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True/False", "tags": [], "metadata": {"description": "Multi choice question week 3", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>See ??</p>", "rulesets": {}, "extensions": [], "variables": {"statements": {"name": "statements", "group": "do not change these", "definition": "map(if(rand[j]=1,\n    statements_true[j],\n    statements_false[j]),j,0..n-1)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "change these", "definition": "random(6..9)", "description": "", "templateType": "anything"}, "max_mark": {"name": "max_mark", "group": "change these", "definition": "4", "description": "", "templateType": "anything"}, "statements_false": {"name": "statements_false", "group": "change these", "definition": "[\"$\\\\displaystyle \\\\int f(x) = \\\\cos(x)+c$\",\n  random([\"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = \\\\cos(x)$\",\n      \"$\\\\displaystyle \\\\int f(x) \\\\, dx = \\\\cos(x)+c$\"]),\n  \"$\\\\displaystyle \\\\int g(t) = -\\\\sin(t)+c$\",\n  random([\"$\\\\displaystyle \\\\int g(t) \\\\, dt = -\\\\sin(x)+c$\",\n      \"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dx = -\\\\sin(t)+c$\"]),\n  \"When integrating, there is no way to check your answer.\",\n  \"You include $+c$ when integrating because it is just a random rule you have to memorise.\",\n  \"The integral of $\\\\frac{1}{x}$ is determined by re-writing it as $x^{-1}$\"  \n]", "description": "", "templateType": "anything"}, "statements_true": {"name": "statements_true", "group": "change these", "definition": "[\"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",\n  \"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = -\\\\cos(x)+c$\",\n  \"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",\n  \"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dt = \\\\sin(t)+c$\",\n  \"When integrating, you should check your answer by differentiating your answer.\",\n  \"The constant of integration summarises the possibility that you can add any number to the function.\",\n  \"The integral of $\\\\frac{1}{x}$ is $\\\\ln(x) + c$\"\n]\n ", "description": "<p><br /> \"<br /><br /><br /><br /><br /> \"To calculate changes in position using areas in a velocity-time graph, you need to think about when the object is moving forwards or backwards\",<br /> \"$\\\\sec(x) = \\\\frac{1}{\\\\cos(x)}$\",<br /> \"$\\\\csc(x) = \\\\frac{1}{\\\\sin(x)}$\" <br /> ]</p>", "templateType": "anything"}, "b": {"name": "b", "group": "change these", "definition": "random(10..18)+random(1..9)/10", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(-2..2)>0,1,0),n-1)+[if(random(0..5)=5,1,0)]", "description": "", "templateType": "anything"}, "error": {"name": "error", "group": "change these", "definition": "1/2", "description": "<p>what proportion of total marks should be lost for each error. e.g. 1/2 would mean a single error costs half of all marks available. 1/3 would mean each error costs a third of all marks.</p>", "templateType": "anything"}, "marks": {"name": "marks", "group": "do not change these", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark*error+max_mark/n],[-max_mark*error+max_mark/n,max_mark/n]),j,0..n-1))\n\n", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "do not change these", "definition": "length(statements_true)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "change these", "definition": "random(3..7)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "error", "a", "b", "c"]}, {"name": "do not change these", "variables": ["n", "rand", "statements", "marks"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>In the following,&nbsp;$f(x) = \\sin(x)$ and $g(t) = \\cos(t)$.&nbsp; Which of the following are true and which are false?&nbsp;&nbsp;</p>\n<p></p>\n<p>If you are unsure of something,&nbsp;find out the answer instead of guessing.&nbsp;<strong>Each error will cost half of the marks available</strong>. 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