// Numbas version: exam_results_page_options
{"name": "MA1002_EXAM_MARCH_18", "metadata": {"description": "<p>Please attempt all questions.</p>", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", ""], "questions": [{"name": "Q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Find the function $y = F(x)$ given that $F'(x) = \\var{a}x -\\var{b}$ and the curve passes through the point $(1,\\var{k})$.&nbsp;&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2, 4, 6, 8, 10, 12)", "description": "<p>F'(x) = ax-b</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..9 except a)", "description": "<p>F'(x) = ax-b</p>", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2..9 except a/2)", "description": "<p>y-intercept</p>", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "k-a/2 +b", "description": "<p>F(x) = a/2 x^2 -bx +c for value of c above</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "k", "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>$F(x) = $ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Q1 Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a/2}x^2 - {b} x + {c} ", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Find the area of the region bounded by the curve $y = -x^2 +\\var{a+b}x -\\var{a b}$ and the line $y = x-\\var{a}$.&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1, 2, 3)", "description": "<p>x coordinate where line and parabola meet</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "a + 1 +random(2, 3)", "description": "<p>parabola is y=(a-x)(x-b)</p>", "templateType": "anything"}, "Area": {"name": "Area", "group": "Ungrouped variables", "definition": "(b-a-1)^3 / 6", "description": "<p>Area between y=x-a and y= (a-x)(x-b)</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "Area"], "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>Area =&nbsp;[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Qu2 Area", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Area", "maxValue": "Area", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Use integration by parts to evaluate each of the following integrals.&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2, 3, 4)", "description": "<p>sin(ax) in the integral part (ii)&nbsp;</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..7)", "description": "<p>b x e^{cx} to integrate in Part (i)</p>", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2, 3, 4, 5)", "description": "<p>b x e^{cx} to integrate in Part (i)</p>", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(2, 3, 7)", "description": "<p>integral of e^{-x} sin(kx) in Part iii</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "k"], "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>$\\displaystyle \\int \\var{b}x e^{\\var{c}x}\\,dx$ =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Ans Part i", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{b/c^2} e^({c} x) ({c} x-1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "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>$\\displaystyle \\int x^2 \\sin(\\var{a} x)\\,dx$ =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Ans Part ii", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({2/a^3} - {1/a}x^2) cos({a}x) + {2/a^2} x sin({a} x)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>In this question, you are asked to find a volume of revolution.&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2, 3, 4, 5)", "description": "<p>Revolving the curve y = a^2 -x^2 about y-axis.&nbsp;</p>", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The region bounded by $y=\\var{a^2} - x^2$, the $x$-axis and the $y$-axis is rotated around the $y$-axis. Find the volume of the solid formed. Give your answer in the form '$\\pi\\ \\text{times a fraction or whole number}$'. (You can enter '$\\pi$' by simply typing 'Pi'.)</p>\n<p>Volume of solid =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Q4 Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "Pi {a^4}/2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Evaluate both of the following integrals.&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2, 3, 4)", "description": "<p>integrating e^(bx) from -a to a</p>", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..5 except a)", "description": "<p>integrating e^(bx) from -a to a</p>", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1, 2, 3, 4)", "description": "<p>integrating x/Sqrt[x^2-c^2] from c+aa to c+bb</p>", "templateType": "anything"}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "random(1, 2)", "description": "", "templateType": "anything"}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(2, 3, 4)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "aa<bb", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "aa", "bb"], "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>Evaluate&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle \\int_{-\\var{a}}^{\\var{a}} \\frac{e^{\\var{b}x} + e^{-\\var{b}x}}{2}\\,dx$</p>\n<p style=\"text-align: left;\">You can leave your answer as an exponential, involving $e$ to a power.</p>\n<p style=\"text-align: left;\">Value of integral =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Part i Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1/{b} (e^({a*b}) - e^(-{a*b}))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "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>Evaluate the following integral, leaving your answer as a surd (i.e. with square roots)&nbsp;</p>\n<p style=\"text-align: center;\">$\\displaystyle&nbsp;\\int_{\\var{{c}+{aa}}}^{\\var{{c}+{bb}}} &nbsp;\\frac{x}{\\sqrt{x^2 - \\var{c^2}}}\\,dx$</p>\n<p>Value of integral equals =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Part ii Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "Sqrt({bb*(bb+2c)}) - Sqrt({aa*(aa+2c)})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Use the information below to find the function $F(x)$.&nbsp;</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..5 except a)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..4 except a)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "random(4, 5, 6)", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "random(5..12 except A)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "A", "B"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $F''(x) = -\\var{2 {a}} + \\var{3{b}}x -\\var{4{c}}x^2$, and if $F'(0) = \\var{A}$ and $F(0) = \\var{B}$, then&nbsp;</p>\n<p>$F(x) =\\ $&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Qu6 Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{B} + {A}x -{a}x^2 + {b/2}x^3 -{c/3}x^4", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Q7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Evaluate both of the following integrals by substitution.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2, 3, 4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..5 except a)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1,2)", "description": "", "templateType": "anything", "can_override": false}, "ee": {"name": "ee", "group": "Ungrouped variables", "definition": "random(1..4)^2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "ee"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Part i", "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 integral&nbsp;</p>\n<p>$\\displaystyle \\int e^{\\var{a}\\sin(\\var{b}x)} \\cos(\\var{b}x)\\,dx$</p>\n<p>Integral =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Part i Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1/({{a} {b}})e^({a}sin({b}x))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Part ii", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the integral&nbsp;</p>\n<p>$\\displaystyle \\int_0^{\\var{c}} \\frac{x^3}{\\sqrt{x^4 + \\var{ee}}} \\,dx$</p>\n<p>Integral =&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Part ii Ans", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "(sqrt({{c}^4+{ee}}) - sqrt({ee}))/2", "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"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "never", "navigatemode": "sequence", "onleave": {"action": "warnifunattempted", "message": "<p>Yuo have not attempted this question. Please check.</p>"}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": false, "advicethreshold": 0, "intro": "", "reviewshowscore": false, "reviewshowfeedback": false, "reviewshowexpectedanswer": false, "reviewshowadvice": false, "feedbackmessages": []}, "contributors": [{"name": "Kieran Mulchrone", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1243/"}], "extensions": [], "custom_part_types": [], "resources": []}