// Numbas version: exam_results_page_options
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Task 7", "tags": [], "metadata": {"description": "<p>The 7th task in HELM book 1.4 section 1.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Simplify</p>", "advice": "<p>First factorise the numerator and the denominator</p>\n<p>\\[ \\frac{\\var{q7num}}{\\var{q7den}} = \\frac{(\\var{q7fc})(\\var{q7f1})}{(\\var{q7fc})(\\var{q7f2})}\\]</p>\n<p>Then cancel out the common terms and simplify.</p>\n<p>\\[ = \\frac{(\\require{enclose} \\enclose{horizontalstrike}{\\var{q7fc}})(\\var{q7f1})}{(\\require{enclose} \\enclose{horizontalstrike}{\\var{q7fc}})(\\var{q7f2})} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"alphabet": {"name": "alphabet", "group": "Ungrouped variables", "definition": "[\"a\",\"b\",\"c\",\"d\",\"f\",\"g\",\"h\",\"k\",\"m\",\"n\",\"p\",\"q\",\"r\",\"s\",\"t\",\"u\",\"v\",\"w\",\"x\",\"y\",\"z\"]", "description": "", "templateType": "anything", "can_override": false}, "q7v": {"name": "q7v", "group": "Q7", "definition": "random(alphabet)", "description": "", "templateType": "anything", "can_override": false}, "q7xcoeff": {"name": "q7xcoeff", "group": "Q7", "definition": "shuffle([1,1,random(1,2,3,5,7)])", "description": "<p>the coefficients of x in the four factors.</p>", "templateType": "anything", "can_override": false}, "q7c": {"name": "q7c", "group": "Q7", "definition": "shuffle(-12..12 except 0)[0..3]", "description": "<p>the four constant terms.</p>", "templateType": "anything", "can_override": false}, "q7fc,q7f1,q7f2": {"name": "q7fc,q7f1,q7f2", "group": "Ungrouped variables", "definition": "[simplify(expression(q7xcoeff[0]+\"*\"+q7v+\"+\"+q7c[0]),\"all\"),\n  simplify(expression(q7xcoeff[1]+\"*\"+q7v+\"+\"+q7c[1]),\"all\"),\n  simplify(expression(q7xcoeff[2]+\"*\"+q7v+\"+\"+q7c[2]),\"all\")]", "description": "<p>the three factors: common factor, numerator, denominator.</p>", "templateType": "anything", "can_override": false}, "q7num": {"name": "q7num", "group": "Q7", "definition": "simplify(expression(\n    \"(\"+string(q7fc)+\")*(\"+string(q7f1)+\")\"\n  ),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}, "q7den": {"name": "q7den", "group": "Q7", "definition": "simplify(expression(\n    \"(\"+string(q7fc)+\")*(\"+string(q7f2)+\")\"\n  ),[\"expandBrackets\",\"all\"])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["q7fc,q7f1,q7f2", "alphabet"], "variable_groups": [{"name": "Q7", "variables": ["q7v", "q7xcoeff", "q7c", "q7num", "q7den"]}], "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></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">$\\var{q7num}$</td>\n<td style=\"text-align: center;\">=</td>\n<td style=\"text-align: center; border-bottom: 1pt solid;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: center;\">$\\var{q7den}$</td>\n<td></td>\n<td style=\"text-align: center;\">[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "stepsPenalty": 0, "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>First factorise the numerator and the denominator</p>"}, {"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>Then cancel out the common terms and simplify.</p>"}], "gaps": [{"type": "jme", "useCustomName": true, "customName": "numerator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q7f1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": true, "customName": "denominator", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{q7f2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}