// Numbas version: exam_results_page_options
{"name": "Algebra: exponential to linear form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra: exponential to linear form", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "", "advice": "<p>See ??</p>", "rulesets": {}, "extensions": [], "variables": {"vari": {"name": "vari", "group": "Ungrouped variables", "definition": "shuffle(['q','r','s','t','v','w','M','K','L','Z'])", "description": "", "templateType": "anything"}, "powera": {"name": "powera", "group": "part a", "definition": "random(2/3, 3/2, 3/5, 5/3, 0.5, 1/3)", "description": "", "templateType": "anything"}, "ca": {"name": "ca", "group": "part a", "definition": "siground(e^intercepta,2)", "description": "", "templateType": "anything"}, "grada": {"name": "grada", "group": "part a", "definition": "powera", "description": "", "templateType": "anything"}, "intercepta": {"name": "intercepta", "group": "part a", "definition": "random([-4,-3,-2,2,3,4]) + random(1..9)*0.1", "description": "", "templateType": "anything"}, "qa": {"name": "qa", "group": "part a", "definition": "expression('{vari[0]} = C {vari[1]}^(gamma)')", "description": "", "templateType": "anything"}, "v0": {"name": "v0", "group": "part a", "definition": "expression('{vari[0]}')", "description": "", "templateType": "anything"}, "v1": {"name": "v1", "group": "part a", "definition": "expression('{vari[1]}')", "description": "", "templateType": "anything"}, "ansa": {"name": "ansa", "group": "part a", "definition": "expression('gamma*x + ln(C)')", "description": "", "templateType": "anything"}, "ansa2": {"name": "ansa2", "group": "part a", "definition": "expression('{ca}*{vari[1]}^{powera}')", "description": "", "templateType": "anything"}, "v2": {"name": "v2", "group": "part b", "definition": "expression('{vari[2]}')", "description": "", "templateType": "anything"}, "v3": {"name": "v3", "group": "part b", "definition": "expression('{vari[3]}')", "description": "", "templateType": "anything"}, "qb": {"name": "qb", "group": "part b", "definition": "expression('{vari[2]} = A *e^(B*{vari[3]})')", "description": "", "templateType": "anything"}, "interceptb": {"name": "interceptb", "group": "part b", "definition": "random([-4,-3,-2,2,3,4]) + random(1..9)*0.1", "description": "", "templateType": "anything"}, "gradb": {"name": "gradb", "group": "part b", "definition": "random(55..99)/10*random([1,-1])", "description": "", "templateType": "anything"}, "ansb": {"name": "ansb", "group": "part b", "definition": "expression('B*x + ln(A)')", "description": "", "templateType": "anything"}, "ansb2": {"name": "ansb2", "group": "part b", "definition": "expression('{A} *e^({gradb}*{vari[3]})')", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "part b", "definition": "siground(e^interceptb,2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["vari"], "variable_groups": [{"name": "part a", "variables": ["powera", "v0", "v1", "qa", "grada", "intercepta", "ca", "ansa", "ansa2"]}, {"name": "part b", "variables": ["v2", "v3", "qb", "gradb", "interceptb", "A", "ansb", "ansb2"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>We are investigating the relationship between the variables $\\simplify{{v0}}$ and $\\simplify{{v1}}$ experimentally.</p>\n<p>We know that they are related via the equation $\\simplify{{qa}}$, where $\\gamma$ and $C$ are constants to be determined.</p>\n<p>This is done by plotting $\\simplify{y = ln({v0})}$ against $\\simplify{x = ln({v1})}$; we should get a straight line.</p>\n<p></p>\n<p>1. Write&nbsp;$y$ in terms of $x$, $\\gamma$ and $C$.&nbsp; To enter \"$\\gamma$\" you type \"gamma\". Use * to indicate multiplication.</p>\n<p>$y =$ [[0]]</p>\n<p></p>\n<p>2. (Calculator). When plotting $y$ against $x$, we get a straight line with gradient $\\simplify[fractionNumbers]{{grada}}$ and $y$-intercept $\\var{intercepta}$.&nbsp; Hence write $\\simplify{{v0}}$&nbsp;in terms of $\\simplify{{v1}}$. $C$ should be provided to 2 s.f..&nbsp;</p>\n<p>$\\simplify{{v0}} = $ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{ansa}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{ansa2}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>We are investigating the relationship between the variables $\\simplify{{v2}}$ and $\\simplify{{v3}}$ experimentally.</p>\n<p>We know that they are related via the equation $\\simplify{{qb}}$, where $A$ and $B$ are constants to be determined.</p>\n<p>This is done by plotting $\\simplify{y = ln({v2})}$ against $\\simplify{x = {v3}}$; we should get a straight line.</p>\n<p></p>\n<p>1. Write&nbsp;$y$ in terms of $x$, $A$ and $B$.&nbsp;Use * to indicate multiplication.</p>\n<p>$y =$ [[0]]</p>\n<p></p>\n<p>2. (Calculator). When plotting $y$ against $x$, we get a straight line with gradient $\\simplify{{gradb}}$ and $y$-intercept $\\var{interceptb}$.&nbsp; Hence write $\\simplify{{v2}}$&nbsp;in terms of $\\simplify{{v3}}$.&nbsp;Constants&nbsp;should be provided to 2 s.f..&nbsp;</p>\n<p>$\\simplify{{v2}} = $ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{ansb}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{ansb2}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}], "sortAnswers": false}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}