TMUA Applied Mathematics 3 — Questions and Answers
Question 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?
- 25 m (Correct answer)
- 15 m
- 20 m
- 30 m
Correct 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.
Question 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)?
- 0.9
- 0.7 (Correct answer)
- 0.6
- 0.8
Correct answer: 0.7
By the addition rule, P(A ∪ B) = 0.4 + 0.5 − 0.2 = 0.7.
Question 3: A car of mass 1200 kg decelerates from 30 m/s to rest in 15 s. What braking force is applied?
- 1200 N
- 2400 N (Correct answer)
- 2000 N
- 1800 N
Correct answer: 2400 N
Deceleration a = 30/15 = 2 m/s², so braking force = 1200 × 2 = 2400 N.
Question 4: The function f(x) = 2x³ − 9x² + 12x has stationary points at which x-values?
- x = 1 and x = 2 (Correct answer)
- x = 0 and x = 3
- x = 1 and x = 3
- x = 2 and x = 4
Correct answer: x = 1 and x = 2
f'(x) = 6x² − 18x + 12 = 6(x−1)(x−2) = 0 gives x = 1 and x = 2.
Question 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)
- 25 N
- 50 N
- 10 N
- 24.5 N (Correct answer)
Correct answer: 24.5 N
By symmetry each string bears half the weight: T = ½ × 5 × 9.8 = 24.5 N.
Question 6: A random variable X ~ N(50, 16). What is P(X < 54)?
- 0.8413 (Correct answer)
- 0.9772
- 0.6915
- 0.7257
Correct answer: 0.8413
Standardizing: z = (54−50)/4 = 1, so P(X < 54) = Φ(1) ≈ 0.8413.
Question 7: A population P satisfies dP/dt = 0.02P with P(0) = 500. What is P(10)?
- 500e^0.2 (Correct answer)
- 500e^0.02
- 600
- 500e^2
Correct answer: 500e^0.2
Solving the separable ODE gives P = 500e^(0.02t), so P(10) = 500e^0.2.
TMUA Applied Mathematics 3
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?