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H2 Mathematics Flashcards

6 cards from real A-LEVEL practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A random variable X ~ N(50, 16). Find P(X > 54).

    Answer: 0.1587

    Z = (54-50)/4 = 1. P(X>54) = P(Z>1) = 1 - Φ(1) = 1 - 0.8413 = 0.1587.

  2. Find the inverse of the matrix [[3,1],[5,2]].

    Answer: [[2,-1],[-5,3]]

    det = 3×2 - 1×5 = 1. Inverse = (1/1)[[2,-1],[-5,3]] = [[2,-1],[-5,3]].

  3. For X ~ B(10, 0.3), find P(X = 3).

    Answer: 0.2668

    P(X=3) = ¹⁰C₃ × (0.3)³ × (0.7)⁷ = 120 × 0.027 × 0.0823... = 120 × 0.02223... ≈ 0.2668.

  4. Find the exact value of ∫₀^(π/2) sin(x) dx.

    Answer: 1

    ∫₀^(π/2) sin(x) dx = [-cos(x)]₀^(π/2) = -cos(π/2) + cos(0) = 0 + 1 = 1.

  5. Differentiate y = ln(3x² + 1).

    Answer: 6x/(3x²+1)

    Using chain rule: dy/dx = 1/(3x²+1) × 6x = 6x/(3x²+1).

  6. Solve the inequality x² - 5x + 6 > 0.

    Answer: x 3

    x²-5x+6 = (x-2)(x-3) > 0. Parabola opens upward; product is positive outside the roots. Solution: x 3.

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