// Numbas version: finer_feedback_settings
{"name": "Differentiation 18 - Applications", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"v": {"templateType": "anything", "name": "v", "description": "", "definition": "random(100..200)", "group": "Ungrouped variables"}, "a": {"templateType": "anything", "name": "a", "description": "", "definition": "siground((2v)^(1/3),3)", "group": "Ungrouped variables"}}, "statement": "<p>An&nbsp;<em>open</em> metal tank of square base has a volume of $\\var{v}\\text{ m}^3$</p>\n<p><strong>Given that the square base has sides of length $x$ metres, find expressions, in terms of $x$, for the following.</strong></p>", "name": "Differentiation 18 - Applications", "parts": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>The height of the tank</p>\n<p>$h=$&nbsp;[[0]] m</p>\n<p></p>", "gaps": [{"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "marks": "2", "checkVariableNames": true, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "answer": "{v}/x^2", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>The surface area of the tank</p>\n<p>$S=$ [[0]]&nbsp;$\\text{m}^2$</p>", "gaps": [{"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "marks": "2", "checkVariableNames": true, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "answer": "x^2+4{v}/x", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"marks": 0, "customMarkingAlgorithm": "", "steps": [{"marks": 0, "customMarkingAlgorithm": "", "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "information", "prompt": "<p><em>Hint:</em> find $x$ at stationary point</p>", "unitTests": [], "useCustomName": false, "variableReplacements": []}], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "type": "gapfill", "prompt": "<p>Given that the surface area is a minimum, find the value of $x$.</p>\n<p>$S'(x)=$&nbsp;[[1]]</p>\n<p>Therefore,</p>\n<p>$x=$&nbsp;[[0]] &nbsp; &nbsp;&nbsp;(give your answer to 2 decimal places)</p>\n<p>Check this is a minimum.</p>\n<p>$S''(x)=$&nbsp;[[2]]</p>\n<p>Substitute your value for $x$ into $S''(x)$ and determine whether is it a minimum.</p>\n<p>Type '$Y$' for yes, '$N$' for no, or '$U$' for undefined.</p>\n<p>[[3]]</p>\n<p></p>\n<p>Hence, the minimum area of metal used is</p>\n<p>$A_{min}=$&nbsp;[[4]] &nbsp; &nbsp;&nbsp;(give your answer to 2 decimal places)</p>", "gaps": [{"correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "minValue": "{a}", "showPrecisionHint": false, "precisionPartialCredit": "50", "showFeedbackIcon": true, "maxValue": "{a}", "notationStyles": ["plain", "en", "si-en"], "marks": "2", "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "allowFractions": false, "strictPrecision": false, "unitTests": [], "useCustomName": false, "correctAnswerFraction": false, "variableReplacements": []}, {"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "marks": 1, "checkVariableNames": true, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "answer": "2x-4{v}/x^2", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": true, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "valuegenerators": [{"name": "x", "value": ""}], "showFeedbackIcon": true, "marks": 1, "checkVariableNames": true, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "answer": "2+8{v}/x^3", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"vsetRangePoints": 5, "customMarkingAlgorithm": "", "showPreview": false, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "checkingAccuracy": 0.001, "valuegenerators": [{"name": "y", "value": ""}], "showFeedbackIcon": true, "marks": 1, "checkVariableNames": true, "answerSimplification": "all", "vsetRange": [0, 1], "failureRate": 1, "answer": "Y", "showCorrectAnswer": true, "scripts": {}, "type": "jme", "unitTests": [], "useCustomName": false, "variableReplacements": []}, {"correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "extendBaseMarkingAlgorithm": true, "customName": "", "variableReplacementStrategy": "originalfirst", "minValue": "{a}^2+4({v}/{a})", "showPrecisionHint": false, "precisionPartialCredit": "50", "showFeedbackIcon": true, "maxValue": "{a}^2+4({v}/{a})", "notationStyles": ["plain", "en", "si-en"], "marks": "1", "precision": "2", "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "allowFractions": false, "strictPrecision": false, "unitTests": [], "useCustomName": false, "correctAnswerFraction": false, "variableReplacements": []}], "unitTests": [], "useCustomName": false, "stepsPenalty": "1", "variableReplacements": []}], "functions": {}, "rulesets": {}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "ungrouped_variables": ["v", "a"], "advice": "<p>This section draws on the skills learnt the previous parts of the&nbsp;<em>'Differentiation'</em> series of questions, and some geometry knowledge.</p>\n<p>The hint&nbsp;under the steps should be all the extra information you need.</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Another practical application of differentiation</p>"}, "type": "question", "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}