// Numbas version: finer_feedback_settings
{"name": "Quader mit quadratischer Grundfl\u00e4che (GGB)", "extensions": ["geogebra"], "custom_part_types": [], "resources": [["question-resources/quadrat-quader.png", "/srv/numbas/media/question-resources/quadrat-quader.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Quader mit quadratischer Grundfl\u00e4che (GGB)", "tags": [], "metadata": {"description": "<p>Variante der Aufgabe&nbsp;<a href=\"https://aufgabenpool.at/ahs/Typ-1/271/Quader%20mit%20quadratischer%20Grundfl%C3%A4che.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>1_562</strong></a> (ehemalige Klausuraufgabe, AHS-Maturatermin: 10. Mai 2017)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<h3>Quader mit quadratischer Grundfl&auml;che</h3>\n<p>Die nachstehende Abbildung zeigt einen Quader, dessen quadratische Grundfl&auml;che in der $xy$-Ebene liegt. Die L&auml;nge einer Grundkante betr&auml;gt {a*multi}&nbsp;L&auml;ngeneinheiten, die K&ouml;rperh&ouml;he&nbsp;betr&auml;gt {b*multi}&nbsp;L&auml;ngeneinheiten. Der Eckpunkt $D$ liegt im Koordinatenursprung, der Eckpunkt $C$ liegt auf der positiven <nobr>$y$-Achse.</nobr></p>\n<p>Der Eckpunkt $E$ hat somit die Koordinaten $E = \\left(\\var{a*multi}\\mid 0\\mid\\var{b*multi}\\right)$.</p>\n<p style=\"text-align: center;\">{app}</p>", "advice": "<p>Man ermittelt als Koordinaten der Eckpunkte:</p>\n<p>$A=\\left(\\var{a*multi}\\mid0\\mid0\\right),B=\\left(\\var{a*multi}\\mid\\var{a*multi}\\mid0\\right),H=\\left(0\\mid0\\mid \\var{b*multi}\\right),G=\\left(0\\mid\\var{a*multi}\\mid\\var{b*multi}\\right)$</p>\n<p>Somit ergibt sich f&uuml;r den gesuchten Vektor (im Bild unten rot) {latex(vektor[auswahl])}$=\\var{loesungen[auswahl]}$</p>\n<p>{app2}</p>", "rulesets": {}, "extensions": ["geogebra"], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(4..8)", "description": "", "templateType": "anything"}, "vektor": {"name": "vektor", "group": "Ungrouped variables", "definition": "['\\\\overrightarrow\\{HB\\}','\\\\overrightarrow\\{BH\\}','\\\\overrightarrow\\{AG\\}','\\\\overrightarrow\\{GA\\}']", "description": "", "templateType": "anything"}, "loesungen": {"name": "loesungen", "group": "Ungrouped variables", "definition": "[vector(a*multi,-a*multi,b*multi),vector(-a*multi,a*multi,-b*multi),vector(-a*multi,a*multi,b*multi),vector(a*multi,-a*multi,-b*multi)]", "description": "", "templateType": "anything"}, "auswahl": {"name": "auswahl", "group": "Ungrouped variables", "definition": "random(0..3)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(8..12)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['a',a],['b',b]]", "description": "", "templateType": "anything"}, "app": {"name": "app", "group": "Ungrouped variables", "definition": "geogebra_applet('https://www.geogebra.org/m/tmwmt8sa',defs)", "description": "", "templateType": "anything"}, "multi": {"name": "multi", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything"}, "defs2": {"name": "defs2", "group": "Ungrouped variables", "definition": "[['a',a],['b',b],['n',auswahl]]", "description": "", "templateType": "anything"}, "app2": {"name": "app2", "group": "Ungrouped variables", "definition": "geogebra_applet('https://www.geogebra.org/m/d7bbz5pz',defs2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "vektor", "loesungen", "auswahl", "b", "defs", "app", "multi", "defs2", "app2"], "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><strong>Aufgabenstellung:</strong></p>\n<p>Geben Sie die Koordinaten (Komponenten) des Vektors {latex(vektor[auswahl])}&nbsp;an!</p>\n<p>{latex(vektor[auswahl])}$=$[[0]]</p>\n<p><sub><em>Variante der Aufgabe-Nr. <strong><a href=\"https://aufgabenpool.at/ahs/Typ-1/271/Quader%20mit%20quadratischer%20Grundfl%C3%A4che.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">1_562</a></strong>,&nbsp;ehemalige Klausuraufgabe, &ouml;sterreichischer AHS-Maturatermin: 10. Mai 2017</em></sub></p>\n<p><span style=\"margin: 0px auto; border: 2px dotted #000000; position: absolute; z-index: 2147483647; visibility: hidden; left: 54px; width: 0px; top: 132px; height: 0px;\"></span><span style=\"z-index: 2147483647; position: absolute; visibility: hidden; left: 39px; width: 50px; top: 117px; height: 20px; font-size: 10px; color: black;\"></span></p>", "gaps": [{"type": "matrix", "useCustomName": true, "customName": "vektor", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "loesungen[auswahl]", "correctAnswerFractions": false, "numRows": "3", "numColumns": 1, "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false}], "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/"}]}