// Numbas version: finer_feedback_settings
{"name": "Bedienung von Numbas: Funktionen eingeben", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Bedienung von Numbas: Funktionen eingeben", "tags": [], "metadata": {"description": "<p>Dealing with functions in Numbas. (Translation to German.)</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Funktionen</strong></p>\n<ol>\n<li>Das Numbas-System erkennt alle \"Standardfunktionen\", aber Sie m&uuml;ssen Klammern setzen, zum Beispiel&nbsp; <code>sin(x)</code> statt <code>sin x</code>, <code>ln(a)</code> statt <code>ln a</code>.</li>\n<li>Den Absolutbetrag der Zahl $a$, den wir &uuml;blicherweise als $|a|$ schreiben, m&uuml;ssen Sie als <code>abs(a)</code> eingeben.</li>\n<li>Die Umkehrfunktionen $\\arcsin(x)$, $\\arccos(x)$ und $\\arctan(x)$ der trigonometrischen Funktionen werden auch erkannt, und k&ouml;nnen wie die anderen Funktionen eingegeben werden: arccos(x) ...</li>\n</ol>\n<p>Hier sind einige Beispiele, an denen Sie es ausprobieren k&ouml;nnen.</p>\n<p>(Um Hilfe dazu zu erhalten, klicken Sie <em>Antworten aufdecken.</em> Sie k&ouml;nnen die Aufgabe danach noch einmal mit ver&auml;nderten Werten bearbeiten.)</p>", "advice": "<p>Die korrekten Eingaben sind (es gibt nat&uuml;rlich auch Varianten, die ebenfalls korrekt sind, probieren Sie ruhig mal ein bisschen herum):&nbsp;</p>\n<h4>a)</h4>\n<ol>\n<li><code>sin(cos({a}x)+{b})</code></li>\n<li><code>cos(sin({a}x + {b}))</code></li>\n</ol>\n<h4>b)</h4>\n<ol>\n<li><code>abs((x + {c}) / (x + {d}))</code></li>\n<li><code>ln(abs((x + {a}) / (x + {d})))</code></li>\n</ol>\n<h4>c)</h4>\n<ol>\n<li><code>{a}t^({-b})*e^({-c}t)*sin({b}t) + (s + {d}t ^ 3)*e ^ ({c}t)</code></li>\n<li><code>arctan(({c}y ^ 2 + {d}) / ((x + {a})*(y + {b})))</code></li>\n</ol>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"d": {"name": "d", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..9)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d"], "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>Geben Sie die folgenden Funktionen ein:</p>\n<ol>\n<li>$\\sin(\\cos(\\var{a}x)+\\var{b})$: [[0]]</li>\n<li>$\\cos(\\sin(\\var{b}x)+\\var{a})$: [[1]]</li>\n</ol>", "gaps": [{"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, "answer": "sin(cos({a}x)+{b})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": true, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"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, "answer": "cos(sin({b}x)+{a})", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "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>Geben Sie die folgenden Funktionen ein:</p>\n<ol>\n<li>$\\displaystyle \\simplify[all]{Abs((x + {c}) / (x + {d}))}$: [[0]]</li>\n<li>$\\displaystyle \\simplify[all]{ln(Abs((x + {a}) / (x + {d})))}$: [[1]]</li>\n</ol>", "gaps": [{"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, "answer": "abs((x + {c}) / (x + {d}))", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, 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"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>Geben Sie die folgenden Funktionen ein:</p>\n<ol>\n<li>$\\simplify[all]{{a} * t ^ { -b} * e ^ (( -{c}) * t) * Sin({b} * t) + (s + {d} * t ^ 3) * e ^ ({c} * t)}$: [[0]]</li>\n<li>$\\displaystyle \\simplify[all]{arctan(({c} * y ^ 2 + {d}) / ((x + {a}) * (y + {b})))}$: [[1]]</li>\n</ol>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], 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