// Numbas version: finer_feedback_settings
{"name": "PreCal Composition of Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "tags": [], "ungrouped_variables": ["p", "q", "A", "B", "C", "D", "F", "fpgCx2", "fpgCx", "fpgCc", "fmgCx2", "fmgCx", "fmgCc", "fdgCx4", "fdgCx3", "fdgCx2", "fdgCx", "fdgCc", "xneq", "gofCx4", "gofCx2", "gofCc"], "functions": {}, "name": "PreCal Composition of Functions", "advice": "", "metadata": {"licence": "All rights reserved", "description": ""}, "extensions": [], "variables": {"fdgCx": {"definition": "A*B", "templateType": "anything", "group": "Ungrouped variables", "name": "fdgCx", "description": ""}, "D": {"definition": "1", "templateType": "anything", "group": "Ungrouped variables", "name": "D", "description": ""}, "q": {"definition": "random(-5..5 except [0,p])", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "fmgCx": {"definition": "-B", "templateType": "anything", "group": "Ungrouped variables", "name": "fmgCx", "description": ""}, "gofCx2": {"definition": "2*F*A*D+B*D", "templateType": "anything", "group": "Ungrouped variables", "name": "gofCx2", "description": ""}, "F": {"definition": "2", "templateType": "anything", "group": "Ungrouped variables", "name": "F", "description": ""}, "fdgCc": {"definition": "A*C", "templateType": "anything", "group": "Ungrouped variables", "name": "fdgCc", "description": ""}, "p": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "fdgCx3": {"definition": "D*B", "templateType": "anything", "group": "Ungrouped variables", "name": "fdgCx3", "description": ""}, "C": {"definition": "p*q", "templateType": "anything", "group": "Ungrouped variables", "name": "C", "description": ""}, "A": {"definition": "-q^2", "templateType": "anything", "group": "Ungrouped variables", "name": "A", "description": ""}, "gofCx4": {"definition": "F*D^2", "templateType": "anything", "group": "Ungrouped variables", "name": "gofCx4", "description": ""}, "fmgCc": {"definition": "A-C", "templateType": "anything", "group": "Ungrouped variables", "name": "fmgCc", "description": ""}, "fpgCx": {"definition": "B", "templateType": "anything", "group": "Ungrouped variables", "name": "fpgCx", "description": ""}, "fdgCx2": {"definition": "D*C+A*F", "templateType": "anything", "group": "Ungrouped variables", "name": "fdgCx2", "description": ""}, "B": {"definition": "p+2*q", "templateType": "anything", "group": "Ungrouped variables", "name": "B", "description": ""}, "fdgCx4": {"definition": "D*F", "templateType": "anything", "group": "Ungrouped variables", "name": "fdgCx4", "description": ""}, "fmgCx2": {"definition": "D-F", "templateType": "anything", "group": "Ungrouped variables", "name": "fmgCx2", "description": ""}, "gofCc": {"definition": "F*A^2+B*A+C", "templateType": "anything", "group": "Ungrouped variables", "name": "gofCc", "description": ""}, "fpgCc": {"definition": "A+C", "templateType": "anything", "group": "Ungrouped variables", "name": "fpgCc", "description": ""}, "fpgCx2": {"definition": "D+F", "templateType": "anything", "group": "Ungrouped variables", "name": "fpgCx2", "description": ""}, "xneq": {"definition": "-p/2", "templateType": "anything", "group": "Ungrouped variables", "name": "xneq", "description": ""}}, "parts": [{"showFeedbackIcon": true, "type": "jme", "prompt": "<p>FIND:&nbsp; $[g \\circ f](x)$</p>\n<p></p>\n<p>$[g \\circ f](x) =$</p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "{gofCx4}*x^4+{gofCx2}*x^2+{gofCc}", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [{"value": "", "name": "x"}], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>FIND:&nbsp;$[f +g](x)$</p>\n<p></p>\n<p>&nbsp;$[f +g](x)=$</p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "({D}+{F})*x^2+{B}*x+{A}+{C}", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [{"value": "", "name": "x"}], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>FIND:&nbsp;&nbsp;&nbsp;$[f -g](x)$</p>\n<p></p>\n<p>&nbsp;$[f -g](x)=$</p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "({D}-{F})*x^2 -{B}*x + ({A}-{C})", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [{"value": "", "name": "x"}], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>FIND:&nbsp;&nbsp;&nbsp;$[f&nbsp; \\cdot g](x)$</p>\n<p></p>\n<p>$[f&nbsp; \\cdot g](x) = $</p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "{fdgCx4}*x^4+{fdgCx3}*x^3+{fdgCx2}*x^2+{fdgCx}*x+{fdgCc}", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [{"value": "", "name": "x"}], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "jme", "prompt": "<p>FIND:&nbsp;&nbsp;$[\\frac{f}{g}](x)$</p>\n<p></p>\n<p>$[\\frac{f}{g}](x)=$</p>", "showPreview": true, "variableReplacements": [], "vsetRangePoints": 5, "failureRate": 1, "customName": "", "answer": "(x-{q})/(2*x+{p})", "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "valuegenerators": [{"value": "", "name": "x"}], "useCustomName": false, "checkingType": "absdiff", "adaptiveMarkingPenalty": 0, "checkingAccuracy": 0.001, "marks": 1, "scripts": {}, "checkVariableNames": false}, {"showFeedbackIcon": true, "type": "numberentry", "correctAnswerStyle": "plain", "variableReplacements": [], "allowFractions": true, "customName": "", "minValue": "{xneq}", "mustBeReduced": true, "correctAnswerFraction": true, "showCorrectAnswer": true, "unitTests": [], "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "<p>For the result $[\\frac{f}{g}](x)$, what is the restriction on the domain of the new function?</p>\n<p></p>\n<p>$x \\ne $?</p>", "variableReplacementStrategy": "originalfirst", "scripts": {}, "useCustomName": false, "mustBeReducedPC": "50", "adaptiveMarkingPenalty": 0, "maxValue": "{xneq}", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true}], "statement": "<p>GIVEN:&nbsp; $f(x) = \\simplify{ {D}*x^2 +{A}}$ and $g(x) = \\simplify{ {F}*x^2 + {B}*x + {C} }$</p>", "type": "question", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}