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chore: add katex, dompurify, vitest; copy sample exam files
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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{
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"title": "Calculus I — Midterm Practice",
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"subtitle": "Limits, derivatives, and applications",
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"author": "Dept. of Mathematics",
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"timeLimitMinutes": 45,
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"feedbackMode": "end",
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"passingScore": 70,
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"categories": ["Limits", "Derivatives", "Applications"],
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"questions": [
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{
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"id": "q1",
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"type": "multiple-choice",
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"category": "Limits",
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"points": 2,
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"prompt": "Evaluate $\\displaystyle\\lim_{x \\to 0} \\frac{\\sin(3x)}{x}$.",
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"choices": [
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{ "id": "a", "text": "$0$" },
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{ "id": "b", "text": "$1$" },
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{ "id": "c", "text": "$3$" },
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{ "id": "d", "text": "$\\infty$" }
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],
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"answer": "c",
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"explanation": "Using the standard limit $\\lim_{u\\to 0}\\frac{\\sin u}{u}=1$ with $u=3x$ gives $3\\cdot 1 = 3$."
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},
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{
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"id": "q2",
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"type": "multiple-select",
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"category": "Derivatives",
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"points": 3,
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"prompt": "Which of the following functions are differentiable at $x=0$? Select all that apply.",
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"choices": [
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{ "id": "a", "text": "$f(x) = |x|$" },
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{ "id": "b", "text": "$f(x) = x^2 \\sin(1/x)$ with $f(0)=0$" },
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{ "id": "c", "text": "$f(x) = \\sqrt{x}$" },
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{ "id": "d", "text": "$f(x) = e^x$" }
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],
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"answer": ["b", "d"],
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"explanation": "$|x|$ has a corner, $\\sqrt{x}$ is not defined for $x<0$. Both $x^2\\sin(1/x)$ (extended) and $e^x$ are differentiable at 0."
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},
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{
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"id": "q3",
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"type": "math-input",
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"category": "Derivatives",
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"points": 3,
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"prompt": "Compute $\\dfrac{d}{dx}\\left[x^2 \\ln x\\right]$. Enter your answer in LaTeX.",
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"answer": "2x\\ln x + x",
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"acceptedForms": ["2x\\ln(x) + x", "x(2\\ln x + 1)", "x + 2x\\ln x"],
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"explanation": "By the product rule: $2x\\ln x + x^2 \\cdot \\frac{1}{x} = 2x\\ln x + x$."
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},
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{
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"id": "q4",
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"type": "short-answer",
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"category": "Limits",
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"points": 2,
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"prompt": "What is the value of $\\displaystyle\\lim_{x \\to \\infty}\\left(1 + \\frac{1}{x}\\right)^x$? Give the standard symbol.",
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"answer": "e",
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"acceptedForms": ["E", "e", " e "],
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"caseSensitive": false,
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"explanation": "This is the definition of Euler's number, $e \\approx 2.71828$."
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},
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{
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"id": "q5",
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"type": "order",
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"category": "Applications",
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"points": 3,
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"prompt": "Order these steps to find the absolute maximum of $f$ on $[a,b]$ (first → last):",
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"items": [
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{ "id": "s1", "text": "Confirm $f$ is continuous on $[a,b]$" },
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{ "id": "s2", "text": "Find critical points in $(a,b)$" },
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{ "id": "s3", "text": "Evaluate $f$ at critical points and endpoints" },
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{ "id": "s4", "text": "Compare values; the largest is the absolute max" }
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],
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"answer": ["s1", "s2", "s3", "s4"],
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"explanation": "The Extreme Value Theorem requires continuity on a closed interval; then candidates are critical points and endpoints."
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},
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{
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"id": "q6",
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"type": "match",
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"category": "Derivatives",
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"points": 4,
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"prompt": "Match each function to its derivative.",
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"left": [
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{ "id": "l1", "text": "$\\sin x$" },
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{ "id": "l2", "text": "$\\tan x$" },
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{ "id": "l3", "text": "$\\ln x$" },
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{ "id": "l4", "text": "$e^{2x}$" }
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],
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"right": [
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{ "id": "r1", "text": "$\\dfrac{1}{x}$" },
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{ "id": "r2", "text": "$\\cos x$" },
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{ "id": "r3", "text": "$2e^{2x}$" },
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{ "id": "r4", "text": "$\\sec^2 x$" }
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],
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"answer": { "l1": "r2", "l2": "r4", "l3": "r1", "l4": "r3" }
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},
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{
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"id": "q7",
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"type": "essay",
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"category": "Applications",
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"points": 5,
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"prompt": "Explain, in your own words, the Mean Value Theorem and give a geometric interpretation.",
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"rubric": [
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"States hypotheses (continuous on $[a,b]$, differentiable on $(a,b)$)",
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"States conclusion: $\\exists c \\in (a,b)$ with $f'(c) = \\frac{f(b)-f(a)}{b-a}$",
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"Explains geometric meaning (tangent parallel to secant)",
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"Gives or references an example"
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]
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}
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]
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}
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{
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"title": "Mixed Demo — Every Question Type",
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"subtitle": "A tour of every renderer in the platform",
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"timeLimitMinutes": null,
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"feedbackMode": "end",
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"categories": ["Demo"],
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"questions": [
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{
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"id": "q1",
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"type": "multiple-choice",
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"category": "Demo",
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"points": 1,
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"prompt": "Which of the following is the capital of Japan?",
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"image": {
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"src": "https://images.unsplash.com/photo-1540959733332-eab4deabeeaf?w=800",
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"alt": "City skyline",
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"caption": "A city skyline — can you identify it?"
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},
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"choices": [
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{ "id": "a", "text": "Kyoto" },
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{ "id": "b", "text": "Osaka" },
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{ "id": "c", "text": "Tokyo" },
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{ "id": "d", "text": "Hiroshima" }
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],
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"answer": "c",
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"explanation": "Tokyo has been Japan's capital since 1868."
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},
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{
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"id": "q2",
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"type": "multiple-choice",
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"category": "Demo",
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"points": 2,
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"prompt": "What does the following function return when called with `fib(6)`?",
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"code": {
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"language": "javascript",
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"content": "function fib(n) {\n if (n < 2) return n;\n return fib(n - 1) + fib(n - 2);\n}"
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},
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"choices": [
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{ "id": "a", "text": "5" },
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{ "id": "b", "text": "8" },
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{ "id": "c", "text": "13" },
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{ "id": "d", "text": "6" }
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],
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"answer": "b",
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"explanation": "The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8 — so fib(6) = 8."
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},
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{
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"id": "q3",
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"type": "short-answer",
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"category": "Demo",
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"points": 1,
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"prompt": "In the data table below, which country had the highest GDP growth?",
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"table": {
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"headers": ["Country", "GDP Growth (%)", "Year"],
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"rows": [
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["Vietnam", "7.2", "2024"],
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["India", "6.8", "2024"],
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["Indonesia", "5.1", "2024"],
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["Philippines", "5.9", "2024"]
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]
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},
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"answer": "Vietnam",
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"caseSensitive": false
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},
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{
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"id": "q4",
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"type": "essay",
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"category": "Demo",
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"points": 5,
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"prompt": "Describe a time you solved a difficult problem. What approach did you take?",
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"minWords": 50,
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"rubric": [
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"Specific situation (not generic)",
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"Clear problem statement",
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"Described methodology",
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"Outcome or reflection"
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]
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}
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]
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}
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{
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"title": "Spanish A2 — Vocabulary & Grammar",
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"subtitle": "Elementary level practice set",
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"timeLimitMinutes": 20,
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"feedbackMode": "immediate",
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"categories": ["Vocabulary", "Grammar", "Listening"],
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"questions": [
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{
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"id": "q1",
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"type": "multiple-choice",
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"category": "Grammar",
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"points": 1,
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"prompt": "Choose the correct form: _____ a la biblioteca todos los días.",
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"choices": [
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{ "id": "a", "text": "Voy" },
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{ "id": "b", "text": "Va" },
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{ "id": "c", "text": "Vamos" },
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{ "id": "d", "text": "Van" }
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],
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"answer": "a",
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"explanation": "First person singular of 'ir' (to go) is 'voy'."
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},
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{
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"id": "q2",
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"type": "translation",
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"category": "Vocabulary",
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"points": 2,
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"sourceLanguage": "English",
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"targetLanguage": "Spanish",
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"prompt": "Translate: \"I would like a coffee with milk, please.\"",
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"answer": "Me gustaría un café con leche, por favor.",
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"acceptedForms": [
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"Quisiera un café con leche, por favor",
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"Me gustaria un cafe con leche por favor",
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"Quiero un café con leche, por favor"
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],
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"caseSensitive": false,
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"ignorePunctuation": true,
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"ignoreAccents": true
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},
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{
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"id": "q3",
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"type": "match",
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"category": "Vocabulary",
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"points": 4,
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"prompt": "Match each Spanish word to its English translation.",
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"left": [
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{ "id": "l1", "text": "perro" },
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{ "id": "l2", "text": "árbol" },
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{ "id": "l3", "text": "lluvia" },
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{ "id": "l4", "text": "manzana" }
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],
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"right": [
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{ "id": "r1", "text": "rain" },
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{ "id": "r2", "text": "apple" },
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{ "id": "r3", "text": "dog" },
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{ "id": "r4", "text": "tree" }
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],
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"answer": { "l1": "r3", "l2": "r4", "l3": "r1", "l4": "r2" }
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},
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{
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"id": "q4",
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"type": "short-answer",
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"category": "Grammar",
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"points": 2,
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"prompt": "Conjugate 'comer' in the first person plural, present tense.",
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"answer": "comemos",
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"caseSensitive": false,
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"explanation": "Regular -er verb: com + emos = comemos ('we eat')."
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},
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{
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"id": "q5",
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"type": "multiple-select",
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"category": "Grammar",
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"points": 2,
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"prompt": "Which of the following are feminine nouns? Select all that apply.",
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"choices": [
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{ "id": "a", "text": "la mesa" },
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{ "id": "b", "text": "el libro" },
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{ "id": "c", "text": "la casa" },
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{ "id": "d", "text": "el perro" },
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{ "id": "e", "text": "la ciudad" }
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],
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"answer": ["a", "c", "e"]
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},
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{
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"id": "q6",
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"type": "order",
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"category": "Grammar",
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"points": 3,
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"prompt": "Arrange these words to form a grammatically correct sentence:",
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"items": [
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{ "id": "w1", "text": "Mi" },
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{ "id": "w2", "text": "hermana" },
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{ "id": "w3", "text": "estudia" },
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{ "id": "w4", "text": "en" },
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{ "id": "w5", "text": "la universidad" }
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],
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"answer": ["w1", "w2", "w3", "w4", "w5"],
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"explanation": "Subject + verb + prepositional phrase: 'My sister studies at the university.'"
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}
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]
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}
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