// Numbas version: exam_results_page_options
{"name": "CLE13. True false", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacements": [], "shuffleChoices": true, "warningType": "none", "maxMarks": "0", "shuffleAnswers": false, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "layout": {"expression": "", "type": "all"}, "scripts": {}, "minAnswers": "{n}", "unitTests": [], "marks": 0, "showFeedbackIcon": true, "answers": ["<p>True</p>", "<p>False</p>"], "prompt": "<p>Which of the following are true and which are false, including correct notation? If you are unsure of something,&nbsp;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.</p>", "choices": "{statements}", "type": "m_n_x", "customMarkingAlgorithm": "", "matrix": "{marks}", "maxAnswers": 0, "showCellAnswerState": true, "displayType": "radiogroup", "minMarks": 0}], "extensions": [], "variables": {"rand": {"definition": "repeat(if(random(0..2)=2,1,0),n)", "name": "rand", "templateType": "anything", "group": "do not change these", "description": ""}, "statements_false": {"definition": "[\"$\\\\displaystyle \\\\int_0^1 \\\\sin(x) = [-\\\\cos(x)]^1_0$\",\n  \"$\\\\displaystyle \\\\int_0^1 \\\\sin(x) \\\\, dx = [-\\\\cos(x)]^0_1$\",\n  \"$\\\\displaystyle \\\\int_0^1 \\\\cos(x) \\\\, dt = [\\\\sin(x)]^1_0$\",\n  \"$\\\\displaystyle \\\\int_0^1 \\\\sin(t) \\\\, dt = [\\\\cos(t)]^1_0$\",\n  \"$\\\\displaystyle \\\\int_0^1 -\\\\sin(t) \\\\, dt = [\\\\cos(t)]$\",\n  \"$\\\\displaystyle \\\\int -\\\\cos(x) \\\\, dx = [-\\\\sin(x)]^1_0$\",\n  \"$\\\\displaystyle \\\\int -\\\\sin(t) \\\\, dt = \\\\cos(t)$\",\n  \"$\\\\displaystyle \\\\int \\\\sin(t) \\\\, dt = \\\\cos(t)+c$\",\n  \"Definite integrals are always equal to areas in a graph\",\n  \"To get from velocity to position, you differentiate.\",\n  \"$\\\\sin^{-1}(1) = \\\\frac{1}{\\\\sin(1)}$\",\n  \"When calculating areas in a graph using integration, there is no way of checking your final answer.\",\n  \"After integrating, there is no way of checking if you did it correctly.\"\n]", "name": "statements_false", "templateType": "anything", "group": "change these", "description": ""}, "statements_true": {"definition": "[\"$\\\\displaystyle \\\\int_0^1 \\\\sin(x) \\\\, dx = [-\\\\cos(x)]^1_0$\",\n  \"$\\\\displaystyle \\\\int_0^1 \\\\sin(x) \\\\, dx = [-\\\\cos(x)]^1_0$\",\n  \"$\\\\displaystyle \\\\int_0^1 \\\\cos(x) \\\\, dx = [\\\\sin(x)]^1_0$\",\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  \"$\\\\displaystyle \\\\int -\\\\cos(x) \\\\, dx = -\\\\sin(x)+c$\",\n  \"$\\\\displaystyle \\\\int -\\\\sin(t) \\\\, dt = \\\\cos(t)+c$\",\n  \"$\\\\displaystyle \\\\int \\\\sin(t) \\\\, dt = -\\\\cos(t)+c$\",\n  \"Definite integrals are closely related to, but not always equal to, areas in a graph.\",\n  \"To get from velocity to position, you integrate.\",\n  \"$\\\\sin^{-1}(1) = \\\\pi/2$\",\n  \"When calculating areas in a graph using integration, doing a simple estimate is a good way of checking your answer.\",\n  \"After integrating, you can often check your answer by differentiating your answer.\"\n]", "name": "statements_true", "templateType": "anything", "group": "change these", "description": "<p>[\"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",<br /> \"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = -\\\\cos(x)+c$\",<br /> \"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",<br /> \"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",<br /> \"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",<br /> \"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dt = \\\\sin(t)+c$\",<br /> \"Integration is the same as undoing differentiation.\",<br /> \"When integrating, you should check your answer by differentiating your answer.\",<br /> \"The constant of integration summarises the possibility that you can add any number to the function.\",<br /> \"$\\\\frac{df}{dx}=\\\\cos(x)$\",<br /> \"$\\\\frac{dg}{dt} = -\\\\sin(t)$\",<br /> \"Areas in a velocity-time graph correspond to distances travelled.\",<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 /> \"To convert from position to velocity, you differentiate.\",<br /> \"$\\\\sec(x) = \\\\frac{1}{\\\\cos(x)}$\",<br /> \"$\\\\csc(x) = \\\\frac{1}{\\\\sin(x)}$\",<br /> \"To integrate $\\\\cos^2(x)$, you need to re-write it in terms of $\\\\cos(2x)$\"<br />]</p>"}, "n": {"definition": "length(statements_true)", "name": "n", "templateType": "anything", "group": "change these", "description": ""}, "statements": {"definition": "map(if(rand[j]=1,\n    statements_true[j],\n    statements_false[j]),j,0..n-1)", "name": "statements", "templateType": "anything", "group": "do not change these", "description": ""}, "max_mark": {"definition": "10", "name": "max_mark", "templateType": "anything", "group": "change these", "description": ""}, "marks": {"definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark/3+max_mark/n],[-max_mark/3+max_mark/n,max_mark/n]),j,0..n-1))", "name": "marks", "templateType": "anything", "group": "do not change these", "description": ""}}, "functions": {}, "tags": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n"]}, {"name": "do not change these", "variables": ["rand", "statements", "marks"]}], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>15 questions based on module&nbsp;so far.&nbsp;</p>"}, "ungrouped_variables": [], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "CLE13. True false", "preamble": {"js": "", "css": ""}, "advice": "<p>See all the lectures and workshops up to this point.</p>", "rulesets": {}, "statement": "", "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}