// Numbas version: exam_results_page_options {"name": "Blathnaid's copy of sp\u00f8rsm\u00e5l 6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "showCorrectAnswer": true, "prompt": "

Løs andregradslikningen $\\simplify{x^2 +{r1+r2}x+{r1*r2}}=0\\text{.}$

\n

Skriv svaret nedenfor som $x_1$ og $x_2$, da $x_1<x_2$

\n\n

$x_1=$ [[0]] (NB:  $x_1<x_2$)

\n

$x_2=$ [[1]]

", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "minValue": "-r2", "variableReplacementStrategy": "originalfirst", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "-r2"}, {"type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "minValue": "-r1", "variableReplacementStrategy": "originalfirst", "marks": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "-r1"}], "unitTests": [], "scripts": {}}, {"type": "gapfill", "showCorrectAnswer": true, "prompt": "

Faktoriser andregradsuttrykket $\\simplify{x^2 +{r1+r2}x+{r1*r2}}\\text{.}$

\n

$\\simplify{x^2 +{r1+r2}x+{r1*r2}}$=[[0]]

", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "gaps": [{"type": "jme", "failureRate": 1, "unitTests": [], "showCorrectAnswer": true, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "variableReplacements": [], "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["^"]}, "answer": "(x+{r2})(x+{r1})", "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "customMarkingAlgorithm": "", "checkVariableNames": false, "musthave": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["(", ")"]}, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "marks": 1, "checkingType": "absdiff", "showFeedbackIcon": true, "showPreview": true, "scripts": {}}], "unitTests": [], "scripts": {}}, {"type": "gapfill", "showCorrectAnswer": true, "prompt": "

Løs ulikheten $\\simplify{x^2 +{r1+r2}x+{r1*r2}}>0\\text{.}$

\n

Svar:

\n

$x>$ [[0]]

\n

[[2]]

\n

$x<$ [[1]]

", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "marks": 0, "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "minValue": "-r1", "variableReplacementStrategy": "originalfirst", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "-r1"}, {"type": "numberentry", "showCorrectAnswer": true, "scripts": {}, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "customMarkingAlgorithm": "", "minValue": "-r2", "variableReplacementStrategy": "originalfirst", "marks": 1, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "unitTests": [], "mustBeReducedPC": 0, "allowFractions": false, "maxValue": "-r2"}, {"matrix": [0, "1"], "choices": ["

Og

", "

eller

"], "showCorrectAnswer": true, "variableReplacements": [], "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "displayType": "radiogroup", "marks": 0, "type": "1_n_2", "showFeedbackIcon": true, "displayColumns": 0, "unitTests": [], "minMarks": 0, "scripts": {}, "shuffleChoices": false}], "unitTests": [], "scripts": {}}], "ungrouped_variables": ["t1", "t2", "t3", "t4"], "variables": {"b": {"definition": "-a", "description": "", "templateType": "anything", "name": "b", "group": "Part A "}, "v2": {"definition": "random(2..6 except [v1,-v1])", "description": "", "templateType": "anything", "name": "v2", "group": "Part A "}, "b1": {"definition": "random(2..6)", "description": "", "templateType": "anything", "name": "b1", "group": "last q"}, "t1": {"definition": "random(1..2)", "description": "", "templateType": "anything", "name": "t1", "group": "Ungrouped variables"}, "r1": {"definition": "random(-9..7 except 0..1)", "description": "", "templateType": "anything", "name": "r1", "group": "Part B"}, "b3": {"definition": "random(1..10)", "description": "", "templateType": "anything", "name": "b3", "group": "last q"}, "t2": {"definition": "random(1..4)", "description": "", "templateType": "anything", "name": "t2", "group": "Ungrouped variables"}, "b2": {"definition": "random(1..6)", "description": "", "templateType": "anything", "name": "b2", "group": "last q"}, "a": {"definition": "random(2..10)", "description": "", "templateType": "anything", "name": "a", "group": "Part A "}, "v3": {"definition": "v5*v6+v4", "description": "", "templateType": "anything", "name": "v3", "group": "Part A "}, "v6": {"definition": "random(2..10 except v5 -v5)", "description": "", "templateType": "anything", "name": "v6", "group": "Part A "}, "v1": {"definition": "random(-9..10 except 0)", "description": "", "templateType": "anything", "name": "v1", "group": "Part A "}, "t4": {"definition": "t2*random(-4..6 except 0)", "description": "", "templateType": "anything", "name": "t4", "group": "Ungrouped variables"}, "v5": {"definition": "random(-8..10 except 0 v1 v2)", "description": "", "templateType": "anything", "name": "v5", "group": "Part A "}, "t3": {"definition": "random(t4*t1/t2..10 #1 except 0)", "description": "", "templateType": "anything", "name": "t3", "group": "Ungrouped variables"}, "r2": {"definition": "random(r1..9 except 0 r1 -r1)", "description": "", "templateType": "anything", "name": "r2", "group": "Part B"}, "b4": {"definition": "random(-8..8 except 0)", "description": "", "templateType": "anything", "name": "b4", "group": "last q"}, "v4": {"definition": "random(2..20)", "description": "", "templateType": "anything", "name": "v4", "group": "Part A "}}, "rulesets": {}, "advice": "", "variable_groups": [{"name": "Part A ", "variables": ["v6", "v5", "v4", "v3", "v2", "v1", "a", "b"]}, {"name": "Part B", "variables": ["r2", "r1"]}, {"name": "last q", "variables": ["b1", "b2", "b3", "b4"]}], "name": "Blathnaid's copy of sp\u00f8rsm\u00e5l 6", "functions": {}, "metadata": {"description": "

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "statement": "

Andregradslikningen $ax^2+bx+c=0$ har løsningene

\n

\$x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a},\\space \\text{når}\\space b^2-4ac\\geq0\\text{.}\$

\n

Dersom andregradsuttrykket $ax^2+bx+c$ har nullpunktene $x=x_{1}$ og $x=x_{2}$ kan det faktoriseres til  $a(x-x_{1})(x-x_{2}).$

", "type": "question", "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}]}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Ida Landg\u00e4rds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2336/"}]}