// Numbas version: exam_results_page_options
{"name": "Algebraiske uttrykk 2", "extensions": [], "custom_part_types": [], "resources": [["question-resources/intervaller_KhNBw2K.PNG", "/srv/numbas/media/question-resources/intervaller_KhNBw2K.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Algebraiske uttrykk 2", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "", "advice": "<p>a) L&oslash;ser likningen $\\var{a}x+\\var{b}=\\var{c}$&nbsp;</p>\n<p>$\\var{a}x=\\var{c}-\\var{b}$</p>\n<p>$\\var{a}x=\\var{c-b}$</p>\n<p>$\\frac{\\var{a}x}{\\var{a}}=\\frac{\\var{c-b}}{\\var{a}}$</p>\n<p>$x=\\simplify{{(c-b)/a}}$</p>\n<p>L&oslash;ser likningen $x^2+\\var{a}x=0$</p>\n<p>$x(x+\\var{a})=0$&nbsp; $\\Leftrightarrow$ $x=0$ $\\vee$ $\\simplify{x+{a}}=0$&nbsp; $\\Leftrightarrow$ $x=0$ $\\vee$ $x=\\simplify{{{-a}}}$</p>\n<p>L&oslash;ser linkningen $\\simplify{x^2+{m+n}x+{m*n}}=0$.&nbsp;</p>\n<p>Bruker $abc$-formelen: $x=\\frac{-(\\var{m+n})\\pm\\sqrt{(\\var{m+n})^2-4\\cdot1\\cdot(\\var{m*n})}}{2\\cdot1}=\\frac{\\simplify{{-m-n}}\\pm\\sqrt{\\simplify{{(m+n)^2-4*m*n}}}}{2}=\\frac{\\simplify{{-m-n}}\\pm{\\simplify{{sqrt((m+n)^2-4*m*n)}}}}{2}$</p>\n<p>$x=\\simplify{{-m}}$ $\\vee$&nbsp;$x=\\simplify{{-n}}$</p>\n<p>b) Nullpunkter til polynomet $\\simplify{x^2+{m+n}x+{m*n}}$ er&nbsp; $x=\\simplify{{-m}}$ og $x=\\simplify{{-n}}$.&nbsp; &nbsp;</p>\n<p>Da uttrykket kan faktoriseres som $\\simplify{x^2+{m+n}x+{m*n}}=\\simplify{(x+{m})(x+{n})}$</p>\n<p>c)$\\simplify{(x^2+{m+n}x+{m*n})/((x+{m})^2)}=\\frac{\\simplify{(x+{m})(x+{n})}}{\\simplify{(x+{m})(x+{m})}}=\\frac{\\simplify{x+{n}}}{\\simplify{x+{m}}}$</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2 .. 8#2)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped 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"description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "max(-m,-n)", "description": "", "templateType": "anything"}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "min(-m,-n)", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "min(0,-a)", "description": "", "templateType": "anything"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "max(0,-a)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "m", "n", "k", "l", "p", "q"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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>Gang sammen de to parentesene og forenkle uttrykket</p>\n<p>$\\var{a}(x-\\var{b})(x-\\var{c})$</p>", "answer": "{a}*x^2-{(a*(b+c))}*x+{a*b*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, "mustmatchpattern": {"pattern": "`+-($n`?*x^2)+`+-($n`?*x) + `+- $n`?", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": 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"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>L&oslash;s f&oslash;lgende likninger med hensyn p&aring; $x$</p>\n<p>$\\var{a}x+\\var{b}=\\var{c}$&nbsp; &nbsp;$\\Leftrightarrow$&nbsp; &nbsp;$x=$ [[0]]</p>\n<p>$x^2+\\var{a}x=0$ $\\Leftrightarrow$ $x=$ [[3]]&nbsp; eller $x=$ [[4]] (skriv inn l&oslash;sningene fra minste til st&oslash;rste)</p>\n<p>$\\simplify{x^2+{m+n}x+{m*n}}=0$&nbsp; &nbsp;$\\Leftrightarrow$&nbsp; &nbsp;$x=$ [[1]]&nbsp; eller $x=$ [[2]] (skriv inn l&oslash;sningene fra minste til st&oslash;rste)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], 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"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": "{k}", "maxValue": "{k}", "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": "{p}", "maxValue": "{p}", "correctAnswerFraction": false, "allowFractions": false, "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": "{q}", "maxValue": "{q}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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>Faktoriser&nbsp;$\\simplify{x^2+{m+n}x+{m*n}}$</p>", "answer": "(x+{m})(x+{n})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "mustmatchpattern": {"pattern": "((`+-($n`?*x) + `+- $n`?)^$n`?)`* * $z", "partialCredit": 0, "message": "", "nameToCompare": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": 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