TMUA Applied Mathematics 4 — Questions and Answers
Question 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?
- 60 m (Correct answer)
- 45 m
- 80 m
- 120 m
Correct answer: 60 m
Time of flight: 80 = ½(10)t² → t = 4 s; horizontal distance = 15 × 4 = 60 m.
Question 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)
- 2 N (Correct answer)
- 6 N
- 8 N
- 4 N
Correct answer: 2 N
Friction = μmg = 0.3 × 2 × 10 = 6 N; net force = 8 − 6 = 2 N.
Question 3: The displacement of a particle is s(t) = t³ − 6t² + 9t. What is the total distance travelled between t = 0 and t = 3?
- 4 m
- 6 m
- 8 m (Correct answer)
- 12 m
Correct 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.
Question 4: Two independent events A and B have P(A) = 0.3 and P(B) = 0.4. What is P(A' ∩ B')?
- 0.42 (Correct answer)
- 0.58
- 0.12
- 0.70
Correct answer: 0.42
P(A' ∩ B') = P(A')P(B') = 0.7 × 0.6 = 0.42.
Question 5: A trapezium rule estimate for ∫₀⁴ x² dx uses 4 equal strips of width 1. What is the estimate?
- 22 (Correct answer)
- 21.5
- 24
- 20
Correct 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.
Question 6: A particle's displacement is x = 4sin(2t). What is the magnitude of the maximum acceleration?
- 4
- 8
- 16 (Correct answer)
- 2
Correct answer: 16
a = d²x/dt² = −16sin(2t); maximum magnitude is 16 when |sin(2t)| = 1.
Question 7: A bag contains 4 red and 6 blue balls. Two are drawn without replacement. What is the probability both are red?
- 2/15 (Correct answer)
- 4/25
- 1/6
- 4/15
Correct answer: 2/15
P(both red) = (4/10) × (3/9) = 12/90 = 2/15.
TMUA Applied Mathematics 4
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?