// Numbas version: exam_results_page_options
{"name": "Factorising: Common factor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "variables": {"pmult": {"templateType": "anything", "definition": "primes[0]", "name": "pmult", "group": "part a", "description": ""}, "ct3": {"templateType": "anything", "definition": "cmult*cc", "name": "ct3", "group": "part c", "description": ""}, "pconstant": {"templateType": "anything", "definition": "primes[2]", "name": "pconstant", "group": "part a", "description": ""}, "bc": {"templateType": "anything", "definition": "bp2/cf", "name": "bc", "group": "part b", "description": ""}, "nconstant": {"templateType": "anything", "definition": "random(2..12)", "name": "nconstant", "group": "part b", "description": ""}, "bp2": {"templateType": "anything", "definition": "nmult*nconstant", "name": "bp2", "group": "part b", "description": ""}, "cprimes": {"templateType": "anything", "definition": "shuffle([2,3,5,7,11])[0..3]", "name": "cprimes", "group": "part c", "description": ""}, "ct2": {"templateType": "anything", "definition": "cmult*cy", "name": "ct2", "group": "part c", "description": ""}, "cy": {"templateType": "anything", "definition": "cprimes[1]", "name": "cy", "group": "part c", "description": ""}, "nxcoeff": {"templateType": "anything", "definition": "random(2..12)", "name": "nxcoeff", "group": "part b", "description": ""}, "bp1": {"templateType": "anything", "definition": "nmult*nxcoeff", "name": "bp1", "group": "part b", "description": ""}, "primes": {"templateType": "anything", "definition": "shuffle([2,3,5,7,11])[0..3]", "name": "primes", "group": "part a", "description": ""}, "bx": {"templateType": "anything", "definition": "bp1/cf", "name": "bx", "group": "part b", "description": ""}, "pxcoeff": {"templateType": "anything", "definition": "primes[1]", "name": "pxcoeff", "group": "part a", "description": ""}, "ct1": {"templateType": "anything", "definition": "cx*cmult", "name": "ct1", "group": "part c", "description": ""}, "cmult": {"templateType": "anything", "definition": "random(2..10)", "name": "cmult", "group": "part c", "description": ""}, "cf": {"templateType": "anything", "definition": "-gcd(bp1,bp2)", "name": "cf", "group": "part b", "description": ""}, "cc": {"templateType": "anything", "definition": "-cprimes[2]", "name": "cc", "group": "part c", "description": ""}, "nmult": {"templateType": "anything", "definition": "random(-12..-2)", "name": "nmult", "group": "part b", "description": ""}, "cx": {"templateType": "anything", "definition": "cprimes[0]", "name": "cx", "group": "part c", "description": ""}}, "advice": "", "functions": {}, "rulesets": {}, "parts": [{"extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "sortAnswers": false, "stepsPenalty": "0", "variableReplacementStrategy": "originalfirst", "prompt": "<p>The expression $\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ is a sum and&nbsp;can be factorised&nbsp;(written as a product) by finding the largest&nbsp;common factor:</p>\n<p>&nbsp;$\\var{pmult*pxcoeff}x+\\var{pconstant*pmult} = $&nbsp;[[0]]&nbsp;$\\large($&nbsp;[[1]]&nbsp;$\\large)$</p>\n<p></p>", "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "variableReplacements": [], "steps": [{"marks": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacements": [], "prompt": "<p><em>We put the common factor out the front of a set of brackets and put the 'left-overs' inside.</em></p>\n<p></p>\n<p>The (largest) common factor of&nbsp;&nbsp;$\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ is $\\var{pmult}$. Once we remove that factor from each term in&nbsp;$\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}$ we are left with&nbsp;$\\var{pxcoeff}x+\\var{pconstant}$.</p>\n<p>That means&nbsp;$\\var{pmult*pxcoeff}x+\\var{pconstant*pmult}= \\var{pmult}(\\var{pxcoeff}x+\\var{pconstant})$.</p>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": []}], "gaps": [{"maxValue": "{pmult}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{pmult}", "unitTests": []}, {"vsetRange": [0, 1], "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "answer": "{pxcoeff}x+{pconstant}", "type": "jme", "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "failureRate": 1, "unitTests": []}], "showCorrectAnswer": true, "unitTests": []}, {"extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "sortAnswers": false, "stepsPenalty": "0", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Factorise $\\simplify{{bp1}a+{bp2}}$</p>\n<p>&nbsp;[[0]]&nbsp;$\\large($&nbsp;[[1]]&nbsp;$\\large)$</p>\n<p></p>\n<p></p>\n<p></p>", "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "variableReplacements": [], "steps": [{"marks": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacements": [], "prompt": "<p><em>We put the common factor out the front of a set of brackets and put the 'left-overs' inside.</em></p>\n<p></p>\n<p>The (largest) common factor of $\\simplify{{bp1}a+{bp2}}$ is $\\var{cf}$. Once we remove that factor from each term in $\\simplify{{bp1}a+{bp2}}$ we are left with&nbsp;$\\var{bx}a+\\var{bc}$.</p>\n<p>That means $\\simplify{{bp1}a+{bp2}}$ is $\\var{cf} = \\var{cf}(\\var{bx}a+\\var{bc})$.</p>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": []}], "gaps": [{"maxValue": "{cf}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{cf}", "unitTests": []}, {"vsetRange": [0, 1], "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": [], "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "answer": "{bx}a+{bc}", "type": "jme", "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "failureRate": 1, "unitTests": []}], "showCorrectAnswer": true, "unitTests": []}, {"extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "sortAnswers": false, "stepsPenalty": "0", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Factorise $\\simplify{{ct1}x+{ct2}y+{ct3}}$</p>\n<p>&nbsp;[[0]]&nbsp;$\\large($&nbsp;[[1]]&nbsp;$\\large)$</p>", "customMarkingAlgorithm": "", "scripts": {}, "type": "gapfill", "variableReplacements": [], "steps": [{"marks": 0, "extendBaseMarkingAlgorithm": true, "scripts": {}, "variableReplacements": [], "prompt": "<p><em>We put the common factor out the front of a set of brackets and put the 'left-overs' inside.</em></p>\n<p></p>\n<p>The (largest) common factor of $\\simplify{{ct1}x+{ct2}y+{ct3}}$ is $\\var{cmult}$. Once we remove that factor from each term in $\\simplify{{ct1}x+{ct2}y+{ct3}}$&nbsp;we are left with&nbsp;$\\simplify{{cx}x+{cy}y+{cc}}$.</p>\n<p>That means $\\simplify{{ct1}x+{ct2}y+{ct3}} = \\simplify{{cmult}({ct1}x+{ct2}y+{ct3})}$.</p>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": []}], "gaps": [{"maxValue": "{cmult}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "minValue": "{cmult}", "unitTests": []}, {"vsetRange": [0, 1], "checkVariableNames": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "expectedVariableNames": ["x", "y"], "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "scripts": {}, "answer": "{cx}x+{cy}y+{cc}", "type": "jme", "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "failureRate": 1, "unitTests": []}], "showCorrectAnswer": true, "unitTests": []}], "variable_groups": [{"name": "part a", "variables": ["pmult", "pxcoeff", "pconstant", "primes"]}, {"name": "part b", "variables": ["nmult", "nxcoeff", "nconstant", "bp2", "bp1", "cf", "bx", "bc"]}, {"name": "part c", "variables": ["cprimes", "cx", "cy", "cc", "cmult", "ct1", "ct2", "ct3"]}], "statement": "", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "name": "Factorising: Common factor", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "tags": [], "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}