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{"name": "Maria's copy of Simon's copy of Inverse Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Rearranging equations to change the subject</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"customName": "", "prompt": "<p>$\\simplify{y={c[0]}x+{c[1]}}$</p>\n<p>$x=$&nbsp;[[0]]</p>\n<p></p>", "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "useCustomName": false, "type": "gapfill", "scripts": {}, "gaps": [{"answer": "(y-{c[1]})/{c[0]}", "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "checkVariableNames": true, 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"(-{c[8]}+{c[7]}{c[9]}-{c[9]}y)/(y-{c[7]})", "checkingType": "absdiff", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "checkVariableNames": true, "valuegenerators": [{"value": "", "name": "y"}], "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "checkingAccuracy": 0.001, "unitTests": [], "answerSimplification": "all", "type": "jme", "customName": "", "vsetRange": [0, 1], "showFeedbackIcon": true, "showPreview": true, "marks": "1", "vsetRangePoints": 5, "adaptiveMarkingPenalty": 0, "useCustomName": false, "failureRate": 1, "scripts": {}, "showCorrectAnswer": true}], "unitTests": [], "marks": 0, "showCorrectAnswer": true}, {"customName": "", "prompt": "<p>$\\simplify{y=sqrt(x+{c[10]})}$</p>\n<p>$x=$&nbsp;[[0]]</p>\n<p></p>", "showFeedbackIcon": true, "sortAnswers": false, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", 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"rulesets": {}, "variables": {"c": {"definition": "repeat(random(-5..5 except 0 except 1 except -1),15)", "description": "", "group": "Ungrouped variables", "name": "c", "templateType": "anything"}}, "advice": "<p><strong>(a)</strong></p>\n<p>$\\simplify{y={c[0]}x+{c[1]}}$</p>\n<p>$\\simplify{y-{c[1]}={c[0]}x}$</p>\n<p>$\\simplify{(y-{c[1]})/{c[0]}={x}}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (dividing both sides by $\\var{c[0]}$)</p>\n<p></p>\n<p><strong>(b)</strong></p>\n<p>$\\simplify{y={c[2]}x/({c[3]}+x)}$</p>\n<p>$\\simplify{y*({c[3]}+x)={c[2]}}x$&nbsp; &nbsp; &nbsp; &nbsp; (multiply both sides by denominator)</p>\n<p>$\\simplify{y*{c[3]}+x y={c[2]}}x$&nbsp; &nbsp; &nbsp; &nbsp; (expanding bracket)</p>\n<p>$\\simplify{y*{c[3]}={c[2]}x- y x}$&nbsp; &nbsp; &nbsp; &nbsp; (moving all $x$ to the same side)</p>\n<p>$\\simplify{y*{c[3]}=x({c[2]}- y)}$&nbsp; &nbsp; &nbsp; &nbsp; (factorising)</p>\n<p>$\\simplify{(y*{c[3]})/({c[2]}- y)=x}$</p>\n<p></p>\n<p><strong>(c)</strong></p>\n<p>$\\simplify{y={c[7]}-{c[8]}/({c[9]}+x)}$</p>\n<p>$\\simplify{y-{c[7]}=-{c[8]}/({c[9]}+x)}$</p>\n<p>$\\simplify{({c[9]}+x)=-{c[8]}/(y-{c[7]})}$</p>\n<p>$\\simplify{x=-{c[9]}-{c[8]}/(y-{c[7]})}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; which is algebraically the same as&nbsp; $\\simplify{x=(-{c[9]}(y-{c[7]})-{c[8]})/(y-{c[7]})}=\\simplify{(-{c[9]}y+{c[7]*c[9]-c[8]})/(y-{c[7]})}$</p>\n<p></p>\n<p><strong>(d)</strong></p>\n<p>$\\simplify{y=sqrt(x+{c[10]})}$</p>\n<p>$\\simplify{y^2=(x+{c[10]})}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (squaring both sides)</p>\n<p>$\\simplify{y^2-{c[10]}=x}$&nbsp; &nbsp;</p>\n<p></p>\n<p><strong>(e)</strong></p>\n<p>$\\simplify{y=1/x+{c[11]}}$</p>\n<p>$\\simplify{y-{c[11]}=1/x}$</p>\n<p>$\\simplify{x(y-{c[11]})=1}$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(multiply both sides by $x$)</p>\n<p>$\\simplify{x=1/(y-{c[11]})}$</p>", "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "ungrouped_variables": ["c"], "functions": {}, "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}