// Numbas version: exam_results_page_options
{"name": "Quadratic modulus graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Quadratic modulus graph", "tags": [], "metadata": {"description": "<p>This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.&nbsp; Student has to decide what kind of map it represents and whether an inverse function exists.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{geogebra_applet('https://ggbm.at/DN6naqhm', defs, [])}</p>\n<p>The graph shows a quadratic function of the form \\[ y = |f(x)| \\] and a straight line $y=\\var{c}$.</p>", "advice": "<p><strong>This is not a function</strong>.&nbsp; The graph&nbsp;fails the vertical line test, because a vertical line would usually touch&nbsp;two&nbsp;points on the curve.&nbsp;&nbsp;</p>\n<p><strong>This is a one-to-many map</strong>.&nbsp;&nbsp;That means each input ($x$-axis, domain) often go to&nbsp;two outputs ($y$-axis, range).</p>\n<p>This&nbsp;relation&nbsp;<strong>does not have an inverse function</strong>.&nbsp; Although it passes the horizontal line test....remember, the horizontal line test only applies to functions!</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"q2": {"name": "q2", "group": "Ungrouped variables", "definition": "a*b+c", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "(-p+sqrt(p^2-4*q1))/2", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "-(a+b)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-6..6 except 0)", "description": "", "templateType": "anything"}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "(-p+sqrt(p^2-4*q2))/2", "description": "", "templateType": "anything"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "(-p-sqrt(p^2-4*q1))/2", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..round(M)-1)", "description": "", "templateType": "anything"}, "M": {"name": "M", "group": "Ungrouped variables", "definition": "abs((a*b)-0.25*(a+b)^2)", "description": "", "templateType": "anything"}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "sort([x1,x2,x3,x4])", "description": "", "templateType": "anything"}, "eps": {"name": "eps", "group": "Ungrouped variables", "definition": "0.5*10^(-4)", "description": "", "templateType": "anything"}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "(-p-sqrt(p^2-4*q2))/2", "description": "", "templateType": "anything"}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "a*b-c", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[\n  ['a',a],\n  ['b',b],\n  ['c',c]\n]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "a<>b and M<11 and M>1", "maxRuns": "200"}, "ungrouped_variables": ["a", "b", "defs", "M", "c", "p", "q1", "q2", "x1", "x2", "x3", "x4", "ans", "eps"], "variable_groups": [], "functions": {"graph": {"parameters": [], "type": "html", "language": "jme", "definition": "geogebra_applet('https://ggbm.at/aXxv2ECN', defs, [])"}}, "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>Input the correct expression for $f(x)$ below.</p>\n<p>$f(x) = $&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hint: You can see from the graph that $x=\\var{a}$ and $x=\\var{b}$ at $y=0$.</p>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "(x-{a})*({b}-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": ""}]}], "answer": "(x-{a})*(x-{b})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "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>The line $y=\\var{c}$ intersects the line at four points. &nbsp;Find the $x$-values of those points and list them in ascending numerical order (smallest value first).</p>\n<p>$x = $&nbsp;[[0]]</p>\n<p>$x = $&nbsp;[[1]]</p>\n<p>$x = $&nbsp;[[2]]</p>\n<p>$x = $&nbsp;[[3]]</p>\n<p>(Give answers to 4 decimal places).</p>", "gaps": [{"type": "numberentry", "useCustomName": false, 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans[2]-{eps}", "maxValue": "ans[2]+{eps}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans[3]-{eps}", "maxValue": "ans[3]+{eps}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "4", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}