// Numbas version: finer_feedback_settings
{"name": "SIT190 - Module 6 - Self-assessment", "metadata": {"description": "", "licence": "None specified"}, "duration": 5400, "percentPass": "80", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "variable_overrides": [[], [], [], [], []], "questions": [{"name": "6.1 Rate of change", "extensions": [], "custom_part_types": [], "resources": ["question-resources/Picture_curve.png"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "tags": [], "metadata": {"description": "<p>Rate of change problem involving velocity &amp; acceleration</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p></p>\n<p></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(100 .. 300#5)", "description": "", "templateType": "randrange", "can_override": false}, "x0": {"name": "x0", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "y0": {"name": "y0", "group": "Ungrouped variables", "definition": "random(1..8)", "description": 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"km3", "group": "Ungrouped variables", "definition": "t3*random(35..59)", "description": "", "templateType": "anything", "can_override": false}, "sec3": {"name": "sec3", "group": "Ungrouped variables", "definition": "random(10,12,15,20,30,40,45)", "description": "", "templateType": "anything", "can_override": false}, "sec4": {"name": "sec4", "group": "Ungrouped variables", "definition": "random(10,12,15,20,30,40,45)", "description": "", "templateType": "anything", "can_override": false}, "tem40": {"name": "tem40", "group": "Ungrouped variables", "definition": "random(10..38)", "description": "", "templateType": "anything", "can_override": false}, "tem41": {"name": "tem41", "group": "Ungrouped variables", "definition": "random(10..38)", "description": "", "templateType": "anything", "can_override": false}, "t4": {"name": "t4", "group": "Ungrouped variables", "definition": "random(3..8)", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": 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"scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><img src=\"resources/question-resources/Picture_curve.png\" width=\"340\" height=\"222\"/></p>\n<p>Calculate the average rate of change over an interval in a graph between points $(x0,y0) = (\\var{x0},\\var{y0})$ and $(x1,y1)= (\\var{x1},\\var{y1})$</p>\n<p>Average rate = [[0]]</p>", "gaps": [{"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, "answer": "({y1}-{y0})/({x1}-{x0})", "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": []}], "sortAnswers": false}, {"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>If it takes {t2} hours to drive a distance of {km2} km on a motorway, what would be your average speed in km/h?</p>\n<p>Average speed = [[0]] km/h</p>", "gaps": [{"type": "jme", 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["question-resources/Picture_curve.png"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "tags": [], "metadata": {"description": "<p>Simple derivatives</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(100 .. 300#5)", "description": "", "templateType": "randrange", "can_override": false}, "x0": {"name": "x0", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "y0": {"name": "y0", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "x0+random(4..12)", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "y0+random(4..12)", "description": "", "templateType": "anything", "can_override": false}, "t2": {"name": "t2", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "km2": {"name": "km2", "group": "Ungrouped variables", "definition": "t2*v2", "description": "", "templateType": "anything", "can_override": false}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "random(55..89)", "description": "", "templateType": "anything", "can_override": false}, "t3": {"name": "t3", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "km3": {"name": "km3", "group": "Ungrouped variables", "definition": "t3*random(35..59)", "description": "", "templateType": "anything", "can_override": false}, "sec3": {"name": "sec3", "group": "Ungrouped variables", "definition": "random(10,12,15,20,30,40,45)", "description": "", "templateType": "anything", "can_override": false}, "sec4": {"name": "sec4", "group": "Ungrouped variables", "definition": "random(10,12,15,20,30,40,45)", "description": "", "templateType": "anything", "can_override": false}, "tem40": {"name": "tem40", "group": "Ungrouped variables", "definition": "random(10..38)", "description": "", "templateType": "anything", "can_override": false}, "tem41": {"name": "tem41", "group": "Ungrouped variables", "definition": "random(10..38)", "description": "", "templateType": "anything", "can_override": false}, "t4": {"name": "t4", "group": "Ungrouped variables", "definition": "random(3..8)", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "random(-9..9 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "bb2": {"name": "bb2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "aa2": {"name": "aa2", "group": "Ungrouped variables", "definition": "random(-9..9 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "nn": {"name": "nn", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "nn1": {"name": "nn1", "group": "Ungrouped variables", "definition": "random(-9..-1)", "description": "", "templateType": "anything", "can_override": false}, "nn2": {"name": "nn2", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "", "templateType": "anything", "can_override": false}, "nn3": {"name": "nn3", "group": "Ungrouped variables", "definition": "random(2..9 except nn2)", "description": "", "templateType": "anything", "can_override": false}, "ann": {"name": "ann", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}, "ann1": {"name": "ann1", "group": "Ungrouped variables", "definition": "random(-9..9 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "ann23": {"name": "ann23", "group": "Ungrouped variables", "definition": "random(-9..9 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "cnn23": {"name": "cnn23", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "ann4": {"name": "ann4", "group": "Ungrouped variables", "definition": "random(-9..9 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "bnn4": {"name": "bnn4", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "cnn4": {"name": "cnn4", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "nn4": {"name": "nn4", "group": "Ungrouped variables", "definition": "random(4..8)", "description": "", "templateType": "anything", "can_override": false}, "nn5": {"name": "nn5", "group": "Ungrouped variables", "definition": "random(2..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "x0", "y0", "x1", "y1", "t2", "km2", "v2", "t3", "km3", "sec3", "sec4", "tem40", "tem41", "t4", "aa", "bb", "bb2", "aa2", "nn", "nn1", "nn2", "nn3", "ann", "ann1", "ann23", "cnn23", "ann4", "bnn4", "cnn4", "nn4", "nn5"], "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>Find derivative of $y=\\var{ann4}x^\\var{nn4}+\\var{bnn4}x^\\var{nn5} +\\var{cnn4}$</p>\n<p>&nbsp;[[0]]</p>", "gaps": [{"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, "answer": "{ann4*nn4}x^{nn4-1} +{bnn4*nn5}x^{nn5-1}", "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": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "6.3 Differentiation - Trigonometric Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}, {"name": "Kevin Bohan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3363/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "tags": [], "metadata": {"description": "<p>More work on differentiation with&nbsp;trigonometric functions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Differentiate the following&nbsp;trigonometric functions using the chain rule.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "advice": "<p><strong></strong>If you don't know how to differentiate trigonometric functions, please see&nbsp;<em>'Differentiation 4 - Trigonometric Functions'</em>.</p>\n<p><strong></strong></p>\n<p><strong>These questions use the chain rule.</strong></p>\n<p>The earlier questions are easy to do by inspection, e.g using Part a:</p>\n<p style=\"text-align: center;\">$y=sin(\\var{c[0]}x)$.</p>\n<p>We differentiate the term(s) inside the function, here the term is $\\var{c[0]}x$.</p>\n<p>Then we derive $sin$ of any function, giving us $cos$.</p>\n<p>Putting our results together, we get</p>\n<p>$\\var{c[0]}cos(\\var{c[0]}x)$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "shuffle(2..8)[0..5]", "description": "<p>coefficients</p>", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "repeat(random(3..6),2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "p"], "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>$y=-5\\cos(\\var{c[3]}x)+\\sin(\\var{c[4]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"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, "answer": "5{c[3]}sin({c[3]}x)+{c[4]}cos({c[4]}x)", "answerSimplification": "all", "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": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "6.4 Differentiation - Exponentials and Logs", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}, {"name": "Simon James", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18202/"}], "tags": [], "metadata": {"description": "<p>Differentiating exponentials and Logs<br></p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Differentiate the following.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>\n<p>Remember to enclose all single powers inside a bracket, for example, $e^{2x}$ is inputted as $e$^$(2x)$, or use $\\ln(2)$ instead of $\\ln2.$</p>", "advice": "<p><strong>The key fact to understand here is that the differentiate of $e^x$ is $e^x$.</strong></p>\n<p>This can be proven by looking at evaluating limits etc. but it is not necessary to do so at this stage.</p>\n<p>The basic steps to differentiate an exponential function are:</p>\n<p>Differentiate the power of $e$, for example in Part b,&nbsp;<strong></strong>$y=\\var{c[1]}e^{\\var{p[1]}x}$, you would differentiate $\\var{p[1]}x$.</p>\n<p>In this example, it is $\\var{p[1]}$.</p>\n<p>Then multiply the coefficient of $e$ by this result.</p>\n<p>Here, you would find $\\simplify{{c[1]}{p[1]}e^({p[1]}x)}$.</p>\n<p>This is your final answer for the derivative.</p>\n<p></p>\n<p>Remember, don't be confused if there is no coefficient. The fact the term is there means the coefficient must be $1$, but we don't tend to write it out as, for example $1x$, we just say $x$.</p>\n<p></p>\n<p>Basic formulas:</p>\n<p>$\\frac{d}{dx} e^x = e^x$</p>\n<p>$\\frac{d}{dx} e^{u(x)} = e^{u(x)}\\frac{d}{dx} u$</p>\n<p>$\\frac{d}{dx} a^x = a^x \\ln(a)$</p>\n<p>$\\frac{d}{dx} a^{u(x)} = a^{u(x)} \\ln(a) \\frac{d}{dx} u$</p>\n<p>$\\frac{d}{dx} \\ln(x) = \\frac{1}{x} ~~ (x&gt;0)$</p>\n<p>$\\frac{d}{dx} \\ln|x| = \\frac{1}{x} ~~ (x\\neq 0)$</p>\n<p>$\\frac{d}{dx} \\log_a(x) = \\frac{1}{x \\ln a} ~~ (a&gt;0, a \\neq 1)$</p>\n<p>$\\frac{d}{dx} x^x = x^x (1+\\ln x)$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "repeat(random(2..4),7)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "repeat(random(2..8),7)", 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You have achieved the minimum threshold for this module's self-assessment.</strong></p>\n<p>Use the \"Print this results summary\" and save your attempt as a pdf.&nbsp; You will need the printout showing all questions for your module submission.</p>", "threshold": "80"}, {"message": "<p><strong>Unfortunately you have not achieved the minimum score.</strong><strong></strong></p>\n<p>If this is your first 'Give it a go' attempt - don't despair! 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