// Numbas version: exam_results_page_options
{"name": "Find coordinates of stationary points of polynomials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"y12": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2(x12^3)-3(x12+x22)*x12^2+6*x12*x22*x12+c02", "description": "", "name": "y12"}, "y03": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "name": "y03"}, "y32": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y12<y22,y12,y22)", "description": "", "name": "y32"}, "c03": {"templateType": "anything", "group": "Ungrouped variables", "definition": "y03-((x03^3)/3-((x13+x23)/2)*x03^2+(x13*x23)*x03)", "description": "", "name": "c03"}, "y13": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(x13^3)/3-(x13+x23)*x13^2/2+x13*x23*x13+c03", "description": "", "name": "y13"}, "y23": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(x23^3)/3-((x13+x23)*x23^2)/2+x13*x23*x23+c03", "description": "", "name": "y23"}, "y43": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y13<y23,y23,y13)", "description": "", "name": "y43"}, "x03": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "name": "x03"}, "c02": {"templateType": "anything", "group": "Ungrouped variables", "definition": "y02-((2x02^3)-3(x12+x22)*x02^2+6(x12*x22)*x02)", "description": "", "name": "c02"}, "x43": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y13<y23,x23,x13)", "description": "", "name": "x43"}, "y0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "name": "y0"}, "y22": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2(x22^3)-3(x12+x22)*x22^2+6x12*x22*x22+c02", "description": "", "name": "y22"}, "c0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "y0-(2x0^3-3(x1+x2)*x0^2+6(x1*x2)*x0)", "description": "", "name": "c0"}, "x4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y1<y2,x2,x1)", "description": "", "name": "x4"}, "x2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except x1)", "description": "", "name": "x2"}, "y02": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "name": "y02"}, "x22": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except [x2,x12])", "description": "", "name": "x22"}, "x0": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "name": "x0"}, "y2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2x2^3-3(x1+x2)*x2^2+6*x1*x2*x2+c0", "description": "", "name": "y2"}, "y33": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y13<y23,y13,y23)", "description": "", "name": "y33"}, "y3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y1<y2,y1,y2)", "description": "", "name": "y3"}, "x3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y1<y2,x1,x2)", "description": "", "name": "x3"}, "x23": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except [x2,x13])", "description": "", "name": "x23"}, "x32": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y12<y22,x12,x22)", "description": "", "name": "x32"}, "x1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "name": "x1"}, "x12": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except x1)", "description": "", "name": "x12"}, "x33": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y13<y23,x13,x23)", "description": "", "name": "x33"}, "y1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "2x1^3-3*(x1+x2)*x1^2+6*x1*x2*x1+c0", "description": "", "name": "y1"}, "x42": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y12<y22,x22,x12)", "description": "", "name": "x42"}, "x02": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "name": "x02"}, "y4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y1<y2,y2,y1)", "description": "", "name": "y4"}, "y42": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(y12<y22,y22,y12)", "description": "", "name": "y42"}, "x13": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-3..3 except x1)", "description": "", "name": "x13"}}, "ungrouped_variables": ["y1", "y0", "y3", "y2", "y4", "y02", "y03", "x1", "x43", "x42", "y42", "y43", "x03", "x02", "y22", "y23", "x23", "x22", "x2", "x3", "x0", "c0", "c02", "x4", "x32", "x33", "x13", "y33", "y32", "x12", "c03", "y13", "y12"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Find coordinates of stationary points of polynomials", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "{x3}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y3}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{x4}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y4}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>For the following function:</p>\n<p>\\[ \\simplify{ y = 2x^3-{3*(x1+x2)}x^2+{x1*x2*6}x+{c0} } \\]</p>\n<p>Determine the coordinates and the nature of the stationary points.</p>\n<p>Minimum point: $\\big($ [[0]] $ , $ [[1]] $\\big)$ and maximum point: $\\big($ [[2]] $ , $ [[3]] $\\big)$</p>\n<p>Enter fractions in their simplest form.</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{x32}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y32}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{x42}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y42}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>For the following function:</p>\n<p>\\[ \\simplify{y = 2x^3-3{(x12+x22)}x^2+6{x12*x22}x+{c02}} \\]</p>\n<p>Determine the coordinates and the nature of the stationary points.</p>\n<p>Minimum point: $\\big($ [[0]] $ , $ [[1]] $\\big)$ and maximum point: $\\big($ [[2]] $ , $ [[3]] $\\big)$</p>\n<p>Enter fractions in their simplest form.</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"answer": "{x33}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y33}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{x43}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}, {"answer": "{y43}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "checkvariablenames": false, "expectedvariablenames": [], "showpreview": false, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "all,fractionNumbers", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "<p>For the following function:</p>\n<p>\\[ \\simplify[All,fractionNumbers]{y = {1}/{3}x^3-{(x13+x23)}/{2}x^2+{x13*x23}x+{c03}} \\]</p>\n<p>Determine the coordinates and the nature of the stationary points.</p>\n<p>Minimum point: $\\big($ [[0]] $ , $ [[1]] $\\big)$ and maximum point: $\\big($ [[2]] $ , $ [[3]] $\\big)$</p>\n<p>Enter fractions in their simplest form.</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "", "tags": ["ACC1012", "acc1012", "checked2015"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Finding the coordinates and determining the nature of the stationary points on a polynomial function</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}