// Numbas version: exam_results_page_options {"name": "CLE15. True false", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variables": {"rand": {"description": "", "templateType": "anything", "group": "do not change these", "name": "rand", "definition": "repeat(if(random(0..2)=2,1,0),n)"}, "marks": {"description": "", "templateType": "anything", "group": "do not change these", "name": "marks", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),j,0..n-1))\n"}, "statements_false": {"description": "", "templateType": "anything", "group": "change these", "name": "statements_false", "definition": "[ \"$\\\\displaystyle \\\\int_0^1 \\\\cos(x) \\\\, dt = [\\\\sin(x)]^1_0$\",\n \"$\\\\displaystyle \\\\int_0^1 \\\\sin(t) \\\\, dt = [\\\\cos(t)]^1_0$\",\n \"$\\\\displaystyle \\\\int_0^1 -\\\\sin(t) \\\\, dt = [\\\\cos(t)]$\",\n \"$\\\\displaystyle \\\\int -\\\\sin(t) \\\\, dt = \\\\cos(t)$\",\n \"$\\\\cos^{-1}(1) = \\\\frac{1}{\\\\cos(1)}$\",\n \"When calculating areas in a graph using integration, there is no way of checking your final answer.\",\n \"You can integrate $x\\\\sin(x), x\\\\cos(x)$ and $xe^x$ using integration by substitution.\",\n \"If $u=\\\\cos(x)$, then $\\\\frac{dx}{du} = -\\\\sin(x)$\",\n \"If $x = \\\\sin(u)$,then $\\\\frac{du}{dx} = \\\\cos(u)$\",\n \"You can integrate $x\\\\sin(x^2), x\\\\cos(x^2)$ and $xe^{x^2}$ using integration by parts.\",\n \"To integrate $e^x (e^{2x}+1)^2$, you can reverse the chain rule.\",\n \"To integrate $e^{2x} (e^{2x}+1)^2$, you have to multiply out the brackets.\",\n \"There are only one or two solutions to differential equations.\",\n \"You cannot use trial-and-error to find a solution to differential equations.\",\n \"In a differential equation, the unknown quantity is a number.\"\n]"}, "n": {"description": "", "templateType": "anything", "group": "change these", "name": "n", "definition": "length(statements_true)"}, "max_mark": {"description": "", "templateType": "anything", "group": "change these", "name": "max_mark", "definition": "10"}, "statements_true": {"description": "", "templateType": "anything", "group": "change these", "name": "statements_true", "definition": "[ \"$\\\\displaystyle \\\\int_0^1 \\\\cos(x) \\\\, dx = [\\\\sin(x)]^1_0$\",\n \"$\\\\displaystyle \\\\int_0^1 \\\\cos(t) \\\\, dt = [\\\\sin(t)]^1_0$\",\n \"$\\\\displaystyle \\\\int_0^1 -\\\\sin(t) \\\\, dt = [\\\\cos(t)]^1_0$\",\n \"$\\\\displaystyle \\\\int -\\\\sin(t) \\\\, dt = \\\\cos(t)+c$\",\n \"$\\\\cos^{-1}(1) = 0$\",\n \"When calculating areas in a graph using integration, doing a simple estimate is a good way of checking your answer.\",\n \"You can integrate $x\\\\sin(x), x\\\\cos(x)$ and $xe^x$ using integration by parts.\",\n \"If $u=\\\\cos(x)$, then $\\\\frac{du}{dx} = -\\\\sin(x)$\",\n \"If $x = \\\\sin(u)$,then $\\\\frac{dx}{du} = \\\\cos(u)$\",\n \"You can integrate $x\\\\sin(x^2), x\\\\cos(x^2)$ and $xe^{x^2}$ by reversing the chain rule.\",\n \"To integrate $e^x (e^{2x}+1)^2$, you have to multiply out the brackets.\",\n \"To integrate $e^{2x} (e^{2x}+1)^2$, you can reverse the chain rule.\",\n \"Differential equations can have infinitely many solutions.\",\n \"Trial-and-improvement is a possible technique for solving differential equations.\",\n \"In a differential equation, the unknown quantity is a function.\"\n]"}, "statements": {"description": "", "templateType": "anything", "group": "do not change these", "name": "statements", "definition": "map(if(rand[j]=1,\n statements_true[j],\n statements_false[j]),j,0..n-1)"}}, "preamble": {"css": "", "js": ""}, "statement": "", "parts": [{"maxAnswers": 0, "showCorrectAnswer": true, "type": "m_n_x", "unitTests": [], "shuffleChoices": true, "prompt": "

Which of the following are true and which are false, including correct notation? If you are unsure of something, find out the answer instead of guessing. A single error will result in a score 0 for the whole question. If you are unable to find out or understand the answer, you are welcome to ask me for help or advice.

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True

", "

False

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See all the lectures and workshops up to this point.