// Numbas version: exam_results_page_options
{"name": "Mat 2A dan 2C - Bab 7 - No 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Mat 2A dan 2C - Bab 7 - No 5", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Fungsi sinus dan kosinus hiperbolik berturut-turut didefinisikan sebagai $\\sinh(x)=\\dfrac{e^x-e^{-x}}{2}$ dan $\\cosh(x)=\\dfrac{e^x+e^{-x}}{2}$. Diberikan $f(x) =\\cosh(\\var{a}x)$ dan $g(x)=\\sinh(\\var{a}x)$.</p>\n<p>Dapat dibuktikan bahwa fungsi $f$ mempunyai invers untuk $x&gt;0$ dan fungsi $g$ mempunyai invers untuk $x\\in\\mathbb{R}$.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2,3,4)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "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>Pilihlah seluruh hubungan yang tepat tentang $f(x)$ dan $g(x)$.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$f'(x)=g'(x)$", "$f^2(x)-g^2(x) = 1$.", "$f^2(x)+g^2(x) = g(2x)$.", "$\\displaystyle \\int f(x)\\, dx = g(x) + C$."], "matrix": ["-0.5", "0.5", "0.5", "-0.5"], "distractors": ["", "", "", ""]}, {"type": "matrix", "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>Diberikan&nbsp;integral $\\displaystyle \\int \\dfrac{\\cosh(x)}{\\sinh^2(x)+\\sinh^4(x)}\\, dx$. Integral tersebut dapat dituliskan dalam bentuk pecahan parsial $\\displaystyle \\int \\cosh(x)\\left(\\dfrac{A}{\\sinh(x)}+\\dfrac{B}{\\sinh^2(x)}+\\dfrac{C\\sinh(x)+D}{\\sinh^2(x)+1}\\right)\\, dx$ dengan $A$, $B$, $C$, dan $D$ berturut-turut adalah $\\ldots$.</p>", "correctAnswer": "matrix([0,1,0,-1])", "correctAnswerFractions": false, "numRows": 1, "numColumns": "4", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"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, "prompt": "<p>Jika $I(x) = \\displaystyle \\int_{0}^{\\cosh^{-1}(x)} \\dfrac{\\cosh(t)}{\\sinh^2(t)+\\sinh^4(t)}\\, dt$ untuk $x&gt;0$, maka $I\\left(\\sqrt{3}\\right) = 1-\\dfrac{1}{\\sqrt{a}}+\\dfrac{\\pi}{b}$ dengan $a +b =\\ldots$.</p>", "minValue": "-9", "maxValue": "-9", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}]}], "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}