// Numbas version: finer_feedback_settings
{"name": "Zero Product Rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "extensions": [], "name": "Zero Product Rule", "ungrouped_variables": ["a", "b", "c", "tworoots", "blist", "d", "f", "g", "h", "j", "k", "l", "plist", "m", "n", "p", "q", "fiveroots"], "functions": {}, "tags": [], "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "variables": {"q": {"name": "q", "group": "Ungrouped variables", "definition": "plist[3]", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything"}, "fiveroots": {"name": "fiveroots", "group": "Ungrouped variables", "definition": "set(0,-d,-g/f,-j/(k*h),(-p*n)/(q*m))", "description": "", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "blist[5]", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "plist[1]", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "abs(j)+1", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "(-1)^(random(0,1))*plist[2]", "description": "", "templateType": "anything"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "blist[2]", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,a*b])", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "blist[0]", "description": "", "templateType": "anything"}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "blist[4]", "description": "", "templateType": "anything"}, "plist": {"name": "plist", "group": "Ungrouped variables", "definition": "shuffle([2,3,5,7,11,13,19,23,29])[0..4]", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "blist[3]", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "(-1)^(random(0,1))*plist[0]", "description": "", "templateType": "anything"}, "tworoots": {"name": "tworoots", "group": "Ungrouped variables", "definition": "set(-a,-c/b)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "blist[1]", "description": "", "templateType": "anything"}, "blist": {"name": "blist", "group": "Ungrouped variables", "definition": "shuffle(-12..12 except 0)[0..6]", "description": "", "templateType": "anything"}}, "statement": "", "parts": [{"customName": "", "type": "gapfill", "customMarkingAlgorithm": "", "steps": [{"customName": "", "type": "information", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "prompt": "<p>Notice, this is a quadratic that has already been factorised. You don't need to expand it since we have the null factor law:</p>\n<p>\\[\\text{If } ab=0, \\text{ then } a=0 \\text{ or } b=0.\\]</p>\n<p></p>\n<p>Since</p>\n<p>\\[(\\simplify{x+{a}})(\\simplify{{b}x+{c}})=0,\\]</p>\n<p>this means $\\simplify{x+{a}}=0$ or $\\simplify{{b}x+{c}}=0$. Solving each of these equations gives $x=\\var{-a}$ or $x=\\simplify{-{c}/{b}}$.</p>\n<p>For this question,&nbsp;we input our answer as set$\\left(\\var{-a},\\simplify{-{c}/{b}}\\right)$.</p>", "scripts": {}, "useCustomName": false, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true}], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "gaps": [{"customName": "", "type": "jme", "vsetRangePoints": 5, "answer": "{tworoots}", "showFeedbackIcon": true, "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "showCorrectAnswer": true, "useCustomName": false, "customMarkingAlgorithm": "", "answerSimplification": "fractionNumbers", "variableReplacementStrategy": "originalfirst", "marks": 1, "valuegenerators": [], "checkingAccuracy": 0.001, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showPreview": true, "unitTests": [], "variableReplacements": [], "vsetRange": [0, 1]}], "sortAnswers": false, "prompt": "<p>Given that $\\displaystyle{(\\simplify{x+{a}})(\\simplify{{b}x+{c}})=0}$. Determine the set of possible values of $x$.</p>\n<p>$x=$&nbsp;[[0]]</p>\n<p><strong>Note:</strong>&nbsp;if your answer is $1$ and $2$ input&nbsp;<strong>set(1,2)</strong></p>\n<p></p>", "scripts": {}, "useCustomName": false, "stepsPenalty": "", "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true}, {"customName": "", "type": "gapfill", "customMarkingAlgorithm": "", "steps": [{"customName": "", "type": "information", "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "prompt": "<p>Notice, this expression that has already been factorised. You don't need to expand it since we have the null factor law:&nbsp;</p>\n<p>\\[\\text{If } ab=0, \\text{ then } a=0 \\text{ or } b=0.\\]</p>\n<p>Since</p>\n<p>\\[\\simplify{{l}a}(\\simplify{a+{d}})(\\simplify{{f}a+{g}})\\left(\\simplify{{h}a+{j}/{k}}\\right)\\left(\\simplify{{m}a/{n}+{p}/{q}}\\right)=0,\\]</p>\n<p>this means $\\simplify{{l}a}=0$, $\\simplify{a+{d}}=0$, $\\simplify{{f}a+{g}}=0$, $\\simplify{{h}a+{j}/{k}}=0$, or $\\simplify{{m}a/{n}+{p}/{q}}=0$. Solving each of these equations gives $x=0$, $x=\\var{-d}$, $x=\\var[fractionnumbers]{-g/f}$, $x=\\var[fractionnumbers]{-j/(k*h)}$, or $x=\\var[fractionnumbers]{(-p*n)/(q*m)}$.</p>\n<p>For this question,&nbsp;we input our answer as set$\\left(0,\\var{-d},\\var[fractionnumbers]{-g/f},\\var[fractionnumbers]{-j/(k*h)},\\var[fractionnumbers]{(-p*n)/(q*m)}\\right)$.</p>", "scripts": {}, "useCustomName": false, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true}], "variableReplacementStrategy": "originalfirst", "marks": 0, "showFeedbackIcon": true, "gaps": [{"customName": "", "type": "jme", "vsetRangePoints": 5, "answer": "{fiveroots}", "showFeedbackIcon": true, "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "showCorrectAnswer": true, "useCustomName": false, "customMarkingAlgorithm": "", "answerSimplification": "fractionNumbers", "variableReplacementStrategy": "originalfirst", "marks": 1, "valuegenerators": [], "checkingAccuracy": 0.001, "scripts": {}, "extendBaseMarkingAlgorithm": true, "showPreview": true, "unitTests": [], "variableReplacements": [], "vsetRange": [0, 1]}], "sortAnswers": false, "prompt": "<p>Solve $\\displaystyle{\\simplify{{l}a}(\\simplify{a+{d}})(\\simplify{{f}a+{g}})\\left(\\simplify{{h}a+{j}/{k}}\\right)\\left(\\simplify{{m}a/{n}+{p}/{q}}\\right)=0}$ for $a$.</p>\n<p>$a=$&nbsp;[[0]]</p>\n<p><strong>Note:</strong>&nbsp;if your answer is $1$, $2$ and $3$ input&nbsp;<strong>set(1,2,3)</strong></p>\n<p></p>", "scripts": {}, "useCustomName": false, "stepsPenalty": 0, "showCorrectAnswer": true, "unitTests": [], "variableReplacements": [], "extendBaseMarkingAlgorithm": true}], "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "heike hoffmann", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2960/"}]}