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Applied Mathematics Flashcards

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

Read the first 7 Applied Mathematics flashcards as text

  1. A particle starts from rest with constant acceleration. It covers 5 m in the first second. How far does it travel in the third second?

    Answer: 25 m

    s₁ = a/2 = 5 gives a = 10 m/s²; distance in nth second = a(2n−1)/2, so for n=3: 10(5)/2 = 25 m.

  2. Two events A and B satisfy P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2. What is P(A ∪ B)?

    Answer: 0.7

    By the addition rule, P(A ∪ B) = 0.4 + 0.5 − 0.2 = 0.7.

  3. A car of mass 1200 kg decelerates from 30 m/s to rest in 15 s. What braking force is applied?

    Answer: 2400 N

    Deceleration a = 30/15 = 2 m/s², so braking force = 1200 × 2 = 2400 N.

  4. The function f(x) = 2x³ − 9x² + 12x has stationary points at which x-values?

    Answer: x = 1 and x = 2

    f'(x) = 6x² − 18x + 12 = 6(x−1)(x−2) = 0 gives x = 1 and x = 2.

  5. A uniform rod of mass 5 kg and length 2 m is suspended horizontally by two vertical strings at each end. What is the tension in each string? (g = 9.8 m/s²)

    Answer: 24.5 N

    By symmetry each string bears half the weight: T = ½ × 5 × 9.8 = 24.5 N.

  6. A random variable X ~ N(50, 16). What is P(X < 54)?

    Answer: 0.8413

    Standardizing: z = (54−50)/4 = 1, so P(X < 54) = Φ(1) ≈ 0.8413.

  7. A population P satisfies dP/dt = 0.02P with P(0) = 500. What is P(10)?

    Answer: 500e^0.2

    Solving the separable ODE gives P = 500e^(0.02t), so P(10) = 500e^0.2.