Parametric differentiation question with customised feedback to catch some common errors.
", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "The following parametric equations describe a curve: $x(t)=4 \\sin t$ and $y(t)=-\\cos t-1$. Find the slope of the tangent to the curve when $\\displaystyle t=\\frac{\\pi}{3}$.
", "advice": "", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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": "First, find $\\displaystyle \\frac{dy}{dx}$:
\n$\\displaystyle \\frac{dy}{dx}=$ [[0]]
", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n [\n [\"cos(t)/(4sin(t))\", \"Have you put $\\\\frac{dx}{dt}$ and $\\\\frac{dy}{dt}$ together in the correct way?\"],\n [\"(sin(t)-1)/(4cos(t))\", \"Double check $\\\\frac{dy}{dt}$.\"],\n [\"-sin(t)/(4cos(t))\", \"Double check $\\\\frac{dy}{dt}$. What is $\\\\frac{d}{dt} \\\\left( \\\\cos t \\\\right)$? $\\\\Rightarrow $ $\\\\frac{d}{dt} \\\\left( - \\\\cos t \\\\right) = ?$\"],\n [\"sin(t)\", \"It looks like you have just found $\\\\frac{dy}{dt}$.\"],\n [\"(-cos(t)-1)/(4sin(t))\", \"You have not differentiated. How is $\\\\frac{dy}{dx}$ calculated for parametric differentiation?\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))$\\displaystyle \\frac{dy}{dx} \\bigg|_{t=\\frac{\\pi}{3}}=$ [[0]]
", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n [\n [\"0.005\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"],\n [\"0.0046\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"],\n [\"0.00457\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"],\n [\"0.004570\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"],\n [\"0.0045698\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"],\n [\"0.00456977\", \"Is your calculator set to radians or degrees? Remember for this module, you should always be in radians.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))