// Numbas version: finer_feedback_settings
{"name": "F\u00fcnfte Proportion", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "F\u00fcnfte Proportion", "tags": [], "metadata": {"description": "<p>Nach Nikomachos: Ermitteln der 5. Proportion</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Nach Nikomachos stehen drei Zahlen $a&lt;b&lt;c$ dann in der \"f&uuml;nften Proportion\", wenn die mittlere Zahl sich zur kleinere Zahl verh&auml;lt, wie sich deren Differenz zur Differenz der gr&ouml;&szlig;eren Zahl und der mittleren Zahl verh&auml;lt.</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 1551px; width: 0px; top: 25px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 1536px; width: 50px; top: 10px; height: 20px; font-size: 10px; color: black;\"></span></p>", "advice": "<p>a) Es gilt: $b:a=(b-a):(c-a)$</p>\n<p>b) Durch probieren (oder aufl&ouml;sen der Gleichung oben) kann man mehrere L&ouml;sungen finden, eine m&ouml;gliche L&ouml;sung ist $2, 4, 5$, sowie alle ganzzahligen Vielfachen dieser L&ouml;sung.</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet('https://www.geogebra.org/m/ezesj2ms')\n\n", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["app"], "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>Beschreiben Sie die Proportion durch eine Gleichung in den Variablen $a,b,c$:</p>\n<p style=\"text-align: center;\">$\\Big($[[0]]$\\Big):\\Big($[[1]]$\\Big)=\\Big($[[2]]$\\Big):\\Big($[[3]]$\\Big)$</p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 149px; width: 0px; top: 28px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 134px; width: 50px; top: 13px; height: 20px; font-size: 10px; color: black;\"></span></p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "t1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "b", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "b", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "t2", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "a", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "a", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "t3", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "b-a", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "a", "value": ""}, {"name": "b", "value": ""}]}, {"type": "jme", "useCustomName": true, "customName": "t4", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "c-b", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": true, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "b", "value": ""}, {"name": "c", "value": ""}]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {"constructor": {"script": "this.marks=3", "order": "after"}}, "customMarkingAlgorithm": "a:\n value(app,\"a\")\n\nb:\n value(app,\"b\")\n\nc:\n value(app,\"c\")\n\nmark:\n  correctif(b/a=(b-a)/(c-b))\n\ninterpreted_answer:\n  [a,b,c]", "extendBaseMarkingAlgorithm": false, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finden Sie drei nat&uuml;rliche Zahlen $a&lt;b&lt;c$, die in f&uuml;nfter Proportion stehen:</p>\n<p>{app}</p>", "gaps": [{"type": "extension", "useCustomName": true, "customName": "ggb", "marks": 1, "scripts": {"constructor": {"script": "this.marks=3", "order": "after"}}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}]}], "contributors": [{"name": "Andreas Vohns", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3622/"}]}