// Numbas version: exam_results_page_options
{"name": "Numbastest uke 41: Integrasjon", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", ""], "variable_overrides": [[], [], [], [], []], "questions": [{"name": "Spesielle integrasjonsregler ubestemte integraler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><strong>Finn de ubestemte integralene under. </strong></p>\n<p>Hint: For &aring; skrive inn f.eks. $\\frac{1}{x^3}$ b&oslash;r man skrive 1/(x^3), for &aring; skrive inn $\\cos^2x$ b&oslash;r man skrive (cos(x))^2. 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"can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>\\[ \\simplify{{out1}}(\\simplify{{inp1}})=\\simplify{{k1}*sin({k3}{inp1})-{k2}*{inp1}^{{a}}+1/{inp1}},&nbsp; \\var{inp1}&gt;0\\]</p>\n<p>\\[ \\int \\simplify{{out1}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-k1/k3}*cos({k3}*{inp1})-{k2/(a+1)}*{inp1}^({a+1})+ln({inp1})+c", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "c", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Bestemte integraler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><strong>Finn de bestemte integralene under</strong></p>", "advice": "<p>Bruk f&oslash;lgende spesielle integrasjonsregler</p>\n<p>\\[ \\int a dx =ax+C\\]&nbsp; ($a$ er et konstant)</p>\n<p>\\[ \\int x^n dx =\\frac{1}{n+1}x^{n+1}+C\\]&nbsp; ($n$ er et reelttall, $n\\neq -1$)</p>\n<p>\\[ \\int \\cos(x) dx =\\sin(kx)+C\\]&nbsp;</p>\n<p>\\[ \\int \\frac{1}{x} dx =\\ln(x)+C\\] ($k$ er et konstant)</p>\n<p>Bruk analysens fundamentalteorem</p>\n<p>Hvis $f$ og $F$ er kontinuerlige p&aring; $[a,b]$ og $F'(x)=f(x)$ for alle $x\\in(a,b)$ s&aring; er</p>\n<p>\\[ \\int\\limits_{a}^{b} f(x)dx=F(b)-F(a)</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp1": {"name": "inp1", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out1": {"name": "out1", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(-3..3 except 0 except -1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..33)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "inp2": {"name": "inp2", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp3": {"name": "inp3", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp4": {"name": "inp4", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp5": {"name": "inp5", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp6": {"name": "inp6", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp7": {"name": "inp7", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp8": {"name": "inp8", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out2": {"name": "out2", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out3": {"name": "out3", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out4": {"name": "out4", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out5": {"name": "out5", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out6": {"name": "out6", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "low1": {"name": "low1", "group": "Ungrouped variables", "definition": "random(-2..1)", "description": "", "templateType": "anything", "can_override": false}, "up1": {"name": "up1", "group": "Ungrouped variables", "definition": "low1+2", "description": "", "templateType": "anything", "can_override": false}, "low2": {"name": "low2", "group": "Ungrouped variables", "definition": "random(-3..0)", "description": "", "templateType": "anything", "can_override": false}, "up2": {"name": "up2", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8", "low1", "up1", "low2", "up2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>\\[ \\simplify{{out1}}(\\simplify{{inp1}})=\\var{a} \\]</p>\n<p>\\[ \\int\\limits_{\\var{low1}}^{\\var{up1}} \\simplify{{out1}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}*{up1}-{a}*{low1}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>\\[ \\simplify{{out3}}(\\simplify{{inp1}})=\\simplify{{inp1}^{k1}}\\]</p>\n<p>\\[ \\int\\limits_{\\var{low2}}^{\\var{up2}} \\simplify{{out3}}(\\simplify{{inp1}})d\\simplify{{inp1}}= \\] [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{1/(k1+1)}*{up2}^({k1+1})-{1/(k1+1)}*{low2}^({k1+1})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>\\[ \\simplify{{out4}}(\\simplify{{inp4}})=\\cos(\\var{inp4})\\]</p>\n<p>\\[ \\int\\limits_{0}^{\\pi} \\simplify{{out4}}(\\simplify{{inp4}})d\\simplify{{inp4}}= \\] [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>\\[ \\simplify{{out2}}(\\simplify{{inp2}})=\\dfrac{1}{\\var{inp2}} \\]</p>\n<p>\\[ \\int\\limits_{1}^{e} \\simplify{{out2}}(\\simplify{{inp2}})d\\simplify{{inp2}}= \\][[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Arealberegning", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>P&aring; grafen under er det gitt en funksjon $f(x)=\\simplify{{a}*x^2+{b}*x+{c}}$ og en linje $l$ som g&aring;r gjennom punktene $(-1,\\simplify{{a-b+c}})$ og $(1,\\simplify{{a+b+c}})$</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/kdcfnghu',defs)}</p>", "advice": "<p>Bruk f&oslash;lgende definisjon:</p>\n<p>Hvis $f(x)\\geq g(x)$ p&aring; $[a,b]$, er arealet avgrenset av grafene til $f(x)$, $g(x)$, $x=a$ of $x=b$ ved folmelen</p>\n<p>\\[ A=\\int\\limits_a^b \\big(f(x)-g(x)\\big) dx \\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..-1)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['a',a],['b',b],['c',c]]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "defs"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>Finn likningen til linja $l: y=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{b}x+{a+c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn arealet avgrenset av funksjonen $f(x)$ og linja $l$ (det bl&aring; omr&aring;det).</p>", "minValue": "-4*{a}/3", "maxValue": "-4*{a}/3", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Volumberegning", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>P&aring; grafen nedenfor er det gitt en funksjon $f(x)=\\simplify{{a}*x+{b}}$ som roterer en gang om $x$-aksen. Omdreiningslegemet er avgrenset av linjene $x=\\var{x1}$ og $x=\\var{x2}$.</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/xsnnedmy',defs)}</p>", "advice": "<p>Volumet i opgavene a) og b) regnes ut ved bruk av formelen&nbsp;</p>\n<p>\\[V=\\pi \\int_a^b (f(x))^2dx \\]</p>\n<p>Volum til kjegle i oppgavene c) og d) regnes ut ved bruk av folmelen&nbsp;</p>\n<p>\\[V=\\dfrac{\\pi r^2 h}{3} \\]</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(3..5)", "description": "", "templateType": "anything", "can_override": false}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['a',a],['b',b],['x1',x1],['x2',x2]]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "x1", "x2", "defs"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "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": "<p>En av m&aring;tene &aring; beregne volumet av dette legemet er &aring; regne ut integralet&nbsp;</p>\n<p>$V=\\pi\\int_{\\var{x1}}^{\\var{x2}}$[[0]]$dx$</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "({a}*x+{b})^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Volumet av legemet er lik (for &aring; skrive inn $\\pi$ skriv pi, eller regn ut med minst tre desimaler)</p>", "answer": "(pi/{3*a})*(({a*x2+b})^3-({a*x1+b})^3)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "gapfill", "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": "<p>Den andre m&aring;ten for &aring; regne volumet av omdeiningslegemet er &aring; finne differansen mellom volumet til en stor kjegle $K_1$ og volumet til en mindre, liten kjegle $K_2$.</p>\n<p>Finner volumet til stor kjegle $K_1$&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/vyvysc6s',defs)}</p>\n<p>H&oslash;yden til kjegle er $h=$[[0]], radius av grunnflaten er $r=$[[1]]</p>\n<p>Volumet til den store kjeglen er $V_{K_1}=$[[2]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x2+b/a}", "maxValue": "{x2+b/a}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a*x2+b}", "maxValue": "{a*x2+b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "pi*({x2+b/a})*({a*x2+b})^2/3", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "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": "<p>Finner volumet til den lille kjeglen $K_2$&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/prqxcdtr',defs)}</p>\n<p>H&oslash;yden til kjegle er $h=$[[0]], radius av grunnflaten er $r=$[[1]]</p>\n<p>Volumet til den lille kjeglen er $V_{K_2}=$[[2]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x1+b/a}", "maxValue": "{x1+b/a}", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a*x1+b}", "maxValue": "{a*x1+b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "pi*({x1+b/a})*({a*x1+b})^2/3", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Regn ut volumet til det opprinnelige legemet</p>\n<p>$V=V_{K_2}-V_{K_1}=$</p>", "answer": "pi*({x2+b/a})*({a*x2+b})^2/3-pi*({x1+b/a})*({a*x1+b})^2/3", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "information", "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": "<p><strong>Sammenlikn resultatene fra oppgave b) og e).</strong></p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}