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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 stone is thrown horizontally at 15 m/s from a cliff 80 m high. Taking g = 10 m/s², how far from the base does it land?

    Answer: 60 m

    Time of flight: 80 = ½(10)t² → t = 4 s; horizontal distance = 15 × 4 = 60 m.

  2. A 2 kg object rests on a horizontal surface with μ = 0.3. A horizontal force of 8 N is applied. What is the net force? (g = 10 m/s²)

    Answer: 2 N

    Friction = μmg = 0.3 × 2 × 10 = 6 N; net force = 8 − 6 = 2 N.

  3. The displacement of a particle is s(t) = t³ − 6t² + 9t. What is the total distance travelled between t = 0 and t = 3?

    Answer: 8 m

    v = 0 at t=1 and t=3; s(0)=0, s(1)=4, s(3)=0; total distance = |4−0| + |0−4| = 8 m.

  4. Two independent events A and B have P(A) = 0.3 and P(B) = 0.4. What is P(A' ∩ B')?

    Answer: 0.42

    P(A' ∩ B') = P(A')P(B') = 0.7 × 0.6 = 0.42.

  5. A trapezium rule estimate for ∫₀⁴ x² dx uses 4 equal strips of width 1. What is the estimate?

    Answer: 22

    Ordinates: y₀=0, y₁=1, y₂=4, y₃=9, y₄=16; estimate = ½(1)[0 + 2(1+4+9) + 16] = ½(44) = 22.

  6. A particle's displacement is x = 4sin(2t). What is the magnitude of the maximum acceleration?

    Answer: 16

    a = d²x/dt² = −16sin(2t); maximum magnitude is 16 when |sin(2t)| = 1.

  7. A bag contains 4 red and 6 blue balls. Two are drawn without replacement. What is the probability both are red?

    Answer: 2/15

    P(both red) = (4/10) × (3/9) = 12/90 = 2/15.