// Numbas version: exam_results_page_options
{"name": "Distributive law: expanding one set of brackets", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "", "notes": ""}, "name": "Distributive law: expanding one set of brackets", "tags": ["algebra", "distributive law", "expanding", "expanding brackets"], "ungrouped_variables": [], "rulesets": {}, "functions": {}, "parts": [{"steps": [{"showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information", "prompt": "<p><em>The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets.</em></p>\n<p></p>\n<p>For example, $3(5x+6)$ means $3\\times (5x+6)$ which means $3\\times 5x+3\\times 6$, and so expanding $3(5x+6)$ gives $15x+18$.</p>", "scripts": {}}], "stepsPenalty": "1", "gaps": [{"allowFractions": false, "minValue": "{pmult*pxcoeff}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{pmult*pxcoeff}", "showPrecisionHint": false}, {"allowFractions": false, "minValue": "{pmult*pconstant}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{pmult*pconstant}", "showPrecisionHint": false}], "variableReplacements": [], "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<p>The expression $\\var{pmult}(\\var{pxcoeff}x+\\var{pconstant})$&nbsp;is factorised (written as a product), we can expand the expression (so it is written as a sum) to get&nbsp;</p>\n<p>[[0]] $x$ +&nbsp;[[1]]</p>", "scripts": {}}, {"steps": [{"showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information", "prompt": "<p><em>The number in front of the bracket is multiplying the bracketed term, that is, each term in the brackets. Further, recall that a negative multiplied by a negative is a positive.</em></p>\n<p></p>\n<p>For example, $-3(5a-6)$ means $-3\\times (5a-6)$ which means $(-3)\\times 5a+(-3)\\times (-6)$, and so expanding $3(5a+6)$ gives $-15a+18$.</p>", "scripts": {}}], "stepsPenalty": "1", "gaps": [{"allowFractions": false, "minValue": "{nmult*nxcoeff}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{nmult*nxcoeff}", "showPrecisionHint": false}, {"allowFractions": false, "minValue": "{nmult*nconstant}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{nmult*nconstant}", "showPrecisionHint": false}], "variableReplacements": [], "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<p>Expand $\\var{nmult}(\\var{nxcoeff}a-\\var{-nconstant})$.</p>\n<p>[[0]]&nbsp;$a$ +&nbsp;[[1]]</p>", "scripts": {}}, {"steps": [{"showCorrectAnswer": true, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "type": "information", "prompt": "<p><em>A negative sign in front of a bracket is a common way to signify $-1$ times the bracketed term. The result is that it changes the sign of everything in the brackets.</em></p>\n<p></p>\n<p>For example, $-(5x-y+6)$ means $-1\\times (5x-y+6)$ which means $(-1)\\times 5x+(-1)\\times (-y)+(-1)\\times 6$, and so expanding $-(5x-y+6)$ gives $-5x+y-6$.</p>", "scripts": {}}], "stepsPenalty": "1", "gaps": [{"allowFractions": false, "minValue": "{-cx}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{-cx}", "showPrecisionHint": false}, {"allowFractions": false, "minValue": "{-cy}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{-cy}", "showPrecisionHint": false}, {"allowFractions": false, "minValue": "{-cc}", "showCorrectAnswer": true, "variableReplacements": [], "type": "numberentry", "marks": 1, "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "maxValue": "{-cc}", "showPrecisionHint": false}], "variableReplacements": [], "type": "gapfill", "marks": 0, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "prompt": "<p>Expand $-(\\var{cx}x-\\var{-cy}y+\\var{cc})$.</p>\n<p>[[0]]&nbsp;$x$ + [[1]]&nbsp;$y$ + [[2]]&nbsp;</p>", "scripts": {}}], "preamble": {"js": "", "css": ""}, "variables": {"nxcoeff": {"name": "nxcoeff", "group": "part b", "description": "", "templateType": "anything", "definition": "random(2..12)"}, "pconstant": {"name": "pconstant", "group": "part a", "description": "", "templateType": "anything", "definition": "primes[2]"}, "primes": {"name": "primes", "group": "part a", "description": "", "templateType": "anything", "definition": "shuffle([2,3,5,7,11])[0..3]"}, "nconstant": {"name": "nconstant", "group": "part b", "description": "", "templateType": "anything", "definition": "random(-12..-2)"}, "pmult": {"name": "pmult", "group": "part a", "description": "", "templateType": "anything", "definition": "primes[0]"}, "pxcoeff": {"name": "pxcoeff", "group": "part a", "description": "", "templateType": "anything", "definition": "primes[1]"}, "nmult": {"name": "nmult", "group": "part b", "description": "", "templateType": "anything", "definition": "random(-12..-2)"}, "cy": {"name": "cy", "group": "part c", "description": "", "templateType": "anything", "definition": "random(-12..1)"}, "cx": {"name": "cx", "group": "part c", "description": "", "templateType": "anything", "definition": "random(2..12)"}, "cc": {"name": "cc", "group": "part c", "description": "", "templateType": "anything", "definition": "random(2..12)"}}, "advice": "", "type": "question", "variable_groups": [{"name": "part a", "variables": ["pmult", "pxcoeff", "pconstant", "primes"]}, {"name": "part b", "variables": ["nmult", "nxcoeff", "nconstant"]}, {"name": "part c", "variables": ["cx", "cy", "cc"]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}