// Numbas version: exam_results_page_options
{"name": "Set Soal Matematika IIB - Bab 8 - 10", "metadata": {"description": "", "licence": "None specified"}, "duration": 3600, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "PG + Isian", "pickingStrategy": "all-shuffled", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "questions": [{"name": "Mat 2B - UAS - No 1", "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>Agar $\\displaystyle \\lim\\limits_{(x,y)\\to(\\var{a},a)}\\dfrac{\\simplify{x*y-b*y-{a}*x+{a}*b}}{\\simplify{{b}x-{b}*{a}}}=\\var{c}$, maka nilai $a$ dan $b$ berturut-turut adalah $\\ldots$.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-7..7 except[0,1])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-7..7 except[0,1,a])", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-7..7 except[0,1,a,b])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_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": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$a=\\var{b*c-a}$ dan $b=\\var{a}$", "$a=\\var{a-b*c}$ dan $b=\\var{a}$", "$a=\\var{b*c-a}$ dan $b=\\var{-a}$", "$a=\\var{a-b*c}$ dan $b=\\var{-a}$"], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mat 2B - UAS - No 2", "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>Misal $A$ dan $B$ adalah matriks persegi berukuran $\\var{b}\\times \\var{b}$ dengan $\\det(A)=\\var{a}$ dan $\\det(B)=\\var{a*b}$.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5..5 except [-1,0,1])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_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>Seluruh pernyataan berikut benar, kecuali $\\ldots$.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\det(A^{-1}BA^2)=\\var{b}\\det(A^2)$.", "$\\det(B^{-1})=\\dfrac{1}{\\var{b}\\det(A)}$.", "$\\det(B^{-1}(AB)^2)=\\var{b}\\det(B^2)$.", "$\\det(A^{-1})=\\dfrac{\\det(B)}{\\var{b}}$."], "matrix": ["0", 0, "1", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mat 2B - UAS - No 3", "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>Pilihlah seluruh matriks $A$ agar sistem persamaan diferensial $\\dfrac{d\\mathbf{x}}{dt}=A\\mathbf{x}$ mempunyai titik kesetimbangan di $(0,0)$ yang bersifat stabil.</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": "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": ["$\\begin{bmatrix} -1 &amp; 0 \\\\ 0 &amp; \\var{-a} \\end{bmatrix}$", "$\\begin{bmatrix} -1 &amp; 1 \\\\ 1 &amp; \\var{-a} \\end{bmatrix}$", "$\\begin{bmatrix} \\var{-a} &amp; 1 \\\\ 1 &amp; \\var{-a} \\end{bmatrix}$", "$\\begin{bmatrix} \\var{a} &amp; 1 \\\\ 1 &amp; \\var{-a} \\end{bmatrix}$", "$\\begin{bmatrix} 0 &amp; \\var{-a} \\\\ \\var{a} &amp; 1 \\end{bmatrix}$"], "matrix": ["1", "1", "1", 0, 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mat 2B - UAS - No 4", "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>Nilai maksimum dari fungsi $f(x,y)=xy^{\\var{a}}$ pada lingkaran $x^2+y^2=\\var{b^2}$ adalah $\\ldots$.</p>\n<p><em>Petunjuk</em>: Suatu persamaan parametrik untuk lingkaran $x^2+y^2=r^2$ adalah $x(t)=r\\cos(t)$, $y(t)=r\\sin(t)$, $t\\in[0,2\\pi]$.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(2..4 except[a])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "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": "b^(1+a)", "maxValue": "b^(1+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": "Mat 2B - UAS - No 5", "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>Turunan berarah fungsi $f$ di titik $(7,24)$ dalam arah $\\mathbf{u}=5\\mathbf{i}+12\\mathbf{j}$ adalah $D_{\\mathbf{u}}f(7,24)=\\var{5*a+12*b}k$ dan dalam arah $\\mathbf{v}=5\\mathbf{i}-12\\mathbf{j}$ adalah $D_{\\mathbf{v}}f(7,24)=\\var{5*a-12*b}k$.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3 except[0])", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3 except[0,a])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "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, "prompt": "<p>Di titik tersebut, turunan berarah fungsi $f$ dalam arah $\\mathbf{w}=4\\mathbf{i}+3\\mathbf{j}$ adalah $D_{\\mathbf{w}}f(7,24)=\\dfrac{ak}{65}$ dengan $a=\\ldots$.</p>", "minValue": "4*a+3*b", "maxValue": "4*a+3*b", "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 - UAS - 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>Model matriks teriterasi suatu populasi membagi populasi menjadi 3 subpopulasi. Jika $\\mathbf{p}_{t+1}=\\begin{bmatrix} 1 &amp; \\var{a} &amp; 1 \\\\ 0 &amp; 3 &amp; \\var{a} \\\\ 0 &amp; 0 &amp; 2 \\end{bmatrix}\\mathbf{p}_t$, maka dalam jangka panjang, perbandingan banyaknya subpopulasi $1$ dan $2$ adalah $1:b$ dengan $b=\\ldots$.</p>\n<p><em>Petunjuk</em>: Jika dibutuhkan, tuliskan nilai $b$ dalam bentuk pecahan paling sederhana.</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2,4,5)", "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": "2/a", "maxValue": "2/a", "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"}]}, {"name": "Isian Terstruktur", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": [""], "questions": [{"name": "Mat 2B - UAS - 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>Suatu model sistem persamaan diferensial untuk model kecukupan vaksinasi suatu wabah adalah</p>\n<p style=\"text-align: center;\">$\\begin{cases} \\dfrac{dN}{dt} &amp;= 2(1-p)N+2(1-p)V-N \\\\ \\dfrac{dV}{dt} &amp;= 2pV+2pN-3V \\end{cases}$</p>\n<p style=\"text-align: left;\">dengan $N$ menyatakan banyaknya orang yang belum divaksin, $V$ menyatakan banyaknya orang yang divaksin, serta $p$ adalah fraksi populasi yang telah divaksin.</p>", "advice": "", "rulesets": {}, "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(20..50)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k"], "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, "prompt": "<p>Perhatikan bahwa titik kesetimbangan model ini adalah di $(0,0)$. Tentukan nilai $p$ terkecil agar titik kesetimbangan ini bersifat stabil. Tuliskan nilainya dalam bentuk pecahan paling sederhana.</p>\n<p><em>Catatan</em>: Nilai $p$ ini disebut juga dengan nilai kritis, yaitu nilai yang dibutuhkan agar wabah dapat mereda.</p>\n<p><em>Petunjuk:</em> Karena $p$ menyatakan fraksi, maka $p\\in[0,1]$.</p>", "minValue": "3/4", "maxValue": "3/4", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Misal $\\mathbf{x}(t)=\\begin{bmatrix} N(t) \\\\ V(t) \\end{bmatrix}$. Dengan menggunakan $p=\\dfrac{15}{16}$, jika diberikan nilai awal $N(0)=\\var{k}$ dan $V(0)=0$, maka solusi khusus dari sistem persamaan diferensial tersebut adalah $\\mathbf{x}(t)=\\begin{bmatrix} c_1e^{\\lambda_1t}+c_2e^{\\lambda_2t} \\\\ c_3e^{\\lambda_1t}+ c_4e^{\\lambda_2t} \\end{bmatrix}$.</p>\n<p style=\"text-align: left;\">Maka $c_1+c_2+c_3+c_4=\\ldots$.</p>", "minValue": "k", "maxValue": "k", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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>Mengacu pada solusi (b), $\\displaystyle \\lim\\limits_{t\\to\\infty}\\dfrac{V(t)}{N(t)} = \\ldots$.</p>", "minValue": "3", "maxValue": "3", "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"}]}], "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": true, "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": []}