// Numbas version: exam_results_page_options
{"name": "Extra time - 2022-23 WM175 Assessment 1", "metadata": {"description": "<p>Topics: Trigonometeric equations and complex numbers<br />Students must complete the exam within 90 mins (standard time).<br />Questions have variables to produce randomised questions.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 9000, "percentPass": "40", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Algebra and calculus", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Solving quadratics - factorisation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}, {"name": "John Wick", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3326/"}], "tags": [], "metadata": {"description": "<p>Some quadratics are to be solved by factorising</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Solve the quadratic equations by factorising. Enter answers into the answer matrix in <strong>ASCENDING ORDER.</strong></p>", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"solmax": {"name": "solmax", "group": "Ungrouped variables", "definition": "vector([max(-d[0]/c[0],-b[0]/a[0])]+[max(-d[1]/c[1],-b[1]/a[1])]+[max(-d[2]/c[2],-b[2]/a[2])]+[max(-d[3]/c[3],-b[3]/a[3])]+[max(-d[4]/c[4],-b[4]/a[4])])", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "vector([random(1..3)]+[random(2..3)]+[random(1..3)]+[random(-2..-4)]+[random(3..6)])", "description": "", "templateType": "anything", "can_override": false}, "solmin": {"name": "solmin", "group": "Ungrouped variables", "definition": "vector([min(-d[0]/c[0],-b[0]/a[0])]+[min(-d[1]/c[1],-b[1]/a[1])]+[min(-d[2]/c[2],-b[2]/a[2])]+[min(-d[3]/c[3],-b[3]/a[3])]+[min(-d[4]/c[4],-b[4]/a[4])])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "vector([random(1..5)] + [random(1..5)] + [random(-1..-5)] + [random(-1..-5)] + [random(2..5)] )", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "vector([1]+[random(2..4)]+[1]+[1]+[random(3..4)])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "vector([1]+[1]+[1]+[1]+[1])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "solmax", "solmin"], "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>Factorise $\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a[0]*c[0]}x^2+{a[0]*d[0]+b[0]*c[0]}x+ {b[0]*d[0]}}=0$.</p>\n<p>[[1]]</p>\n<p>Use fractions or integers for your answers.</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a[0]}x+{b[0]})({c[0]}x+{d[0]})", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "musthave": {"strings": [")("], "showStrings": false, "partialCredit": 0, "message": ""}, "notallowed": {"strings": ["x^2", "x*x", "x x", "x(", "x*("], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "matrix([{solmin[0]}],[{solmax[0]}])", "correctAnswerFractions": false, "numRows": "2", "numColumns": "1", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Factorise $\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}$.&nbsp;[[0]]</p>\n<p>Hence solve $\\simplify{{a[1]*c[1]}x^2+{a[1]*d[1]+b[1]*c[1]}x+ {b[1]*d[1]}}=0$.</p>\n<p>[[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a[1]}x+{b[1]})({c[1]}x+{d[1]})", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "musthave": {"strings": [")("], "showStrings": false, "partialCredit": 0, "message": ""}, "notallowed": {"strings": ["x^2", "x*x", "x x", "x(", "x*("], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "matrix([{solmin[1]}],[{solmax[1]}])", "correctAnswerFractions": false, "numRows": "2", "numColumns": "1", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Simple simultaneous equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Paul Hancock", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1738/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}, {"name": "Johnny Yi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2810/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}], "tags": [], "metadata": {"description": "<p>This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"g": {"name": "g", "group": "Part b", "definition": "d*x2+f*y2", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Part b", "definition": "random(-5..-1)*sgn(x2)", "description": "<p>Value of $y$ in part b</p>", "templateType": "anything", "can_override": false}, "numerator": {"name": "numerator", "group": "part a", "definition": "m*(j/h)-n", "description": "", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "part a", "definition": "random(2..3)", "description": "<p>$x$ coefficient of the second equation in part a. An integer multiple of the $x$ coefficient of the second equation.</p>", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Part b", "definition": "random(-5..5)", "description": "<p>Value of $x$ in part b</p>", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "part a", "definition": "random(1..6)", "description": "<p>Constant part of the LHS of the first equation in part a</p>", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "part a", "definition": "h*x1 + k*y1", "description": "<p>RHS of the first equation in part a</p>", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Part b", "definition": "random(a+1..9 except map(j*a,j,0..10/a))", "description": "<p>$x$ coefficient in the second equation of part b. Never an integer multiple of the $x$ coefficient in the first equation.</p>", "templateType": "anything", "can_override": false}, "divisor": {"name": "divisor", "group": "part a", "definition": "k*(j/h)+l", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "part a", "definition": "random(-5..-1)*(x1)", "description": "<p>Value of $x$ in part a</p>", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "part a", "definition": "j*x1 + l*y1", "description": "<p>RHS of the second equation in part a</p>", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Part b", "definition": "random(max(a,b)+1..12 except map(j*b,j,0..10/b))", "description": "<p>$y$ coefficient of the second equation in part b. Never an integer multiple of the $y$ coefficient in the first equation.</p>", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Part b", "definition": "a*x2+b*y2", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Part b", "definition": "random(a+1..7)", "description": "<p>Coefficient of $y$ in the first equation of part b.</p>\n<p></p>", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "part a", "definition": "random(1..6)", "description": "<p>Constant part of the LHS of the second equation in part a</p>", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "part a", "definition": "random(2..5)", "description": "<p>$x$ coefficient of the first equation in part a</p>", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Part b", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "part a", "definition": "3", "description": "<p>Value of $x$ in part a</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "lcm(a,d)<lcm(b,f)", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Part b", "variables": ["a", "b", "c", "d", "f", "g", "x2", "y2"]}, {"name": "part a", "variables": ["h", "j", "k", "l", "m", "n", "y1", "x1", "numerator", "divisor"]}], "functions": {}, "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>Solve this set of simultaneous equations and give your answers for $x$ and $y$ below.</p>\n<p>\\begin{align}<br/>\\simplify{{h}x+{k}y} &amp;= \\var{m} \\text{,} \\\\<br/>\\simplify{{j}x+{l}y} &amp;= \\var{n} \\text{.}<br/>\\end{align}</p>\n<p>$x =$&nbsp;[[0]]</p>\n<p>$y =$ [[1]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "x1", "maxValue": "x1", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "y1", "maxValue": "y1", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Derivative (Function of a Function)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/chain_rule_example_mathcentre.JPG", "/srv/numbas/media/question-resources/chain_rule_example_mathcentre.JPG"]], "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": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Differentiate $\\displaystyle (ax^m+b)^{n}$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find the derivative of $y$ using the function of a function rule (also known as <em>the chain rule</em>).</p>\n<p>Note, you should check that the preview of your answer shown is correct before submitting.&nbsp;&nbsp;</p>", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"result": "(sqrt(b)*a)/b", "pattern": "a/sqrt(b)"}]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(5..9)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "s1", "b", "m", "n"], "variable_groups": [], "functions": {}, "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>\\[\\simplify[std]{y = ({a} * x^{m}+{b})^{n}}\\]</p>\n<p></p>\n<p>$\\displaystyle{u}=$&nbsp; [[0]]</p>\n<p>$\\displaystyle \\frac{\\mathrm{d}u}{\\mathrm{d}x}=$&nbsp; [[1]]</p>\n<p>$\\displaystyle \\frac{\\mathrm{d}y}{\\mathrm{d}u}=$&nbsp; [[2]]</p>\n<p>Hence,</p>\n<p>$\\displaystyle \\frac{\\mathrm{d}y}{\\mathrm{d}x}=$&nbsp; [[3]]</p>\n<p></p>\n<p>For help, you may wish to click on <em>Show steps</em> - but be aware this will cost you 2 marks.&nbsp;</p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>This example shows how to differentiate a similar function of a function - use it to help you answer the one above.</p>\n<p><img src=\"resources/question-resources/chain_rule_example_mathcentre.JPG\"/></p>\n<p></p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a} * x^{m} + {b}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": false, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a*m}x ^ {m-1} ", "answerSimplification": "std", "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": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{n}u ^ {n-1}", "answerSimplification": "std", "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": "u", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a*m*n}x ^ {m-1}) (({a} * x^{m}+{b})^{n-1})", "answerSimplification": "std", "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": "Integration", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Definite integation of basic functions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p><em>Make sure your calculator is in radians for this question.</em></p>\n<p></p>", "advice": "<p>(a) and (b):</p>\n<p>\\[\\int_\\var{d-2}^\\var{d}\\simplify[all]{{a}*x-sin({b}*x)}\\,dx=\\left[\\simplify{{a}*x^2/2+cos({b}*x)/{b}}\\right]_\\var{d-2}^\\var{d}=\\var{a1}\\]</p>\n<p>(c) and (d):</p>\n<p>\\[\\int_\\var{d}^\\var{d+3}\\simplify[all]{{c}/x^{a+1}+{b}*sqrt(x)}\\,dx=\\left[\\simplify{{-c/a}/x^{a}+{2*b/3}*x^(3/2)}\\right]_\\var{d}^\\var{d+3}=\\var{a2}\\]</p>\n<p>(e) and (f):</p>\n<p>\\[\\int_{-2}^\\var{a-2}\\simplify[all]{{c+1}*exp(x/{b})-{a}}\\,dx=\\left[\\simplify{{b*(c+1)}*exp(x/{b})-{a}*x}\\right]_{-2}^\\var{a-2}=\\var{a3}\\]</p>\n<p>(g) and (h):</p>\n<p>\\[\\int_\\var{b}^\\var{b+a}\\simplify[all]{{c}/({b}*x)+{b}/{a+1}*cos({c}*x)}\\,dx=\\left[\\simplify{{c}/{b}*ln(x)+{b}/{c*(a+1)}*sin({c}*x)}\\right]_\\var{b}^\\var{b+a}=\\var{a4}\\]</p>\n<p>(i) and (j):</p>\n<p>\\[\\int_\\var{a}^\\var{a+1}\\simplify[all]{x^{b-1}/{b+2}-{d}+{c}*exp({-a}*x)}\\,dx=\\left[\\simplify{x^{b}/{b*(b+2)}-{d}*x-{c/a}*exp({-a}*x)}\\right]_\\var{a}^\\var{a+1}=\\var{a5}\\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a2": {"name": "a2", "group": "Ungrouped variables", "definition": "-c/(a*(d+3)^a)+(2*b/3)*(d+3)^(3/2)+c/(a*d^a)-(2*b/3)*d^(3/2)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "b*(c+1)*exp((a-2)/b)-a*(a-2)-b*(c+1)*exp(-2/b)-2*a", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-5..5 except [-1,0])", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "a*d^2/2+cos(b*d)/b-a*(d-2)^2/2-cos(b*(d-2))/b", "description": "", "templateType": "anything", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "(a+1)^b/(b*(b+2))-d*(a+1)-c/a*exp(-a*(a+1))-a^{b}/(b*(b+2))+d*a+c/a*exp(-a^2)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..8)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..15)", "description": "", "templateType": "anything", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "c/b*ln(b+a)+b/(c*(a+1))*sin(c*(b+a))-c/b*ln(b)-b/(c*(a+1))*sin(c*b)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "a1", "a2", "a3", "a4", "a5"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Integrate this expression with respect to x</p>\n<p><em>Don't forget the constant of integration + c</em></p>\n<p>\\[\\int\\simplify[all]{{a}*x-sin({b}*x)}\\,dx\\]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Remember that</p>\n<p><br/>the integral of&nbsp; &nbsp; $x^n$&nbsp; &nbsp;is&nbsp; &nbsp; $x^{n+1} / {n+1}$ ,&nbsp; and</p>\n<p>the integral of&nbsp; &nbsp; sin$(ax)$&nbsp; &nbsp;is&nbsp; &nbsp; $-$cos$(ax) / a$</p>"}], "alternatives": [{"type": "jme", "useCustomName": true, "customName": "No constant", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "<p>You have forgotten the constant of integration&nbsp;(condoned on this occasion).</p>", "useAlternativeFeedback": false, "answer": "{a}*x^2/2+cos({b}*x)/{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "answer": "{a}*x^2/2+cos({b}*x)/{b}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}, {"name": "x", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hence evaluate</p>\n<p>\\[\\int_\\var{d-2}^\\var{d}\\simplify[all]{{a}*x-sin({b}*x)}\\,dx\\]</p>\n<p></p>\n<p><em>Remember to use radians and give your answer correct to 3 significant figures</em>.</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Example:</p>\n<p>The definite intgeral is calculated by substituting $x$ with the values of the limits.<br/>e.g.&nbsp;</p>\n<p>$ \\int_1^4\\ {{x}^4}\\,dx = 4^5 / 5 - 1^4/5=204.6=205$ (3 significant figures)</p>"}], "minValue": "{a1}", "maxValue": "{a1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Trigonometric equations", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "Trigonometry: degrees and radians", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Sanka Balasuriya", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/738/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Convert degrees to radians and radians to degrees.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find the value of</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"radians2": {"name": "radians2", "group": "Ungrouped variables", "definition": "radians1/pi", "description": "", "templateType": "anything", "can_override": false}, "degrees": {"name": "degrees", "group": "Ungrouped variables", "definition": "random(1..360)", "description": "", "templateType": "anything", "can_override": false}, "radians": {"name": "radians", "group": "Ungrouped variables", "definition": "random(2,3,4,5,9,12,15,18,20,30,36,45,60,90)", "description": "", "templateType": "anything", "can_override": false}, "radians1": {"name": "radians1", "group": "Ungrouped variables", "definition": "(pi/radians)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["radians", "degrees", "radians1", "radians2"], "variable_groups": [], "functions": {}, "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>An angle of $\\var{degrees}^{\\circ}$ corresponds in radians to [[0]] radians.</p>\n<p>(Note: you should leave your answer as a fraction in terms of $\\pi,$ which can be entered by typing \"pi\" without the quotation marks)</p>\n<p>An angle of $\\frac{\\pi}{\\var{radians}}$ radians corresponds to&nbsp;[[1]]&nbsp;degrees.</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(pi*{degrees})/180", "answerSimplification": "all ", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "180*{radians2}", "answerSimplification": "all ", "showPreview": true, "checkingType": "dp", "checkingAccuracy": "2", "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Trigonometric Equations  - Simple (Radians)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Simple trig equations with radians</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Solve the following equation in <em>radians</em>, for $\\theta$ in the range $0\\leq\\theta\\leq2\\pi$.</strong></p>\n<p>Give your answers correct to 2 decimal places in ascending order.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Q1", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "Q1", "definition": "(a-1)/a", "description": "", "templateType": "anything", "can_override": false}, "f2": {"name": "f2", "group": "Q2", "definition": "c/b", "description": "", "templateType": "anything", "can_override": false}, "f3": {"name": "f3", "group": "Q4", "definition": "(1-b)/(b+1)", "description": "", "templateType": "anything", "can_override": false}, "f4": {"name": "f4", "group": "Q3", "definition": "-c/(c+3)", "description": "", "templateType": "anything", "can_override": false}, "s3": {"name": "s3", "group": "Q4", "definition": "arccos(f3)", "description": "", "templateType": "anything", "can_override": false}, "s2": {"name": "s2", "group": "Q2", "definition": "arccos(f2)", "description": "", "templateType": "anything", "can_override": false}, "s1": {"name": "s1", "group": "Q1", "definition": "arcsin(f1)", "description": "", "templateType": "anything", "can_override": false}, "s31": {"name": "s31", "group": "Q4", "definition": "precround(s3,2)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Q2", "definition": "random(2..b-1)", "description": "", "templateType": "anything", "can_override": false}, "s4": {"name": "s4", "group": "Q3", "definition": "arcsin(f4)", "description": "", "templateType": "anything", "can_override": false}, "s22": {"name": "s22", "group": "Q2", "definition": "precround(2*pi-s2,2)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Q2", "definition": "random(5..12)", "description": "", "templateType": "anything", "can_override": false}, "s41": {"name": "s41", "group": "Q3", "definition": "precround(pi-s4,2)", "description": "", "templateType": "anything", "can_override": false}, "s42": {"name": "s42", "group": "Q3", "definition": "precround(2*pi+s4,2)", "description": "", "templateType": "anything", "can_override": false}, "s12": {"name": "s12", "group": "Q1", "definition": "precround(pi-s1,2)", "description": "", "templateType": "anything", "can_override": false}, "s21": {"name": "s21", "group": "Q2", "definition": "precround(s2,2)", "description": "", "templateType": "anything", "can_override": false}, "s32": {"name": "s32", "group": "Q4", "definition": "precround(2*pi-s3,2)", "description": "", "templateType": "anything", "can_override": false}, "s11": {"name": "s11", "group": "Q1", "definition": "precround(s1,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Q1", "variables": ["a", "f1", "s1", "s11", "s12"]}, {"name": "Q2", "variables": ["b", "c", "f2", "s2", "s21", "s22"]}, {"name": "Q4", "variables": ["f3", "s31", "s32", "s3"]}, {"name": "Q3", "variables": ["f4", "s4", "s41", "s42"]}], "functions": {}, "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>\\[\\var{c+3}\\sin(\\theta)=-\\var{c}\\]</p>\n<p>$\\sin(\\theta)=$ [[0]]</p>\n<p>$\\theta=$ [[1]]&nbsp;or&nbsp;[[2]]</p>\n<p>Discard any solutions out of range.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f4}-0.01", "maxValue": "{f4}+0.01", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{s41}", "maxValue": "{s41}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{s42}", "maxValue": "{s42}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Trigonometric Equations  - Core (Degrees)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Trigonometric equations with degrees</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Solve the following equation in <em>degrees</em>, for $x$ in the range $0^\\circ\\leq x\\leq720^\\circ$.</strong></p>\n<p>\\[\\var{a+1}\\cos(x-\\var{b})=\\var{a-2}\\]</p>\n<p>Give your final answers correct to the nearest degree in ascending order.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "p", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(10..p-5)", 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"exploreObjective": null, "answer": "{4*s2*s4*(s2^2-s4^2)}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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>\\[z=(\\var{z3})^{\\var{-d1}}\\]<br/>$z=\\;\\;$[[0]] + [[1]] i</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{re(conj(z3^d1))}/{abs(z3^(2*d1))}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "notallowed": {"strings": ["."], "showStrings": false, "partialCredit": 0, "message": "<p>Make sure that you input the real and imaginary parts as fractions and not as decimals</p>"}, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{im(conj(z3^d1))}/{round(abs(z3)^(2*d1))}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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>Use integers or letters only for part (c) answers below.</p>\n<p></p>\n<p>when&nbsp; \\[z=i^0\\] $z=\\;\\;$ [[0]]</p>\n<p>when&nbsp; \\[z=i^1\\] $z=\\;\\;$ [[1]]</p>\n<p>when&nbsp; \\[z=i^2\\] $z=\\;\\;$ [[2]] &nbsp;</p>\n<p>when&nbsp; \\[z=i^3\\]$z=\\;\\;$ [[3]]</p>\n<p>Hence, or otherwise calculate</p>\n<p>\\[z=i^{\\var{n}}\\]<br/>$z=\\;\\;$[[4]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1", "answerSimplification": "std", "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": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "i", "answerSimplification": "std", "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": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-1", "answerSimplification": "std", "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": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-i", "answerSimplification": "std", "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": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{i^n}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Modulus and argument calculations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p><span style=\"color: #222222; font-family: sans-serif;\"><span style=\"line-height: 20px;\">Finding&nbsp;</span></span>the modulus and argument (in radians) of four complex numbers; the arguments between $-\\pi$ and $\\pi$ and careful with quadrants!</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Find the modulus and argument (in radians) of the following complex number, where the argument lies between $-\\pi$ and $\\pi$.</p>\n<p>When calculating the argument pay particular attention to the quadrant in which the complex number lies.</p>\n<p>Input final answers to 3 decimal places.</p>", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"arg3": {"name": "arg3", "group": "Ungrouped variables", "definition": "precround(arg(z3),3)", "description": "", "templateType": "anything", "can_override": true}, "z3": {"name": "z3", "group": "Ungrouped variables", "definition": "c2+d2*i", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "precround(abs(z3),3)", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ans3", "arg3", "z3", "c2", "d2", "tol"], "variable_groups": [], "functions": {}, "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>$|\\var{z3}|=\\;\\;$[[0]], $\\arg(\\var{z3})=\\;\\;$[[1]] radians</p>\n<p>Input both answers to 3 decimal places.</p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>HINT<br/><br/>Remember that</p>\n<p>$|\\var{z3}|=\\;\\;sqrt (\\var{c2}^2+\\var{d2}^2)$&nbsp; &nbsp;and&nbsp; &nbsp;$\\arg(\\var{z})=\\;\\;tan (\\var{d2}/\\var{c2})$</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans3-tol", "maxValue": "ans3+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "arg3-tol", "maxValue": "arg3+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Harder practice Q - roots of a cubic ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Using either algebraic division or the factor theorem, choose which one of these complex numbers is a root of the given equation $f(z)=0$ , and hence find all the roots.</p>", "advice": "", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "tx2a2": {"name": "tx2a2", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "s5": {"name": "s5", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "s4": {"name": "s4", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "x3b2": {"name": "x3b2", "group": "Ungrouped variables", "definition": "xs1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x1a1": {"name": "x1a1", "group": "Ungrouped variables", "definition": "if(tx1a1=a1,a1+1,tx1a1)", "description": "", "templateType": "anything", "can_override": false}, "x2a1": {"name": "x2a1", "group": "Ungrouped variables", "definition": "if(tx2a1=a1,a1+1,tx2a1)", "description": "", "templateType": "anything", "can_override": false}, "tx1a1": {"name": "tx1a1", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z3": {"name": "z3", "group": "Ungrouped variables", "definition": "x2a1+x2b1*i", "description": "", "templateType": "anything", "can_override": false}, "x2b2": {"name": "x2b2", "group": "Ungrouped variables", "definition": "xs3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "xs2": {"name": "xs2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x1a2": {"name": "x1a2", "group": "Ungrouped variables", "definition": "if(tx1a2=a2,a2+1,tx1a2)", "description": "", "templateType": "anything", "can_override": false}, "tx3a2": {"name": "tx3a2", "group": "Ungrouped variables", "definition": "s6*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "a1+ b1*i", "description": "", "templateType": "anything", "can_override": false}, "tx1a2": {"name": "tx1a2", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "tx2a1": {"name": "tx2a1", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "if(abs(a1)=f1,f1+1,f1)", "description": "", "templateType": "anything", "can_override": false}, "z4": {"name": "z4", "group": "Ungrouped variables", "definition": "x3a1+x3b1*i", "description": "", "templateType": "anything", "can_override": false}, "x1b2": {"name": "x1b2", "group": "Ungrouped variables", "definition": "xs2*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "x1a1+x1b1*i", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Ungrouped variables", "definition": "s5*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x2b1": {"name": "x2b1", "group": "Ungrouped variables", "definition": "xs2*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x2a2": {"name": "x2a2", "group": "Ungrouped variables", "definition": "if(tx2a2=a2,a2+1,tx2a2)", "description": "", "templateType": "anything", "can_override": false}, "x3a1": {"name": "x3a1", "group": "Ungrouped variables", "definition": "if(tx3a1=a1,a1+1,tx3a1)", "description": "", "templateType": "anything", "can_override": false}, "tx3a1": {"name": "tx3a1", "group": "Ungrouped variables", "definition": "s4*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "s3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x3a2": {"name": "x3a2", "group": "Ungrouped variables", "definition": "if(tx3a2=a2,a2+1,tx3a2)", "description": "", "templateType": "anything", "can_override": false}, "s3": {"name": "s3", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "s6": {"name": "s6", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "xs1": {"name": "xs1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "xs3": {"name": "xs3", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything", "can_override": false}, "x3b1": {"name": "x3b1", "group": "Ungrouped variables", "definition": "xs3*random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "x1b1": {"name": "x1b1", "group": "Ungrouped variables", "definition": "xs1*random(1..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["tx3a1", "f1", "tx3a2", "b2", "tx2a2", "x1b2", "x1b1", "b1", "tx1a1", "tx2a1", "xs2", "xs3", "xs1", "x3a1", "x3a2", "s3", "s2", "s1", "s6", "s5", "s4", "x2a1", "x2a2", "x1a2", "x1a1", "a1", "a2", "z4", "c2", "c1", "z1", "z2", "z3", "x3b1", "x3b2", "x2b1", "x2b2", "tx1a2"], "variable_groups": [], "functions": {}, "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>Given &nbsp;$\\displaystyle f(z) = \\simplify[std]{z ^ 3 + {( -2) * a1 -c1}*z ^ 2 + {2 * a1 * c1 + a1 ^ 2 + b1 ^ 2} * z -{c1 * (a1 ^ 2 + b1 ^ 2)}}$, one of the following complex numbers is a root $z_1$ of the equation $f(z)=0$.</p>\n        <p>Choose the correct value for $z_1$:[[0]]</p>", "gaps": [{"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": 4, "showCellAnswerState": true, "choices": ["<p>$\\simplify{{a1}+{b1}i}$</p>", "<p>$\\simplify{{x1a1}+{x1b1}i}$</p>", "<p>$\\simplify{{x2a1}+{x2b1}i}$</p>", "<p>$\\simplify{{x3a1}+{x3b1}i}$</p>"], "matrix": ["5", 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}, {"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>The remaining roots of $f(z)$ are:</p>\n        <p>$z_2=\\;\\;$[[0]] (enter the complex root here)</p>\n        <p>$z_3=\\;\\;$[[1]] (enter the real root here)</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a1}-{b1}i", "answerSimplification": "std", "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": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c1}", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Considering efficiency - roots of a quartic real polynomial", "extensions": [], "custom_part_types": [], "resources": [["question-resources/wm175_method_1.png", "/srv/numbas/media/question-resources/wm175_method_1.png"], ["question-resources/20210608_165320.jpg", "/srv/numbas/media/question-resources/20210608_165320.jpg"], ["question-resources/wm175_method_1_jNN3Dz7.png", "/srv/numbas/media/question-resources/wm175_method_1_jNN3Dz7.png"], ["question-resources/method_1.jpg", "/srv/numbas/media/question-resources/method_1.jpg"], ["question-resources/method_2.jpg", "/srv/numbas/media/question-resources/method_2.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], "tags": [], "metadata": {"description": "<p>Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Consider both methods shown to get the correct answer to the question below.<br/>After looking through both methods, choose which one you prefer and say why, giving a full explanation of your choice.</p>\n<p>Remember to compare efficiency, clarity of setting out, the reader's ability to follow the logic used easily in your answer.<br/><br/><strong>Question</strong></p>\n<p>Given &nbsp;$\\displaystyle f(z) = \\simplify[std]{z ^ 4+ 4*z ^ 3+ 28 * z^2 +240z+800}$, one of the following complex numbers is a root $z_1$ of the equation $f(z)=0$.</p>\n<p>Choose the correct value for $z_1$:&nbsp; &nbsp; &nbsp;(i)&nbsp; $1-4i$ &nbsp; &nbsp; &nbsp;or&nbsp; &nbsp; &nbsp;(ii)&nbsp; $-4+2i$</p>\n<p><br/><img src=\"resources/question-resources/method_1.jpg\" width=\"545\" height=\"726\"/>&nbsp; &nbsp; <img src=\"resources/question-resources/method_2.jpg\" width=\"543\" height=\"725\"/></p>\n<p></p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"></span></p>", "advice": "<p></p>\n<p>&nbsp;</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {"ch": {"parameters": [["a", "number"], ["s", "number"], ["b", "number"], ["r", "number"], ["t", "number"]], "type": "number", "language": "jme", "definition": "if(round(a^2+b^2)|round(s),ch(a,s,random(r..t except 0),r,t),b)"}}, "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>Please give your full reasoning for which of the methods shown above you prefer.<br/><br/></p>\n<p>You should aim to write about 50 words in your answer.</p>\n<p>Then send it to Shaheen Charlwood via Teams direct chat before the submission time given (usually the end time of the exam).</p>\n<p></p>", "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": false, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "never", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": "WM175A1"}, "timing": {"allowPause": false, "timeout": {"action": "warn", "message": "<p>This assessment has now finished.&nbsp;<br/><br/></p>"}, "timedwarning": {"action": "warn", "message": "<p>You have 5 minutes left.</p>\n<p>Please ensure you have submitted all answers and sent your explanation for the last question to Shaheen via Teams direct chat now!</p>"}}, "feedback": {"showactualmark": false, "showtotalmark": true, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "<ul>\n<li>You have 2.5 hours to complete all the questions.</li>\n<li>Make sure you submit your answers as you complete them and ensure all anwers are submitted before the end of the exam - you will see a reminder when there are 5 minutes left.</li>\n<li>The last question requires you to write an explanation of about 50 words that needs to be sent to Shaheen via Teams direct chat before the end of the exam.</li>\n<li>You may use a scientific calculator throughout this exam - if it not a casio fx series calculator then please ensure it has been verified as acceptable by the invigilator.</li>\n<li>You will need paper for your rough work - this is not usully required to be handed in although you should keep it safe in case the marker wishes to see it.&nbsp;</li>\n<li>You may take a comfort break but be ensure to let the invigilator know via Teams chat.</li>\n<li>If you have any questions during the exam please use the Teams chat feature to send a message to Shaheen.</li>\n</ul>\n<p>&nbsp; &nbsp;</p>", "reviewshowscore": false, "reviewshowfeedback": false, "reviewshowexpectedanswer": false, "reviewshowadvice": false, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Shaheen Charlwood", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1809/"}], 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