// Numbas version: finer_feedback_settings
{"name": "Numeracy and A-level skills test for health science - University of Hertfordshire", "metadata": {"description": "<p><a href=\"https://web.archive.org/web/20090123035303/http://www.staff.ncl.ac.uk/john.appleby/diagpage/diagindx.htm\">DIAGNOSYS</a> is a knowledge-based test of mathematics background knowledge for first-year university students, created by John Appleby at Newcastle University.</p>\n<p>The questions have been translated directly into Numbas, with as few changes as possible.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "percentPass": "0", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "101, Multiplication of negative numbers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Multiplication of negative numbers", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "skill: 101, Multiplication of negative numbers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-3,-5],\n  [-4,-6],\n  [-6,-3],\n  [-2,-7],\n  [-4,-5]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate: $(\\var{a}) \\times (\\var{b})$</p>", "minValue": "a*b", "maxValue": "a*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "0", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "102, Multiply negative and positive", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Multiplying a negative and a positive number", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 101, Multiplication of negative numbers", "skill: 102, Multiply negative and positive"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [4,-1.5],\n  [5,-0.5],\n  [6,-0.5],\n  [7,-3],\n  [6,-4]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate: $\\var{a} \\times (\\var{b})$</p>", "minValue": "a*b", "maxValue": "a*b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "103, Negative Numbers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Negative numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 102, Multiply negative and positive", "leads to: 201, Use of < and > signs", "skill: 103, Negative Numbers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-3,-4],\n  [-5,-6],\n  [-6,-8],\n  [-2.5,-3.5],\n  [-4,-7]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate: $(\\var{a}) + (\\var{b})$</p>", "minValue": "a+b", "maxValue": "a+b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "104, Size of decimals", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Size of decimals", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 201, Use of < and > signs", "skill: 104, Size of decimals"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "[\n  [\n    [\"1/100\", \"0.00099963\",\"0.00997\",\"0.010003\",\"1/150\"],\n    [0,0,0,1,0]\n  ],\n  [\n    [\"1/250\",\"0.0049931\",\"0.0050014\",\"0.0009814\",\"1/200\"],\n    [0,0,1,0,0]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "scenario[0]", "description": "", "templateType": "anything", "can_override": false}, "correct_matrix": {"name": "correct_matrix", "group": "Ungrouped variables", "definition": "scenario[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "choices", "correct_matrix"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which is the <strong>largest</strong> of the following?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "2", "showCellAnswerState": true, "choices": "choices", "matrix": "correct_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "107, Ratios", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Ratios", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 205, Inverse ratios", "leads to: 206, Cancelling numerical fractions", "skill: 107, Ratios"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "[\n  [\n    [\"10 : 15\", \"18 : 24\", \"2 : 3\", \"8 : 12\", \"-4 : -6\"],\n    [0,1,0,0,0]\n  ],\n  [\n    [\"6 : 8\", \"-3 : -4\", \"15 : 20\", \"9 : 12\", \"12 : 18\"],\n    [0,0,0,0,1]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "scenario[0]", "description": "", "templateType": "anything", "can_override": false}, "choice_marks": {"name": "choice_marks", "group": "Ungrouped variables", "definition": "scenario[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "choices", "choice_marks"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following ratios is <strong>not</strong> equal to the others?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "2", "showCellAnswerState": true, "choices": "choices", "matrix": "choice_marks"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "108, Factors of an integer", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Factors of Integers", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 107, Ratios", "leads to: 206, Cancelling numerical fractions", "leads to: 208, Factors of algebraic products", "skill: 108, Factors of an integer"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "[\n  [\n    [\n      \"15 and 25 are both factors of 75\", \n      \"8 is a factor of 100\",\n      \"6, 8 and 16 are all factors of 48\",\n      \"5, 8 and 12 are all factors of 60\",\n    ],\n    [1,0,1,0]\n  ],\n  [\n    [\n      \"6 and 9 are both factors of 96\",\n      \"6, 16 and 24 are all factors of 64\",\n      \"3, 8 and 18 are all factors of 72\",\n      \"35 is a factor of 105\"\n    ],\n    [0,0,1,1]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "scenario[0]", "description": "", "templateType": "anything", "can_override": false}, "correct_matrix": {"name": "correct_matrix", "group": "Ungrouped variables", "definition": "scenario[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "choices", "correct_matrix"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following are true?</p>", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "2", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": "choices", "matrix": "correct_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "109, Simple fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simple fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 216, Add/subtract numerical fractions", "skill: 109, Simple fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [1,2,3,4],\n  [1,6,1,3],\n  [1,4,1,3],\n  [1,2,1,10],\n  [1,2,1,6]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add: $\\simplify[]{ {a}/{b} + {c}/{d}}$ leaving your answer in the <strong>simplest possible form</strong>.</p>", "minValue": "a/b+c/d", "maxValue": "a/b+c/d", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "201, Use of < and > signs", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Use of < > signs", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 301, Solution of simple inequalities", "skill: 201, Use of < and > signs"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "[\n  [\n    [\n      \"8.9 < 9.1\",\n      \"-4 > -5.1\",\n      \"2.5 < -13.6\",\n      \"-3 < 7\",\n      \"19.98 > 20.03\"\n    ],\n    [2,2,0,2,0]\n  ],\n  [\n    [\n      \"-183 > -182\",\n      \"0.4991 < 0.5007\",\n      \"-11.9 < 10.95\",\n      \"0.997 > 1.003\",\n      \"-49.601 < -52.48\"\n    ],\n    [0,3,3,0,0]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "scenario[0]", "description": "", "templateType": "anything", "can_override": false}, "correct_matrix": {"name": "correct_matrix", "group": "Ungrouped variables", "definition": "scenario[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "choices", "correct_matrix"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Select <strong>all</strong> of the following that are <strong>true</strong>.</p>", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "2", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": "choices", "matrix": "correct_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "205, Inverse ratios", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Inverse ratios", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "skill: 205, Inverse ratios"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"scenarios": {"name": "scenarios", "group": "Ungrouped variables", "definition": "[\n  [5,80,25,16],\n  [15,40,75,8],\n  [6,50,120,2.5],\n  [12,40,16,30],\n  [20,26,10,52]\n]", "description": "", "templateType": "anything"}, "scenario": {"name": "scenario", "group": "Ungrouped variables", "definition": "random(scenarios)", "description": "", "templateType": "anything"}, "hours1": {"name": "hours1", "group": "Ungrouped variables", "definition": "scenario[0]", "description": "", "templateType": "anything"}, "speed1": {"name": "speed1", "group": "Ungrouped variables", "definition": "scenario[1]", "description": "", "templateType": "anything"}, "speed2": {"name": "speed2", "group": "Ungrouped variables", "definition": "scenario[2]", "description": "", "templateType": "anything"}, "hours2": {"name": "hours2", "group": "Ungrouped variables", "definition": "scenario[3]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["scenarios", "scenario", "hours1", "speed1", "speed2", "hours2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If a car takes {hours1} hours for a journey travelling at {speed1} miles per hour (mph), how many hours would it take if it travelled at {speed2} mph?</p>", "minValue": "hours2", "maxValue": "hours2", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "206, Cancelling numerical fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Cancelling Numerical Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 207, Multiply algebraic fractions", "leads to: 216, Add/subtract numerical fractions", "leads to: 303, Simplification of fractions with powers", "skill: 206, Cancelling numerical fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [72,90],\n  [36,60],\n  [48,18],\n  [30,24],\n  [60,45]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Cancel <strong>all</strong> possible common factors to leave the fraction in its <strong>simplest</strong> form.</p>\n<p>$\\frac{\\var{a}}{\\var{b}} =$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a/b", "maxValue": "a/b", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "216, Add/subtract numerical fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Addition + Subtraction of Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 308, Add/subtract algebraic fractions", "skill: 216, Add/subtract numerical fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [5,6,7,15],\n  [5,4,7,6],\n  [7,12,3,8],\n  [7,6,5,9],\n  [5,4,11,14]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate $\\simplify[]{ {a}/{b} - {c}/{d} }$.</p>\n<p>Enter your answer in the <strong>simplest possible form</strong>.</p>", "minValue": "a/b-c/d", "maxValue": "a/b-c/d", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "301, Solution of simple inequalities", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Solve simple inequalities", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "skill: 301, Solution of simple inequalities"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [3,2,4,3],\n  [3,3,7,5],\n  [4,3,7,5],\n  [8,5,2,2],\n  [6,4,1,2]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The following inequality can be solved to give $x &lt; a$.</p>\n<p>\\[ \\simplify[]{ {a}-{b} &lt; {c} - {d}x } \\]</p>\n<p>Enther the number $a$.</p>", "minValue": "(c-a+b)/d", "maxValue": "(c-a+b)/d", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "105, Decimal places", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Decimal places", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 202, Significant figures", "skill: 105, Decimal places"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [251.49251,3],\n  [107.36612,2],\n  [61.24416,4],\n  [17.00361,3],\n  [99.9876,2]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "dp": {"name": "dp", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "n", "dp"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the number $\\var{n}$ rounded to <strong>{dp}</strong> decimal places.</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "dp", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "106, Definition of positive powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Definition of positive powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 203, Definition of negative powers", "leads to: 204, Rules for positive powers", "skill: 106, Definition of positive powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [3,3],\n  [2,4],\n  [5,3],\n  [10,3],\n  [2,5]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the value of $\\var{a}^\\var{b}$.</p>", "minValue": "a^b", "maxValue": "a^b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "202, Significant figures", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Significant figures", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 302, Scientific Notation", "skill: 202, Significant figures"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-173.26148,4],\n  [0.0431858,3],\n  [1467.2,2],\n  [304.271,4],\n  [0.0030456,3]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "sf": {"name": "sf", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "n", "sf"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the number $\\var{n}$ rounded to <strong>{sf}</strong> significant figures.</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "sf", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "203, Definition of negative powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Definition of negative powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 302, Scientific Notation", "leads to: 304, Rules for negative powers", "leads to: 306, Definition of fractional powers", "skill: 203, Definition of negative powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [3,2],\n  [2,3],\n  [4,2],\n  [3,3],\n  [2,4]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter (as a fraction) the number given by $\\var{a}^{\\var{-b}}$.</p>", "minValue": "a^-b", "maxValue": "a^-b", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "204, Rules for positive powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Rules for positive powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 304, Rules for negative powers", "skill: 204, Rules for positive powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"x\",2,4,2],\n  [\"u\",3,5,2],\n  [\"y\",4,2,3],\n  [\"z\",3,7,5],\n  [\"t\",6,4,2]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "name(group[0])", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "x", "a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\simplify[]{ {x}^{a} * {x}^{b} = ({x}^{c})^n}$, what is the number $n$?</p>", "minValue": "(a+b)/c", "maxValue": "(a+b)/c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "302, Scientific Notation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Scientific notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 401, Simplify with scientific notation", "skill: 302, Scientific Notation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "[\n  0.00736,\n  0.000438,\n  0.00301,\n  340.62,\n  4107.2\n]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(numbers)", "description": "", "templateType": "anything"}, "significand": {"name": "significand", "group": "Ungrouped variables", "definition": "n/10^power", "description": "", "templateType": "anything"}, "power": {"name": "power", "group": "Ungrouped variables", "definition": "floor(log(n,10))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbers", "n", "power", "significand"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>We can write the number $\\var{n}$ in the form $\\var{significand} \\times 10^n$. Enter the number $n$.</p>", "minValue": "power", "maxValue": "power", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "303, Simplification of fractions with powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simplify fractions and powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 401, Simplify with scientific notation", "skill: 303, Simplification of fractions with powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"exprs": {"name": "exprs", "group": "Ungrouped variables", "definition": "[\n  \"(4^-2 * 2^6) / (2^-3 * 4^3)\",\n  \"(9^-1 * 3^2) / (3^-2 * 9^2)\",\n  \"(2^3 * 4^-1) / (4^2 * 2^-2)\",\n  \"(3^-2 * 9^3) / (9^4 * 3^-1)\",\n  \"(5^-1 * 25^2) / (25^4 * 5^-3)\"\n]", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(random(exprs))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["exprs", "expr"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Express the following in its simplest form (without powers/indices):</p>\n<p>\\[ \\var{expr} \\]</p>", "minValue": "eval(expr)", "maxValue": "eval(expr)", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "304, Rules for negative powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Rules for negative Powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 303, Simplification of fractions with powers", "leads to: 305, Rules for fractional powers", "leads to: 402, Logs", "leads to: 403, Arbitrary factors", "skill: 304, Rules for negative powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"p^-3 * p^-4 = p^n\",-7],\n  [\"(q^-3)^2 = q^n\",-6],\n  [\"x^-2 * x^-5 = x^n\",-7],\n  [\"(y^-2)^4 = y^n\",-8],\n  [\"s^-4 * s^-2 = s^n\",-6]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\var{expr}$, what is the value of $n$?</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "305, Rules for fractional powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Rules for fractional powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "skill: 305, Rules for fractional powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"x^(1/2) * x^(1/3) = (x^5)^a\",1/6],\n  [\"(y^4)^(1/6) = y^(1/2) * y^a\",1/6],\n  [\"p^(1/4) * p^(5/4) = (p^3)^a\",1/2],\n  [\"(q^3)^(1/2) = q^2 * q^a\",-1/2],\n  [\"t^(2/3) * t^(1/2) = (t^7)^a\",1/6]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\var[fractionnumbers]{expr}$ give the value of $a$.</p>", "minValue": "a", "maxValue": "a", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "306, Definition of fractional powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Definition of Fractional Powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "leads to: 305, Rules for fractional powers", "skill: 306, Definition of fractional powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [8,1/3],\n  [16,1/2],\n  [25,1/2],\n  [27,1/3],\n  [16,1/4]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Give the value of $\\simplify[fractionnumbers,flatfractions]{ {a}^{b} }$.</p>", "minValue": "a^b", "maxValue": "a^b", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "401, Simplify with scientific notation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simplify + Scientific notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "skill: 401, Simplify with scientific notation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [-2.5,-2,0.2,-3],\n  [24,3,-0.3,-1],\n  [7,-1,0.2,2],\n  [180,2,0.6,5],\n  [5,-1,-20,-4]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}, "prod": {"name": "prod", "group": "Ungrouped variables", "definition": "(a*10^b) / (c*10^d)", "description": "", "templateType": "anything"}, "power": {"name": "power", "group": "Ungrouped variables", "definition": "floor(log(abs(prod)))", "description": "", "templateType": "anything"}, "significand": {"name": "significand", "group": "Ungrouped variables", "definition": "prod/10^power", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c", "d", "prod", "power", "significand"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The number $\\frac{\\var{a} \\times 10^{\\var{b}}}{\\var{c} \\times 10^{\\var{d}}}$ can be simplified to give $\\var{significand} \\times 10^n$.</p>\n<p>Enter the value of $n$.</p>", "minValue": "power", "maxValue": "power", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "402b, Log rules", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "skill: 402, Logs"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [1,4,2,6],\n  [1,25,2,10],\n  [3,2,2,3],\n  [2,4,1,5],\n  [1,9,3,3]\n]", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "b^a/d^c", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "b", "a", "c", "d", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\simplify{ {a}ln({b}) - {c}ln({d})} = \\ln(a)$, give the number $a$.</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "403, Arbitrary factors", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Arbitrary Factors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: powers", "skill: 403, Arbitrary factors"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [3,\"4w^2 + w^3 = w^3(1+4w^n)\",1],\n  [2,\"2+w^2 = w^2(2w^n + 1)\",-2],\n  [-1,\"w+3/w = w^-1(3+w^n)\",2],\n  [3,\"4w-3w^3=w^3(4w^n-3)\",-2],\n  [-2,\"1/w + 1/w^2 = w^-2(w^n+1)\",1]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(group[1])", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "expr", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In the following, the factor $w^\\var{a}$ has been taken out of the left-hand side to give the right-hand side.</p>\n<p>\\[ \\var{expr} \\]</p>\n<p>Enter the value of the number $n$.</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "110, Collect terms (simple)", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "Collect terms (simple)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 211, Collecting terms", "leads to: 312, Expanding two brackets", "leads to: 317, Complex numbers", "skill: 110, Collect terms (simple)"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"2x-3y+1+y+4x\",\"6x-2y-4\"],\n  [\"y-3x-5y+3+x-2\",\"1-2x-4y\"],\n  [\"3u-2-u+4v-3-2v\",\"2u+2v-5\"],\n  [\"1-3p-4-q+4p+3q\",\"p+2q-3\"],\n  [\"-g-3h+7-4g+5+2h\",\"12-5g-h\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Collect terms in the following expression</p>\n<p>\\[ \\var{expr} \\]</p>\n<p>leaving your answer in the simplest possible form.</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "[\"n\": `+-$n`?] `@ ((n*x)`? + (n*y)`? + (n*u)`? + (n*v)`? + (n*p)`? + (n*q)`? + (n*g)`? + (n*h)`? + n)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}, {"name": "Collecting like terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["algebra", "Algebra", "collecting like terms", "like terms", "simplifying"], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify the following by collecting like terms.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10)+[0,0])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10)+[0,0])[0..2]", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10))[0..2]", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10))[0..2]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10))[0..3]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "shuffle(list(-10..10)+[0,0,0,0])[0..3]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify[!collectnumbers]{{a[1]}x+{b[1]}y+{c[1]}z+{b[2]}y+{a[2]}x+{c[2]}z+{a[0]}x+{c[0]}z+{b[0]}y}$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Like terms are terms where the variable part is the same. For example, $4x$ and $-x$ have the same variable part $x$. However, $3x$ and $-2y$ have different variable parts and are therefore unlike terms (or not like terms).&nbsp;</p>\n<p>We can only collect like terms! Just like we can't say 2&nbsp;m + 3&nbsp;cm equals&nbsp;5&nbsp;m or 5&nbsp;cm, we can't say $2x+3y$ equals $5x$ or $5y$! We can, however, say $2a+3a=5a$.</p>\n<p>In our question we look at all the terms with a variable part of $x$ and add up all the corresponding&nbsp;coefficients, we do the same for the $y$ terms and the $z$ terms:</p>\n<p>\\[\\begin{align}<br/>&amp;\\simplify[!collectnumbers]{{a[1]}x+{b[1]}y+{c[1]}z+{b[2]}y+{a[2]}x+{c[2]}z+{a[0]}x+{c[0]}z+{b[0]}y}\\\\<br/>&amp;=\\simplify[basic]{({a[1]}+{a[2]}+{a[0]})x+({b[1]}+{b[2]}+{b[0]})y+({c[1]}+{c[2]}+{c[0]})z}\\end{align}\\]</p>\n<p>We present this as the sum of three unlike terms:</p>\n<p>\\[\\simplify{{sum(a)}x+{sum(b)}y+{sum(c)}z}\\]</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum(a)}*x+{sum(b)}*y+{sum(c)}*z", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "maxlength": {"length": "14", "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}, {"name": "z", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify[!collectnumbers]{{d[1]}x^2+{f[1]}x+{g[1]}+{d[0]}x^2+{f[0]}x+{g[0]}}$ =&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Like terms are terms where the variable part is the same. For example, $4x$ and $-x$ have the same variable part $x$. However, $3x^2$ and $-2x$ have different variable parts and are therefore unlike terms (or not like terms).&nbsp;</p>\n<p>We can only collect like terms! Just like we can't say 2&nbsp;m + 3&nbsp;cm equals&nbsp;5&nbsp;m or 5&nbsp;cm, we can't say $2x^2+3x$ equals $5x^2$ or $5x$! We can, however, say $2x^2+3x^2=5x^2$.</p>\n<p>In our question we look at all the terms with a variable part of $x^2$ and add up all the corresponding&nbsp;coefficients (the numbers in front of the variables), we do the same for the $x$ terms and the constant&nbsp;terms (the terms with no variable part):</p>\n<p>\\[\\begin{align}&amp;\\simplify[!collectnumbers]{{d[1]}x^2+{f[1]}x+{g[1]}+{d[0]}x^2+{f[0]}x+{g[0]}}\\\\&amp;=\\simplify[basic]{({d[1]}+{d[0]})x^2+({f[1]}+{f[0]})x+({g[1]}+{g[0]})}\\end{align}\\]</p>\n<p>We present this as the sum of three unlike terms:</p>\n<p>\\[\\simplify[!noleadingminus, basic]{{sum(d)}x^2+{sum(f)}x+{sum(g)}}\\]</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum(d)}x^2+{sum(f)}x+{sum(g)}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`?`+-$n*`?(x^2) + `?`+-$n*`?x + `?`+-$n", "partialCredit": 0, "message": "", "nameToCompare": "", "warningTime": "submission"}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "111, Solving a simple equation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Solving a simple equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 212, Solving linear equations", "skill: 111, Solving a simple equation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"3x+1=13\",4],\n  [\"4x-3=9\",3],\n  [\"5x+2=17\",3],\n  [\"3-2x=9\",-3],\n  [\"2-5x=-8\",2]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the equation, and give the value of $x$:</p>\n<p>\\[ \\var{expr} \\]</p>", "minValue": "x", "maxValue": "x", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "112, Simple calculation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simple calculation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "leads to: 210, Expanding one bracket", "leads to: 214, Evaluating formula", "leads to: 215, Precedence Rules", "skill: 112, Simple calculation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [17,3,4],\n  [14,2,3],\n  [13,4,2],\n  [21,5,3],\n  [20,4,3]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Simplify: $\\simplify[]{ {a} - {b}*{c} }$.</p>", "minValue": "a-b*c", "maxValue": "a-b*c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "113, Evaluating a simple expression", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Evaluating a simple expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 214, Evaluating formula", "skill: 113, Evaluating a simple expression"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [2,3,3,\"x\"],\n  [5,2,4,\"x\"],\n  [4,5,5,\"y\"],\n  [2,4,3,\"z\"],\n  [6,2,4,\"p\"]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "name(group[3])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "a", "b", "c", "x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Evaluate $\\var{a} + \\var{b}\\var{x}$ if $\\var{x} = \\var{c}$.</p>", "minValue": "a+b*c", "maxValue": "a+b*c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "207, Multiply algebraic fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Multiplication of Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 307, Division of algebraic fractions", "skill: 207, Multiply algebraic fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"6/y\", \"y^2/12\", \"y/2\"],\n  [\"4/y^2\", \"3y/2\", \"6/y\"],\n  [\"3/y^3\", \"5y^2/6\", \"5/(2y)\"],\n  [\"2y/9\", \"3/(4y^2)\",\"1/(6y)\"],\n  [\"4/y\", \"y^3/8\",\"y^2/2\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[2])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is $\\var{a} \\times \\var{b}$?</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "($n `| $v^$n`?)/($n`? * $v`?)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "208, Factors of algebraic products", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Factors of Algebraic Products", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 209, Simple Factorisation", "skill: 208, Factors of algebraic products"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"12x^3y=3x^2y\",\"4x\"],\n  [\"15p*q^2=5p*q\",\"3q\"],\n  [\"18u^2v^2=6u*v^2\", \"3u\"],\n  [\"10g^3h=5g^2\",\"2*g*h\"],\n  [\"14m*n^3=2n^2\",\"7m*n\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the other factor in the equation:</p>\n<p>\\[ \\var{expr}( ? ) \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "209, Simple Factorisation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simple Factorisation", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 309, Simple Quadratic equations", "leads to: 311, Factorising a quadratic", "leads to: 412, Difficult linear equation", "skill: 209, Simple Factorisation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"2z-6z^2\",\"2z*(1-3z)\"],\n  [\"10t^2-5t\",\"5t*(2t-1)\"],\n  [\"12y-8y^2\",\"4y*(3-2y)\"],\n  [\"6p^2-9p\",\"3p*(2p-3)\"],\n  [\"14w-6w^2\",\"2w*(7-3w)\"]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Factorise the following, taking out the highest factor possible:</p>\n<p>\\[ \\var{expr} \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "$n`? * $v * ?", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "210, Expanding one bracket", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "Expand one bracket", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 209, Simple Factorisation", "leads to: 312, Expanding two brackets", "skill: 210, Expanding one bracket"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"2x*(x-3x^2)\",\"2x^2-6x^3\"],\n  [\"3y*(2y-1)\",\"6y^2-3y\"],\n  [\"4z*(z-2z^2)\",\"4z^2-8z^3\"],\n  [\"2u*(u^2-3)\",\"2u^3-6u\"],\n  [\"3v*(v^3-2v)\",\"3v^4-6v^2\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Expand the bracket in:</p>\n<p>\\[ \\var{expr} \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+-($n`?*$v^$n`?))`* + $z", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}, {"name": "Distributive law: expanding one set of brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": ["algebra", "Algebra", "distributive law", "expanding", "Expanding", "expanding brackets"], "metadata": {"description": "<p>Things like \"expand 4(5a-3)\"</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"nconstant": {"name": "nconstant", "group": "part b", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "nxcoeff": {"name": "nxcoeff", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "nmult": {"name": "nmult", "group": "part b", "definition": "random(-12..-2)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "x", "y"], "variable_groups": [{"name": "part b", "variables": ["nmult", "nxcoeff", "nconstant"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The expression $\\simplify{{nmult}({nxcoeff}a+{nconstant})}$ is factorised (written as a product). We can expand the expression (so it is written as a sum) to get&nbsp;</p>\n<p>[[0]]$a$ +&nbsp;[[1]]</p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets. Also, recall that a negative multiplied by a negative is a positive.</p>\n<p><em>$\\begin{align*}<br/>\\simplify{{nmult}({nxcoeff}a+{nconstant})}&amp;=\\simplify[!noleadingminus]{{nmult}*{nxcoeff}a+{nmult} * {nconstant}}\\\\&amp;=\\simplify[!noLeadingMinus]{{nmult*nxcoeff}a+{nmult*nconstant}}<br/>\\end{align*}$</em></p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{nmult*nxcoeff}", "maxValue": "{nmult*nxcoeff}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{nmult*nconstant}", "maxValue": "{nmult*nconstant}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "211, Collecting terms", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Collect Terms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "skill: 211, Collecting terms"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"2p-4+p^2+11p+2-3p^2\", \"-2+13p-2p^2\"],\n  [\"1-3y+4+4y^2-5y+3-y^2\", \"8-8y+3y^2\"],\n  [\"2z^2-5-z+7-3z-4z^2\", \"2-4z-2z^2\"],\n  [\"-5^2-4t+3t^2+6-t+5\", \"11-5t+2t^2\"],\n  [\"4m-2-2m+4m^2+3-2m^2\", \"1+2m+2m^2\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Collect the terms in the following expression:</p>\n<p>\\[ \\var{expr} \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+- $n`?) + (`+- $n`?*$v) + (`+- $n`? * $v^2)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "212, Solving linear equations", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Linear Equations", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 309, Simple Quadratic equations", "leads to: 310, Relation between roots and factors", "leads to: 314, Simultaneous Equations", "leads to: 315, Unusual linear equation", "skill: 212, Solving linear equations"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"7-3c=-5c-4\",\"c\",-5.5],\n  [\"2d+3=-4d+18\",\"d\",2.5],\n  [\"1-3t=-6t-2\",\"t\",-1],\n  [\"4c+4=-2c-5\",\"c\",-1.5],\n  [\"3-2n=6n+11\",\"n\",-1]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "latex(pair[1])", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "pair[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "x", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the equation:</p>\n<p>\\[ \\var{expr} \\]</p>\n<p>Enter the value of $\\var{x}$.</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "213, Transposition of formula", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Transposition of formulae", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 315, Unusual linear equation", "skill: 213, Transposition of formula"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"c=a*b/2\",\"b\",\"2c/a\"],\n  [\"v=2u/3\",\"u\",\"3v/2\"],\n  [\"d=5e/3\",\"e\",\"3d/5\"],\n  [\"s=-(3t/5)\",\"t\",\"-5s/3\"],\n  [\"x=y*z/4\",\"y\",\"4x/z\"]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(group[0])", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "latex(group[1])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(group[2])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "expr", "x", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\var{expr}$ then what is $\\var{x}$?</p>\n<p>Enter an expression for $\\var{x}$.</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "214, Evaluating formula", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Evaluation of Formulae", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: basic algebra", "leads to: 316, Use of quadratic formula", "leads to: 410, Substituting into a formula", "skill: 214, Evaluating formula"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"(p^2+2r)/(t-1)\",[p:4,r:-2,t:5]],\n  [\"(3a+b)/(2c^2)\",[a:5,b:-3,c:2]],\n  [\"(2f-g^3)/(4h)\",[f:7,g:2,h:1.5]],\n  [\"(3r^2-2s)/(t+4)\",[r:3,s:6,t:-1]],\n  [\"(x^2-3y^2)/(1-3z)\",[x:4,y:-2,z:1]]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "values": {"name": "values", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "eval(expr,values)", "description": "", "templateType": "anything"}, "values_string": {"name": "values_string", "group": "Ungrouped variables", "definition": "latex(join(map(\"{x} = {v}\",[x,v],items(values)),\", \"))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "values", "n", "values_string"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $Q = \\var{expr}$ and $\\var{values_string}$, then what value has $Q$?</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "215, Precedence Rules", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Order of Operations", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Laura Midgley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18287/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: numbers", "skill: 215, Precedence Rules"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\n    latex(safe(\"\\\\frac{12}{6 \\\\times 3}\")),\n    [\n      safe(\"12 \u00f7 (6 \u00d7 3) =\"),\n      safe(\"12 \u00f7 6 \u00d7 3 =\"),\n      safe(\"(12) \u00f7 (6 \u00d7 3) =\"),\n      safe(\"(12 \u00f7 6) \u00d7 3 =\")\n    ],\n    [0,1,0,0]\n  ],\n  [\n    latex(safe(\"\\\\frac{15+27}{3}\")),\n    [\n      safe(\"(15+27) \u00f7 3 =\"),\n      safe(\"15 + 27 = \u00f7 3 =\"),\n      safe(\"15 + 27 \u00f7 3 =\"),\n      safe(\"15 \u00f7 3 + 27 \u00f7 3 =\")\n    ],\n    [0,0,1,0]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "map(\"<code>\"+x+\"</code>\",x,group[1])", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything", "can_override": false}, "correct_matrix": {"name": "correct_matrix", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "expr", "choices", "correct_matrix"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>To calculate $\\var{expr}$ you press a sequence of keys on your calculator.</p>\n<p>Which one of the following would give you the <strong>WRONG</strong> answer?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": "choices", "matrix": "correct_matrix"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "307, Division of algebraic fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Division of Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "skill: 307, Division of algebraic fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"12/y\",\"6/y^2\",\"2y\"],\n  [\"z^2/4\",\"z/8\",\"2z\"],\n  [\"6/u^2\",\"3/u\",\"2/u\"],\n  [\"v/4\",\"v^2/8\",\"2/v\"],\n  [\"1/(2m)\",\"4/m^2\",\"m/8\"]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "expr1": {"name": "expr1", "group": "Ungrouped variables", "definition": "expression(group[0])", "description": "", "templateType": "anything"}, "expr2": {"name": "expr2", "group": "Ungrouped variables", "definition": "expression(group[1])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(group[2])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "expr1", "expr2", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\var{expr1}$ is divided by $\\var{expr2}$ then the result (when simplified) is:</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "308, Add/subtract algebraic fractions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Addition/Subtraction of Algebraic Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "leads to: 404, L.c.d. of an algebraic fraction", "leads to: 405, Identification of common errors", "skill: 308, Add/subtract algebraic fractions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"3/(x+1)+2/(x+2)\",\"(x+1)(x+2)\",\"5x+8\"],\n  [\"4/(x-1)+3/(x+3)\",\"(x-1)(x+3)\",\"7x+9\"],\n  [\"2/(x-2)+3/(x-1)\",\"(x-2)(x-1)\",\"5x-8\"],\n  [\"3/(x+3)-1/(x+1)\",\"(x+3)(x+1)\",\"2x\"],\n  [\"2/(x-2)-1/(x+2)\",\"(x-2)(x+2)\",\"x+6\"]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(group[0])", "description": "", "templateType": "anything"}, "denom": {"name": "denom", "group": "Ungrouped variables", "definition": "expression(group[1])", "description": "", "templateType": "anything"}, "numerator": {"name": "numerator", "group": "Ungrouped variables", "definition": "expression(group[2])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "expr", "denom", "numerator"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Two fractions are put over a common denominator as shown:</p>\n<p>\\[ \\var{expr} = \\frac{?}{\\var{denom}} \\]</p>\n<p>Enter the numerator (shown as $?$) in simplified form:</p>", "answer": "{numerator}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "309, Simple Quadratic equations", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simple Quadratic Equations", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "skill: 309, Simple Quadratic equations"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\n    \"x^2+4x=0\",\n    [\n      safe(\"has only one solution, $x=-4$\"),\n      safe(\"has only one solution, $x=4$\"),\n      safe(\"has only one solution, $x=0$\"),\n      safe(\"has two solutions, $x=0$ and $x=-4$\"),\n      safe(\"has two solutions, $x=0$ and $x=4$\")\n    ],\n    [0,0,0,1,0]\n  ],\n  [\n    \"3x=x^2\",\n    [\n      safe(\"has only one solution, $x=3$\"),\n      safe(\"has only one solution, $x=-3$\"),\n      safe(\"has only one solution, $x=0$\"),\n      safe(\"has two solutions, $x=0$ and $x=3$\"),\n      safe(\"has two solutions, $x=0$ and $x=-3$\")\n    ],\n    [0,0,0,1,0]\n  ],\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(group[0])", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "choice_marks": {"name": "choice_marks", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "expr", "choices", "choice_marks"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which <strong>one</strong> of the following statements about this quadratic equation is true?</p>\n<p>\\[ \\var{expr} \\]</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": "choices", "matrix": "choice_marks"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "310, Relation between roots and factors", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Relationship of Roots and Factors", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "skill: 310, Relation between roots and factors"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-2,1],\n  [3,-1],\n  [2,-3],\n  [1,-4],\n  [-3,1]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "-x1-x2", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "x1*x2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "x1", "x2", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The quadratic equation $x^2+ax+b=0$ has roots $x = \\var{x1}$ and $x=\\var{x2}$.</p>\n<p>Enter the values of $a$ and $b$.</p>\n<p>$a = $ [[0]]</p>\n<p>$b = $ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "$a$", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a", "maxValue": "a", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$b$", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b", "maxValue": "b", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "311, Factorising a quadratic", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Factorising a Quadratic Function", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "leads to: 310, Relation between roots and factors", "leads to: 407, Quadratics - completing the square", "skill: 311, Factorising a quadratic"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"x\",5,-3],\n  [\"v\",-4,2],\n  [\"y\",1,-3],\n  [\"z\",-2,3],\n  [\"u\",3,-4]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "name(group[0])", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "simplify(expression(\"{x}^2 + {-a-b}{x} + {a*b}\"),\"all\")", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "simplify(expression(\"({x}-{a})({x}-{b})\"),\"all\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "x", "a", "b", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Factorise the following expression into two brackets:</p>\n<p>\\[ \\var{expr} \\]</p>\n<p>that is, into the form $(\\var{x}\\ldots)(\\var{x}\\ldots)$.</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+- $n`? * $v + `+- $n`?)`* * $z", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "312, Expanding two brackets", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Expanding Two Brackets", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "leads to: 311, Factorising a quadratic", "leads to: 313, Difference of squares", "leads to: 405, Identification of common errors", "leads to: 408, Multiplication of complex numbers", "leads to: 410, Substituting into a formula", "skill: 312, Expanding two brackets"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"(2+v)(3-v)\",\"6+v-v^2\"],\n  [\"(r-4)(r+2)\",\"r^2-2r-8\"],\n  [\"(t-2)(t+4)\",\"t^2+2t-8\"],\n  [\"(1-s)(2+s)\",\"2-s-s^2\"],\n  [\"(y+3)(y-5)\",\"y^2-2y-15\"]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Expand the brackets and collect terms:</p>\n<p>\\[ \\var{expr} \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "`+-($n`? * $v^2) + `+-($n`? * $v)`? + `+-$n`?", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "313, Difference of squares", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Difference of squares", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "skill: 313, Difference of squares"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"4y^2-9\",\"(2y+3)(2y-3)\"],\n  [\"9v^2-1\",\"(3v-1)(3v+1)\"],\n  [\"4b^2-9\",\"(2b+3)(2b-3)\"],\n  [\"9d^2-4\",\"(3d+2)(3d-2)\"],\n  [\"25-f^2\",\"(5-f)(5+f)\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Factorise the following expression</p>\n<p>\\[ \\var{expr} \\]</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(`+-$n`?*`+-$v + `+-$n`?)`* * $z", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "314, Simultaneous Equations", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Simultaneous Equations", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "skill: 314, Simultaneous Equations"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [2,3,12,3,4,17],\n  [2,2,4,4,3,5],\n  [3,2,2,2,5,-6],\n  [4,2,-10,2,5,-1],\n  [3,2,1,2,3,4]\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "group[4]", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "group[5]", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "(y2*c1-y1*c2)/(y2*x1-y1*x2)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "(x2*c1-x1*c2)/(x2*y1-x1*y2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "x1", "y1", "c1", "x2", "y2", "c2", "x", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the simultaneous equations</p>\n<p>\\begin{align}<br/>\\simplify{ {x1}x + {y1}y} &amp;=\\var{c1} \\\\<br/>\\simplify{ {x2}x + {y2}y} &amp;= \\var{c2}<br/>\\end{align}</p>\n<p>Enter the values for $x$ and $y$:</p>\n<p>$x = $ [[0]]</p>\n<p>$y = $ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "$x$", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "x", "maxValue": "x", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "$y$", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "y", "maxValue": "y", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "315, Unusual linear equation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Unusual Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "leads to: 412, Difficult linear equation", "skill: 315, Unusual linear equation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"3/y=5/(y-1)\",-1.5],\n  [\"2/(y+2)=4/(y+3)\",-1],\n  [\"2/(1-y)=3/(1+y)\",0.2],\n  [\"2/(y+4)=-1/(y+1)\",-2],\n  [\"4/(y-3)=1/(y+3)\",-5]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "y"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve $\\var{expr}$</p>\n<p>Enter the value of $y$.</p>", "minValue": "y", "maxValue": "y", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "316, Use of quadratic formula", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Formula for Quadratic Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "leads to: 411, Solutions of a quadratic", "skill: 316, Use of quadratic formula"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-6,4],\n  [-8,5],\n  [-4,-2],\n  [4,-1],\n  [6,2]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "-a/2", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "(a^2-4b)/4", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If we solve the quadratic equation</p>\n<p>\\[ \\simplify{ x^2 + {a}x + {b} = 0 } \\]</p>\n<p>we obtain two solutions in the form $x=\\var{c} \\pm \\sqrt{n}$.</p>\n<p>Enter the value of $n$.</p>", "minValue": "d", "maxValue": "d", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "405, Identification of common errors", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Common Errors", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "skill: 405, Identification of common errors"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\n    [\n      \"(x-1)^2=x^2+1\",\n      \"1/(x^2-x)=1/x^2-1/x\",\n      \"(x+1/x)^2=2+x^2+1/x^2\",\n      \"x^2+2x-8=(x-4)(x+2)\",\n      \"(-3x)^2=-9x^2\"\n    ],\n    [0,0,2,0,0]\n  ],\n  [\n    [\n      \"(x^(3/2)-2x)/sqrt(x) = x-2sqrt(x)\",\n      \"x^2+6x+1=(x+3)^2+8\",\n      \"ln(x+x^2)=ln(x)+ln(x^2)\",\n      \"(x-2/x)^2=x^2-4-4/x^2\",\n      \"2x^2-x-6=(2x+3)(x-2)\"\n    ],\n    [1,0,0,0,1]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "map(\"$\"+latex(expression(x))+\"$\",x,pair[0])", "description": "", "templateType": "anything", "can_override": false}, "choice_marks": {"name": "choice_marks", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "choices", "choice_marks"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following are correct?</p>", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": "1", "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": "choices", "matrix": "choice_marks"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "406, Solve quad. by comp. the square", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Solution of quadratic by c.t.s.", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "skill: 406, Solve quad. by comp. the square"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"p\",-4,-21],\n  [\"z\",-6,-27],\n  [\"y\",-4,-12],\n  [\"w\",-8,7],\n  [\"m\",-6,-7]\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "name(group[0])", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "sqrt((c1/2)^2-c2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "x", "c1", "c2", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If we solve the equation $\\simplify{{x}^2+{c1}{x}+{c2}=0}$ by completing the square, we get an answer in the form $(\\var{x}-a) = \\pm b$.</p>\n<p>Enter the number $b$.</p>", "minValue": "b", "maxValue": "b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "407, Quadratics - completing the square", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Completing the square", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "leads to: 406, Solve quad. by comp. the square", "skill: 407, Quadratics - completing the square"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [6,13],\n  [-4,9],\n  [-6,10],\n  [8,13],\n  [-8,11]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Put the expression $\\simplify{ x^2 + {b}x + {c}}$ into the form $(\\ldots)^2 + \\text{number}$ by completing the square.</p>", "answer": "(x+{b/2})^2+{c-b^2/4}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "(`+-$n`? * $v + `+-$n)^2 + `+-$n", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "410, Substituting into a formula", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Substituting into a formula", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra methods", "skill: 410, Substituting into a formula"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"z^2-2z\",\"2z+3\",\"4z^2+8z+3\"],\n  [\"z-2z^2\",\"3z-1\",\"15z-18z^2-3\"],\n  [\"3z^2-z\",\"1-2z\",\"12z^2-10z+2\"],\n  [\"z^2-3z\",\"2-3z\",\"9z^2-3z-2\"],\n  [\"2z^2-4z\",\"2+3z\",\"18z^2+12z\"]\n]", "description": "", "templateType": "anything"}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "expression(group[0])", "description": "", "templateType": "anything"}, "val": {"name": "val", "group": "Ungrouped variables", "definition": "expression(group[1])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(group[2])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "f", "val", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $f(z) = \\var{f}$, what is $f(\\var{val})$?</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "411, Solutions of a quadratic", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Solutions to a quadratic equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "leads to: 409, Divide by zero (possible solution)", "skill: 411, Solutions of a quadratic"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [3,4],\n  [6,9],\n  [2,-5],\n  [-3,5],\n  [-8,16]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "discriminant": {"name": "discriminant", "group": "Ungrouped variables", "definition": "b^2-4c", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "switch(\n  discriminant<0,0,\n  discriminant>0,2,\n  1\n)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "b", "c", "discriminant", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How many real solutions are there to the equation $\\simplify{x^2+{b}x+{c}}=0$?</p>", "minValue": "n", "maxValue": "n", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "412, Difficult linear equation", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Difficult Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: equations", "skill: 412, Difficult linear equation"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"(2T-1)/(1-3T)\",\"(a+1)/(2+3a)\"],\n  [\"(1-4T)/(2+4T)\",\"(1-2a)/(4a+4)\"],\n  [\"(3T+2)/(3T-2)\",\"(2+2a)/(3a-3)\"],\n  [\"(2T-1)/(T-2)\",\"(2a-1)/(a-2)\"],\n  [\"(6T+5)/(5-6T)\",\"(5a-5)/(6a+6)\"]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the following equation for $T$ in terms of the constant $a$:</p>\n<p>(i.e. make $T$ the subject of the formula):</p>\n<p>\\[ a = \\var{expr} \\]</p>\n<p>Enter your expression for $T$.</p>", "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "T={answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "T=?;expr", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "t", "value": ""}]}], "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "341, Differentiation of powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Differentiate powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "leads to: 342, Finding Max/Min of a quadratic", "leads to: 441, Product rule", "leads to: 442, Integration of powers", "skill: 341, Differentiation of powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"x\",3],\n  [\"y\",4],\n  [\"z\",5],\n  [\"t\",6],\n  [\"s\",7]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "name(pair[0])", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "x", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Differentiate $\\var{x}^\\var{n}$ with respect to $\\var{x}$.</p>", "answer": "{n}*{x}^{n-1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "342, Finding Max/Min of a quadratic", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Max/Min of quadratics", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "skill: 342, Finding Max/Min of a quadratic"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"3x+x^2\",-1.5],\n  [\"2x^2-x\",0.25],\n  [\"5x^2-2x\",0.2],\n  [\"-3x+3x^2\",0.5],\n  [\"-4x+x^2\",2]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "x"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What value of $x$ gives the <strong>minimum</strong> of the function $f(x) = \\var{expr}$?</p>", "minValue": "x", "maxValue": "x", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "343, Geometric Progression", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Geometric progression", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Krishna Kedia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25454/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "skill: 343, Geometric Progression"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Definition of Geometric Progression: A series of the form a, ar, ar<sup>2</sup>, ar<sup>3</sup>, ... so on; where a is the inital value and r is the common ratio</p>", "advice": "<p>n<sup>th</sup> term of a GP is given by:</p>\n<p>a<sub>n</sub> = a r<sup>n-1</sup></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [3,-2],\n  [-1,3],\n  [2,-3],\n  [4,-2],\n  [-3,2]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "r"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>A Geometric Progression has first term $\\var{a}$ and ratio $\\var{r}$.</p>\n<p>What is the <strong>4<sup>th</sup></strong> term?</p>\n<p></p>", "minValue": "a*r^3", "maxValue": "a*r^3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "441, Product rule", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Product rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "skill: 441, Product rule"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"x*e^x\",\"x*e^x+e^x\"],\n  [\"x*sin(x)\",\"x*cos(x)+sin(x)\"],\n  [\"x*cos(x)\",\"cos(x)-x*sin(x)\"],\n  [\"x^2*sin(x)\",\"2x*sin(x)+x^2*cos(x)\"],\n  [\"x^2*e^x\",\"2x*e^x+x^2*e^x\"]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(pair[0])", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "Ungrouped variables", "definition": "expression(pair[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "expr", "answer"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Differentiate $\\var{expr}$ with respect to $x$.</p>", "answer": "{answer}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "442, Integration of powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Integrate powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: algebra+calculus", "skill: 442, Integration of powers"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [2,3],\n  [6,2],\n  [10,4],\n  [6,3],\n  [9,2]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $\\frac{\\mathrm{d}y}{\\mathrm{d}t} = \\simplify{ {a}t^{b} }$ find $y$, given $y=0$ when $t=0$.</p>\n<p>Enter $y$.</p>", "answer": "{a}/{(b+1)}*t^{b+1}", "answerSimplification": "all,fractionnumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "t", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "151, Coordinates", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Coordinates", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: graphs", "leads to: 251, Gradient of a straight line", "skill: 151, Coordinates"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [-1,2],\n  [3,-1],\n  [2,-1],\n  [-3,-2],\n  [-2,3]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "x", "y"], "variable_groups": [], "functions": {"graph": {"parameters": [["x", "number"], ["y", "number"]], "type": "html", "language": "javascript", "definition": "// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n    {boundingBox: [-5,5,5,-5],\n     axis: true,\n     showNavigation: false,\n     grid: true\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\nboard.create('point',[x,y],{fixed:true, name:''});\nboard.removeObject(board.infobox);\n\n// Then do whatever you want with the board....\n\n// and return the container div\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the $x$ and $y$ coordinates of the point shown:</p>\n<p>{graph(x,y)}</p>\n<p>( [[0]] , [[1]] )</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "First component", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "x", "maxValue": "x", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Second component", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "y", "maxValue": "y", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "251, Gradient of a straight line", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Gradient of straight line", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Krishna Kedia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25454/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: graphs", "leads to: 351, Equation of a straight line", "skill: 251, Gradient of a straight line"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Gradient or slope of a straight line is given by:</p>\n<p>slope = (y<sub>2</sub>-y<sub>1</sub>)/(x<sub>2</sub>-x<sub>1</sub>)</p>\n<p>where (x<sub>1</sub>,y<sub>1</sub>) and (x<sub>2</sub>,y<sub>2</sub>) are two points on the line</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [[1,2],[3,8]],\n  [[2,0],[6,2]],\n  [[-1,-2],[1,2]],\n  [[-1,2],[2,-4]],\n  [[2,3],[6,1]]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "vector(pair[0])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "vector(pair[1])", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b[1]-a[1])/(b[0]-a[0])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the gradient of the straight line joing the points $\\var[rowvector]{a}$ and $\\var[rowvector]{b}$?</p>", "minValue": "g", "maxValue": "g", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "351, Equation of a straight line", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Equation of a straight line", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: graphs", "leads to: 451, Recognise formula of quad. graph", "leads to: 452, Recognise formula of recip. graph", "skill: 351, Equation of a straight line"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [[0,2],[3,8]],\n  [[2,0],[5,9]],\n  [[1,3],[3,11]],\n  [[-1,5],[2,-1]],\n  [[2,-7],[3,-10]]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "vector(pair[0])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "vector(pair[1])", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "(b[1]-a[1])/(b[0]-a[0])", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "a[1]-g*a[0]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "g", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The equation (in $x$ and $y$) of the straight line joining the points $\\var[rowvector]{a}$ and $\\var[rowvector]{b}$ is $y = ?$</p>\n<p>Enter the <strong>right-hand side</strong> of the equation.</p>", "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "y={g}x+{c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "y=?;expr", "partialCredit": 0, "message": "", "nameToCompare": "expr"}, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "answer": "{g}x+{c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "451, Recognise formula of quad. graph", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Quadratic Graphs", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: graphs", "skill: 451, Recognise formula of quad. graph"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\n    [\"$x^2-x$\",\"$x^2-1$\",\"$(x-1)^2$\",\"$x^2+x$\",\"$1-x^2$\"],\n    [1,0,0,0,0]\n  ],\n  [\n    [\"$(x-3)^2$\",\"$x^2-3x$\",\"$x^2+2$\",\"$4-x^2$\",\"$x^2+2x$\"],\n    [0,1,0,0,0]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything", "can_override": false}, "choice_marks": {"name": "choice_marks", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "choices", "choice_marks"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "javascript", "definition": "// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n    {boundingBox: [-2,3,3,-1],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\nboard.create('axis',[[0,0],[1,0]],{ticks:{visible:false}})\nboard.create('axis',[[0,0],[0,1]],{ticks:{visible:false}});\nboard.create('functiongraph',[function(x){return x*x-x}],{fixed:true, name:''});\nboard.removeObject(board.infobox);\n\n// Then do whatever you want with the board....\n\n// and return the container div\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Choose the function whose graph looks like this.</p>\n<p>{graph()}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": "choices", "matrix": "choice_marks"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "452, Recognise formula of recip. graph", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Reciprocal Graphs", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: graphs", "skill: 452, Recognise formula of recip. graph"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\n    [\"1/x\",\"1/x-1\",\"-(1/-x)\",\"-1/x\",\"1-1/x\"],\n    [0,0,0,1,0]\n  ],\n  [\n    [\"2/x\",\"-(2/-x)\",\"2/x-1\",\"2/x-2\",\"-2/x\"],\n    [0,0,0,0,1]\n  ]\n]", "description": "", "templateType": "anything", "can_override": false}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything", "can_override": false}, "choices": {"name": "choices", "group": "Ungrouped variables", "definition": "map(\"$\"+latex(expression(x))+\"$\",x,pair[0])", "description": "", "templateType": "anything", "can_override": false}, "choice_marks": {"name": "choice_marks", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "choices", "choice_marks"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "javascript", "definition": "// First, make the JSXGraph board.\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n    {boundingBox: [-3,3,3,-3],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\nboard.create('axis',[[0,0],[1,0]],{ticks:{visible:false}})\nboard.create('axis',[[0,0],[0,1]],{ticks:{visible:false}});\nboard.create('functiongraph',[function(x){return x-1/x}],{fixed:true, name:''});\nboard.removeObject(board.infobox);\n\n// Then do whatever you want with the board....\n\n// and return the container div\nreturn div;"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Choose the function whose graph looks like this.</p>\n<p>{graph()}</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": "choices", "matrix": "choice_marks"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "221, Pythagoras", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Pythagoras Theorem", "extensions": ["eukleides"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: miscellaneous", "leads to: 321, Equation of a circle", "leads to: 322, Sin and Cos formula", "skill: 221, Pythagoras"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"graph": {"name": "graph", "group": "Ungrouped variables", "definition": "eukleides(\"Right-angled triangle\",\n  let(\n    scale,1/2,\n    pa,point(scale*b,0),\n    pb,point(scale*b,scale*a),\n    pc,point(0,0),\n    [\n      pa..pb..pc,\n      pb..pa label(a),\n      pc..pb label(b),\n      pa..pc label(\"\u221an\")\n    ]\n  ),\n  [\"a\":a,\"b\":b]\n)", "description": "", "templateType": "anything"}, "pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [4,10],\n  [3,6],\n  [3,8],\n  [3,7],\n  [2,5]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "cs": {"name": "cs", "group": "Ungrouped variables", "definition": "b*b-a*a", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "cs", "graph"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the number $n$ (under the square root):</p>\n<p>{max_width(20,graph)}</p>", "minValue": "cs", "maxValue": "cs", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "222, Definition of sin and cos", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Sine and Cosine", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: miscellaneous", "leads to: 322, Sin and Cos formula", "leads to: 422, Sin and Cos as functions", "skill: 222, Definition of sin and cos"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"graph": {"name": "graph", "group": "Ungrouped variables", "definition": "eukleides(\"Right-angled triangle\",\n  let(\n    scale,1,\n    pa,point(4,0),\n    pb,point(4,3),\n    pc,point(0,0),\n    [\n      pa..pb..pc,\n      pb..pa label(b),\n      pc..pb label(c),\n      pa..pc label(a),\n      angle(pa,pc,pb) label(\"\u03b8\")\n    ]\n  ),\n  [\"a\":a,\"b\":b,\"c\":c]\n)", "description": "", "templateType": "anything", "can_override": false}, "groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n  [\"sine\",12,5],\n  [\"cosine\",12,5],\n  [\"sine\",24,7],\n  [\"cosine\",24,7],\n  [\"sine\",8,6]\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "fn": {"name": "fn", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "round(sqrt(a^2+b^2))", "description": "", "templateType": "anything", "can_override": false}, "theta": {"name": "theta", "group": "Ungrouped variables", "definition": "if(\n  fn=\"cosine\",\n    a/c,\n    b/c\n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "fn", "a", "b", "c", "theta", "graph"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter the <strong>{fn}</strong> of the angle $\\theta$</p>\n<p>{max_width(20,graph)}</p>", "minValue": "theta", "maxValue": "theta", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "322, Sin and Cos formula", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Sine/Cosine Relationships", "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: miscellaneous", "skill: 322, Sin and Cos formula"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following statements are true for <strong>all</strong> values of $x$?</p>", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": ["$\\sin^2(x) + \\cos^2(x) = 1$", "$\\sin(2x) + \\cos(2x) = 1$", "$\\sin(x) + \\cos(x) = 1$", "$(\\sin(x))^2 + (\\cos(x))^2=1$", "$\\sin(x^2) + \\cos(x^2)=1$"], "matrix": ["1", 0, 0, "1", 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "323, Definition of radians", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: miscellaneous", "skill: 323, Definition of radians"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [5,6],\n  [2,3],\n  [1,3],\n  [3,4],\n  [5,4]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "degrees": {"name": "degrees", "group": "Ungrouped variables", "definition": "180*a/b", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "a", "b", "degrees"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Express the angle $\\simplify{ {a}pi/{b} }$ radians in degrees.</p>", "minValue": "degrees", "maxValue": "degrees", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "422, Sin and Cos as functions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Sine and Cosine Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["category: miscellaneous", "skill: 422, Sin and Cos as functions"], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "variables": {"pairs": {"name": "pairs", "group": "Ungrouped variables", "definition": "[\n  [\"sin\",3],\n  [\"cos\",4],\n  [\"sin\",5],\n  [\"cos\",6],\n  [\"cos\",3]\n]", "description": "", "templateType": "anything"}, "pair": {"name": "pair", "group": "Ungrouped variables", "definition": "random(pairs)", "description": "", "templateType": "anything"}, "fn": {"name": "fn", "group": "Ungrouped variables", "definition": "pair[0]", "description": "", "templateType": "anything"}, "scale": {"name": "scale", "group": "Ungrouped variables", "definition": "pair[1]", "description": "", "templateType": "anything"}, "expr": {"name": "expr", "group": "Ungrouped variables", "definition": "expression(\"sin({scale}x)\")", "description": "", "templateType": "anything"}, "period": {"name": "period", "group": "Ungrouped variables", "definition": "expression(\"2*pi/{scale}\")", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pairs", "pair", "fn", "scale", "expr", "period"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the period of the function $\\var{expr}$?</p>\n<p>($\\pi$ should appear in your answer)</p>", "answer": "{period}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "exam"}]}, {"name": "502, Solve equation using log", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Solving equations using logs", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>Solving an equation of the form $a^x=b$ using logarithms to find $x$.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Solve for $x$:</p>\n<p>\\[ \\var{a}^x = \\var{b} \\,. \\]</p>", "advice": "<p>To solve $\\var{a}^x = \\var{b}$ for $x$, since $x$ is the exponent we want to make use of the following logarithm rule:</p>\n<ul>\n<li>$\\log(a^n) = n \\log(a)$.</li>\n</ul>\n<p></p>\n<p>By taking the logarithm of each side and applying the above rule:</p>\n<p>\\[ \\begin{split}\\var{a}^x &amp;\\,= \\var{b} \\\\ \\log_{10}(\\var{a}^x) &amp; \\,= \\log_{10}(\\var{b})\\\\ x \\log_{10}(\\var{a}) &amp;\\,= \\log_{10}(\\var{b}) \\\\\\\\ x&amp;\\,=\\simplify{log({b})/log({a})} \\\\\\\\ x &amp;\\,= \\var{sol} \\text{ (2 d.p.)}.&nbsp; \\end{split} \\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Logs\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise how logarithms.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..9 except [a,a^2,a^3])", "description": "", "templateType": "anything", "can_override": false}, "sol": {"name": "sol", "group": "Ungrouped variables", "definition": "precround(log(b)/log(a),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "sol"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$x=$ [[0]] (<em>Give you answer to 2 decimal places where necessary)</em></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "402, Logs definition", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Logs - definition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Megan Oliver", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23526/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>Finding $x$ from a logarithmic equation of the form $\\log_ax = b$, where $a$ and $b$ are positive integers.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Find the value of $x$:</p>\n<p>\\[ \\log_\\var{a}x = \\var{n} \\]</p>", "advice": "<p>To find the value of $x$, recall that $\\log_a(x)=b$ is equivalent to $x=a^b$.&nbsp;</p>\n<p>Therefore, \\[\\log_\\var{a}(x) = \\var{n} \\implies \\simplify[!collectNumbers]{x={a}^{n}}.\\]</p>\n<p>Hence, \\[x=\\var{a^n}\\,.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Logs\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise logarithms.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "n"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$x=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a^n}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "442b, Integration of Powers, Trig and Exp", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Integration - powers, trig and exp", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "functions": {}, "tags": ["Calculus", "Steps", "calculus", "constant of integration", "exponential function", "indefinite integration", "integrals", "integrating powers", "integration", "integration of exponential function", "integration of powers", "integration of trigonometric functions", "standard integrals", "steps", "trigonometric functions"], "advice": "\n  <p>Note that \\[\\begin{eqnarray*} &amp;\\int&amp; \\;x^n\\;dx&amp;=&amp;\\frac{x^{n+1}}{n+1}+C,\\;\\;n \\neq -1\\\\ &amp;\\int&amp; \\;\\sin(ax)\\;dx &amp;=&amp; -\\frac{1}{a}\\cos(ax)+C\\\\ &amp;\\int&amp; \\;e^{ax}\\;dx &amp;=&amp; \\frac{1}{a}e^{ax}+C\\\\ \\end{eqnarray*}\\]</p>\n  <p>Splitting the integral into three parts and using the above information we have: <br/>\\[\\begin{eqnarray*}\\simplify[std]{Int({b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3},x)}&amp;=&amp;\\simplify[std]{Int({b} * e ^ ({a}*x),x)+Int({b1} * Sin({a1}*x),x)+Int({a2} * x ^ {c3},x) }\\\\ &amp;=&amp;\\simplify[std]{({b}/{a}) * (e ^({a}*x)) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C} \\end{eqnarray*}\\]</p>\n  ", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}]}, "parts": [{"stepspenalty": 0.0, "prompt": "\n      <p>$\\simplify[std]{f(x) = {b} * e ^ ({a}*x) + {b1} * Sin({a1}*x) + {a2} * x ^ {c3}}$</p>\n        <p>$\\displaystyle \\int\\;f(x)\\,dx=\\;$[[0]]</p>\n        <p>Input all numbers as integers or fractions and not decimals. Remember to include the constant of integration $C$.</p>\n        <p>Click on Show steps to get more information. You will not lose any marks by doing so.</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Input all numbers as integers or fractions and not decimals.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [1.0, 2.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 3.0, "answer": "({b}/{a}) * (e ^({a}*x)) + (({(-b1)}/{a1}) * Cos({a1}*x)) + ({a2}/{c3+1}) * (x ^ {(c3 + 1)})+C", "type": "jme"}], "steps": [{"prompt": "<p>Note that \\[\\begin{eqnarray*} &amp;\\int&amp; \\;x^n\\;dx&amp;=&amp;\\frac{x^{n+1}}{n+1}+C,\\;\\;n \\neq -1\\\\ &amp;\\int&amp; \\;\\sin(ax)\\;dx &amp;=&amp; -\\frac{1}{a}\\cos(ax)+C\\\\ &amp;\\int&amp; \\;e^{ax}\\;dx &amp;=&amp; \\frac{1}{a}e^{ax}+C\\\\ \\end{eqnarray*}\\]</p>", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "statement": "\n  <p>Integrate the following function $f(x)$.</p>\n  <p>&nbsp;<br/>Input the constant of integration as $C$.</p>\n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "s1*random(2..5)", "name": "a"}, "b": {"definition": "s2*random(2..9)", "name": "b"}, "s3": {"definition": "random(1,-1)", "name": "s3"}, "s2": {"definition": "random(1,-1)", "name": "s2"}, "s1": {"definition": "random(1,-1)", "name": "s1"}, "s5": {"definition": "random(1,-1)", "name": "s5"}, "s4": {"definition": "random(1,-1)", "name": "s4"}, "a1": {"definition": "random(2..5)", "name": "a1"}, "a2": {"definition": "s4*random(3..9)", "name": "a2"}, "b1": {"definition": "s3*random(2..9)", "name": "b1"}, "c3": {"definition": "s5*random(2..8)", "name": "c3"}}, "metadata": {"notes": "\n    \t\t<p><strong>2/08/2012:</strong></p>\n    \t\t<p>Added tags.</p>\n    \t\t<p>Added description.</p>\n    \t\t<p>Corrected mistake in formula for integrating $\\sin(ax)$ in Steps and Advice.</p>\n    \t\t<p>Checked calculation. OK.</p>\n    \t\t<p>Added decimal point to forbidden strings along with message to user re input of numbers.</p>\n    \t\t<p>Message about Show steps included. Also another message about including the constant of integration.</p>\n    \t\t<p>Changed checking range from 0 to 1 to 1 to 2 as we can have negative powers of $x$.</p>\n    \t\t<p>Improved display of Steps by aligning integral signs.</p>\n    \t\t", "description": "<p>Find $\\displaystyle \\int ae ^ {bx}+ c\\sin(dx) + px ^ {q}\\;dx$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}, {"name": "443, Definite Integrals", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Definite Integral - Powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>Calculating the definite integral $\\int_{n_1}^{n_2}a_1x^{b_1}+a_2x^{b_2}+a_3x^{b_3} dx$.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Evaluate \\[ \\int_{\\var{n_1}}^{\\var{n_2}}\\simplify[unitFactor, unitPower, fractionNumbers]{{a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3}} \\,dx.\\]</p>\n<p></p>", "advice": "<p>Integrating a function of the form&nbsp;&nbsp;\\[ f(x)=x^n \\] has the integral \\[ \\int_a^b x^n dx&nbsp; =&nbsp; \\left[\\frac{x^{n+1}}{n+1}\\right]_a^b,\\]</p>\n<p>and \\[\\int_a^b kf(x) dx = k \\int_a^b f(x) dx.\\]</p>\n<p>Additionally, the&nbsp;integral of the sum or difference of two or more functions is equal to the sum or difference of the&nbsp;integrals of each function: \\[ \\int(f(x)\\pm g(x))\\, dx = \\int f(x)\\, dx&nbsp; \\pm \\int g(x) \\, dx.\\]</p>\n<p></p>\n<p>Therefore,</p>\n<p>\\[ \\begin{split}\\simplify[unitFactor,unitPower]{defint({a_1}*x^{b_1}+{a_2}*x^{b_2}+{a_3}*x^{b_3},x,{n_1},{n_2})} &amp;\\,= \\simplify{{a_1}defint(x^{b_1},x,{n_1},{n_2})+{a_2}defint(x^{b_2},x,{n_1},{n_2})+{a_3}defint(x^{b_3},x,{n_1},{n_2})} \\\\ &amp;\\,= \\left[\\simplify[all,fractionNumbers]{{a_1}x^{b_1+1}/{b_1+1}+{a_2}x^{b_2+1}/{b_2+1}+{a_3}x^{b_3+1}/{b_3+1}}\\right]_\\var{n_1}^\\var{n_2} \\\\ &amp;\\,= \\left[\\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_2^(b_1+1)}/{b_1+1}+{a_2*n_2^(b_2+1)}/{b_2+1}+{a_3*n_2^(b_3+1)}/{b_3+1}}\\right] -\\left[\\simplify[all,fractionNumbers,!collectNumbers]{{a_1*n_1^(b_1+1)}/{b_1+1}+{a_2*n_1^(b_2+1)}/{b_2+1}+{a_3*n_1^(b_3+1)}/{b_3+1}}\\right]&nbsp;\\\\ &amp;\\,= \\simplify[!collectNumbers]{{eval2a}-{eval1a}} \\\\ &amp;\\,=\\var{sol1} \\end{split} \\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/first-steps#Int\"><span style=\"font-weight: 400;\">Use this link to find some resources on areas under curves which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a_1": {"name": "a_1", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "b_1": {"name": "b_1", "group": "Ungrouped variables", "definition": "3", "description": "", "templateType": "anything", "can_override": false}, "a_2": {"name": "a_2", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b_2": {"name": "b_2", "group": "Ungrouped variables", "definition": "2", "description": "", "templateType": "anything", "can_override": false}, "b_3": {"name": "b_3", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a_3": {"name": "a_3", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything", "can_override": false}, "n_1": {"name": "n_1", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "n_2": {"name": "n_2", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "eval2": {"name": "eval2", "group": "Ungrouped variables", "definition": "a_1*n_2^(b_1+1)/(b_1+1)+a_2*n_2^(b_2+1)/(b_2+1)+a_3*n_2^(b_3+1)/(b_3+1)", "description": "", "templateType": "anything", "can_override": false}, "eval1": {"name": "eval1", "group": "Ungrouped variables", "definition": "a_1*n_1^(b_1+1)/(b_1+1)+a_2*n_1^(b_2+1)/(b_2+1)+a_3*n_1^(b_3+1)/(b_3+1)", "description": "", "templateType": "anything", "can_override": false}, "eval2a": {"name": "eval2a", "group": "Ungrouped variables", "definition": "precround(eval2,3)", "description": "", "templateType": "anything", "can_override": false}, "eval1a": {"name": "eval1a", "group": "Ungrouped variables", "definition": "precround(eval1,3)", "description": "", "templateType": "anything", "can_override": false}, "sol": {"name": "sol", "group": "Ungrouped variables", "definition": "eval2-eval1", "description": "", "templateType": "anything", "can_override": false}, "sol1": {"name": "sol1", "group": "Ungrouped variables", "definition": "precround(sol,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "b_1>b_2 and b_2>b_3 and n_2>n_1", "maxRuns": "100"}, "ungrouped_variables": ["a_1", "a_2", "a_3", "b_1", "b_2", "b_3", "n_1", "n_2", "eval2", "eval1", "eval2a", "eval1a", "sol", "sol1"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]&nbsp;<em>(Give answers to 2 decimal places where necessary)</em></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Gap 0", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sol1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "444, Integration by substitution", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Integration - Substitution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>Calculating the integral of a function of the form $\\frac{nx^{n-1}}{x^n+a}$ using integration by substitution.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate \\[ \\simplify[all]{int(({n}x^{n-1})/(x^{n}+{a}),x)}\\]</p>\n<p>by using the substitution \\[ \\simplify[all]{u=x^{n}+{a}}.\\]</p>", "advice": "<p>Since this integral is of the form \\[ \\int g'(x)f(g(x))\\,dx,\\] we can use the method of substitution to calculate the solution.&nbsp;</p>\n<p>Firstly, we must make a change of variables from $x$ to $u$, where $u$ is equal to the 'inner' function $g(x)$.</p>\n<p>So, for \\[\\simplify[fractionNumbers]{int(({n}x^{n-1})/((x^{n}+{a})),x)}\\]</p>\n<p>let $\\color{red}{u=\\simplify[fractionNumbers]{x^{n}+{a}}}.$</p>\n<p>Now, we need to calculate the differential, $du$, where \\[ du = \\left(\\frac{du}{dx}\\right)dx. \\]</p>\n<p>Differentiating $u$ with respect to $x$:</p>\n<p>\\[ \\frac{du}{dx}= \\simplify[fractionNumbers]{{n}x^{n-1}}.\\]</p>\n<p>Therefore, \\[ \\color{blue}{du = \\simplify[fractionNumbers]{{n}x^{n-1}}\\, dx}.\\]</p>\n<p>We can now rewrite the original integral in terms of $u$:</p>\n<p>\\[ \\int \\frac{\\color{blue}{\\simplify{{n}x^{n-1}}}}{\\color{red}{\\simplify{x^{n}+{a}}}}\\color{blue}{\\text{d}x} =&nbsp;\\int \\frac{1}{\\color{red}{u}}\\color{blue}{\\text{d}u}.\\]</p>\n<p><strong>(Note: It is important to see that both the function we are integrating, and the variable we are integrating with respect to, has changed.)</strong></p>\n<p>\\[ \\simplify[fractionNumbers]{int(1/u,u) = ln(abs(u)) + c}.\\]</p>\n<p>Finally, we must rewrite our solution back in terms of the original variable $x$:</p>\n<p>\\[ \\simplify[fractionNumbers]{ln(abs(u)) + c = ln(abs(x^{n}+{a}))&nbsp;+ c}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/next-steps#Int\">Use this link to find some resources which will help you revise this topic.</a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["a", "n"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Correct answer", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": true, "customName": "Alternative using brackets", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>Technically we should use the absolute value symbols for the logs. This can be done in NUMBAS by using \"abs(*function*)\".</p>", "useAlternativeFeedback": false, "answer": "ln(x^{n}+{a})+c", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "Alternative using \"+k\"", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "ln(abs(x^{n}+{a})) + k", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "k", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "Alternative using brackets and \"+k\"", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>Technically we should use the absolute value symbols for the logs. This can be done in NUMBAS by using \"abs(*function*)\".</p>", "useAlternativeFeedback": false, "answer": "ln(x^{n}+{a})+k", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "k", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "Forgotten constant", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>It looks like you forgot to include the integration constant. You should always remember the \"+C\" when doing an indefinite integral.</p>", "useAlternativeFeedback": false, "answer": "ln(abs(x^{n}+{a}))", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "ln(abs(x^{n}+{a}))+c", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": "0.01", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "505, Integration by parts", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Integration - by Parts", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>Calculating the integral of a function of the form $ax^2 \\cos(bx)$ using integration by parts.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the integral \\[ \\simplify{int({a}x^2 cos({b}x),x)}\\]</p>", "advice": "<p>If we have a function of $x$ which is the product of two functions of $x$, to integrate such a function it is often necessary to use Integration by Parts. The formula for Integration by Parts is:</p>\n<p>\\[ \\int u(x) \\frac{dv}{dx} dx = u(x)v(x) - \\int v(x) \\frac{du}{dx} dx.\\]</p>\n<p>Using this method can be broken down into steps:</p>\n<ol>\n<li>Identify $u(x)$ and $\\tfrac{dv}{dx}$ (The function you pick for each is important, in general you want $u(x)$ to become simpler when differentiating it, and you must be able to integrate $\\tfrac{dv}{dx}$ to find $v(x)$);</li>\n<li>Calculate $\\tfrac{du}{dx}$ and $v(x)$;</li>\n<li>Put the functions $u(x)$, $v(x)$, and their derivatives into the Integration by Parts formula;</li>\n<li>Calculate the integral $\\int v(x) \\tfrac{du}{dx} dx$ (This may require you to use Integration by Parts again, this is OK!);</li>\n<li>Simplify your answer where possible and don't forget to add the constant of integration.</li>\n</ol>\n<p></p>\n<p>For the integral</p>\n<p>\\[ \\simplify{int({a}x^2 cos({b}x),x)},\\]</p>\n<p>we must first identify $u(x)$ and $\\tfrac{dv}{dx}$. In this case, let \\[ u(x)=\\simplify{{a}x^2},\\quad \\frac{dv}{dx}= \\simplify{cos({b}x)}. \\]</p>\n<p>Next, we need to calculate $\\tfrac{du}{dx}$ and $v(x)$:</p>\n<p>\\[ \\begin{split} u(x) = \\var{a}x^2 \\quad &amp;\\implies \\frac{du}{dx} = \\simplify{{2a}x}; \\\\ \\frac{dv}{dx} = \\cos(\\var{b}x) &amp;\\implies v(x) = \\simplify[fractionNumbers]{1/{b} sin({b}x)}. \\end{split} \\]</p>\n<p>Plugging these 4 terms into the integration by parts formula:</p>\n<p>\\[&nbsp; \\begin{split} \\simplify{int({a}x^2 cos({b}x),x)} &amp;\\,= \\simplify[fractionNumbers]{{a/b}x^2 sin({b}x) - int({2a/b}x sin({b}x),x)},&nbsp; \\\\ \\\\ &amp;\\,= \\simplify[fractionNumbers]{{a/b}x^2 sin({b}x) -{2a/b}int(x sin({b}x),x)}.\\end{split} \\]</p>\n<p>Since the integral on the right-hand side is still the product of two functions of $x$, we need to use integration by parts again.&nbsp;</p>\n<p>So, for&nbsp;</p>\n<p>\\[ \\simplify{int(x sin({b}x),x)}, \\]</p>\n<p>&nbsp;Let $u=x$ and $\\tfrac{dv}{dx} = \\sin(\\var{b}x)$. Therefore, $\\tfrac{du}{dx}=1$ and $v(x)=\\simplify{-1/{b} cos({b}x)}$.</p>\n<p>Hence,</p>\n<p>\\[ \\begin{split} \\simplify{int(x sin({b}x),x)} &amp;\\,= \\simplify{-1/{b}x cos({b}x)- int(-1/{b} cos({b}x),x)} \\\\ \\\\ &amp;\\,= \\simplify{-1/{b}x cos({b}x)+1/{b^2}sin({b}x)}. \\end{split}\\]</p>\n<p>Plugging this back into the original calculation:</p>\n<p>\\[&nbsp; \\begin{split} \\simplify{int({a}x^2 cos({b}x),x)} &amp;\\,= \\simplify[fractionNumbers]{{a/b}x^2 sin({b}x) -{2a/b}int(x cos({b}x),x)} \\\\ \\\\ &amp;\\,=&nbsp;\\simplify[fractionNumbers]{{a/b}x^2 sin({b}x) -{2a/b}[-1/{b}x cos({b}x)+1/{b^2}sin({b}x)]} \\\\ \\\\ &amp;\\,=\\simplify[fractionNumbers]{{a/b}x^2 sin({b}x) +{2a/b^2}x cos({b}x)-{2a/b^3}sin({b}x)} + c.\\end{split} \\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/next-steps#Int\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..7)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "gcd(a,b)=1 and b>a", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Correct Answer", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": true, "customName": "Alt constant +k", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "{a/b}x^2 sin({b}x)+{2a/b^2}x cos({b}x)-{2a/b^3}sin({b}x)+k", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "k", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "Forgotten constant", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>It looks like you forgot to include the integration constant. You should always remember the \"+C\" when doing an indefinite integral.</p>", "useAlternativeFeedback": false, "answer": "{a/b}x^2 sin({b}x)+{2a/b^2}x cos({b}x)-{2a/b^3}sin({b}x)", "answerSimplification": "all,!collectLikeFractions,fractionNumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a/b}x^2 sin({b}x)+{2a/b^2}x cos({b}x)-{2a/b^3}sin({b}x)+c", "answerSimplification": "fractionNumbers, basic", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}]}, {"name": "341b, Differentiation of polynomials", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Differentiation - Polynomials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "functions": {}, "ungrouped_variables": ["ac", "bc", "cc", "dc", "d"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p style=\"text-align: center;\">If $y=ax^n$,</p>\n<p style=\"text-align: center;\">$\\frac{dy}{dx}=anx^{n-1}$ for all rational $n$.</p>\n<p style=\"text-align: left;\">We'll take the following term as an example:</p>\n<p style=\"text-align: left;\">$\\frac{3}{8}x^2$</p>\n<p style=\"text-align: left;\">All we have to do to terms where $x$ is to a power of anything is times the coefficient of $x$ by the original power, and then take one away from the original power.</p>\n<p style=\"text-align: left;\">If you are not familiar with this kind of work, these instructions may sound confusing, but it is much easier once you have seen it in practice.</p>\n<p style=\"text-align: left;\">We take</p>\n<p style=\"text-align: left;\">$\\frac{3}{8}x^2$</p>\n<p style=\"text-align: left;\">and times $\\frac{3}{8}$ by $2$, to get</p>\n<p style=\"text-align: left;\">$(\\frac{3}{8}\\times2)x^2=\\frac{6}{8}x^2=\\frac{3}{4}x^2$.</p>\n<p style=\"text-align: left;\">We then subtract one from the original power, $2$.</p>\n<p style=\"text-align: left;\">This gives us the final answer of</p>\n<p style=\"text-align: left;\"><strong>$\\frac{3}{4}x^1=\\frac{3}{4}x$</strong>.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">Remember, don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$, but we don't tend to write it out as, for example $1x$, we just say $x$.</p>", "rulesets": {}, "parts": [{"vsetrangepoints": 5, "prompt": "<p>$\\simplify{({ac[0]}/{d[0]})x^3+({bc[0]}/{d[1]})x^2+({cc[0]}/{d[2]})x+({dc[0]}/{d[3]})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3{ac[0]}/{d[0]}x^2+2{bc[0]}/{d[1]}x+{cc[0]}/{d[2]}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{({ac[1]}/{d[4]})x^3+({bc[1]}/{d[5]})x^2+({cc[1]}/{d[6]})x+({dc[1]}/{d[7]})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3{ac[1]}/{d[4]}x^2+2{bc[1]}/{d[5]}x+{cc[1]}/{d[6]}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>$\\simplify{({ac[2]}/{d[8]})x^3+({bc[2]}/{d[9]})x^2+({cc[2]}/{d[10]})x+({dc[2]}/{d[11]})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3{ac[2]}/{d[8]}x^2+2{bc[2]}/{d[9]}x+{cc[2]}/{d[10]}", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "statement": "<p><strong>Differentiate the following polynomials.</strong></p>", "type": "question", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"cc": {"definition": "repeat(random(-15..15),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "ac": {"definition": "repeat(random(-3..3),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "ac", "description": ""}, "d": {"definition": "repeat(random(1..9),12)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "dc": {"definition": "repeat(random(-30..30),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "dc", "description": ""}, "bc": {"definition": "repeat(random(-10..10),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "bc", "description": ""}}, "metadata": {"description": "<p>More work on differentiation with fractional coefficients.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}, {"name": "341c, Differentiation of exponential, log, trig functions", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Differentiation - exponentials, log, trig functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}, {"name": "Sid Gurjar", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3870/"}, {"name": "Venkata Lakshmipathi Raju Chinthalapati", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4574/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": ["calculus", "Calculus", "Differentiation", "differentiation"], "metadata": {"description": "<p>A question to test basic&nbsp;differentiation of functions, including powers of x, trig, log and exponential functions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Differentiate the&nbsp;following functions with respect to $x$, simplifying your answers where possible.</p>", "advice": "<p>This&nbsp;<a href=\"http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-table1-2009-1.pdf\">leaflet</a> from Mathcentre will remind you of the rules for differentiating these functions.</p>\n<p></p>", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..5)//Use as a power", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-5..5 except -1..1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$x^\\var{a}-\\sin(\\var{b}x)$</p>", "answer": "{a}x^{a-1}-{b}cos({b}x)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{a}e^{-\\var{b}x}+\\frac{\\var{c}}{x}$</p>", "answer": "-{a}{b}e^(-{b}x)-{c}/x^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{d}\\ln(\\var{c}x)-\\var{a*b}\\cos(x/\\var{b})$</p>", "answer": "{d}/x+{a}sin(x/{b})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{a}\\sqrt{x}-\\var{c}e^{\\var{d}x}$</p>", "answer": "{a}/(2sqrt(x))-{c}{d}e^({d}x)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{d}-\\frac{\\var{b}}{x^2}$</p>", "answer": "2{b}/x^3", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$\\var{10*d}\\sin(\\var{c/10}x)+\\var{b}x$</p>", "answer": "{c}*{d}cos({c}/10*x)+{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}], "type": "question"}]}, {"name": "503, Chain rule - powers", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Chain rule - powers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "functions": {}, "ungrouped_variables": ["c"], "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>This question is the chain rule again.</strong></p>\n<p>This time, the function that is being differentiated is the term inside the brackets.</p>\n<p>This is another 'chain rule by inspection' kind of question to save time and paper.</p>\n<p>Firstly, differentiate everything inside the brackets.</p>\n<p>Then multiply the existing coefficient of the bracket by this result.</p>\n<p>Finally, multiply by the original magnitude of the power and decrease the power by one.</p>\n<p>If these steps confuse you, look back at <em>'Differentiation - Basic Polynomial Expressions'</em>&nbsp;and make sure you understand fully how to work those types of questions out.</p>", "rulesets": {}, "parts": [{"prompt": "<p>$y=(\\var{c[0]}x-1)^3$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3*{c[0]}({c[0]}x-1)^2", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$y=(\\var{c[1]}-x)^5$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-5({c[1]}-x)^4", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$y=(x^2+\\var{c[2]})^4$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "8x*(x^2+{c[2]})^3", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$y=(x^3-\\var{c[3]})^2$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "6x^2*(x^3-{c[3]})", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$y=(1-\\var{c[4]}x^2)^3$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-6{c[4]}x*(1-{c[4]}x^2)^2", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Differentiate the following using the chain rule.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"definition": "repeat(random(2..9),8)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}}, "metadata": {"notes": "", "description": "<p>Using the chain rule with polynomials</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}, {"name": "504, Quotient rule", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Differentiation - Quotient Rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "functions": {}, "ungrouped_variables": ["c", "p"], "tags": [], "advice": "<p><strong>These questions use the&nbsp;quotient&nbsp;rule.</strong></p>\n<p>The quotient&nbsp;rule is defined as</p>\n<p style=\"text-align: center;\">$\\frac{dy}{dx}=\\frac{v\\frac{du}{dx}+u\\frac{dv}{dx}}{v^2}$</p>\n<p style=\"text-align: center;\">when $y=\\frac{u}{v}$</p>\n<p><strong>Worked example using Part a:</strong></p>\n<p style=\"text-align: center;\"><fraction><numerator>$x$</numerator><denominator>$\\simplify{x+{c[0]}}$</denominator></fraction></p>\n<p style=\"text-align: left;\">This expression is the result of&nbsp;$x$ divided by&nbsp;($\\simplify{x+{c[0]}}$).</p>\n<p style=\"text-align: left;\">We can therefore say:</p>\n<p style=\"text-align: left;\">$u=x$</p>\n<p style=\"text-align: left;\">and</p>\n<p style=\"text-align: left;\">$v=\\simplify{x+{c[0]}}$,</p>\n<p style=\"text-align: left;\">Hence meaning that $y=\\frac{u}{v}$.</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">We already have what $u$ and $v$ equal, so all we have to do is find what $\\frac{du}{dx}$ and $\\frac{dv}{dx}$ are, and then substitute everything into the rule.</p>\n<p style=\"text-align: left;\">Differentiating with respect to $x$, we get:</p>\n<p style=\"text-align: left;\">$\\frac{du}{dx}=1$</p>\n<p style=\"text-align: left;\">and</p>\n<p style=\"text-align: left;\">$\\frac{dv}{dx}=1$.</p>\n<p style=\"text-align: left;\">As there are no powers or coefficients of $x$ that are $&gt;1$, this is a very simple version of the quotient&nbsp;rule, but knowing how to work out this equation formally will make more difficult looking problems just as simple.</p>\n<p style=\"text-align: left;\">Substituting in all the results we've found, we get:</p>\n<p style=\"text-align: left;\">$\\frac{dy}{dx}=\\frac{1(\\simplify{x+{c[0]}})+1(x)}{\\simplify{(x+{c[0]})^2}}$</p>\n<p style=\"text-align: left;\">We then simplify, collecting all the terms, to get our final answer of:</p>\n<p style=\"text-align: center;\">$\\frac{dy}{dx}=\\simplify{((2x+{c[0]}))/(x+{c[0]})^2}$</p>", "rulesets": {"std": ["all"]}, "parts": [{"variableReplacements": [], "prompt": "<p><fraction><numerator>$\\simplify{{c[1]}x+{c[2]}}$</numerator><denominator>$\\simplify{x+{c[3]}}$</denominator></fraction></p>", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c[1]}*{c[3]}-{c[2]})/(x+{c[3]})^2", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p><fraction><numerator>$\\simplify{{c[6]}-sqrt(x)}$</numerator><denominator>$\\simplify{({c[7]}+x)^2}$</denominator></fraction></p>", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(-1({c[7]}+x)-4(sqrt(x)*({c[6]}-sqrt(x))))/(2sqrt(x)({c[7]}+x)^3)", "marks": "3", "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "statement": "<p><strong>Differentiate the following expressions with respect to $x$ using the quotient rule.</strong></p>\n<p><strong></strong>Simplify your answers as much as possible.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "variables": {"p": {"definition": "repeat(random(2..7),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "repeat(random(-9..9 except 0),12)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}}, "metadata": {"notes": "", "description": "<p>An introduction to using the quotient rule</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}]}, {"name": "505, Chain rule - trigonometry", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Chain rule - trigonometry", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}], "tags": [], "metadata": {"description": "<p>More work on differentiation with&nbsp;trigonometric functions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Differentiate the following&nbsp;trigonometric functions using the chain rule.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "advice": "<p><strong></strong>If you don't know how to differentiate trigonometric functions, please see&nbsp;<em>'Differentiation 4 - Trigonometric Functions'</em>.</p>\n<p><strong></strong></p>\n<p><strong>These questions use the chain rule.</strong></p>\n<p>The earlier questions are easy to do by inspection, e.g using Part a:</p>\n<p style=\"text-align: center;\">$y=sin(\\var{c[0]}x)$.</p>\n<p>We differentiate the term(s) inside the function, here the term is $\\var{c[0]}x$.</p>\n<p>Then we derive $sin$ of any function, giving us $cos$.</p>\n<p>Putting our results together, we get</p>\n<p>$\\var{c[0]}cos(\\var{c[0]}x)$.</p>\n<p></p>\n<p></p>\n<p></p>\n<p><strong>We will now go through an entire worked example of the formal method of the chain rule using Part e.</strong></p>\n<p>The expression we will be differentiating here is</p>\n<p style=\"text-align: center;\">$y=tan^\\var{p[0]}(x)$.</p>\n<p style=\"text-align: left;\">As a reminder, the chain rule is defined as</p>\n<p style=\"text-align: center;\">$\\frac{dy}{dx}=\\frac{dy}{du}\\times\\frac{du}{dx}$.</p>\n<p style=\"text-align: left;\">Now we let $u=tanx$, so then $y=u^\\var{p[0]}$</p>\n<p style=\"text-align: left;\">This becomes an easy differentiation using $\\frac{dy}{du}\\times\\frac{du}{dx}$:</p>\n<p style=\"text-align: left;\">Differentiate $y$ with respect to $u$, giving $\\simplify{{p[0]}u^{{p[0]}-1}}$.</p>\n<p style=\"text-align: left;\">Then differentiate $u$ with respect to $x$, giving $sec^2x$.</p>\n<p style=\"text-align: left;\">Multiply these results together, and substitue $tan$ back in for $u$.</p>\n<p style=\"text-align: left;\">Your final result is therefore</p>\n<p style=\"text-align: center;\">$\\simplify{{p[0]}(tan^{{p[0]}-1}(x))*sec^2(x)}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "repeat(random(3..6),2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "shuffle(2..8)[0..5]", "description": "<p>coefficients</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "p"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\sin(\\var{c[0]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c[0]}cos({c[0]}x)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\cos(\\var{c[1]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-{c[1]}sin({c[1]}x)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=-\\sin(\\var{c[2]}x^2)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-2{c[2]}x*cos({c[2]}x^2)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=-5\\cos(\\var{c[3]}x)+\\sin(\\var{c[4]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "5{c[3]}sin({c[3]}x)+{c[4]}cos({c[4]}x)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\tan^\\var{p[0]}(x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{p[0]}(tan(x)^({p[0]}-1))*sec(x)^2", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$y=\\cos(x^\\var{p[1]}-1)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-{p[1]}x^({p[1]}-1)*sin(x^{p[1]}-1)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": false, "browse": false, "allowsteps": true, "showfrontpage": true, "navigatemode": "diagnostic", "onleave": {"action": "warnifunattempted", "message": "<p>You have not attempted this question.</p>"}, "preventleave": false, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": true, "downloadEncryptionKey": "", "showresultspage": "oncompletion"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showpartfeedbackmessageswhen": "never", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": false, "intro": "<p>The purpose of this test is to establish your background knowledge of mathematics before beginning a university degree course.</p>\n<p>The system chooses which questions to ask you based on your answers to previous questions.</p>\n<p>If the test feels too long, use the PAUSE button and save the page (don't close the tab!); you can get back to it at a later time.</p>\n<p>When the test is over, you will be shown a summary of the system's estimates of your understanding of each of the topics covered in the test.</p>\n<p>The test is anonymous and won't appear in any record, so don't be afraid to test your skills!</p>", "end_message": "<p>Depending on your results, you may wish to access the Math helpdesk <a href=\"https://ask.herts.ac.uk/maths-drop-in-centre\">here</a>, or book a one to one appointment with a tutor. They can help you assess the best way to improve your skills and fill in the gaps. Save the page with your results to have a reference on what are your weaker and stronger topics, and bring it to the appointment.</p>\n<p>Use the \"print this result summary\" button and save the file, it will contain all your attempted questions with your answers; it will be useful to go through the questions with the tutor.</p>\n<p>Click <a href=\"https://helpdesk.herts.ac.uk:8443/helpdesk/WebObjects/Helpdesk.woa/wa/TicketActions/new?rt=146\">here</a> to book your appointment.</p>", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": true, "showanswerstate": false, "reviewshowfeedback": true, "showactualmark": true, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [{"name": "101, Multiplication of negative numbers", "description": "", "depends_on": ["102, Multiply negative and positive"], "learning_objectives": ["Numbers"]}, {"name": "102, Multiply negative and positive", "description": "", "depends_on": ["103, Negative Numbers"], "learning_objectives": ["Numbers"]}, {"name": "103, Negative Numbers", "description": "", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "104, Size of decimals", "description": "", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "105, Decimal places", "description": "", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "106, Definition of positive powers", "description": "", "depends_on": [], "learning_objectives": ["Powers"]}, {"name": "107, Ratios", "description": "", "depends_on": ["108, Factors of an integer"], "learning_objectives": ["Numbers"]}, {"name": "108, Factors of an integer", "description": "<p>Can the student find the factors of a given integer?</p>", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "109, Simple fractions", "description": "", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "201, Use of < and > signs", "description": "", "depends_on": ["103, Negative Numbers", "104, Size of decimals"], "learning_objectives": ["Numbers"]}, {"name": "205, Inverse ratios", "description": "", "depends_on": ["107, Ratios"], "learning_objectives": ["Numbers"]}, {"name": "206, Cancelling numerical fractions", "description": "", "depends_on": ["107, Ratios", "108, Factors of an integer"], "learning_objectives": ["Numbers"]}, {"name": "216, Add/subtract numerical fractions", "description": "", "depends_on": ["109, Simple fractions", "206, Cancelling numerical fractions"], "learning_objectives": ["Numbers"]}, {"name": "301, Solution of simple inequalities", "description": "", "depends_on": ["201, Use of < and > signs"], "learning_objectives": ["Numbers"]}, {"name": "202, Significant figures", "description": "", "depends_on": ["105, Decimal places"], "learning_objectives": ["Numbers"]}, {"name": "203, Definition of negative powers", "description": "", "depends_on": ["106, Definition of positive powers"], "learning_objectives": ["Powers"]}, {"name": "204, Rules for positive powers", "description": "", "depends_on": ["106, Definition of positive powers"], "learning_objectives": ["Powers"]}, {"name": "302, Scientific Notation", "description": "", "depends_on": ["202, Significant figures", "203, Definition of negative powers"], "learning_objectives": ["Numbers"]}, {"name": "303, Simplification of fractions with powers", "description": "", "depends_on": ["206, Cancelling numerical fractions", "304, Rules for negative powers"], "learning_objectives": ["Powers"]}, {"name": "304, Rules for negative powers", "description": "", "depends_on": ["203, Definition of negative powers", "204, Rules for positive powers"], "learning_objectives": ["Powers"]}, {"name": "305, Rules for fractional powers", "description": "", "depends_on": ["304, Rules for negative powers", "306, Definition of fractional powers"], "learning_objectives": ["Powers"]}, {"name": "306, Definition of fractional powers", "description": "", "depends_on": ["203, Definition of negative powers"], "learning_objectives": ["Powers"]}, {"name": "401, Simplify with scientific notation", "description": "", "depends_on": ["302, Scientific Notation", "303, Simplification of fractions with powers"], "learning_objectives": ["Powers"]}, {"name": "402b, Log rules", "description": "", "depends_on": ["304, Rules for negative powers", "402, Logs definition"], "learning_objectives": ["Powers"]}, {"name": "403, Arbitrary factors", "description": "", "depends_on": ["304, Rules for negative powers"], "learning_objectives": ["Powers"]}, {"name": "110, Collect terms (simple)", "description": "", "depends_on": [], "learning_objectives": ["Basic algebra"]}, {"name": "111, Solving a simple equation", "description": "", "depends_on": [], "learning_objectives": ["Basic algebra"]}, {"name": "112, Simple calculation", "description": "", "depends_on": [], "learning_objectives": ["Numbers"]}, {"name": "113, Evaluating a simple expression", "description": "", "depends_on": [], "learning_objectives": ["Basic algebra"]}, {"name": "207, Multiply algebraic fractions", "description": "", "depends_on": ["206, Cancelling numerical fractions"], "learning_objectives": ["Basic algebra"]}, {"name": "208, Factors of algebraic products", "description": "", "depends_on": ["108, Factors of an integer"], "learning_objectives": ["Basic algebra"]}, {"name": "209, Simple Factorisation", "description": "", "depends_on": ["208, Factors of algebraic products", "210, Expanding one bracket"], "learning_objectives": ["Basic algebra"]}, {"name": "210, Expanding one bracket", "description": "", "depends_on": ["112, Simple calculation"], "learning_objectives": ["Basic algebra"]}, {"name": "211, Collecting terms", "description": "", "depends_on": ["110, Collect terms (simple)"], "learning_objectives": ["Basic algebra"]}, {"name": "212, Solving linear equations", "description": "", "depends_on": ["111, Solving a simple equation"], "learning_objectives": ["Basic algebra"]}, {"name": "213, Transposition of formula", "description": "", "depends_on": [], "learning_objectives": ["Basic algebra"]}, {"name": "214, Evaluating formula", "description": "", "depends_on": ["112, Simple calculation", "113, Evaluating a simple expression"], "learning_objectives": ["Basic algebra"]}, {"name": "215, Precedence Rules", "description": "", "depends_on": ["112, Simple calculation"], "learning_objectives": ["Numbers"]}, {"name": "307, Division of algebraic fractions", "description": "", "depends_on": ["207, Multiply algebraic fractions"], "learning_objectives": ["Algebra methods"]}, {"name": "308, Add/subtract algebraic fractions", "description": "", "depends_on": ["216, Add/subtract numerical fractions"], "learning_objectives": ["Algebra methods"]}, {"name": "309, Simple Quadratic equations", "description": "", "depends_on": ["209, Simple Factorisation", "212, Solving linear equations"], "learning_objectives": ["Trigonometry"]}, {"name": "310, Relation between roots and factors", "description": "", "depends_on": ["212, Solving linear equations", "311, Factorising a quadratic"], "learning_objectives": ["Trigonometry"]}, {"name": "311, Factorising a quadratic", "description": "", "depends_on": ["209, Simple Factorisation", "312, Expanding two brackets"], "learning_objectives": ["Algebra methods"]}, {"name": "312, Expanding two brackets", "description": "", "depends_on": ["110, Collect terms (simple)", "210, Expanding one bracket"], "learning_objectives": ["Algebra methods"]}, {"name": "313, Difference of squares", "description": "", "depends_on": ["312, Expanding two brackets"], "learning_objectives": ["Algebra methods"]}, {"name": "314, Simultaneous Equations", "description": "", "depends_on": ["212, Solving linear equations"], "learning_objectives": ["Trigonometry"]}, {"name": "315, Unusual linear equation", "description": "", "depends_on": ["212, Solving linear equations", "213, Transposition of formula"], "learning_objectives": ["Trigonometry"]}, {"name": "316, Use of quadratic formula", "description": "", "depends_on": ["214, Evaluating formula"], "learning_objectives": ["Trigonometry"]}, {"name": "405, Identification of common errors", "description": "", "depends_on": ["308, Add/subtract algebraic fractions", "312, Expanding two brackets"], "learning_objectives": ["Algebra and calculus"]}, {"name": "406, Solve quad. by comp. the square", "description": "", "depends_on": ["407, Quadratics - completing the square"], "learning_objectives": ["Trigonometry"]}, {"name": "407, Quadratics - completing the square", "description": "", "depends_on": ["311, Factorising a quadratic"], "learning_objectives": ["Algebra methods"]}, {"name": "410, Substituting into a formula", "description": "", "depends_on": ["214, Evaluating formula", "312, Expanding two brackets"], "learning_objectives": ["Algebra methods"]}, {"name": "411, Solutions of a quadratic", "description": "", "depends_on": ["316, Use of quadratic formula"], "learning_objectives": ["Trigonometry"]}, {"name": "412, Difficult linear equation", "description": "", "depends_on": ["209, Simple Factorisation", "315, Unusual linear equation"], "learning_objectives": ["Trigonometry"]}, {"name": "341, Differentiation of powers", "description": "", "depends_on": [], "learning_objectives": ["Algebra and calculus"]}, {"name": "342, Finding Max/Min of a quadratic", "description": "", "depends_on": ["341, Differentiation of powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "343, Geometric Progression", "description": "", "depends_on": [], "learning_objectives": ["Algebra and calculus"]}, {"name": "441, Product rule", "description": "", "depends_on": ["341, Differentiation of powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "442, Integration of powers", "description": "", "depends_on": ["341, Differentiation of powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "151, Coordinates", "description": "", "depends_on": [], "learning_objectives": ["Graphs"]}, {"name": "251, Gradient of a straight line", "description": "", "depends_on": ["151, Coordinates"], "learning_objectives": ["Graphs"]}, {"name": "351, Equation of a straight line", "description": "", "depends_on": ["251, Gradient of a straight line"], "learning_objectives": ["Graphs"]}, {"name": "451, Recognise formula of quad. graph", "description": "", "depends_on": ["351, Equation of a straight line"], "learning_objectives": ["Graphs"]}, {"name": "452, Recognise formula of recip. graph", "description": "", "depends_on": ["351, Equation of a straight line"], "learning_objectives": ["Graphs"]}, {"name": "221, Pythagoras", "description": "", "depends_on": [], "learning_objectives": ["Trigonometry"]}, {"name": "222, Definition of sin and cos", "description": "", "depends_on": [], "learning_objectives": ["Trigonometry"]}, {"name": "322, Sin and Cos formula", "description": "", "depends_on": ["221, Pythagoras", "222, Definition of sin and cos"], "learning_objectives": ["Trigonometry"]}, {"name": "323, Definition of radians", "description": "", "depends_on": [], "learning_objectives": ["Trigonometry"]}, {"name": "422, Sin and Cos as functions", "description": "", "depends_on": ["222, Definition of sin and cos"], "learning_objectives": ["Trigonometry"]}, {"name": "502, Solve equation using log", "description": "", "depends_on": ["402b, Log rules"], "learning_objectives": ["Powers"]}, {"name": "402, Logs definition", "description": "", "depends_on": ["304, Rules for negative powers"], "learning_objectives": ["Powers"]}, {"name": "442b, Integration of Powers, Trig and Exp", "description": "", "depends_on": ["442, Integration of powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "443, Definite Integrals", "description": "", "depends_on": ["442b, Integration of Powers, Trig and Exp"], "learning_objectives": ["Algebra and calculus"]}, {"name": "444, Integration by substitution", "description": "", "depends_on": ["442b, Integration of Powers, Trig and Exp"], "learning_objectives": ["Algebra and calculus"]}, {"name": "505, Integration by parts", "description": "", "depends_on": ["444, Integration by substitution"], "learning_objectives": ["Algebra and calculus"]}, {"name": "506, Integration using partial fractions", "description": "", "depends_on": ["505, Integration by parts"], "learning_objectives": ["Algebra and calculus"]}, {"name": "341b, Differentiation of polynomials", "description": "", "depends_on": ["341, Differentiation of powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "341c, Differentiation of exponential, log, trig functions", "description": "", "depends_on": ["341b, Differentiation of polynomials"], "learning_objectives": ["Algebra and calculus"]}, {"name": "503, Chain rule - powers", "description": "", "depends_on": ["441, Product rule"], "learning_objectives": ["Algebra and calculus"]}, {"name": "504, Quotient rule", "description": "", "depends_on": ["503, Chain rule - powers"], "learning_objectives": ["Algebra and calculus"]}, {"name": "505, Chain rule - trigonometry", "description": "", "depends_on": ["503, Chain rule - powers"], "learning_objectives": ["Algebra and calculus"]}], "learning_objectives": [{"name": "Numbers", "description": ""}, {"name": "Powers", "description": ""}, {"name": "Basic algebra", "description": ""}, {"name": "Algebra methods", "description": ""}, {"name": "Trigonometry", "description": ""}, {"name": "Algebra and calculus", "description": ""}, {"name": "Graphs", "description": ""}, {"name": "Trigonometry", "description": ""}]}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Alessandro Palazio", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25453/"}, {"name": "Krishna Kedia", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/25454/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "http://localhost:8000/accounts/profile/1/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": ["eukleides", "jsxgraph"], "custom_part_types": [], "resources": []}