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{"name": "Algebra. Trigonometric identities. I", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebra. Trigonometric identities. I", "tags": [], "metadata": {"description": "<p>several statements are given regarding trig identities. student is to select which are true and which are false</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>See&nbsp;?? and the formula sheet.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"statements_false": {"name": "statements_false", "group": "change these", "definition": "[\"The formula $\\\\tan(A) = \\\\frac{\\\\sin(A)}{\\\\cos(A)}$ is not in the formula sheet\",\n  \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is in the formula sheet\",\n  \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is not in the formula sheet\",\n  \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)- \\\\frac{1}{2} $\",\n  \"$\\\\sin^2(z) = \\\\frac{1}{2} \\\\cos(2z) -\\\\frac{1}{2}$\",\n  \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n  \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n  \"$\\\\cot(\\\\theta) = \\\\tan^{-1}(x)$\",\n  \"$\\\\sin(-a) = \\\\sin\\\\times (-a) $\",\n  \"$-\\\\cos(q) = \\\\cos(-q) $\"\n]", "description": "", "templateType": "anything", "can_override": false}, "statements_true": {"name": "statements_true", "group": "change these", "definition": "[\"The formula $\\\\tan(A) = \\\\frac{\\\\sin(A)}{\\\\cos(A)}$ is in the formula sheet\",\n  \"The formula $\\\\cos(A+2\\\\pi) = \\\\cos(A)$ is not in the formula sheet\",\n  \"The formula $\\\\cos(2A) = 1-2\\\\sin^2(A)$ is in the formula sheet\",\n  \"$\\\\cos^2(t) = \\\\frac{1}{2} \\\\cos(2t)+ \\\\frac{1}{2} $\",\n  \"$\\\\sin^2(z) = \\\\frac{1}{2} - \\\\frac{1}{2} \\\\cos(2z) $\",\n  \"$\\\\sec(\\\\theta) = \\\\frac{1}{\\\\cos(\\\\theta)}$\",\n  \"$\\\\csc(\\\\theta) = \\\\frac{1}{\\\\sin(\\\\theta)}$\",\n  \"$\\\\cot(\\\\theta) = \\\\frac{1}{\\\\tan(\\\\theta)}$\",\n  \"$\\\\sin(-a) = -\\\\sin(a) $\",\n  \"$\\\\cos(q) = \\\\cos(-q) $\"\n]\n ", "description": "", "templateType": "anything", "can_override": false}, "error": {"name": "error", "group": "change these", "definition": "1/4", "description": "", "templateType": "anything", "can_override": false}, "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))", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "change these", "definition": "len(statements_true)", "description": "", "templateType": "anything", "can_override": false}, "max_mark": {"name": "max_mark", "group": "change these", "definition": "4", "description": "", "templateType": "anything", "can_override": false}, "rand": {"name": "rand", "group": "do not change these", "definition": "repeat(if(random(0..3)=3,1,0),n)", "description": "", "templateType": "anything", "can_override": false}, "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", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "change these", "variables": ["statements_true", "statements_false", "max_mark", "n", "error"]}, {"name": "do not change these", "variables": ["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": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<ul>\n<li>Which of the following are true and which are false? If you are unsure of something,&nbsp;find out the answer instead of guessing.</li>\n<li>Each error will cost&nbsp;1 of the available marks.</li>\n<li>The formula sheet is at the end of the module handbook. A digital copy of the handbook is available on Blackboard.</li>\n</ul>", "minMarks": 0, "maxMarks": "0", "minAnswers": "{n}", "maxAnswers": 0, "shuffleChoices": true, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": "{statements}", "matrix": "{marks}", "layout": {"type": "all", "expression": ""}, "answers": ["<p>True</p>", "<p>False</p>"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}, {"name": "Doug Satterford", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3185/"}]}