// Numbas version: exam_results_page_options
{"name": "Gleichungen bei Diophant", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Gleichungen bei Diophant", "tags": [], "metadata": {"description": "<p>L&ouml;sen einer quadratischen Gleichung im Stile Diophants</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Wir betrachten ein weiteres Problem der Form: Zwei Zahlen finden, deren Summe und deren Summe der Quadrate der Zahlen gegeben sind.</p>\n<p>Summe sei $\\var{sum}$, Quadratsumme&nbsp;$\\var{qsum}$.</p>\n<p>Wir bezeichnen die Differenz der beiden Zahlen mit $2\\cdot x$.</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 709px; width: 0px; top: 36px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 694px; width: 50px; top: 21px; height: 20px; font-size: 10px; color: black;\"></span></p>", "advice": "<p>a) Es ist $a=\\frac{\\var{sum}}{2}-x=\\var{sum/2}-x$,&nbsp;$b=\\frac{\\var{sum}}{2}+x=\\var{sum/2}+x$.</p>\n<p>b) Es ergibt sich: $\\var{qsum}=2\\cdot\\var{(sum/2)^2}+2x^2\\Leftrightarrow x^2=\\frac{\\var{qsum}-\\var{2*(sum/2)^2}}{2}=\\frac{\\var{(qsum-2*(sum/2)^2)}}{2}=\\var{(qsum-2*(sum/2)^2)/2}\\Leftrightarrow x=\\var{x}$</p>", "rulesets": {}, "extensions": [], "variables": {"sum": {"name": "sum", "group": "Ungrouped variables", "definition": "random(4..8)*10", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "sum/2-x", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "sum/2+x", "description": "", "templateType": "anything"}, "qsum": {"name": "qsum", "group": "Ungrouped variables", "definition": "a^2+b^2", "description": "", "templateType": "anything"}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(5..15)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["sum", "a", "b", "qsum", "x"], "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>Dann ist die kleinere der beiden Zahlen $a=$[[0]] und die gr&ouml;&szlig;ere der beiden Zahlen $b=$[[1]].</p>\n<p><em>Jeweils einen Term in Abh&auml;ngigkeit von $x$ eintragen!</em></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "a", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum/2}-x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "musthave": {"strings": ["x"], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "b", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{sum/2}+x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "musthave": {"strings": ["x"], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": [{"name": "x", "value": ""}]}], "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>Durch Einsetzen dieser Terme in $\\var{qsum}=a^2+b^2$ ermittelt man daraus:</p>\n<p>$x=$[[2]] ,&nbsp;$a=$[[0]] ,&nbsp;$b=$[[1]]</p>\n<p><span style=\"margin: 0px auto; 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