// Numbas version: exam_results_page_options
{"name": "Rachel's copy of 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": [{"extensions": [], "preamble": {"js": "", "css": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "parts": [{"gaps": [{"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{pmult*pxcoeff}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{pmult*pxcoeff}", "correctAnswerFraction": false, "showCorrectAnswer": true}, {"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{pmult*pconstant}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{pmult*pconstant}", "correctAnswerFraction": false, "showCorrectAnswer": true}], "stepsPenalty": "1", "marks": 0, "variableReplacements": [], "prompt": "<p>Expand the expression $\\var{pmult}(\\var{pxcoeff}x+\\var{pconstant})$.</p>\n<p>[[0]] $x$ +&nbsp;[[1]]</p>", "steps": [{"marks": 0, "variableReplacements": [], "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>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "type": "gapfill", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"gaps": [{"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{nmult*nxcoeff}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{nmult*nxcoeff}", "correctAnswerFraction": false, "showCorrectAnswer": true}, {"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{nmult*nconstant}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{nmult*nconstant}", "correctAnswerFraction": false, "showCorrectAnswer": true}], "stepsPenalty": "1", "marks": 0, "variableReplacements": [], "prompt": "<p>Expand $\\var{nmult}(\\var{nxcoeff}a-\\var{-nconstant})$.</p>\n<p>[[0]]&nbsp;$a$ +&nbsp;[[1]]</p>", "steps": [{"marks": 0, "variableReplacements": [], "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>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "type": "gapfill", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}, {"gaps": [{"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{-cx}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{-cx}", "correctAnswerFraction": false, "showCorrectAnswer": true}, {"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{-cy}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{-cy}", "correctAnswerFraction": false, "showCorrectAnswer": true}, {"correctAnswerStyle": "plain", "marks": 1, "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "minValue": "{-cc}", "type": "numberentry", "showFeedbackIcon": true, "maxValue": "{-cc}", "correctAnswerFraction": false, "showCorrectAnswer": true}], "stepsPenalty": "1", "marks": 0, "variableReplacements": [], "prompt": "<p>Expand $-(\\var{cx}x-\\var{-cy}y+\\var{cc})$.</p>\n<p>[[0]]&nbsp;$x$ + [[1]]&nbsp;$y$ + [[2]]&nbsp;</p>", "steps": [{"marks": 0, "variableReplacements": [], "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>", "type": "information", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "type": "gapfill", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "scripts": {}}], "variables": {"pmult": {"description": "", "group": "part a", "templateType": "anything", "definition": "primes[0]", "name": "pmult"}, "nxcoeff": {"description": "", "group": "part b", "templateType": "anything", "definition": "random(2..12)", "name": "nxcoeff"}, "pconstant": {"description": "", "group": "part a", "templateType": "anything", "definition": "primes[2]", "name": "pconstant"}, "nconstant": {"description": "", "group": "part b", "templateType": "anything", "definition": "random(-12..-2)", "name": "nconstant"}, "cc": {"description": "", "group": "part c", "templateType": "anything", "definition": "random(2..12)", "name": "cc"}, "nmult": {"description": "", "group": "part b", "templateType": "anything", "definition": "random(-12..-2)", "name": "nmult"}, "pxcoeff": {"description": "", "group": "part a", "templateType": "anything", "definition": "primes[1]", "name": "pxcoeff"}, "primes": {"description": "", "group": "part a", "templateType": "anything", "definition": "shuffle([2,3,5,7,11])[0..3]", "name": "primes"}, "cy": {"description": "", "group": "part c", "templateType": "anything", "definition": "random(-12..1)", "name": "cy"}, "cx": {"description": "", "group": "part c", "templateType": "anything", "definition": "random(2..12)", "name": "cx"}}, "functions": {}, "advice": "", "variable_groups": [{"variables": ["pmult", "pxcoeff", "pconstant", "primes"], "name": "part a"}, {"variables": ["nmult", "nxcoeff", "nconstant"], "name": "part b"}, {"variables": ["cx", "cy", "cc"], "name": "part c"}], "ungrouped_variables": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "name": "Rachel's copy of Distributive law: expanding one set of brackets", "rulesets": {}, "statement": "<p>For all questions in this quiz, if you want to show indices (e.g., $x^2$) then input this as x^2 for&nbsp;$x^2$, y^3 for&nbsp;$y^3$, etc.</p>", "type": "question", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}