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{"name": "Set Soal Matematika IIB - Bab 8 Bagian 2", "metadata": {"description": "", "licence": "None specified"}, "duration": 2700, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Mat 2B - Bab 8 - No 6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Pillihlah semua matriks yang memenuhi syarat Teorema Perron-Frobenius.</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": ["\\(\\begin{bmatrix} 1 &amp;&nbsp;5 \\\\ 0 &amp; 3 \\end{bmatrix}\\)", "\\(\\begin{bmatrix}&nbsp;2 &amp; 0 \\\\ 0 &amp; -2 \\end{bmatrix}\\)", "\\(\\begin{bmatrix}&nbsp;2 &amp;&nbsp;5 \\\\&nbsp;1 &amp; 3 \\end{bmatrix}\\)", "\\(\\begin{bmatrix}&nbsp;9 &amp; 1 \\\\ 0 &amp; 0 \\end{bmatrix}\\)", "\\(\\begin{bmatrix} 1 &amp; 1 \\\\ 1 &amp; 0 \\end{bmatrix}\\)"], "matrix": [0, 0, "1", 0, "1"], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mat 2B - Bab 8 - No 7", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Pilih semua matriks yang mempunyai invers.</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "score per matched cell", "choices": ["\\(\\begin{bmatrix} 1 &amp; 2\\\\ 3 &amp; 4 \\end{bmatrix}\\)", "\\(\\begin{bmatrix} 1 &amp; 4\\\\ 2 &amp; 3 \\end{bmatrix}\\)", "\\(\\begin{bmatrix} 1 &amp; 0 &amp; 5\\\\ 4 &amp; 2 &amp; 6\\\\ 3 &amp; 2 &amp; 1\\end{bmatrix}\\)", "\\(\\begin{bmatrix} 1 &amp; 1 &amp; 2\\\\ 0 &amp; 2 &amp; 3\\\\ 0 &amp; 0 &amp; 4\\end{bmatrix}\\)", "\\(\\begin{bmatrix} 1 &amp; 0 &amp; 0\\\\ 0 &amp; 0 &amp; 0\\\\ 0 &amp; 0 &amp; -1\\end{bmatrix}\\)"], "matrix": ["1", "1", 0, "1", 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mat 2B - Bab 8 - No 8", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Matriks \\(A=\\begin{bmatrix} \\var{2+3*a} &amp; \\var{-2-2*a}\\\\ \\var{3+3*a} &amp; \\var{-3-2*a} \\end{bmatrix}\\) mempunyai vektor eigen \\(\\mathbf{v}=\\begin{bmatrix} 2\\\\3 \\end{bmatrix}\\) yang bersesuaian dengan nilai eigen \\(\\lambda=\\ldots\\).</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..5)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minValue": "-1", "maxValue": "-1", "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"}, {"name": "Mat 2B - Bab 8 - No 9", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Diketahui \\( \\mathbf{v}=\\begin{bmatrix} \\var{a*0.01} \\\\ a \\\\ b \\end{bmatrix} \\) merupakan suatu vektor eigen yang berkaitan dengan nilai eigen \\(\\lambda = 5\\) dari matriks \\(A=\\begin{bmatrix} 1 &amp; -4 &amp; 0 \\\\ -4 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 2 \\end{bmatrix}\\). Maka nilai \\(a+b=\\ldots\\).</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(200..400)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minValue": "-a", "maxValue": "-a", "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"}]}, {"name": "Isian Terstruktur", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": [""], "questions": [{"name": "Mat 2B - Bab 8 - No 10", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Penyebaran populasi capung yang berada di dua kolam&nbsp;\\(P\\) dan \\(Q\\) dapat dimodelkan sebagai berikut. Setiap hari, \\(20\\%\\) capung yang berada dalam kolam \\(P\\) akan pindah ke kolam \\(Q\\). Sebaliknya, \\(30\\%\\) capung yang berada dalam kolam&nbsp;\\(Q\\) akan pindah ke kolam \\(P\\). Misalkan \\(P_t\\) dan \\(Q_t\\) berturut-turut menyatakan banyaknya capung pada kolam&nbsp;\\(P\\) dan&nbsp;\\(Q\\) setiap waktu. Maka&nbsp;dapat diperoleh sistem persamaan beda \\(\\begin{cases} P_{t+1}&amp;=0.8P_t+0.3Q_t \\\\&nbsp;Q_{t+1}&amp;=0.2P_t+0.7Q_t \\end{cases}\\).</p>", "advice": "", "rulesets": {}, "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Misalkan \\(\\mathbf{x}_t=\\begin{bmatrix} P_t \\\\Q_t \\end{bmatrix}\\). Bentuk iterasi model tersebut dapat ditulis sebagai \\(\\mathbf{x}_{t+1}=A\\mathbf{x}_t\\). Tentukan matriks \\(A\\).</p>", "correctAnswer": "matrix([0.8,0.3],[0.2,0.7])", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "1.6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Diketahui</p>\n<ul>\n<li>Nilai eigen dari matriks $A$ adalah $\\lambda_1$ dan $\\lambda_2$ dengan $\\lambda_1\\geq \\lambda_2$.</li>\n<li>Vektor \\(\\mathbf{v}_1=\\begin{bmatrix} 3 \\\\ a \\end{bmatrix}\\) merupakan vektor eigen yang bersesuaian dengan $\\lambda_1$, dan vektor \\(\\mathbf{v}_2=\\begin{bmatrix} 3 \\\\ b \\end{bmatrix}\\) merupakan vektor eigen yang bersesuaian dengan $\\lambda_2$.</li>\n<li>Populasi awal capung di kedua kolam tersebut adalah \\(\\mathbf{x}_0=\\begin{bmatrix} 600 \\\\ 80 \\end{bmatrix}\\).</li>\n</ul>\n<p>Tentukan nilai $\\lambda_1$, $\\lambda_2$, $a$, dan $b$ berturut-turut.</p>", "correctAnswer": "matrix([1,0.5,2,-3])", "correctAnswerFractions": true, "numRows": 1, "numColumns": "4", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": true, "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>Dalam waktu yang cukup lama, misalkan banyaknya capung pada kolam $P$ sebanyak $P_\\infty$, sedangkan banyaknya capung pada kolam $Q$ sebanyak $Q_\\infty$. Tentukan nilai dari $\\dfrac{P_\\infty}{Q_\\infty}$.</p>", "minValue": "1.5", "maxValue": "1.5", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": false, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "warn", "message": "<p>Waktunya 5 menit lagi ya.</p>"}}, "feedback": {"showactualmark": false, "showtotalmark": false, "showanswerstate": false, "allowrevealanswer": false, "advicethreshold": 0, "intro": "<p>Selamat datang!</p>\n<p>Silakan gunakan set soal ini dengan bijak.&nbsp;Kalian bisa mencoba set soal ini terus-menerus.</p>\n<p>Set soal ini dapat digunakan oleh siapapun secara gratis.</p>\n<p>Petunjuk pengerjaan soal:</p>\n<ul>\n<li>Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.</li>\n<li>Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan&nbsp;bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \\(\\frac{2}{3}\\).</li>\n<li>Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik&nbsp;2/3 untuk menjawab \\(\\frac{2}{3}\\).</li>\n</ul>\n<p>Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.</p>", "reviewshowscore": true, "reviewshowfeedback": false, "reviewshowexpectedanswer": true, "reviewshowadvice": false, "feedbackmessages": []}, "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}], "extensions": [], "custom_part_types": [], "resources": []}