True

", "False

"], "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.

", "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": "[\"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",

\"$\\\\displaystyle \\\\int \\\\sin(x) \\\\, dx = -\\\\cos(x)+c$\",

\"$\\\\displaystyle \\\\int f(x) \\\\, dx = -\\\\cos(x)+c$\",

\"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",

\"$\\\\displaystyle \\\\int g(t) \\\\, dt = \\\\sin(t)+c$\",

\"$\\\\displaystyle \\\\int \\\\cos(t) \\\\, dt = \\\\sin(t)+c$\",

\"Integration is the same as undoing differentiation.\",

\"When integrating, you should check your answer by differentiating your answer.\",

\"The constant of integration summarises the possibility that you can add any number to the function.\",

\"$\\\\frac{df}{dx}=\\\\cos(x)$\",

\"$\\\\frac{dg}{dt} = -\\\\sin(t)$\",

\"Areas in a velocity-time graph correspond to distances travelled.\",

\"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\",

\"To convert from position to velocity, you differentiate.\",

\"$\\\\sec(x) = \\\\frac{1}{\\\\cos(x)}$\",

\"$\\\\csc(x) = \\\\frac{1}{\\\\sin(x)}$\",

\"To integrate $\\\\cos^2(x)$, you need to re-write it in terms of $\\\\cos(2x)$\"

]

15 questions based on module so far.

"}, "ungrouped_variables": [], "variablesTest": {"condition": "", "maxRuns": 100}, "name": "CLE13. True false", "preamble": {"js": "", "css": ""}, "advice": "See all the lectures and workshops up to this point.

", "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/"}]}