// Numbas version: finer_feedback_settings
{"name": "Marlon's copy of Factorising: Common factor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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"]}], "advice": "", "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "showQuestionGroupNames": false, "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "rulesets": {}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "notes": ""}, "statement": "", "type": "question", "tags": ["algebra", "common factor", "distributive law", "factor", "factorisation", "Factorisation", "factorising"], "parts": [{"showCorrectAnswer": true, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "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", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{pmult}", "type": "numberentry", "variableReplacements": [], "minValue": "{pmult}", "scripts": {}}, {"checkvariablenames": false, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "type": "jme", "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "vsetrangepoints": 5, "answer": "{pxcoeff}x+{pconstant}", "showpreview": true, "vsetrange": [0, 1], "expectedvariablenames": []}], "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>", "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"showCorrectAnswer": true, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "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", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{cf}", "type": "numberentry", "variableReplacements": [], "minValue": "{cf}", "scripts": {}}, {"checkvariablenames": false, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "type": "jme", "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "vsetrangepoints": 5, "answer": "{bx}a+{bc}", "showpreview": true, "vsetrange": [0, 1], "expectedvariablenames": []}], "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>", "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"showCorrectAnswer": true, "variableReplacements": [], "steps": [{"showCorrectAnswer": true, "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", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "maxValue": "{cmult}", "type": "numberentry", "variableReplacements": [], "minValue": "{cmult}", "scripts": {}}, {"checkvariablenames": true, "checkingtype": "absdiff", "checkingaccuracy": 0.001, "type": "jme", "marks": 1, "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "vsetrangepoints": 5, "answer": "{cx}x+{cy}y+{cc}", "showpreview": true, "vsetrange": [0, 1], "expectedvariablenames": ["x", "y"]}], "prompt": "<p>Factorise $\\simplify{{ct1}x+{ct2}y+{ct3}}$</p>\n<p>&nbsp;[[0]]&nbsp;$\\large($&nbsp;[[1]]&nbsp;$\\large)$</p>", "type": "gapfill", "stepsPenalty": "1", "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "name": "Marlon's copy of Factorising: Common factor", "preamble": {"js": "", "css": ""}, "variables": {"cy": {"name": "cy", "group": "part c", "definition": "cprimes[1]", "description": "", "templateType": "anything"}, "bx": {"name": "bx", "group": "part b", "definition": "bp1/cf", "description": "", "templateType": "anything"}, "cprimes": {"name": "cprimes", "group": "part c", "definition": "shuffle([2,3,5,7,11])[0..3]", "description": "", "templateType": "anything"}, "cmult": {"name": "cmult", "group": "part c", "definition": "random(2..10)", "description": "", "templateType": "anything"}, "cx": {"name": "cx", "group": "part c", "definition": "cprimes[0]", "description": "", "templateType": "anything"}, "pmult": {"name": "pmult", "group": "part a", "definition": "primes[0]", "description": "", "templateType": "anything"}, "pconstant": {"name": "pconstant", "group": "part a", "definition": "primes[2]", "description": "", "templateType": "anything"}, "pxcoeff": {"name": "pxcoeff", "group": "part a", "definition": "primes[1]", "description": "", "templateType": "anything"}, "cc": {"name": "cc", "group": "part c", "definition": "-cprimes[2]", "description": "", "templateType": "anything"}, "ct2": {"name": "ct2", "group": "part c", "definition": "cmult*cy", "description": "", "templateType": "anything"}, "nmult": {"name": "nmult", "group": "part b", "definition": "random(-12..-2)", "description": "", "templateType": "anything"}, "primes": {"name": "primes", "group": "part a", "definition": "shuffle([2,3,5,7,11])[0..3]", "description": "", "templateType": "anything"}, "ct1": {"name": "ct1", "group": "part c", "definition": "cx*cmult", "description": "", "templateType": "anything"}, "bp1": {"name": "bp1", "group": "part b", "definition": "nmult*nxcoeff", "description": "", "templateType": "anything"}, "bc": {"name": "bc", "group": "part b", "definition": "bp2/cf", "description": "", "templateType": "anything"}, "ct3": {"name": "ct3", "group": "part c", "definition": "cmult*cc", "description": "", "templateType": "anything"}, "nxcoeff": {"name": "nxcoeff", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything"}, "bp2": {"name": "bp2", "group": "part b", "definition": "nmult*nconstant", "description": "", "templateType": "anything"}, "nconstant": {"name": "nconstant", "group": "part b", "definition": "random(2..12)", "description": "", "templateType": "anything"}, "cf": {"name": "cf", "group": "part b", "definition": "-gcd(bp1,bp2)", "description": "", "templateType": "anything"}}, "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}