// Numbas version: exam_results_page_options
{"name": "INTO Diagnostic Test", "metadata": {"description": "<p>A practice test to get used to the NUMBAS environment.</p>", "licence": "None specified"}, "duration": 2400, "percentPass": "0", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Number", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], []], "questions": [{"name": "Simple arithmetic", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "functions": {}, "parts": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{ans1}", "prompt": "<p>$\\var{a}+\\var{b}$</p>", "allowFractions": false, "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans1}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacements": []}, {"type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{ans2}", "prompt": "<p>$\\var{c}-\\var{d}$</p>", "allowFractions": false, "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans2}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacements": []}, {"type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{ans3}", "prompt": "<p>$\\var{f}\\times\\var{g}$</p>", "allowFractions": false, "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "maxValue": "{ans3}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacements": []}, {"type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{n}", "prompt": "<p>$\\var{p}\\div\\var{q}$</p>", "allowFractions": false, "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "correctAnswerFraction": false, "scripts": {}, "maxValue": "{n}", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "variableReplacements": []}], "tags": [], "metadata": {"licence": "None specified", "description": ""}, "ungrouped_variables": ["a", "b", "ans1", "c", "d", "ans2", "f", "g", "ans3", "n", "q", "p"], "statement": "<p>Answer the following questions (without a calculator!)</p>", "variable_groups": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": "ans2>10"}, "rulesets": {}, "advice": "", "variables": {"ans2": {"definition": "c-d", "name": "ans2", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "c": {"definition": "random(50..120)", "name": "c", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "f": {"definition": "random(2..12)", "name": "f", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "d": {"definition": "random(20..50)", "name": "d", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "g": {"definition": "random(2..12)", "name": "g", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "q": {"definition": "random(2..10)", "name": "q", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "n": {"definition": "random(3..20)", "name": "n", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "p": {"definition": "n*q", "name": "p", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "b": {"definition": "random(11..50 except a)", "name": "b", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "a": {"definition": "random(11..50)", "name": "a", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans1": {"definition": "a+b", "name": "ans1", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans3": {"definition": "f*g", "name": "ans3", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "type": "question"}, {"name": "Multiplying numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "metadata": {"description": "", "licence": "None specified"}, "preamble": {"css": "", "js": ""}, "advice": "", "variable_groups": [], "statement": "<p>Carry out the following calculations.</p>", "parts": [{"variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "prompt": "<p>&nbsp;$\\var{a} \\times\\var{b}$</p>", "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "a*b", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "a*b", "type": "numberentry", "scripts": {}}, {"variableReplacements": [], "showCorrectAnswer": true, "correctAnswerFraction": false, "prompt": "<p>$\\var{c} \\times\\var{d}$</p>", "mustBeReduced": false, "marks": 1, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst", "minValue": "c*d", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "c*d", "type": "numberentry", "scripts": {}}], "tags": [], "rulesets": {}, "variables": {"d": {"definition": "random(-0.9..0.9 except 0)", "description": "", "templateType": "anything", "name": "d", "group": "Ungrouped variables"}, "b": {"definition": "random(-9..9 except 0)", "description": "", "templateType": "anything", "name": "b", "group": "Ungrouped variables"}, "c": {"definition": "random(-0.9..0.9 except 0)", "description": "", "templateType": "anything", "name": "c", "group": "Ungrouped variables"}, "a": {"definition": "random(-9..9 except 0)", "description": "", "templateType": "anything", "name": "a", "group": "Ungrouped variables"}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["a", "b", "c", "d"], "functions": {}, "type": "question"}, {"name": "Rounding values", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "parts": [{"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a1}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a1}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "<p>Round $\\var{d1}$ to $\\var{n1}$ decimal places.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a2}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a2}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "<p>Round $\\var{d2}$ to $\\var{n2}$ decimal places.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "type": "numberentry", "allowFractions": false, "minValue": "{a3}", "correctAnswerStyle": "plain", "scripts": {}, "marks": 1, "showCorrectAnswer": true, "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "{a3}", "mustBeReduced": false, "showFeedbackIcon": true, "prompt": "<p>Round $\\var{d3}$ to $\\var{n3}$ decimal places.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "statement": "<p>Round the following numbers to the specified number of decimal places.</p>", "rulesets": {}, "variablesTest": {"condition": "n2<>n1 and n3<>n1 and n2<>n3 and isint(a1)<>true and isint(a2)<>true and isint(a3)<>true", "maxRuns": "200"}, "variables": {"d1": {"description": "", "definition": "random(0..1#0.00001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d1", "templateType": "anything", "group": "Ungrouped variables"}, "n2": {"description": "", "definition": "random(1,2,3)", "name": "n2", "templateType": "anything", "group": "Ungrouped variables"}, "a1": {"description": "", "definition": "precround(d1,n1)", "name": "a1", "templateType": "anything", "group": "Ungrouped variables"}, "d2": {"description": "", "definition": "random(0..1#0.0001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d2", "templateType": "anything", "group": "Ungrouped variables"}, "a2": {"description": "", "definition": "precround(d2,n2)", "name": "a2", "templateType": "anything", "group": "Ungrouped variables"}, "d3": {"description": "", "definition": "random(0..1#0.0001)*random(0..1#0.0001)*10^(random(-2..5))", "name": "d3", "templateType": "anything", "group": "Ungrouped variables"}, "n3": {"description": "", "definition": "random(1,2,3)", "name": "n3", "templateType": "anything", "group": "Ungrouped variables"}, "n1": {"description": "", "definition": "random(1,2,3)", "name": "n1", "templateType": "anything", "group": "Ungrouped variables"}, "a3": {"description": "", "definition": "precround(d3,n3)", "name": "a3", "templateType": "anything", "group": "Ungrouped variables"}}, "ungrouped_variables": ["d1", "d2", "d3", "n1", "n2", "n3", "a1", "a2", "a3"], "metadata": {"licence": "None specified", "description": ""}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "type": "question"}, {"name": "Simple ratio", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Two people decide to split some money between them.</p>\n<p>They have &pound;$\\var{(a+b)*n}$ and decide to divide the cash in the ratio $\\var{a}:\\var{b}$.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(a+1..a+2)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "v1": {"name": "v1", "group": "Ungrouped variables", "definition": "a*n", "description": "", "templateType": "anything", "can_override": false}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "b*n", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "n", "v1", "v2"], "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>How much does each person get?</p>\n<p>&pound; [[0]]</p>\n<p>&pound; [[1]]</p>\n<p>(Input amounts in any order).</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": "{v1}", "maxValue": "{v1}", "correctAnswerFraction": false, "allowFractions": true, "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": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{v2}", "maxValue": "{v2}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": true}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Simple percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "metadata": {"description": "", "licence": "None specified"}, "variable_groups": [], "tags": [], "functions": {}, "advice": "", "rulesets": {}, "variables": {"a": {"description": "", "name": "a", "definition": "random(41..99#1)", "templateType": "randrange", "group": "Ungrouped variables"}}, "statement": "<p>Calculate the following percentages and give the exact answer in decimal form.</p>", "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a"], "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Calculate &nbsp;10% of {a}.</p>", "marks": 1, "type": "jme", "answer": "0.1{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Calculate &nbsp;5% of {a}.</p>", "marks": 1, "type": "jme", "answer": "0.05{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "showpreview": true, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacements": [], "scripts": {}, "expectedvariablenames": [], "variableReplacementStrategy": "originalfirst", "prompt": "<p>Calculate &nbsp;15% of {a}.</p>", "marks": 1, "type": "jme", "answer": "0.15{a}", "checkingtype": "absdiff", "showCorrectAnswer": true, "checkingaccuracy": 0.001, "vsetrange": [0, 1]}], "type": "question"}, {"name": "Fraction Arithmetic with answers in simplest form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "tags": [], "variables": {"simpleden4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den4/gcd(num4,den4)", "description": "", "name": "simpleden4"}, "answer4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum4+\"/\"+simpleden4", "description": "", "name": "answer4"}, "m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..10) //random denominator", "description": "", "name": "m"}, "z": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..10) //random denominator", "description": "", "name": "z"}, "n": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..m-l) //random numerator less than denominator", "description": "", "name": "n"}, "qq": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..rr-1) //random numerator less than denominator", "description": "", "name": "qq"}, "den3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{m}*{multiple_m}", "description": "", "name": "den3"}, "den1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2*{b}{b}", "description": "<p>den1</p>", "name": "den1"}, "hh": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "hh"}, "p": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "p"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12) //random denominator", "description": "", "name": "b"}, "num4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{w}*{z}+{y}*{x}", "description": "", "name": "num4"}, "simpleden3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den3/gcd(num3,den3)", "description": "", "name": "simpleden3"}, "t": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "t"}, "l": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..m-1) //random numerator less than denominator", "description": "", "name": "l"}, "j": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "j"}, "r": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "r"}, "ss": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..tt-1) //random numerator less than denominator", "description": "", "name": "ss"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..b-1) //random numerator less than denominator", "description": "", "name": "a"}, "answer1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum1+\"/\"+simpleden1", "description": "", "name": "answer1"}, "pp": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "pp"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "f"}, "gg": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..hh-1) //random numerator less than denominator", "description": "", "name": "gg"}, "answer3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum3+\"/\"+simpleden3", "description": "", "name": "answer3"}, "multiple": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(3,4,5,6,7,8,9)", "description": "", "name": "multiple"}, "simplenum1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num1/gcd(num1,den1)", "description": "", "name": "simplenum1"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..f-1) //random numerator less than denominator", "description": "", "name": "d"}, "dd": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "dd"}, "num2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{d}", "description": "", "name": "num2"}, "jj": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "jj"}, "nn": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "nn"}, "multiple_d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{multiple}*{d}", "description": "", "name": "multiple_d"}, "s": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..t-1) //random numerator less than denominator", "description": "", "name": "s"}, "y": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..x-1) //random numerator less than denominator", "description": "", "name": "y"}, "aa": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..bb-1) //random numerator less than denominator", "description": "", "name": "aa"}, "ii": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..jj-1) //random numerator less than denominator", "description": "", "name": "ii"}, "answer2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "simplenum2+\"/\"+simpleden2", "description": "", "name": "answer2"}, "simplenum4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num4/gcd(num4,den4)", "description": "", "name": "simplenum4"}, "ll": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "ll"}, "kk": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..ll-1) //random numerator less than denominator", "description": "", "name": "kk"}, "simpleden1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den1/gcd(num1,den1)", "description": "", "name": "simpleden1"}, "v": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "v"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..b-a) //random numerator less than denominator", "description": "", "name": "c"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..f-d) //random numerator less than denominator", "description": "", "name": "g"}, "simpleden2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "den2/gcd(num2,den2)", "description": "", "name": "simpleden2"}, "num3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{l}*multiple_m}-{n}*{m}", "description": "", "name": "num3"}, "oo": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..pp-1) //random numerator less than denominator", "description": "", "name": "oo"}, "u": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..v-1) //random numerator less than denominator", "description": "", "name": "u"}, "h": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..j-1) //random numerator less than denominator", "description": "", "name": "h"}, "cc": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..dd-1) //random numerator less than denominator", "description": "", "name": "cc"}, "den4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{x}*{z}", "description": "", "name": "den4"}, "bb": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "bb"}, "rr": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "rr"}, "num1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "{a}{c}", "description": "", "name": "num1"}, "x": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(4..10) //random denominator", "description": "", "name": "x"}, "ee": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..ff-1) //random numerator less than denominator", "description": "", "name": "ee"}, "den2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "multiple_d", "description": "", "name": "den2"}, "simplenum2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num2/gcd(num2,den2)", "description": "", "name": "simplenum2"}, "mm": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..nn-1) //random numerator less than denominator", "description": "", "name": "mm"}, "k": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..j-h) //random numerator less than denominator", "description": "", "name": "k"}, "q": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..r-1) //random numerator less than denominator", "description": "", "name": "q"}, "simplenum3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "num3/gcd(num3,den3)", "description": "", "name": "simplenum3"}, "tt": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "tt"}, "multiple_m": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(m*3,m*4,m*5,m*6,m*7)", "description": "", "name": "multiple_m"}, "ff": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..20) //random denominator", "description": "", "name": "ff"}, "w": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..3) ", "description": "", "name": "w"}, "o": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..p-1) //random numerator less than denominator", "description": "", "name": "o"}}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "j", "m", "p", "r", "t", "v", "x", "z", "bb", "dd", "ff", "hh", "jj", "ll", "nn", "pp", "rr", "tt", "h", "k", "l", "n", "o", "q", "s", "u", "w", "y", "aa", "cc", "ee", "gg", "ii", "kk", "mm", "oo", "qq", "ss", "num1", "den1", "simplenum1", "simpleden1", "answer1", "num2", "den2", "simplenum2", "simpleden2", "answer2", "multiple", "multiple_d", "multiple_m", "num3", "den3", "simplenum3", "simpleden3", "answer3", "num4", "den4", "simplenum4", "simpleden4", "answer4"], "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p></p>\n<p>$\\frac{\\var{a}}{\\var{b}} \\times \\frac{\\var{c}}{\\var{2*b}}$</p>\n<p>&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "matchMode": "regex", "showFeedbackIcon": true, "answer": "{answer1}", "displayAnswer": "{answer1}", "showCorrectAnswer": true, "marks": 1, "type": "patternmatch", "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>$\\frac{\\var{d}}{\\var{f}} \\div \\frac{\\var{multiple_d}}{\\var{f}}$</p>\n<p>&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "matchMode": "regex", "showFeedbackIcon": true, "answer": "{answer2}", "displayAnswer": "{answer2}", "showCorrectAnswer": true, "marks": 1, "type": "patternmatch", "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>$\\frac{\\var{l}}{\\var{m}} - \\frac{\\var{n}}{\\var{multiple_m}}$</p>\n<p>&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "matchMode": "regex", "showFeedbackIcon": true, "answer": "{answer3}", "displayAnswer": "{answer3}", "showCorrectAnswer": true, "marks": 1, "type": "patternmatch", "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>$\\frac{\\var{w}}{\\var{x}} + \\frac{\\var{y}}{\\var{z}}$</p>\n<p>&nbsp;[[0]]</p>", "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "variableReplacements": [], "matchMode": "regex", "showFeedbackIcon": true, "answer": "{answer4}", "displayAnswer": "{answer4}", "showCorrectAnswer": true, "marks": 1, "type": "patternmatch", "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}], "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "preamble": {"js": "", "css": ""}, "statement": "<p>Give your answer as a fraction <strong>in its simplest form.</strong></p>\n<p>In the form a/b</p>", "rulesets": {}, "variable_groups": [], "type": "question"}, {"name": "Formula for temperature (conversion/substitution)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "advice": "", "rulesets": {}, "preamble": {"css": "", "js": ""}, "parts": [{"prompt": "<p>Convert $\\var{C}^{\\circ}\\textrm{C}$ to Fahrenheit.</p>", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "minValue": "1.8*C+32", "scripts": {}, "maxValue": "1.8*C+32", "variableReplacements": [], "correctAnswerStyle": "plain"}, {"prompt": "<p>Convert $\\var{F}^{\\circ}\\textrm{F}$ to Celsius.</p>\n<p>(Don't input decimals unless it is exact; use fractions if necessary)</p>", "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": true, "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "mustBeReducedPC": "50", "correctAnswerFraction": true, "marks": 1, "minValue": "5*(F-32)/9", "scripts": {}, "maxValue": "5*(F-32)/9", "variableReplacements": [], "correctAnswerStyle": "plain"}], "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["C", "F"], "functions": {}, "variables": {"F": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(-100..500 except 0)", "name": "F"}, "C": {"templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(-40..300 except 0)", "name": "C"}}, "tags": [], "statement": "<p>The formula for converting a temperature in Celsius (C) to Fahrenheit (F) is given by:</p>\n<p>$F = \\frac{9}{5}C+32$</p>", "type": "question"}]}, {"name": "Algebra", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], []], "questions": [{"name": "Expanding brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Multiply out the brackets and select the correct answer.</p>", "advice": "<p>(a) To expand the brackets&nbsp;$\\simplify{(x+{a})^2}$ - there are different ways to do this!&nbsp; You could write it out like this&nbsp;</p>\n<p>\\[&nbsp;\\simplify{(x+{a})^2} \\equiv \\simplify[!cancelTerms]{(x+{a})(x+{a})} \\equiv \\simplify[basic,collectNumbers]{x^2 + {a}x+{a}x+{a}^2} \\equiv \\simplify{x^2+{2*a}x +{a^2} } \\]</p>\n<p></p>\n<p>(b) Same process for this part:</p>\n<p>\\[&nbsp;\\simplify{({b}x+{c})^2} \\equiv \\simplify[collectNumbers,!cancelTerms]{({b}x+{c})({b}x+{c})} \\equiv \\simplify[basic,collectNumbers]{{b^2}x^2 + {b*c}x+{b*c}x+{c}^2} \\equiv \\simplify{{b^2}x^2 + {2*b*c}x+{c^2}} \\]</p>", "rulesets": {}, "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2 .. 10#1)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-9 .. 9#1)", "description": "", "templateType": "randrange"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "a<>0 and b<>0 and c<>0", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "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>$\\simplify{(x+{a})^2}$</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$\\simplify{x^2 + 2{a}x+{a^2}}$</p>", "<p>$\\simplify{x^2 +{a^2}}$</p>", "<p>$\\simplify{x^2 +3{a}x+{a}}$</p>", "<p>$\\simplify{x^2 -{a^2}}$</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"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>$\\simplify{({b}x+{c})^2}$</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$\\simplify{{b^2}x^2 + 2{b}{c}x+{c^2}}$</p>", "<p>$\\simplify{{b^2}x^2 +{c^2}}$</p>", "<p>$\\simplify{{b}x^2 + 3{a}{b}x+{c^2}}$</p>", "<p>$\\simplify{{b}x^2 - 3{a}x-{c^3}}$</p>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Factorise an expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Factorise the following expression.</p>", "advice": "", "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)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-9..9 except 0 except a except b)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "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{{a*b}x+{a*c}x^2} \\equiv $&nbsp;[[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}x({b}+{c}x)", "answerSimplification": "!alwaysTimes", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": false, "implicitFunctionComposition": true, "caseSensitive": false, "mustmatchpattern": {"pattern": "m_nogather(\n    ?;factors*?`+;factors\n    `where\n    all(map(not numerical_compare(x,expression(\"1\")),x,factors))\n)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Simple equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["a", "b", "ans", "c", "ans2"], "statement": "<p>Solve these equations to find the value of $x$</p>", "advice": "", "metadata": {"description": "", "licence": "None specified"}, "variable_groups": [], "parts": [{"gaps": [{"notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": true, "minValue": "{ans}", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "showFeedbackIcon": true, "maxValue": "{ans}", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "showFeedbackIcon": true, "scripts": {}, "prompt": "<p>$\\dfrac{\\var{a}}{x}=\\var{b}$</p>\n<p>$x = $&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "marks": 0}, {"gaps": [{"notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": true, "scripts": {}, "correctAnswerStyle": "plain", "allowFractions": true, "minValue": "{ans2}", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "mustBeReduced": false, "showFeedbackIcon": true, "maxValue": "{ans2}", "variableReplacements": [], "marks": 1, "mustBeReducedPC": 0}], "showFeedbackIcon": true, "scripts": {}, "prompt": "<p>$\\sqrt{x}=\\var{c}$</p>\n<p>$x = $&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "marks": 0}], "functions": {}, "rulesets": {}, "variables": {"a": {"group": "Ungrouped variables", "description": "", "name": "a", "definition": "random(2..20)", "templateType": "anything"}, "ans2": {"group": "Ungrouped variables", "description": "", "name": "ans2", "definition": "c^2", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "", "name": "b", "definition": "random(-50..50)", "templateType": "anything"}, "ans": {"group": "Ungrouped variables", "description": "", "name": "ans", "definition": "a/b", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "description": "", "name": "c", "definition": "random(3..15)", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "preamble": {"js": "", "css": ""}, "type": "question"}, {"name": "Solve a linear equation $ax+b = cx+d$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["d", "f", "g", "h", "x", "gcd_hfdg", "hf_coprime", "dg_coprime", "finalb"], "parts": [{"variableReplacements": [], "prompt": "<p>What is the value of $x$?</p>\n<p>$x = $ [[0]]</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"maxValue": "finalb", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "correctAnswerFraction": false, "marks": "2", "mustBeReduced": false, "minValue": "finalb", "scripts": {}, "mustBeReducedPC": 0, "showCorrectAnswer": true, "variableReplacements": [], "allowFractions": false, "type": "numberentry"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true}], "rulesets": {}, "variables": {"finalb": {"definition": "hf_coprime/dg_coprime", "group": "Ungrouped variables", "templateType": "anything", "name": "finalb", "description": ""}, "f": {"definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "f", "description": ""}, "gcd_hfdg": {"definition": "gcd((h+f),(d-g))", "group": "Ungrouped variables", "templateType": "anything", "name": "gcd_hfdg", "description": ""}, "d": {"definition": "random(g+2..8)", "group": "Ungrouped variables", "templateType": "anything", "name": "d", "description": ""}, "h": {"definition": "(x*(d-g))-f", "group": "Ungrouped variables", "templateType": "anything", "name": "h", "description": ""}, "dg_coprime": {"definition": "(d-g)/gcd_hfdg", "group": "Ungrouped variables", "templateType": "anything", "name": "dg_coprime", "description": ""}, "x": {"definition": "random(2..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "x", "description": ""}, "hf_coprime": {"definition": "(h+f)/gcd_hfdg", "group": "Ungrouped variables", "templateType": "anything", "name": "hf_coprime", "description": ""}, "g": {"definition": "random(2..5)", "group": "Ungrouped variables", "templateType": "anything", "name": "g", "description": ""}}, "statement": "<p>Consider the equation \\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]</p>", "advice": "<p>We are asked to solve the equation</p>\n<p>\\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]</p>\n<p>In this equation, there are $x$ terms and constant terms on both sides of the equals sign.</p>\n<p>To solve this equation, we must rearrange it&nbsp;to get $x$ on its own.</p>\n<p>\\begin{align}<br/>\\var{d}x-\\var{f} &amp;= \\var{g}x+\\var{h} \\\\[0.5em]<br/>\\var{d}x-\\var{g}x &amp;= \\var{h}+\\var{f} &amp; \\text{Move } x \\text{ terms to the left, and constant terms to the right.}\\\\[0.5em]<br/>\\simplify{{d-g}*x} &amp;= {\\var{h+f}} &amp; \\text{Collect like terms together.}\\\\[0.5em]<br/>x &amp;=\\frac{\\var{h+f}}{\\var{d-g}} &amp; \\text{Divide both sides by } \\var{d-g} \\text{.} \\\\[0.5em]<br/>x &amp;= \\simplify{{h+f}/{d-g}}<br/>\\end{align}</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "tags": [], "preamble": {"js": "", "css": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.</p>"}, "variable_groups": [], "type": "question"}, {"name": "Solutions to equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Which of the following equations has no solutions?</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "random(2..10 except n)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "p"], "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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$0x =\\var{n} $", "$0x =0 $", "$\\var{p}x =\\var{n} $", "$\\var{p}x =0 $"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Simultaneous equations (harder)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "Amy Barker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4520/"}], "tags": [], "metadata": {"description": "<p>Solve a pair of simultaneous equations.</p>", "licence": "None specified"}, "statement": "<p>Simultaneous equations have two equations with two unknowns.</p>", "advice": "<p>We can't immediately eliminate $x$ or $y$ from each equation so there are couple of ways to approach this. &nbsp;One possibility is to multiply each equation by a constant so that we can do elimination.</p>\n<p>For example: multiply the first equation by $\\var{c}$ and the second equation by $\\simplify{-{a}}$: &nbsp;\\[ \\simplify{ {c}{a}x+{c}{b}y = {c}{b1}} \\\\ \\simplify{ {-a}{c}x+{-a}{d}y = {-a}{b2}} \\] Now we have two equations with the same coefficient on $x$.</p>\n<p>We can do elimination (of $x$) by adding the equations. \\[ \\simplify{{c}{b}y + {-a}{d}y} = \\simplify{{c}{b1}} + \\simplify{{-a}{b2}&nbsp;} \\\\ \\simplify{({c}{b}+{-a}{d})y ={c}{b1}+{-a}{b2}&nbsp;}&nbsp; \\]</p>\n<p>Therefore $y=\\var{y}$.</p>\n<p>Substitute this value into one of the original equations. &nbsp;For example, using the first: \\[ \\simplify{ {a}x+{b}{y} = {b1}} \\\\ \\simplify{ {a}x = {b1} - {b}{y} } \\]</p>\n<p>Therefore $x=\\var{x}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Coefficients", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Coefficients", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b1": {"name": "b1", "group": "RHS", "definition": "a*x+b*y", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Coefficients", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Coefficients", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b2": {"name": "b2", "group": "RHS", "definition": "c*x+d*y", "description": "", "templateType": "anything", "can_override": false}, "det": {"name": "det", "group": "RHS", "definition": "a*d-b*c", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(a)>1 and abs(b)>1 and abs(c)>1 and abs(d)>1 and det<>0", "maxRuns": "250"}, "ungrouped_variables": ["x", "y"], "variable_groups": [{"name": "Coefficients", "variables": ["a", "b", "c", "d"]}, {"name": "RHS", "variables": ["b1", "b2", "det"]}], "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 equations \\[ \\begin{eqnarray} \\simplify{ {a}x + {b}y } &amp; = &amp; \\var{b1} \\\\ \\simplify{{c}x + {d}y} &amp;=&amp; \\var{b2}&nbsp; \\end{eqnarray}&nbsp; \\]</p>\n<p>Solutions &nbsp;$x = $&nbsp;[[0]]&nbsp;, &nbsp;$y = $&nbsp;[[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1.5", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1.5", "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, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Factorise a quadratic expression", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "<p>This question will generate a quadratic expression which can be expressed in terms of rational factors.</p>", "licence": "None specified"}, "statement": "<p>Factorise the following quadratic expressions:</p>", "advice": "", "rulesets": {}, "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..4 except a)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(-10..10 except 0 except p except -p)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "300"}, "ungrouped_variables": ["a", "b", "c", "d", "p", "q"], "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>$\\simplify{ x^2 + {p+q}x + {p*q}}$.</p>", "answer": "(x + {p})(x + {q})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "(x+?)(x+?)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{a*c} x^2 + {b*c+a*d}x + {b*d}}$.</p>", "answer": "({a} x + {b})({c} x + {d})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "mustmatchpattern": {"pattern": "m_nogather(\n    ?;factors*?`+;factors\n    `where\n    all(map(not numerical_compare(x,expression(\"1\")),x,factors))\n)", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Shape, space and trigonometry", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], []], "questions": [{"name": "Drag points to given Cartesian coordinates", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "<p>Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Move the points to the required coordinates on the graph.</p>", "advice": "<p>Coordinates are given as $(x\\text{-coordinate},y\\text{-coordinate})$. So, for example $(2,5)$ has $x$-coordinate $= 2$ and $y$-coordinate$= 5$.</p>\n<p>Plot the first coordinate ($x$-coordinate) against the horizontal axis and then plot the second coordinate ($y$-coordinate) against the vertical axis.</p>\n<p>{correctPoints()}</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"b2": {"name": "b2", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "2", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "1", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "Ungrouped variables", "definition": "0", "description": "", "templateType": "anything", "can_override": false}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(-10..-1)", "description": "", "templateType": "anything", "can_override": false}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(1..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x", "y", "a1", "a2", "b1", "b2", "c1", "c2", "d1", "d2", "e1", "e2", "e3", "f1", "f2"], "variable_groups": [], "functions": {"correctPoints": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true});\nvar board = div.board;\nquestion.board = board;\n\nvar a1 = Numbas.jme.unwrapValue(scope.variables.a1);\nvar a2 = Numbas.jme.unwrapValue(scope.variables.a2);\nvar b1 = Numbas.jme.unwrapValue(scope.variables.b1);\nvar b2 = Numbas.jme.unwrapValue(scope.variables.b2);\nvar c1 = Numbas.jme.unwrapValue(scope.variables.c1);\nvar c2 = Numbas.jme.unwrapValue(scope.variables.c2);\nvar d1 = Numbas.jme.unwrapValue(scope.variables.d1);\nvar d2 = Numbas.jme.unwrapValue(scope.variables.d2);\nvar e1 = Numbas.jme.unwrapValue(scope.variables.e1);\nvar e2 = Numbas.jme.unwrapValue(scope.variables.e2);\nvar f1 = Numbas.jme.unwrapValue(scope.variables.f1);\nvar f2 = Numbas.jme.unwrapValue(scope.variables.f2);\n\n\nvar a = board.create('point',[a1,a2],{name: 'A', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar b = board.create('point',[b1,b2],{name: 'B', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar c = board.create('point',[c1,c2],{name: 'C', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar d = board.create('point',[d1,d2],{name: 'D', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar e = board.create('point',[e1,e2],{name: 'E', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\nvar f = board.create('point',[f1,f2],{name: 'F', size: 7, fillColor: 'limegreen' , strokeColor: 'yellow' , highlightFillColor: 'green', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: true});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n  ko.computed(function(){ \n  var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n  var y = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n  if(!(isNaN(x) || isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n     a.moveTo([x,y],100);\n  }\n  });\n});\n*/\n\nreturn div;"}, "dragpoints": {"parameters": [], "type": "html", "language": "javascript", "definition": "var div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',{boundingBox:[-11,11,11,-11],grid: true});\nvar board = div.board;\nquestion.board = board;\n\n//var x = Numbas.jme.unwrapValue(scope.variables.x);\n//var y = Numbas.jme.unwrapValue(scope.variables.y);\n\nvar a = board.create('point',[10,10],{name: 'A', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow', snapToGrid: true, showInfobox: false});\nvar b = board.create('point',[10,9],{name: 'B', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar c = board.create('point',[10,8],{name: 'C', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar d = board.create('point',[10,7],{name: 'D', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar e = board.create('point',[10,6],{name: 'E', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\nvar f = board.create('point',[10,5],{name: 'F', size: 7, fillColor: 'blue' , strokeColor: 'lightblue' , highlightFillColor: 'lightblue', highlightStrokeColor: 'yellow',snapToGrid: true, showInfobox: false});\n\nquestion.points = {\n  a:a,b:b,c:c,d:d,e:e,f:f\n}\n\na.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[0].gaps[0].display.studentAnswer(a.X());\n  Numbas.exam.currentQuestion.parts[0].gaps[1].display.studentAnswer(a.Y());\n});\nb.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[1].gaps[0].display.studentAnswer(b.X());\n  Numbas.exam.currentQuestion.parts[1].gaps[1].display.studentAnswer(b.Y());\n});\nc.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[2].gaps[0].display.studentAnswer(c.X());\n  Numbas.exam.currentQuestion.parts[2].gaps[1].display.studentAnswer(c.Y());\n});\nd.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[3].gaps[0].display.studentAnswer(d.X());\n  Numbas.exam.currentQuestion.parts[3].gaps[1].display.studentAnswer(d.Y());\n});\ne.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[4].gaps[0].display.studentAnswer(e.X());\n  Numbas.exam.currentQuestion.parts[4].gaps[1].display.studentAnswer(e.Y());\n});\nf.on('drag',function(){\n  Numbas.exam.currentQuestion.parts[5].gaps[0].display.studentAnswer(f.X());\n  Numbas.exam.currentQuestion.parts[5].gaps[1].display.studentAnswer(f.Y());\n});\n\n/*\nquestion.signals.on('HTMLAttached',function(e) {\n  ko.computed(function(){ \n  var x = parseFloat(question.parts[0].gaps[0].display.studentAnswer());\n  var y = parseFloat(question.parts[0].gaps[1].display.studentAnswer());\n  if(!(isNaN(x) || isNaN(y)) && board.mode!=board.BOARD_MODE_DRAG) {\n     a.moveTo([x,y],100);\n  }\n  });\n});\n*/\n\nreturn div;\n\n"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.a.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>{dragpoints()}</p>\n<p>Move the points as follows:</p>\n<p>A to $(\\var{a1},\\var{a2})$.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a1}", "maxValue": "{a1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a2}", "maxValue": "{a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.b.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>B to $(\\var{b1},\\var{b2})$.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b1}", "maxValue": "{b1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b2}", "maxValue": "{b2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.c.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>C to $(\\var{c1},\\var{c2})$.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c1}", "maxValue": "{c1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c2}", "maxValue": "{c2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.d.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});\n", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>D to $(\\var{d1},\\var{d2})$.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{d1}", "maxValue": "{d1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{d2}", "maxValue": "{d2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.e.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>E to $(\\var{e1},\\var{e2})$.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{e1}", "maxValue": "{e1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{e2}", "maxValue": "{e2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"mark": {"script": "console.log(this.question.points);\nthis.question.points.f.setAttribute({fillColor: this.credit==1 ? 'green' : 'red'});", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>F to $(\\var{f1},\\var{f2})$.</p>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}", "maxValue": "{f1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f2}", "maxValue": "{f2}", "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": "Straight line graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "<p>This uses an embedded Geogebra graph of a&nbsp;line $y=mx+c$ with random coefficients set by NUMBAS.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The graph shows a straight line on a graph.</p>\n<p>{geogebra_applet('https://ggbm.at/FTsrJUzg', defs, [])}</p>\n<p></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['m',m],\n  ['c',c]\n]", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(random(random(0..3),random(1/2,2/3,1/4,3/4,1/3)))*random(-1,1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "200"}, "ungrouped_variables": ["defs", "m", "c"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "jme", "definition": ""}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the equation of this line?</p>\n<p>$y = $&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": "{m}x+{c}", "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, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Graph recognition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Match the graph with the correct function description.</p>", "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": "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><iframe width=\"500\" height=\"500\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/vumw2jpj29?embed\" frameborder=\"0\"></iframe></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\displaystyle y = \\mathrm{e}^{-x}$", "$\\displaystyle y = \\mathrm{e}^{x}$", "$\\displaystyle y = \\ln (x)$", "$\\displaystyle y = -\\ln (x)$"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><iframe width=\"500\" height=\"500\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/l5kgbcqtnf?embed\" frameborder=\"0\"></iframe></p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\displaystyle y = 2\\cos (x)$", "$\\displaystyle y = \\cos (2x)$", "$\\displaystyle y = \\sin (2x)$", "$\\displaystyle y = 2\\sin (x)$"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Graph recognition (2)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Which of the following is the graph of $y=x^3$?</p>", "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": "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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "2", "showCellAnswerState": true, "choices": ["<iframe width=\"250\" height=\"250\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/ftjwwyb8pl?embed\" frameborder=\"0\"></iframe>", "<iframe width=\"250\" height=\"250\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/fb5e1kefok?embed\" frameborder=\"0\"></iframe>", "<iframe width=\"250\" height=\"250\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/rk3s25oswm?embed\" frameborder=\"0\"></iframe>", "<iframe width=\"250\" height=\"250\" style=\"border: 1px solid #ccc;\" src=\"https://www.desmos.com/calculator/vvjktsmrdv?embed\" frameborder=\"0\"></iframe>"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Angle facts", "extensions": [], "custom_part_types": [], "resources": [["question-resources/angle_line.JPG", "/srv/numbas/media/question-resources/angle_line.JPG"], ["question-resources/angle_circle.JPG", "/srv/numbas/media/question-resources/angle_circle.JPG"], ["question-resources/triangle_angles.JPG", "/srv/numbas/media/question-resources/triangle_angles.JPG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "preamble": {"js": "", "css": ""}, "statement": "<p>Calculate the missing angles in the diagrams below.</p>", "metadata": {"licence": "None specified", "description": ""}, "tags": [], "advice": "", "ungrouped_variables": ["x1", "a", "b", "c", "p", "q"], "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "functions": {}, "parts": [{"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "180-x1", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "180-x1", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "<p>These two angles $x$ and $y$ lie on a straight line. &nbsp;This picture is not drawn accurately!</p>\n<p><img src=\"resources/question-resources/angle_line.JPG\" width=\"536\" height=\"194\"/></p>\n<p>Given that $x = \\var{x1}^{\\circ}$, calculate $y$.</p>", "correctAnswerFraction": false, "marks": 1}, {"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "360-(a+b+c)", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "360-(a+b+c)", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "<p>Angles around a point. &nbsp;This picture is not drawn accurately!</p>\n<p><img src=\"resources/question-resources/angle_circle.JPG\" width=\"250\" height=\"229\"/></p>\n<p>Given that $a = \\var{a}^{\\circ}$, $b = \\var{b}^{\\circ}$ and $c = \\var{c}^{\\circ}$</p>\n<p>Calculate the angle $d$.</p>", "correctAnswerFraction": false, "marks": 1}, {"showCorrectAnswer": true, "mustBeReducedPC": 0, "showFeedbackIcon": true, "maxValue": "180-(p+q)", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "correctAnswerStyle": "plain", "minValue": "180-(p+q)", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "prompt": "<p>Angles in triangle. &nbsp;This picture is not drawn accurately!</p>\n<p><img src=\"resources/question-resources/triangle_angles.JPG\" width=\"289\" height=\"271\"/></p>\n<p>Given that $p = \\var{p}^{\\circ}$ and $q = \\var{q}^{\\circ}$</p>\n<p>Calculate the angle $x$.</p>", "correctAnswerFraction": false, "marks": 1}], "rulesets": {}, "variables": {"a": {"group": "Ungrouped variables", "name": "a", "templateType": "randrange", "definition": "random(15..45#1)", "description": ""}, "c": {"group": "Ungrouped variables", "name": "c", "templateType": "randrange", "definition": "random(95..130#1)", "description": ""}, "q": {"group": "Ungrouped variables", "name": "q", "templateType": "randrange", "definition": "random(95..129#1)", "description": ""}, "p": {"group": "Ungrouped variables", "name": "p", "templateType": "randrange", "definition": "random(11..29#1)", "description": ""}, "x1": {"group": "Ungrouped variables", "name": "x1", "templateType": "randrange", "definition": "random(18..44#1)", "description": ""}, "b": {"group": "Ungrouped variables", "name": "b", "templateType": "randrange", "definition": "random(35..50#1)", "description": ""}}, "type": "question"}, {"name": "Sphere and cuboid", "extensions": [], "custom_part_types": [], "resources": [["question-resources/sphere.JPG", "/srv/numbas/media/question-resources/sphere.JPG"], ["question-resources/cuboid.JPG", "/srv/numbas/media/question-resources/cuboid.JPG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "ungrouped_variables": ["w", "l", "h"], "advice": "", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "", "licence": "None specified"}, "tags": [], "variables": {"h": {"name": "h", "templateType": "randrange", "definition": "random(20..30#1)", "description": "", "group": "Ungrouped variables"}, "l": {"name": "l", "templateType": "randrange", "definition": "random(20..50#1)", "description": "", "group": "Ungrouped variables"}, "w": {"name": "w", "templateType": "randrange", "definition": "random(5..30#1)", "description": "", "group": "Ungrouped variables"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}, "prompt": "<p>The picture shows a cuboid of of width $w$, length $l$ and height $h$.</p>\n<p><img src=\"resources/question-resources/cuboid.JPG\" width=\"283\" height=\"205\"/></p>\n<p>Given that $w=\\var{w}$, $l=\\var{l}$ and $h=\\var{h}$. &nbsp;Calculate the <strong>value</strong> of the following:</p>\n<p>Volume =&nbsp;[[0]]</p>\n<p>Surface area =&nbsp;[[1]]</p>", "gaps": [{"scripts": {}, "minValue": "w*l*h", "type": "numberentry", "correctAnswerFraction": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "marks": "2", "maxValue": "w*l*h", "allowFractions": false, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "mustBeReducedPC": 0, "variableReplacements": []}, {"scripts": {}, "minValue": "2*(w*l+l*h+w*h)", "type": "numberentry", 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"showCorrectAnswer": true, "checkvariablenames": false, "expectedvariablenames": ["pi"], "checkingaccuracy": 0.001, "variableReplacements": []}], "statement": "<p>Answer the following questions about these 3D shapes.</p>", "variable_groups": [], "rulesets": {}, "type": "question"}, {"name": "Adrian's copy of Using Pythagoras to find a missing side (Eukleides diagrams)", "extensions": ["eukleides"], "custom_part_types": [], "resources": [["question-resources/Q2_0UOrG2O.png", "/srv/numbas/media/question-resources/Q2_0UOrG2O.png"]], "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": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Deirdre Casey", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/681/"}], "tags": [], "metadata": {"description": "<p>Using Pythagoras' Theorem to find a missing side. Illustrated using simple Eukleides diagram</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Use Pythagoras's Theorem to find the length the value of $x^2$.</p>\n<p>{RightAngledTriangle}</p>", "advice": "<p>&nbsp;$x^2 = \\var{lent1}^2 + \\var{lent2}^2$</p>\n<p></p>\n<p>That means the length is:</p>\n<p>$x = \\sqrt(\\var{lent1}^2 + \\var{lent2}^2)$</p>\n<p>$x = \\var{ans1}$</p>\n<p>(You were not asked to find this in the question!)</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"lent2": {"name": "lent2", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "lent1": {"name": "lent1", "group": "Ungrouped variables", "definition": "random(5..10)", "description": "", "templateType": "anything", "can_override": false}, "ang1": {"name": "ang1", "group": "Ungrouped variables", "definition": "random(63..65)", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "lent1^2+lent2^2", "description": "", "templateType": "anything", "can_override": false}, "RightAngledTriangle": {"name": "RightAngledTriangle", "group": "Ungrouped variables", "definition": "\neukleides(\"Right Angled Triangle\",[\n    let(\n      [a,b,c], right(length1,length2)\n     \n  \n        ,[\n      a..b..c filled color4,\n        (a..b) label(length1+\" mm\",deg(-90),0.5),\n        (b..c) label(length2+\" mm\",deg(0),0.1),\n        (a..c) label(\"x\"),\n        angle(a,b,c) right\n        ]\n      )\n    ],[length1:lent1,length2:lent2]\n  )", "description": "<p>A diagram of a right angled triangle.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ang1", "lent1", "ans1", "lent2", "RightAngledTriangle"], "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>Find the value of $x^2$:</p>\n<p>$x^2 = $ [[0]] $\\mathrm{mm^2}$</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>You were asked for $x^2$, not $x$.</p>", "useAlternativeFeedback": false, "minValue": "{0.99*sqrt(ans1)}", "maxValue": "{1.01*sqrt(ans1)}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "{ans1}", "maxValue": "{ans1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "never", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": "easyaspi", "allowAttemptDownload": false, "downloadEncryptionKey": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "warn", "message": "<p>You have 5 minutes remaining!</p>"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "<p>This is a practice test to help you get used to the NUMBAS environment.&nbsp; The questions cover a range of topics:</p>\n<ul>\n<li>Numbers</li>\n<li>Algebra</li>\n<li>Shape, space and geometry</li>\n</ul>\n<p><strong>You have a maximum of 40 minutes.</strong></p>\n<p><strong>Please submit answers as you move through the test.&nbsp;&nbsp;</strong>You can go back and change asnwers if needed.&nbsp; Make sure you submit answers before the test ends.</p>\n<p><strong> You may not use a calculator.</strong></p>\n<p>This test <strong>does not</strong> count towards your final module mark.&nbsp; The marks will only be seen by your teachers and used for providing you with extra help if needed.</p>", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}], "extensions": ["eukleides", "geogebra", "jsxgraph"], "custom_part_types": [], "resources": [["question-resources/angle_line.JPG", "/srv/numbas/media/question-resources/angle_line.JPG"], ["question-resources/angle_circle.JPG", "/srv/numbas/media/question-resources/angle_circle.JPG"], ["question-resources/triangle_angles.JPG", "/srv/numbas/media/question-resources/triangle_angles.JPG"], ["question-resources/sphere.JPG", "/srv/numbas/media/question-resources/sphere.JPG"], ["question-resources/cuboid.JPG", "/srv/numbas/media/question-resources/cuboid.JPG"], ["question-resources/Q2_0UOrG2O.png", "/srv/numbas/media/question-resources/Q2_0UOrG2O.png"]]}