// Numbas version: exam_results_page_options
{"name": "Integration: standard integrals, multiple simple terms, randomised", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Integration: standard integrals, multiple simple terms, randomised", "tags": [], "metadata": {"description": "<p>Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)</p>", "licence": "None specified"}, "statement": "", "advice": "<p>See&nbsp;??</p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "coeffs etc", "definition": "shuffle(repeat(random(2..9),5) + [-1,-1,1,random(-1,1)])", "description": "", "templateType": "anything"}, "var": {"name": "var", "group": "coeffs etc", "definition": "random(['x','z','t','p','s','r','w'])", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f[rand[j]][0]+var+ f[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "coeffs etc", "definition": "2", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "coeffs etc", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "f": {"name": "f", "group": "functions", "definition": "[\n  [\"(1*\",\")\"],\n  [\"(\",\")^\"+n1],\n  [\"(\",\")^\"+n2],\n  [\"1/(\",\")\"],\n  [\"1/((\",\")^\"+n3+\")\"],\n  [\"sqrt(\",\")\"],\n  [\"sin(\",\")\"],\n  [\"cos(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"ln(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "shuffle([1,2,random(6..7),8,9])+shuffle([6,7,1,random(8,9)])", "description": "<p>[<br />0[\"(\"+b0[0]+\"*\",\")\"],<br />1[\"(\",\")^\"+n1],<br />2[\"(\",\")^\"+n2],<br />3[\"1/(\",\")\"],<br />4[\"1/((\",\")^\"+n3+\")\"],<br />5[\"sqrt(\",\")\"],<br />6[\"sin(\",\")\"],<br />7[\"cos(\",\")\"],<br />8[\"e^(\",\")\"],<br />9[\"ln(\",\")\"]<br /> ]</p>\n<p></p>\n<p>don't use 0 for product rule</p>", "templateType": "anything"}, "f'": {"name": "f'", "group": "functions", "definition": "[\n  [\"(1*(\",\"^0))\"],\n  [n1+\"*(\",\")^\"+(n1-1)],\n  [n2+\"*(\",\")^\"+(n2-1)],\n  [\"-1/((\",\")^2)\"],\n  [\"-\"+n3+\"/((\",\")^\"+(n3+1)+\")\"],\n  [\"0.5/(sqrt(\",\"))\"],\n  [\"cos(\",\")\"],\n  [\"-sin(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"1/(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "f0'": {"name": "f0'", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f'[rand[j]][0]+var+ f'[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "coeffs etc", "definition": "1", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rand"], "variable_groups": [{"name": "coeffs etc", "variables": ["var", "n1", "n2", "n3", "a"]}, {"name": "functions", "variables": ["f", "f'", "f0", "f0'"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Integrate the following with respect to&nbsp;$\\simplify{{expression(var)}}$.</p>\n<p></p>\n<p>$\\simplify{{f0'[0]}+{f0'[1]}}$.</p>\n<p>[[0]]</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>$\\simplify{{f0'[2]}+{f0'[3]}+{f0'[4]}}$.</p>\n<p>[[1]]</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p>$\\simplify{{f0'[5]}+{f0'[6]}+{f0'[7]}+{f0'[8]}}$.</p>\n<p>[[2]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[0]}+{f0[1]}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[2]}+{f0[3]}+{f0[4]}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0[5]}+{f0[6]}+{f0[7]}+{f0[8]}+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": [{"name": "c", "value": ""}]}], "sortAnswers": false}], "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/"}]}