// Numbas version: exam_results_page_options
{"name": "Test", "metadata": {"description": "<p>Answer all the questions</p>", "licence": "All rights reserved"}, "duration": 120, "percentPass": "75", "showQuestionGroupNames": true, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Wonder", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "variable_overrides": [[], [], [], [], []], "questions": [{"name": "Application of differentiation (optimisation)", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Picture1_6woS8OC.jpg", "/srv/numbas/media/question-resources/Picture1_6woS8OC.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>A metal box will be constructed. The base length must be three times the base width, and the volume must be {volume} m<sup>3</sup>.&nbsp;The metal used to build the top and bottom costs &pound;{tb_cost} per m<sup>2</sup> and the metal used to build the sides costs just &pound;{side_cost} per m<sup>2</sup>.</p>\n<p><img src=\"resources/question-resources/Picture1_6woS8OC.jpg\"/></p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "volume": {"name": "volume", "group": "Ungrouped variables", "definition": "3*random(10..30)", "description": "", "templateType": "anything", "can_override": false}, "tb_cost": {"name": "tb_cost", "group": "Ungrouped variables", "definition": "random(8..12)", "description": "", "templateType": "anything", "can_override": false}, "side_cost": {"name": "side_cost", "group": "Ungrouped variables", "definition": "random(3..tb_cost-2)", "description": "", "templateType": "anything", "can_override": false}, "w_opt": {"name": "w_opt", "group": "Ungrouped variables", "definition": "(2*side_cost*volume/(9*tb_cost))^(1/3)", "description": "", "templateType": "anything", "can_override": false}, "secder": {"name": "secder", "group": "Ungrouped variables", "definition": "16*side_cost*volume/3/w_opt^3+12*tb_cost", "description": "", "templateType": "anything", "can_override": false}, "h_opt": {"name": "h_opt", "group": "Ungrouped variables", "definition": "volume/3/w_opt^2", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "volume", "tb_cost", "side_cost", "w_opt", "secder", "h_opt"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter a formula for the volume of the box in terms of $w$ and $h$, simplifying where possible.</p>", "answer": "3*w^2*h", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "musthave": {"strings": ["w^2"], "showStrings": false, "partialCredit": 0, "message": "Simplify by using $w^2$."}, "valuegenerators": [{"name": "h", "value": ""}, {"name": "w", "value": ""}]}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The volume must be {volume} m<sup>3</sup>. Use this volume constraint to write $h$ in terms of $w$.</p>\n<p>$h=\\;$[[0]]</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Equate the volume to {volume} and rearrange to make $h$ the subject.</p>"}], "gaps": [{"type": "jme", "useCustomName": true, "customName": "h", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{volume/3}/w^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter a formula (in terms of $w$ only) for the total area of the top and bottom of the box. Simplify where possible.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add together the area of the top and the area of the bottom.</p>"}], "answer": "6*w^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The metal used to build the top and bottom costs &pound;{tb_cost} per m<sup>2</sup>. Enter a formula for the cost of the top and bottom.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Multiply the area by the cost per square metre.</p>"}], "answer": "{6*tb_cost}*w^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Enter a formula (in terms of $w$ and $h$) for the total area of the four sides of the box.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Add together the area of the 4 sides of the box. Don't include the top or bottom.</p>"}], "answer": "8*w*h", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "w", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The metal used to build the sides costs &pound;{side_cost} per m<sup>2</sup>. Enter a formula for the cost of the four sides.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Multiply the area by the cost per square metre.</p>"}], "answer": "{8*side_cost}*w*h", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "w", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Using your answer from part (b), write the formula above in terms of $w$ only.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Substitute your formula for $h$ in part (b) into the formula in part (f).</p>"}], "answer": "{8*side_cost*volume/3}/w", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Now write down a formula for the total cost $C$ of building the box in terms of $w$.</p>\n<p>$C=\\;$[[0]]</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>This is the cost of the top, bottom and sides. So add together the costs for these.</p>"}], "gaps": [{"type": "jme", "useCustomName": true, "customName": "cost", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{8*side_cost*volume/3}/w+{6*tb_cost}*w^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Differentiate the formula for $C$ to obtain $\\frac{dC}{dw}$.</p>", "answer": "-{8*side_cost*volume/3}/w^2+{12*tb_cost}*w", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "w", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the value of $w$ for which $C$ has a stationary point.</p>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve the equation</p>\n<p>\\[\\frac{dC}{dw}=0\\]</p>\n<p>by collecting all the $w$ terms together, and taking the cube root.</p>"}], "minValue": "{w_opt}", "maxValue": "{w_opt}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Verify that the stationary point is a minimum by calculating the second derivative $\\frac{d^2C}{dw^2}$ at this value of $w$. (A positive second derivative implies a minimum.)</p>", "minValue": "{secder}", "maxValue": "{secder}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Hence enter the dimensions of the box which minimise the cost of materials.</p>\n<p>Width:&nbsp;[[0]] m</p>\n<p>Length:&nbsp;[[1]] m</p>\n<p>Height:&nbsp;[[2]] m</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "width", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "w_opt", "maxValue": "w_opt", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "length", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "3*w_opt", "maxValue": "3*w_opt", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "height", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "h_opt", "maxValue": "h_opt", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "100", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "The Exponential distribution", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Stefan Siegert", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4982/"}], "tags": [], "metadata": {"description": "<p><em>No description</em></p>", "licence": "All rights reserved"}, "statement": "<p>Let the random variable $X$ have an Exponential distribution with rate parameter $\\lambda$:</p>\n<p style=\"padding-left: 40px;\">$X \\sim Exp(\\lambda)$</p>", "advice": "<p>The random variable $X\\sim Exp(\\lambda)$ has</p>\n<ul>\n<li>probability density function $f_X(x) = \\lambda e^{-\\lambda x}$ for $x&gt;0$ and $f_X(x)=0$ for $x\\le 0$</li>\n<li>cumulative distribution function $F_X(x) = 1 - e^{-\\lambda x}$ for $x&gt;0$ and $F_X(x)=0$ for $x\\le 0$</li>\n<li>$E[X] = 1/\\lambda$</li>\n<li>$Var[X] = \\frac{1}{\\lambda^2}$</li>\n<li>$Median[X] = \\log(2) / \\lambda$</li>\n<li>$P(X&gt;1) = e^{-\\lambda}$</li>\n</ul>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"lambda": {"name": "lambda", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Rate parameter of the Exponential distribution.</p>", "templateType": "randrange", "can_override": true}, "lambda2": {"name": "lambda2", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "<p>Rate parameter of the Exponential distribution.</p>", "templateType": "randrange", "can_override": false}, "lambda3": {"name": "lambda3", "group": "Ungrouped variables", "definition": "random(1 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "lambda4": {"name": "lambda4", "group": "Ungrouped variables", "definition": "random(1 .. 5#0.5)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["lambda", "lambda2", "lambda3", "lambda4"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The probability density function of $X$ is given by $f_X(x) =&nbsp; \\dots$ (for $x &gt; 0$)</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\lambda e^{-\\lambda x}$", "$e^{-\\lambda x}$", "$1 - e^{-\\lambda x}$", "$e^{\\lambda x}$"], "matrix": ["2", 0, "1", 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The cumulative distribution function of $X$ is given by $F_X(x)=&nbsp; \\dots $ (for $x &gt; 0$</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\lambda e^{-\\lambda x}$", "$\\lambda x$", "$1 - e^{-\\lambda x}$", "$1+e^{\\lambda x}$"], "matrix": ["1", "0", "2", 0], "distractors": ["", "", "", ""]}, {"type": "numberentry", "useCustomName": true, "customName": "Expectation", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate $E[X]$ when $\\lambda=$ {lambda}.</p>", "minValue": "1 / lambda", "maxValue": "1 / lambda", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Variance", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate $Var[X]$ when $\\lambda=$ {lambda2}.</p>", "minValue": "1 / lambda2^2", "maxValue": "1 / lambda2^2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": "50", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Median", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the Median of $X$ when $\\lambda=$ {lambda3}.</p>", "minValue": "ln(2) / lambda3", "maxValue": "ln(2) / lambda3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "50", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "75", "precisionMessage": "You have not given the correct number of significant figures.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Exceedance probability", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate $P(X &gt;1)$ when $\\lambda=$ {lambda4}.</p>", "minValue": "exp(-lambda4)", "maxValue": "exp(-lambda4)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": "50", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": "65", "precisionMessage": "You have not given the correct number of significant figures.", "strictPrecision": false, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Multiplication 3 digit by 2 digit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "<p>Multiplication algorithm with integers</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Write the following question down on paper and evaluate&nbsp;it without using a calculator.</p>\n<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ab0t0last": {"name": "ab0t0last", "group": "2digit", "definition": "mod(ab0t0,10)", "description": "", "templateType": "anything", "can_override": false}, "threedigit3": {"name": "threedigit3", "group": "Ungrouped variables", "definition": "random(101..999 except list(200..900#100) )", "description": "", "templateType": "anything", "can_override": false}, "aanstho": {"name": "aanstho", "group": "2digit", "definition": "mod((aans-aansone-aansten*10-aanshun*100)/1000,10)", "description": "", "templateType": "anything", "can_override": false}, "aanstth": {"name": "aanstth", "group": "2digit", "definition": "mod((aans-aansone-aansten*10-aanshun*100-aanstho*1000)/10000,10)", "description": "", "templateType": "anything", "can_override": false}, "ab0t1": {"name": "ab0t1", "group": "2digit", "definition": "abot[0]*atop[1]", "description": "", "templateType": "anything", "can_override": false}, "threedigit2": {"name": "threedigit2", "group": "Ungrouped variables", "definition": "random(101..999 except list(200..900#100) )", "description": "", "templateType": "anything", "can_override": false}, "ab1t2pluscarry": {"name": "ab1t2pluscarry", "group": "2digit", "definition": "ab1t2+ab1t1carry", "description": "", "templateType": "anything", "can_override": false}, "twodigit1": {"name": "twodigit1", "group": "Ungrouped variables", "definition": "random(11..99 except list(20..90#10) )", "description": "", "templateType": "anything", "can_override": false}, "asum1": {"name": "asum1", "group": "2digit", "definition": "abot[0]*atopnum", "description": "", "templateType": "anything", "can_override": false}, "aanshun": {"name": "aanshun", "group": "2digit", "definition": "mod((aans-aansone-aansten*10)/100,10)", "description": "", "templateType": "anything", "can_override": false}, "abot": {"name": "abot", "group": "2digit", "definition": "[adigs[4],adigs[3]]", "description": "<p><g class=\"gr_ gr_3 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"3\" data-gr-id=\"3\">abot</g></p>", "templateType": "anything", "can_override": false}, "threedigit1": {"name": "threedigit1", "group": "Ungrouped variables", "definition": "random(101..999 except list(200..900#100) )", "description": "", "templateType": "anything", "can_override": false}, "ab1t1last": {"name": "ab1t1last", "group": "2digit", "definition": "mod(ab1t1pluscarry,10)", "description": "", "templateType": "anything", "can_override": false}, "twodigit3": {"name": "twodigit3", "group": "Ungrouped variables", "definition": "random(11..99 except list(20..90#10) )", "description": "", "templateType": "anything", "can_override": false}, "adigs": {"name": "adigs", "group": "2digit", "definition": "shuffle(1..9)[0..5]", "description": "<p>we want distinct digits so it is easier to refer to digits unambiguously.&nbsp;</p>", "templateType": "anything", "can_override": false}, "ab1t1": {"name": "ab1t1", "group": "2digit", "definition": "abot[1]*atop[1]", "description": "", "templateType": "anything", "can_override": false}, "ab1t2carry": {"name": "ab1t2carry", "group": "2digit", "definition": "(ab1t2pluscarry-ab1t2last)/10", "description": "", "templateType": "anything", "can_override": false}, "asum2": {"name": "asum2", "group": "2digit", "definition": "10*abot[1]*atopnum", "description": "<p>sum2</p>", "templateType": "anything", "can_override": false}, "atop": {"name": "atop", "group": "2digit", "definition": "[adigs[2],adigs[1],adigs[0]]", "description": "", "templateType": "anything", "can_override": false}, "ab1t0last": {"name": "ab1t0last", "group": "2digit", "definition": "mod(ab1t0,10)", "description": "", "templateType": "anything", "can_override": false}, "ab0t2last": {"name": "ab0t2last", "group": "2digit", "definition": "mod(ab0t2pluscarry,10)", "description": "", "templateType": "anything", "can_override": false}, "ab1t1pluscarry": {"name": "ab1t1pluscarry", "group": "2digit", "definition": "ab1t1+ab1t0carry", "description": "", "templateType": "anything", "can_override": false}, "ab1t0": {"name": "ab1t0", "group": "2digit", "definition": "abot[1]*atop[0]", "description": "", "templateType": "anything", "can_override": false}, "ab1t0carry": {"name": "ab1t0carry", "group": "2digit", "definition": "(ab1t0-ab1t0last)/10", "description": "", "templateType": "anything", "can_override": false}, "ab0t1last": {"name": "ab0t1last", "group": "2digit", "definition": "mod(ab0t1pluscarry,10)", "description": "", "templateType": "anything", "can_override": false}, "ab1t2last": {"name": "ab1t2last", "group": "2digit", "definition": "mod(ab1t2pluscarry,10)", "description": "", "templateType": "anything", "can_override": false}, "ab1t2": {"name": "ab1t2", "group": "2digit", "definition": "abot[1]*atop[2]", "description": "", "templateType": "anything", "can_override": false}, "ab0t2pluscarry": {"name": "ab0t2pluscarry", "group": "2digit", "definition": "ab0t2+ab0t1carry", "description": "", "templateType": "anything", "can_override": false}, "ab0t2carry": {"name": "ab0t2carry", "group": "2digit", "definition": "(ab0t2pluscarry-ab0t2last)/10", "description": "", "templateType": "anything", "can_override": false}, "twodigit2": {"name": "twodigit2", "group": "Ungrouped variables", "definition": "random(11..99 except list(20..90#10) )", "description": "", "templateType": "anything", "can_override": false}, "ab0t0carry": {"name": "ab0t0carry", "group": "2digit", "definition": "(ab0t0-ab0t0last)/10", "description": "", "templateType": "anything", "can_override": false}, "ab1t1carry": {"name": "ab1t1carry", "group": "2digit", "definition": "(ab1t1pluscarry-ab1t1last)/10", "description": "", "templateType": "anything", "can_override": false}, "ab0t2": {"name": "ab0t2", "group": "2digit", "definition": "abot[0]*atop[2]", "description": "", "templateType": "anything", "can_override": false}, "ab0t1carry": {"name": "ab0t1carry", "group": "2digit", "definition": "(ab0t1pluscarry-ab0t1last)/10", "description": "", "templateType": "anything", "can_override": false}, "abotnum": {"name": "abotnum", "group": "2digit", "definition": "abot[1]*10+abot[0]", "description": "<p><g class=\"gr_ gr_3 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"3\" data-gr-id=\"3\">botnum</g></p>", "templateType": "anything", "can_override": false}, "ab0t1pluscarry": {"name": "ab0t1pluscarry", "group": "2digit", "definition": "ab0t1+ab0t0carry", "description": "<p>ab</p>", "templateType": "anything", "can_override": false}, "atopnum": {"name": "atopnum", "group": "2digit", "definition": "atop[2]*100+atop[1]*10+atop[0]", "description": "", "templateType": "anything", "can_override": false}, "aans": {"name": "aans", "group": "2digit", "definition": "atopnum*abotnum", "description": "", "templateType": "anything", "can_override": false}, "aansone": {"name": "aansone", "group": "2digit", "definition": "mod(aans,10)", "description": "", "templateType": "anything", "can_override": false}, "aansten": {"name": "aansten", "group": "2digit", "definition": "mod((aans-aansone)/10,10)", "description": "", "templateType": "anything", "can_override": false}, "ab0t0": {"name": "ab0t0", "group": "2digit", "definition": "atop[0]*abot[0]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "\n", "maxRuns": 100}, "ungrouped_variables": ["twodigit1", "twodigit2", "threedigit1", "threedigit2", "twodigit3", "threedigit3"], "variable_groups": [{"name": "2digit", "variables": ["adigs", "atop", "abot", "atopnum", "abotnum", "aans", "ab0t0", "ab0t0last", "ab0t0carry", "ab0t1", "ab0t1pluscarry", "ab0t1last", "ab0t1carry", "ab0t2", "ab0t2pluscarry", "ab0t2last", "ab0t2carry", "ab1t0", "ab1t0last", "ab1t0carry", "ab1t1", "ab1t1pluscarry", "ab1t1last", "ab1t1carry", "ab1t2", "ab1t2pluscarry", "ab1t2last", "ab1t2carry", "asum1", "asum2", "aansone", "aansten", "aanshun", "aanstho", "aanstth"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{atopnum}\\times\\var{abotnum} = $&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Generally&nbsp;we set up $\\var{atopnum}\\times\\var{abotnum}$&nbsp;with the <em>ones </em>and<em>&nbsp;</em><em>tens</em>&nbsp;columns lined up vertically:</p>\n<table>\n<tbody>\n<tr>\n<td>$\\var{atop[2]}$</td>\n<td>$\\var{atop[1]}$</td>\n<td>$\\var{atop[0]}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\var{abot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td>$\\phantom{0}$</td>\n<td></td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>We need to multiply each digit in the bottom number by each digit in the top number whilst respecting their place values.</p>\n<p></p>\n<p><strong>We multiply the digits in the ones column, that is, $\\color{green}{\\var{abot[0]}\\times \\var{atop[0]}}$.</strong></p>\n<p><span data-jme-visible=\"ab0t0&lt;10\">Since this is just $\\var{ab0t0}$ we&nbsp;write $\\var{ab0t0}$ under the line in the ones column.</span></p>\n<p><span data-jme-visible=\"ab0t0&gt;=10\">Since this is $\\var{ab0t0}$ we write the $\\var{ab0t0last}$ under the line in the ones column and carry the&nbsp;$\\var{ab0t0carry}$ into the tens column to be dealt with in the next step.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td>$\\overset{\\phantom{1}}{\\var{atop[2]}}$</td>\n<td><span data-jme-visible=\"ab0t0carry&lt;&gt;0\">$\\overset{\\color{red}{\\var{ab0t0carry}}}{\\var{atop[1]}}$</span> <span data-jme-visible=\"ab0t0carry=0\">$\\overset{\\phantom{1}}{\\var{atop[1]}}$</span></td>\n<td>&nbsp;$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[0]}}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\color{green}{\\var{abot[0]}}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ab0t0last}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p><strong>We now multiply&nbsp;diagonally, $\\color{green}{\\var{abot[0]}\\times \\var{atop[1]}}$.&nbsp;</strong></p>\n<p><span data-jme-visible=\"ab0t1&lt;10 and ab0t0carry=0\">This just gives us $\\var{ab0t1}$ so we write&nbsp;$\\var{ab0t1}$ under the line in the tens column.</span></p>\n<p><span data-jme-visible=\"ab0t1&gt;=10 and ab0t0carry=0\">This gives us $\\var{ab0t1}$ so we write this under the line with the $\\var{ab0t1last}$ in the tens column.</span></p>\n<p><span data-jme-visible=\"ab0t0carry&lt;&gt;0 and ab0t1pluscarry&gt;=10\">This gives us $\\var{ab0t1}$ but we have to add the $\\var{ab0t0carry}$ we carried earlier and so we write&nbsp;$\\var{ab0t1last}$ under the line in the tens column and carry the $\\var{ab0t1carry}$ into the hundreds column to be dealt with in the next step.</span></p>\n<p><span data-jme-visible=\"ab0t0carry&lt;&gt;0 and ab0t1pluscarry&lt;10\">This gives us $\\var{ab0t1}$ but we have to add the $\\var{ab0t0carry}$ we carried earlier and so we write&nbsp;$\\var{ab0t1pluscarry}$ under the line in the tens column.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td><span data-jme-visible=\"ab0t1carry&lt;&gt;0\">$\\overset{\\color{red}{\\var{ab0t1carry}}}{\\var{atop[2]}}$</span> <span data-jme-visible=\"ab0t1carry=0\">$\\overset{\\phantom{1}}{\\var{atop[2]}}$</span></td>\n<td><span data-jme-visible=\"ab0t0carry&lt;&gt;0\">${\\overset{{\\var{ab0t0carry}}}{\\color{green}{\\var{atop[1]}}}}$</span> <span data-jme-visible=\"ab0t0carry=0\">$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[1]}}}$</span></td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\color{green}{\\var{abot[0]}}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td>$\\color{red}{\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><strong>We now multiply&nbsp;diagonally, $\\color{green}{\\var{abot[0]}\\times \\var{atop[2]}}$.&nbsp;</strong></p>\n<p><span data-jme-visible=\"ab0t2&lt;10 and ab0t1carry=0\">This just gives us $\\var{ab0t2}$ so we write&nbsp;$\\var{ab0t2}$ under the line in the&nbsp;hundreds&nbsp;column.</span></p>\n<p><span data-jme-visible=\"ab0t2&gt;=10 and ab0t1carry=0\">This gives us $\\var{ab0t2}$ so we write this under the line with the $\\var{ab0t2last}$ in the&nbsp;hundreds&nbsp;column.</span></p>\n<p><span data-jme-visible=\"ab0t1carry&lt;&gt;0 and ab0t2pluscarry&gt;=10\">This gives us $\\var{ab0t2}$ but we have to add the $\\var{ab0t1carry}$ we carried earlier and so we write&nbsp;$\\var{ab0t2pluscarry}$ under the line with the $\\var{ab0t2last}$ in the&nbsp;hundreds column.</span></p>\n<p><span data-jme-visible=\"ab0t1carry&lt;&gt;0 and ab0t2pluscarry&lt;10\">This gives us $\\var{ab0t2}$ but we have to add the $\\var{ab0t1carry}$ we carried earlier and so we write&nbsp;$\\var{ab0t2pluscarry}$ under the line in the&nbsp;hundreds column.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td><span data-jme-visible=\"ab0t1carry&lt;&gt;0\">$\\overset{{\\var{ab0t1carry}}}{\\color{green}{\\var{atop[2]}}}$</span> <span data-jme-visible=\"ab0t1carry=0\">$\\overset{\\phantom{1}}{\\color{green}{\\var{atop[2]}}}$</span></td>\n<td><span data-jme-visible=\"ab0t0carry&lt;&gt;0\">${\\overset{{\\var{ab0t0carry}}}{\\var{atop[1]}}}$</span> <span data-jme-visible=\"ab0t0carry=0\">${\\overset{\\phantom{1}}{\\var{atop[1]}}}$</span></td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\color{green}{\\var{abot[0]}}$</td>\n<td></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ab0t2carry&lt;&gt;0\">$\\color{red}{\\var{ab0t2carry}}$</span><span data-jme-visible=\"ab0t2carry=0\">$\\phantom{0}$</span></td>\n<td>$\\color{red}{\\var{ab0t2last}}$</td>\n<td>${\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>We are now finished with the digit $\\var{abot[0]}$ and move on to work with the $\\var{abot[1]}$ in the tens column. Since this is really a $\\var{abot[1]*10}$ <strong>we place a zero in the ones column on the next line</strong> to pad our numbers out. <span data-jme-visible=\"ab0t0carry&lt;&gt;0\">We also cross out or erase any carry marks that we have used.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\overset{\\phantom{1}}{\\var{atop[2]}}$</td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[1]}}$</td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\var{abot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td>&nbsp;<span data-jme-visible=\"ab0t1carry&lt;&gt;0\">$\\var{ab0t2carry}$</span><span data-jme-visible=\"ab0t1carry=0\">$\\phantom{0}$</span></td>\n<td>${\\var{ab0t2last}}$</td>\n<td>${\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{red}0$</td>\n<td>&nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p><strong>We now multiply along the other diagonal, that is, $\\color{green}{\\var{abot[1]}\\times\\var{atop[0]}}$.</strong></p>\n<p><span data-jme-visible=\"ab1t0&lt;10\">Since this is just $\\var{ab1t0}$ we&nbsp;write $\\var{ab1t0}$ under the line in the tens column.</span></p>\n<p><span data-jme-visible=\"ab1t0&gt;=10\">Since this is $\\var{ab1t0}$ we write the $\\var{ab1t0last}$ under the line in the tens column and carry the&nbsp;$\\var{ab1t0carry}$ into the tens column to be dealt with in the next step.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>$\\overset{\\phantom{1}}{\\var{atop[2]}}$</td>\n<td><span data-jme-visible=\"ab1t0carry&lt;&gt;0\">$\\overset{\\color{red}{\\var{ab1t0carry}}}{\\var{atop[1]}}$</span> <span data-jme-visible=\"ab1t0carry=0\">$\\overset{\\phantom{1}}{\\var{atop[1]}}$</span></td>\n<td>&nbsp;$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[0]}}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td>$\\color{green}{\\var{abot[1]}}$</td>\n<td>$\\var{abot[0]}$</td>\n<td></td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ab0t2carry&lt;&gt;0\">$\\var{ab0t2carry}$</span><span data-jme-visible=\"ab0t2carry=0\">$\\phantom{0}$</span></td>\n<td>${\\var{ab0t2last}}$</td>\n<td>${\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td></td>\n</tr>\n<tr>\n<td></td>\n<td></td>\n<td>$\\color{red}{\\var{ab1t0last}}$</td>\n<td>${0}$</td>\n<td></td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p><strong>We now multiply the digits in the tens column, that is, $\\color{green}{\\var{abot[1]}\\times \\var{atop[1]}}$.&nbsp;</strong></p>\n<p><span data-jme-visible=\"ab1t1&lt;10 and ab1t0carry=0\">This just gives us $\\var{ab1t1}$ so we write&nbsp;$\\var{ab1t1}$ under the line in the&nbsp;hundreds column.</span></p>\n<p><span data-jme-visible=\"ab1t1&gt;=10 and ab1t0carry=0\">This gives us $\\var{ab1t1}$ so we write this under the line with the $\\var{ab1t1last}$ in the&nbsp;hundreds&nbsp;column.</span></p>\n<p><span data-jme-visible=\"ab1t0carry&lt;&gt;0 and ab1t1pluscarry&gt;=10\">This gives us $\\var{ab1t1}$ but we have to add the $\\var{ab1t0carry}$ we carried earlier and so we write&nbsp;$\\var{ab1t1last}$ under the line in the hundreds column and carry the $\\var{ab1t1carry}$ into the hundreds&nbsp;column to be dealt with in the next step.</span></p>\n<p><span data-jme-visible=\"ab1t0carry&lt;&gt;0 and ab1t1pluscarry&lt;10\">This gives us $\\var{ab1t1}$ but we have to add the $\\var{ab1t0carry}$ we carried earlier and so we write&nbsp;$\\var{ab1t1pluscarry}$ under the line in the&nbsp;hundreds column.</span></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td>&nbsp;<span data-jme-visible=\"ab1t1carry&lt;&gt;0\">$\\overset{\\color{red}{\\var{ab1t1carry}}}{\\var{atop[2]}}$</span>&nbsp;<span data-jme-visible=\"ab1t1carry=0\">$\\overset{\\phantom{1}}{\\var{atop[2]}}$</span></td>\n<td>&nbsp;<span data-jme-visible=\"ab1t0carry&lt;&gt;0\">${\\overset{{\\var{ab1t0carry}}}{\\color{green}{\\var{atop[1]}}}}$</span> <span data-jme-visible=\"ab1t0carry=0\">$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[1]}}}$</span></td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td>$\\color{green}{\\var{abot[1]}}$</td>\n<td>$\\var{abot[0]}$</td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ab0t2carry&lt;&gt;0\">${\\var{ab0t2carry}}$</span><span data-jme-visible=\"ab0t2carry=0\">$\\phantom{0}$</span></td>\n<td>${\\var{ab0t2last}}$</td>\n<td>${\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td></td>\n<td>$\\color{red}{\\var{ab1t1last}}$</td>\n<td>${\\var{ab1t0last}}$</td>\n<td>${0}$</td>\n<td>&nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p><strong>We now multiply the final pair of digits, that is, $\\color{green}{\\var{abot[1]}\\times \\var{atop[2]}}$.&nbsp;</strong></p>\n<p><span data-jme-visible=\"ab1t2&lt;10 and ab1t1carry=0\">This just gives us $\\var{ab1t2}$ so we write&nbsp;$\\var{ab1t2}$ under the line in the&nbsp;thousands column.</span></p>\n<p><span data-jme-visible=\"ab1t2&gt;=10 and ab1t1carry=0\">This gives us $\\var{ab1t2}$ so we write this under the line with the $\\var{ab1t2last}$ in the&nbsp;thousands column.</span></p>\n<p><span data-jme-visible=\"ab1t1carry&lt;&gt;0 and ab1t2pluscarry&gt;=10\">This gives us $\\var{ab1t2}$ but we have to add the $\\var{ab1t1carry}$ we carried earlier and so we write&nbsp;$\\var{ab0t2pluscarry}$ under the line with the $\\var{ab1t2last}$ in the&nbsp;thousands column.</span></p>\n<p><span data-jme-visible=\"ab1t1carry&lt;&gt;0 and ab1t2pluscarry&lt;10\">This gives us $\\var{ab1t2}$ but we have to add the $\\var{ab1t1carry}$ we carried earlier and so we write&nbsp;$\\var{ab1t2pluscarry}$ under the line in the&nbsp;thousands column.</span></p>\n<p></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td></td>\n<td><span data-jme-visible=\"ab1t1carry&lt;&gt;0\">$\\overset{{\\var{ab1t1carry}}}{\\color{green}{\\var{atop[2]}}}$</span>&nbsp;<span data-jme-visible=\"ab1t1carry=0\">$\\overset{\\phantom{1}}{\\color{green}{\\var{atop[2]}}}$</span></td>\n<td><span data-jme-visible=\"ab1t0carry&lt;&gt;0\">${\\overset{{\\var{ab1t0carry}}}{{\\var{atop[1]}}}}$</span> <span data-jme-visible=\"ab1t0carry=0\">${\\overset{\\phantom{1}}{\\var{atop[1]}}}$</span></td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td></td>\n<td>$\\color{green}{\\var{abot[1]}}$</td>\n<td>$\\var{abot[0]}$</td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td>&nbsp;&nbsp;</td>\n<td><span data-jme-visible=\"ab0t2carry&lt;&gt;0\">$\\var{ab0t2carry}$</span><span data-jme-visible=\"ab0t2carry=0\">$\\phantom{0}$</span></td>\n<td>${\\var{ab0t2last}}$</td>\n<td>${\\var{ab0t1last}}$</td>\n<td>${\\var{ab0t0last}}$</td>\n<td>&nbsp;&nbsp;</td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"ab1t2carry&lt;&gt;0\">$\\color{red}{\\var{ab1t2carry}}$</span><span data-jme-visible=\"ab1t2carry=0\">$\\phantom{0}$</span></td>\n<td>$\\color{red}{\\var{ab1t2last}}$</td>\n<td>${\\var{ab1t1last}}$</td>\n<td>${\\var{ab1t0last}}$</td>\n<td>${0}$</td>\n<td>&nbsp; &nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p><strong>We now add the two results to get the total, that is, $\\color{green}{\\var{asum1}+\\var{asum2}}$.</strong></p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td></td>\n<td></td>\n<td><span data-jme-visible=\"ab1t1carry&lt;&gt;0\">$\\overset{{\\var{ab1t1carry}}}{\\var{atop[2]}}$ </span> <span data-jme-visible=\"ab1t1carry=0\"> $\\overset{\\phantom{1}}{\\var{atop[2]}}$ </span></td>\n<td><span data-jme-visible=\"ab1t0carry&lt;&gt;0\">$\\overset{{\\var{ab1t0carry}}}{\\var{atop[1]}}$</span> <span data-jme-visible=\"ab1t0carry=0\">$\\overset{\\phantom{1}}{\\var{atop[1]}}$</span></td>\n<td>&nbsp;$\\overset{\\phantom{1}}{\\var{atop[0]}}$</td>\n<td>$\\times$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td></td>\n<td></td>\n<td></td>\n<td>$\\var{abot[1]}$</td>\n<td>$\\var{abot[0]}$</td>\n<td>&nbsp;</td>\n</tr>\n<tr>\n<td>&nbsp;</td>\n<td><span data-jme-visible=\"ab0t2carry&lt;&gt;0\">$\\color{green}{\\var{ab0t2carry}}$</span><span data-jme-visible=\"ab0t2carry=0\">$\\phantom{0}$</span></td>\n<td>$\\color{green}{\\var{ab0t2last}}$</td>\n<td>$\\color{green}{\\var{ab0t1last}}$</td>\n<td>$\\color{green}{\\var{ab0t0last}}$</td>\n<td>$+$</td>\n</tr>\n<tr style=\"border-bottom: 1px solid black;\">\n<td><span data-jme-visible=\"ab1t2carry&lt;&gt;0\">$\\color{green}{\\var{ab1t2carry}}$</span><span data-jme-visible=\"ab1t2carry=0\">$\\phantom{0}$</span></td>\n<td>$\\color{green}{\\var{ab1t2last}}$</td>\n<td>$\\color{green}{\\var{ab1t1last}}$</td>\n<td>$\\color{green}{\\var{ab1t0last}}$</td>\n<td>$\\color{green}{0}$</td>\n<td>&nbsp;&nbsp;</td>\n</tr>\n<tr>\n<td><span data-jme-visible=\"aanstth&lt;&gt;0\">$\\color{red}{\\var{aanstth}}$</span> <span data-jme-visible=\"aanstth=0\">$\\phantom{0}$</span></td>\n<td>$\\color{red}{\\var{aanstho}}$</td>\n<td>$\\color{red}{\\var{aanshun}}$</td>\n<td>$\\color{red}{\\var{aansten}}$</td>\n<td>$\\color{red}{\\var{aansone}}$</td>\n<td>&nbsp;&nbsp;</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>\n<p>The answer is therefore $\\var{aans}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "aans", "maxValue": "aans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Fractions: adding and subtracting, numerical, already with common denominator", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "tags": [], "metadata": {"description": "<p>Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Express the following as a single fraction (using / as the fraction bar).</p>", "advice": "<p>Since both denominators are the same, i.e. $\\var{den}$. We can simply <span data-jme-visible=\"addSub=1\">add</span><span data-jme-visible=\"addSub=-1\">subtract</span> the numerators, $\\var{num1}$ and $\\var{num2}$, and put that over the common denominator.</p>\n<p><span data-jme-visible=\"addSub=1\">$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den}}+\\dfrac{\\var{num2}}{\\var{den}}&amp;=\\dfrac{\\var{num1}+\\var{num2}}{\\var{den}}\\\\[3pt]&amp;=\\dfrac{\\var{ansNum}}{\\var{den}}\\end{align*}$</span></p>\n<p><span data-jme-visible=\"addSub=-1\">$\\begin{align*}\\dfrac{\\var{num1}}{\\var{den}}-\\dfrac{\\var{num2}}{\\var{den}}&amp;=\\dfrac{\\var{num1}-\\var{num2}}{\\var{den}}\\\\[3pt]&amp;=\\dfrac{\\var{ansNum}}{\\var{den}}\\end{align*}$</span></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"den": {"name": "den", "group": "Ungrouped variables", "definition": "numbers[2]", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "numbers[0]", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "numbers[1]", "description": "", "templateType": "anything", "can_override": false}, "addSub": {"name": "addSub", "group": "Ungrouped variables", "definition": "random(-1,1)", "description": "<p>adding or subtracting</p>", "templateType": "anything", "can_override": false}, "ansnum": {"name": "ansnum", "group": "Ungrouped variables", "definition": "if(addSub=1,num1+num2,num1-num2)", "description": "", "templateType": "anything", "can_override": false}, "numbers": {"name": "numbers", "group": "Ungrouped variables", "definition": "random(tempnumbers,[tempnumbers[1],tempnumbers[0],tempnumbers[2]])", "description": "", "templateType": "anything", "can_override": false}, "tempnumbers": {"name": "tempnumbers", "group": "Ungrouped variables", "definition": "sort(shuffle([3,5,7,11,13,17,19,23,29])[0..3])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["tempnumbers", "numbers", "den", "num1", "num2", "addSub", "ansnum"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><span data-jme-visible=\"addSub=1\">$\\dfrac{\\var{num1}}{\\var{den}}+\\dfrac{\\var{num2}}{\\var{den}}$</span> <span data-jme-visible=\"addSub=-1\">$\\dfrac{\\var{num1}}{\\var{den}}-\\dfrac{\\var{num2}}{\\var{den}}$</span>&nbsp; $=$ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ansNum/den", "maxValue": "ansNum/den", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Equilibrium of a rigid body: raise pole", "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}], "tags": ["angle from reference", "Equilibrium", "equilibrium", "Mechanics", "mechanics", "Rigid Body", "rigid body", "Statics", "statics"], "metadata": {"description": "<p>Equilibrium of a rigid body. &nbsp;Find tension to raise a pole.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>{geogebra_applet('pf8c3vcn',[['&alpha;',alpha +'&deg;'],['&beta;',beta&nbsp;+'&deg;']])}</p>\n<p>A {mass} homogeneous pole with a length of {L} is being raised by pulling with a cable at $B$.</p>", "advice": "<p>This problem can be solved by the standard method:</p>\n<ol>\n<li>Draw a free body diagram of the pole. &nbsp;Include the weight of the pole at the center of gravity. &nbsp;Note that mass must be converted to weight.</li>\n<li>Use $\\Sigma M_A = 0$&nbsp;to find <em>$T$.</em></li>\n<li>Use $\\Sigma F_x = 0$ and&nbsp; $\\Sigma F_y = 0$ to find $A_x$ and $A_y$.</li>\n<li>Resolve&nbsp; $A_x$ and $A_y$ to find magnitude and direction of $\\mathbf{A}$.</li>\n</ol>\n<p>It can also be solved using the three force body principle.</p>\n<ol>\n<li>Find the point of intersection of the lines of action of the weight and the tension.</li>\n<li>Determine the direction of force $\\mathbf{A}$. &nbsp;Its line of action must pass through the point.</li>\n<li>Draw a force triangle.</li>\n<li>Determine the angles in the force triangle.</li>\n<li>Use the known weight and the law of sines to solve for the tension and the reaction at $A$.</li>\n</ol>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"L": {"name": "L", "group": "inputs", "definition": "qty(random(3..5#0.2),'m')", "description": "", "templateType": "anything", "can_override": false}, "theta_T": {"name": "theta_T", "group": "Ungrouped variables", "definition": "180 + alpha - beta", "description": "", "templateType": "anything", "can_override": false}, "T": {"name": "T", "group": "Ungrouped variables", "definition": "scalar(weight)  cos(radians(alpha))/(2 sin(radians(beta)) )\nvector(cos(radians(theta_t)),sin(radians(theta_t)))", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "Ungrouped variables", "definition": "-(W+T)", "description": "", "templateType": "anything", "can_override": false}, "W": {"name": "W", "group": "Ungrouped variables", "definition": "vector(0,-scalar(weight))", "description": "", "templateType": "anything", "can_override": false}, "theta_A": {"name": "theta_A", "group": "Ungrouped variables", "definition": "mod(degrees(atan2(A[1],A[0])),360)", "description": "", "templateType": "anything", "can_override": false}, "mass": {"name": "mass", "group": "inputs", "definition": "qty(random(10..150#5),'kg')", "description": "", "templateType": "anything", "can_override": false}, "beta": {"name": "beta", "group": "inputs", "definition": "random(20..(90+alpha-20))", "description": "<p>angle between pole and rope</p>", "templateType": "anything", "can_override": false}, "weight": {"name": "weight", "group": "inputs", "definition": "mass * qty(9.81,'m/s^2') in 'N'", "description": "", "templateType": "anything", "can_override": false}, "debug": {"name": "debug", "group": "Ungrouped variables", "definition": "false", "description": "", "templateType": "anything", "can_override": false}, "alpha": {"name": "alpha", "group": "inputs", "definition": "random(20..80)", "description": "<p>angle of pole</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["W", "T", "theta_T", "A", "theta_A", "debug"], "variable_groups": [{"name": "inputs", "variables": ["alpha", "mass", "beta", "weight", "L"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Tension", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the tension in the cable?</p>\n<p>$T$= [[0]] &nbsp;<span data-jme-visible=\"debug\">T = {siground(abs(T),4)} N</span></p>", "gaps": [{"type": "engineering-answer", "useCustomName": true, "customName": "Tension", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(abs(T),'N')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Reaction at A", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "interpreted_angle:  // a qty string corrected to standard angle\n  student_angle[2]  + student_angle[1] * student_angle[0] + student_units\n\nmagnitude:\n  studentAnswer[3]\n\nstudent_angle:\n  [mod(matchnumber(studentAnswer[0],['plain','en'])[1],360), // angle\n  [1,-1][indices(studentAnswer[1],[true])[0]],      // ccw = 1 cw = -1\n  [0,90,180,-90][indices(studentAnswer[2],[true])[0]]] // reference axis\n\nstudent_units:\n  studentAnswer[0][len(matchnumber(studentAnswer[0],['plain','en'])[0])..len(studentAnswer[0])]\n\ninterpreted_answers:\n  [interpreted_angle, studentAnswer[1], studentAnswer[2], studentAnswer[3]]\n\ngap_feedback (Feedback on each of the gaps):\n    map(\n        try(\n            let(\n                result, submit_part(gaps[gap_number][\"path\"],answer),\n                gap, gaps[gap_number],\n                name, gap[\"name\"],  \n                noFeedbackIcon, not gap[\"settings\"][\"showFeedbackIcon\"],\n                assert(name=\"\" or len(gaps)=1,feedback(translate('part.gapfill.feedback header',[\"name\": name])));\n                concat_feedback(filter(x[\"op\"]<>\"warning\",x,result[\"feedback\"]), if(marks>0,result[\"marks\"]/marks,1), noFeedbackIcon);\n                    result\n            ),\n            err,\n            fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n        ),\n        [gap_number,answer,index],\n        zip([3,0],[studentAnswer[3], interpreted_angle],[1,2])\n    )\n\n", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the magnitude and direction of the reaction force at point <em>A</em>?</p>\n<p>$\\mathbfy{A}$ = [[3]]</p>\n<p>at an angle of&nbsp;&nbsp;[[0]]&nbsp;measured [[1]]&nbsp;from the &nbsp;[[2]].</p>\n<p><span data-jme-visible=\"debug\">A= {siground(abs(A),4)} N @ {siground(theta_A,4)}&deg;</span></p>", "gaps": [{"type": "angle", "useCustomName": true, "customName": "angle", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"expected_answer": "precround(qty(theta_A,'deg'),2)", "unit_penalty": "20", "close_penalty": "20", "close_tol": "0.5", "right_tol": "0.2"}}, {"type": "1_n_2", "useCustomName": true, "customName": "sign", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["CCW", "CW"], "matrix": [0, 0], "distractors": ["", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "ref", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["+x axis", "+y axis", "-x axis", "-yaxis"], "matrix": [0, 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "engineering-answer", "useCustomName": true, "customName": "Mag A", "marks": "10", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "settings": {"correctAnswer": "qty(siground(abs(A),4),'N')", "right": "0.2", "close": "1.0", "C1": "75", "C2": "50", "C3": "25"}}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "warnifunattempted", "message": "<p>Work hard please</p>"}, "preventleave": true, "startpassword": "123"}, "timing": {"allowPause": true, "timeout": {"action": "warn", "message": "<p>Time over</p>"}, "timedwarning": {"action": "warn", "message": "<p>Get ready ,soon you are going to commerce a test</p>"}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "<p>Answer all the questions</p>", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": [{"message": "<p>Good job</p>", "threshold": "3"}]}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "John Chigongo", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16986/"}], "extensions": ["geogebra", "quantities"], "custom_part_types": [{"source": {"pk": 12, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/12/edit"}, "name": "Angle quantity 2020", "short_name": "angle", "description": "<p>Adjusts all angles to 0 &lt; $\\theta$ &lt; 360.</p>\n<p>Accepts '&deg;' and 'deg' as units.</p>\n<p>Penalizes if not close enough or no units.</p>\n<p>90&deg; = -270&deg; = 450&deg;</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings['expected_answer']) ", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "original_student_scalar:\nmatchnumber(studentAnswer,['plain','en'])[1]\n\nstudent_scalar:\nmod(original_student_scalar,360)\n\n\nstudent_unit:\nstudentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]\n\ninterpreted_unit:\nif(trim(student_unit)='\u00b0','deg',student_unit)\n\ninterpreted_answer:\nqty(mod(student_scalar,360),'deg')\n\nclose:\nwithintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))\n\ncorrect_scalar:\nmod(scalar(settings['expected_answer']),360)\n\nright:\nwithintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))\n\ngood_unit:\nsame(qty(1,interpreted_unit),qty(1,'deg'))\n\nmark:\nassert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))", "marking_notes": [{"name": "original_student_scalar", "description": "<p>Retuns the scalar part of students answer (which is a quantity) as a number.</p>", "definition": "matchnumber(studentAnswer,['plain','en'])[1]"}, {"name": "student_scalar", "description": "<p>Normalize angle with mod 360</p>", "definition": "mod(original_student_scalar,360)\n"}, {"name": "student_unit", "description": "<p>matchnumber(studentAnswer,['plain','en'])[0] is a string \"12.34\"</p>", "definition": "studentAnswer[len(matchnumber(studentAnswer,['plain','en'])[0])..len(studentAnswer)]"}, {"name": "interpreted_unit", "description": "<p>Allows student to use degree symbol or 'deg' for units.</p>", "definition": "if(trim(student_unit)='\u00b0','deg',student_unit)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(mod(student_scalar,360),'deg')"}, {"name": "close", "description": "", "definition": "withintolerance(student_scalar, correct_scalar,decimal(settings['close_tol']))"}, {"name": "correct_scalar", "description": "<p>Normalize expected_answer with mod 360</p>", "definition": "mod(scalar(settings['expected_answer']),360)"}, {"name": "right", "description": "", "definition": "withintolerance(student_scalar, correct_scalar, decimal(settings['right_tol']))"}, {"name": "good_unit", "description": "", "definition": "same(qty(1,interpreted_unit),qty(1,'deg'))"}, {"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "assert(close,incorrect('Incorrect.');end());\nif(right,correct('Correct angle.'), set_credit(1 - settings['close_penalty'],'Angle is close.'));\nassert(good_unit,sub_credit(settings['unit_penalty'], 'Missing or incorrect units.'))"}], "settings": [{"name": "expected_answer", "label": "Expected Answer", "help_url": "", "hint": "Expected angle as a quantity.", "input_type": "code", "default_value": "qty(30,'deg')", "evaluate": true}, {"name": "unit_penalty", "label": "Unit penalty", "help_url": "", "hint": "Penalty for not including degree sign or 'deg'.", "input_type": "percent", "default_value": "20"}, {"name": "close_penalty", "label": "Close Penalty", "help_url": "", "hint": "Penalty for close answer.", "input_type": "percent", "default_value": "20"}, {"name": "close_tol", "label": "Close", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked close. &nbsp;&nbsp;", "input_type": "code", "default_value": "0.5", "evaluate": false}, {"name": "right_tol", "label": "Right ", "help_url": "", "hint": "Angle must be $\\pm$ this many degrees to be marked correct. &nbsp;", "input_type": "code", "default_value": "0.1", "evaluate": false}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}, {"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "<p>A value with units marked right if within an adjustable % error of the correct value. &nbsp;Marked close if within a wider margin of error.</p>", "help_url": "", "input_widget": "string", "input_options": {"correctAnswer": "siground(settings['correctAnswer'],4)", "hint": {"static": true, "value": ""}, "allowEmpty": {"static": true, "value": true}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nswitch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n\n\ninterpreted_answer:\nqty(student_scalar, student_units)\n\n\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\n\n\ncorrect_units:\nunits(correct_quantity)\n\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_scalar:\nmatch_student_number[1]\n\nstudent_units:\nreplace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")\n\ngood_units:\ntry(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n\n\nstudent_quantity:\nswitch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n\n\npercent_error:\ntry(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   \n\nright:\npercent_error <= settings['right']\n\n\nclose:\nright_sign and percent_error <= settings['close']\n\nright_sign:\nsign(student_scalar) = sign(correct_quantity)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "switch( \n  right and good_units and right_sign, add_credit(1.0,'Correct.'),\n  right and good_units and not right_sign, add_credit(settings['C2'],'Wrong sign.'),\n  right and right_sign and not good_units, add_credit(settings['C2'],'Correct value, but wrong or missing units.'),\n  close and good_units, add_credit(settings['C1'],'Close.'),\n  close and not good_units, add_credit(settings['C3'],'Answer is close, but wrong or missing units.'),\n  incorrect('Wrong answer.')\n)\n"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "qty(student_scalar, student_units)\n\n"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]\n\n"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)\n"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_scalar", "description": "", "definition": "match_student_number[1]"}, {"name": "student_units", "description": "<p>Modify&nbsp;the&nbsp;unit portion of&nbsp;the student's answer by</p>\n<p>1. replacing \"ohms\" with \"ohm\" &nbsp;case insensitive</p>\n<p>2.&nbsp;replacing '-'&nbsp;with ' '&nbsp;</p>\n<p>3. replacing '&deg;' with ' deg'&nbsp;</p>\n<p>to allow answers like 10 ft-lb and 30&deg;</p>", "definition": "replace_regex('ohms','ohm',\n  replace_regex('\u00b0', ' deg',\n    replace_regex('-', ' ' ,\n      studentAnswer[len(match_student_number[0])..len(studentAnswer)])),\"i\")"}, {"name": "good_units", "description": "", "definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n"}, {"name": "student_quantity", "description": "<p>This fixes the student answer for two common errors. &nbsp;</p>\n<p>If student_units are wrong&nbsp;&nbsp;- replace with correct units</p>\n<p>If student_scalar has the wrong sign - replace with right sign</p>\n<p>If student makes both errors, only one gets fixed.</p>", "definition": "switch(not good_units, \n       student_scalar * correct_units, \n       not right_sign,\n       -quantity(student_scalar, student_units),\n       quantity(student_scalar,student_units)\n)\n  \n"}, {"name": "percent_error", "description": "", "definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100  \n,msg,\nif(student_quantity=correct_quantity,0,100))\n   "}, {"name": "right", "description": "", "definition": "percent_error <= settings['right']\n"}, {"name": "close", "description": "<p>Only marked close if the student actually has the right sign.</p>", "definition": "right_sign and percent_error <= settings['close']"}, {"name": "right_sign", "description": "", "definition": "sign(student_scalar) = sign(correct_quantity) "}], "settings": [{"name": "correctAnswer", "label": "Correct Quantity.", "help_url": "", "hint": "The correct answer given as a JME quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "right", "label": "% Accuracy for right.", "help_url": "", "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "0.2", "evaluate": true}, {"name": "close", "label": "% Accuracy for close.", "help_url": "", "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "input_type": "code", "default_value": "1.0", "evaluate": true}, {"name": "C1", "label": "Close with units.", "help_url": "", "hint": "Partial Credit for close value with appropriate units. &nbsp;if correct answer is 100 N and close is &plusmn;1%,<br />99 &nbsp;N is accepted.", "input_type": "percent", "default_value": "75"}, {"name": "C2", "label": "No units or wrong sign", "help_url": "", "hint": "Partial credit for forgetting units or using wrong sign.<br />If the correct answer is 100 N, both 100 and -100 N are accepted.", "input_type": "percent", "default_value": "50"}, {"name": "C3", "label": "Close, no units.", "help_url": "", "hint": "Partial Credit for close value but forgotten units.<br />This value would be close&nbsp;if the expected units were provided. &nbsp;If the correct answer is 100 N, and close is &plusmn;1%,<br />99 is accepted.", "input_type": "percent", "default_value": "25"}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/Picture1_6woS8OC.jpg", "/srv/numbas/media/question-resources/Picture1_6woS8OC.jpg"]]}