// Numbas version: exam_results_page_options
{"name": "CLE16. True false", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "CLE16. True false", "tags": [], "metadata": {"description": "<p>15 questions based on module&nbsp;so far.&nbsp;</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>See all the lectures and workshops up to this point.</p>", "rulesets": {}, "extensions": [], "variables": {"max_mark": {"name": "max_mark", "group": "change these", "definition": "10", "description": "", "templateType": "anything"}, "marks": {"name": "marks", "group": "do not change these", "definition": "matrix(map(if(rand[j]=1,[max_mark/n,-max_mark],[-max_mark,max_mark/n]),j,0..n-1))\n", "description": "", "templateType": "anything"}, "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"}, "statements_true": {"name": "statements_true", "group": "change these", "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  \"$\\\\sin^{-1}(1) = \\\\pi/2$\",\n  \"If $u=\\\\cos(x)$, then $\\\\frac{du}{dx} = -\\\\sin(x)$\",\n  \"If $x = \\\\sin(u)$,then $\\\\frac{dx}{du} = \\\\cos(u)$\",\n  \"In a differential equation, the unknown quantity is a function.\",\n  \"The formula $\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{b} = a_1b_1+a_2b_2+a_3b_3$ is not in the formula booklet.\",\n  \"The formula $\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{b} = |\\\\boldsymbol{a}||\\\\boldsymbol{b}| \\\\cos(\\\\theta)$ is in the formula booklet.\",\n  \"$\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{a}$ equals $a^2$\",\n  \"If $\\\\boldsymbol{a}$ and $\\\\boldsymbol{b}$ are perpendicular, then $\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{b}=0$\",\n  \"$A_{12}$ is the entry in the 1st row and 2nd column of $A$\",\n  \"To calculate $C_{21}$, you use the 2nd row of $A$ and the 1st column of $B$.\",\n  \"To calculate $C_{22}$, you use the 2nd row of $A$ and the 2nd column of $B$.\",\n  \"To calculate $D_{12}$, you use the 1st row of $B$ and the 2nd column of $A$.\",\n  \"$C$ will be a $2 \\\\times 2$-matrix\"\n]", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(0..2)=2,1,0),n)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "change these", "definition": "length(statements_true)", "description": "", "templateType": "anything"}, "statements_false": {"name": "statements_false", "group": "change these", "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  \"$\\\\sin^{-1}(1) = \\\\frac{1}{\\\\sin(1)}$\",\n  \"If $u=\\\\cos(x)$, then $\\\\frac{dx}{du} = -\\\\sin(x)$\",\n  \"If $x = \\\\sin(u)$,then $\\\\frac{du}{dx} = \\\\cos(u)$\",\n  \"In a differential equation, the unknown quantity is a number.\",\n  \"The formula $\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{b} = a_1b_1+a_2b_2+a_3b_3$ is in the formula booklet.\",\n  \"The formula $a \\\\cdot b = |\\\\boldsymbol{a}||\\\\boldsymbol{b}| \\\\cos(\\\\theta)$ is in the formula booklet.\",\n  \"$\\\\boldsymbol{a} \\\\cdot \\\\boldsymbol{a}$ equals $\\\\boldsymbol{a}^2$\",\n  \"If $\\\\boldsymbol{a}$ and $\\\\boldsymbol{b}$ are perpendicular, then $a \\\\cdot b=0$.\",\n  \"$A_{12}$ is the entry in the 2nd row and 1st column of $A$.\",\n  \"To calculate $C_{21}$, you use the 1st row of $A$ and the 2nd column of $B$.\",\n  \"To calculate $C_{22}$, you use the 2nd row of $A$ and the 2nd row of $B$.\",\n  \"To calculate $D_{12}$, you multiply $B_{12}$ and $C_{12}$.\",\n  \"The size of $A$ is $4$.\"\n]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n"]}, {"name": "do not change these", "variables": ["rand", "statements", "marks"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "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>\n<p></p>\n<p>For the following:</p>\n<ul>\n<li>$\\boldsymbol{a} = \\simplify{matrix([a_1],[a_2],[a_3])}$</li>\n<li>$\\boldsymbol{b} = \\simplify{matrix([b_1],[b_2],[b_3])}$</li>\n<li>$a = |\\boldsymbol{a}|$ and $b&nbsp;= |\\boldsymbol{b}|$</li>\n<li>$A$ and $B$ are $2 \\times 2$-matrices.</li>\n<li>$C=AB$ and $D=BA$.</li>\n</ul>\n<p></p>\n<p>Make sure you check for the difference between bold letters (e.g. $\\boldsymbol{a}$) and non-bold letters (e.g. $a$).</p>", "minMarks": 0, "maxMarks": "0", "minAnswers": "{n}", "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "choices": "{statements}", "matrix": "{marks}", "layout": {"type": "all", "expression": ""}, "answers": ["<p>True</p>", "<p>False</p>"]}], "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/"}]}