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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 5 m ladder of mass 20 kg rests against a smooth vertical wall, its foot on rough ground at 60° to horizontal. What is the reaction at the wall? (g = 10 m/s²)

    Answer: 57.7 N

    Moments about the foot: R_w × 5sin60° = 100 × 2.5cos60°, giving R_w = 250cos60°/(5sin60°) = 100/(2√3) ≈ 57.7 N.

  2. A sample of 5 values has mean 8 and variance 4. What is Σx²?

    Answer: 340

    Variance = Σx²/n − x̄² gives 4 = Σx²/5 − 64, so Σx² = 5 × 68 = 340.

  3. A car accelerates from 10 m/s to 30 m/s over 200 m. What is the constant acceleration?

    Answer: 2 m/s²

    v² = u² + 2as: 900 = 100 + 400a → a = 800/400 = 2 m/s².

  4. The function y = xe^(−x) has a local maximum at x = 1. What is the maximum value of y?

    Answer: e^(−1)

    Substituting x = 1: y = 1 × e^(−1) = e^(−1) ≈ 0.368.

  5. A Poisson random variable has mean λ = 3. What is the probability of exactly 2 events?

    Answer: 9e^(−3)/2

    P(X=2) = e^(−3) × 3²/2! = 9e^(−3)/2.

  6. An object slides down a frictionless incline at 30° to the horizontal. What is its acceleration? (g = 10 m/s²)

    Answer: 5 m/s²

    The component of gravity along the slope is g sin30° = 10 × 0.5 = 5 m/s².

  7. A recurrence relation is defined by a_{n+1} = 2a_n − 3. What is the fixed point L where L = 2L − 3?

    Answer: 3

    Setting L = 2L − 3 gives −L = −3, so L = 3.