{ "version": 1, "note": "Quick-fire single-answer questions for the Live Game. answer = canonical value (accepts numeric variations e.g. 540 == 540.0 == '£540'). altAnswers = extra accepted strings.", "courses": { "slai": [ { "id": "slai-qf-1", "topic": "Financial Math", "prompt": "Marcus invests £2000 at 4.5% p.a. simple interest for 6 years. What is the total interest earned?", "answer": "540", "unit": "£" }, { "id": "slai-qf-2", "topic": "Financial Math", "prompt": "Convert 300 USD to EUR at rate 1 USD = 0.92 EUR.", "answer": "276", "unit": "€" }, { "id": "slai-qf-3", "topic": "Number & Algebra","prompt": "Round 45,678 to 3 significant figures.", "answer": "45700" }, { "id": "slai-qf-4", "topic": "Statistics", "prompt": "Find the mean of 4, 7, 9, 12, 18.", "answer": "10" }, { "id": "slai-qf-5", "topic": "Statistics", "prompt": "Find the median of 3, 5, 8, 12, 15, 22.", "answer": "10" }, { "id": "slai-qf-6", "topic": "Probability", "prompt": "P(rolling a 6 on a fair die) as a fraction in lowest terms.", "answer": "1/6" }, { "id": "slai-qf-7", "topic": "Functions", "prompt": "f(x) = 3x + 5. Find f(4).", "answer": "17" }, { "id": "slai-qf-8", "topic": "Geometry", "prompt": "Area of a circle with radius 6 cm (to 3 s.f., use π ≈ 3.14159).", "answer": "113", "unit": "cm²", "altAnswers": ["113.1", "113.10", "113.097"] }, { "id": "slai-qf-9", "topic": "Geometry", "prompt": "Volume of a cube with side length 4 cm.", "answer": "64", "unit": "cm³" }, { "id": "slai-qf-10", "topic": "Calculus", "prompt": "Differentiate f(x) = x². Give f'(2).", "answer": "4" }, { "id": "slai-qf-11", "topic": "Statistics", "prompt": "Standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 (population).", "answer": "2", "altAnswers": ["2.0"] }, { "id": "slai-qf-12", "topic": "Number & Algebra","prompt": "Solve 3x - 7 = 14. Give x.", "answer": "7" } ], "slaa": [ { "id": "slaa-qf-1", "topic": "Algebra", "prompt": "Solve x² - 5x + 6 = 0. Give the larger root.", "answer": "3" }, { "id": "slaa-qf-2", "topic": "Algebra", "prompt": "Solve x² - 5x + 6 = 0. Give the smaller root.", "answer": "2" }, { "id": "slaa-qf-3", "topic": "Sequences", "prompt": "Arithmetic sequence: 3, 7, 11, ... . Find u₁₀.", "answer": "39" }, { "id": "slaa-qf-4", "topic": "Functions", "prompt": "f(x) = 2x + 1, g(x) = x². Find (f∘g)(3).", "answer": "19" }, { "id": "slaa-qf-5", "topic": "Trigonometry", "prompt": "sin(30°) as a fraction.", "answer": "1/2", "altAnswers": ["0.5"] }, { "id": "slaa-qf-6", "topic": "Trigonometry", "prompt": "cos(60°) as a fraction.", "answer": "1/2", "altAnswers": ["0.5"] }, { "id": "slaa-qf-7", "topic": "Calculus", "prompt": "Differentiate f(x) = 3x² + 2x. Find f'(1).", "answer": "8" }, { "id": "slaa-qf-8", "topic": "Calculus", "prompt": "∫ 2x dx from 0 to 3.", "answer": "9" }, { "id": "slaa-qf-9", "topic": "Trigonometry", "prompt": "Solve 2sin(x) = 1 for x in [0°, 90°].", "answer": "30°", "altAnswers": ["30", "30 degrees"] }, { "id": "slaa-qf-10", "topic": "Statistics", "prompt": "Median of 2, 5, 7, 8, 12.", "answer": "7" }, { "id": "slaa-qf-11", "topic": "Probability", "prompt": "P(A) = 0.3, P(B) = 0.4, independent. P(A ∩ B) =", "answer": "0.12" }, { "id": "slaa-qf-12", "topic": "Logarithms", "prompt": "log₂(32) = ", "answer": "5" } ], "hlai": [ { "id": "hlai-qf-1", "topic": "Statistics", "prompt": "Correlation coefficient r = 0.85. Is this strong positive, strong negative or weak? (answer: strong-positive / strong-negative / weak)", "answer": "strong-positive" }, { "id": "hlai-qf-2", "topic": "Statistics", "prompt": "Sample size n = 100, mean = 50, SD = 5. Standard error of the mean.", "answer": "0.5" }, { "id": "hlai-qf-3", "topic": "Probability", "prompt": "P(X = 3) for X ~ Binomial(5, 0.5). Answer as a fraction with denominator 32.", "answer": "10/32", "altAnswers": ["5/16", "0.3125"] }, { "id": "hlai-qf-4", "topic": "Financial Math", "prompt": "€1000 at 5% compound interest, annually, for 3 years. Final value (to nearest €).", "answer": "1158", "unit": "€" }, { "id": "hlai-qf-5", "topic": "Calculus", "prompt": "Newton's method: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ). With f(x) = x²-2, x₀ = 1, find x₁.", "answer": "1.5" }, { "id": "hlai-qf-6", "topic": "Matrices", "prompt": "det([[2,3],[1,4]]) = ", "answer": "5" }, { "id": "hlai-qf-7", "topic": "Graphs", "prompt": "In a graph with 6 vertices where each is connected to 3 others, how many edges?", "answer": "9" }, { "id": "hlai-qf-8", "topic": "Statistics", "prompt": "Chi-square degrees of freedom for a 3×4 table.", "answer": "6" }, { "id": "hlai-qf-9", "topic": "Calculus", "prompt": "Euler's method: y' = x + y, y(0)=1, h=0.1. Find y(0.1).", "answer": "1.1" }, { "id": "hlai-qf-10", "topic": "Complex Numbers", "prompt": "|3 + 4i| = ", "answer": "5" } ], "hlaa": [ { "id": "hlaa-qf-1", "topic": "Complex Numbers", "prompt": "(1 + i)² = a + bi. Find a + b.", "answer": "2" }, { "id": "hlaa-qf-2", "topic": "Complex Numbers", "prompt": "|3 + 4i| =", "answer": "5" }, { "id": "hlaa-qf-3", "topic": "Sequences", "prompt": "Geometric sequence with u₁ = 4, r = 1/2. Sum to infinity S∞ =", "answer": "8" }, { "id": "hlaa-qf-4", "topic": "Calculus", "prompt": "Differentiate f(x) = ln(x). Find f'(2). Give a fraction.", "answer": "1/2", "altAnswers": ["0.5"] }, { "id": "hlaa-qf-5", "topic": "Calculus", "prompt": "∫ 1/x dx from 1 to e. (Answer in exact form.)", "answer": "1" }, { "id": "hlaa-qf-6", "topic": "Trigonometry", "prompt": "tan(45°) =", "answer": "1" }, { "id": "hlaa-qf-7", "topic": "Vectors", "prompt": "(1,2,2) · (2,0,1) =", "answer": "4" }, { "id": "hlaa-qf-8", "topic": "Proof", "prompt": "Sum 1+2+...+n = n(n+1)/2. Value for n = 100.", "answer": "5050" }, { "id": "hlaa-qf-9", "topic": "Series", "prompt": "Coefficient of x² in (1 + x)⁵.", "answer": "10" }, { "id": "hlaa-qf-10", "topic": "Probability", "prompt": "Bayes: P(A|B) if P(B|A)=0.8, P(A)=0.5, P(B)=0.5.", "answer": "0.8" } ] } }