TMUA Applied Mathematics 5 — Questions and Answers
Question 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)
- 57.7 N (Correct answer)
- 100 N
- 173 N
- 86.6 N
Correct 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.
Question 2: A sample of 5 values has mean 8 and variance 4. What is Σx²?
- 340 (Correct answer)
- 320
- 360
- 400
Correct answer: 340
Variance = Σx²/n − x̄² gives 4 = Σx²/5 − 64, so Σx² = 5 × 68 = 340.
Question 3: A car accelerates from 10 m/s to 30 m/s over 200 m. What is the constant acceleration?
- 2 m/s² (Correct answer)
- 4 m/s²
- 3 m/s²
- 1 m/s²
Correct answer: 2 m/s²
v² = u² + 2as: 900 = 100 + 400a → a = 800/400 = 2 m/s².
Question 4: The function y = xe^(−x) has a local maximum at x = 1. What is the maximum value of y?
- e^(−1) (Correct answer)
- 1
- e
- 2e^(−1)
Correct answer: e^(−1)
Substituting x = 1: y = 1 × e^(−1) = e^(−1) ≈ 0.368.
Question 5: A Poisson random variable has mean λ = 3. What is the probability of exactly 2 events?
- 3e^(−3)/2
- 9e^(−3)/2 (Correct answer)
- 3e^(−3)
- 6e^(−3)
Correct answer: 9e^(−3)/2
P(X=2) = e^(−3) × 3²/2! = 9e^(−3)/2.
Question 6: An object slides down a frictionless incline at 30° to the horizontal. What is its acceleration? (g = 10 m/s²)
- 5 m/s² (Correct answer)
- 8.66 m/s²
- 10 m/s²
- 2.5 m/s²
Correct answer: 5 m/s²
The component of gravity along the slope is g sin30° = 10 × 0.5 = 5 m/s².
Question 7: A recurrence relation is defined by a_{n+1} = 2a_n − 3. What is the fixed point L where L = 2L − 3?
- 3 (Correct answer)
- 5
- 6
- 1
Correct answer: 3
Setting L = 2L − 3 gives −L = −3, so L = 3.
TMUA Applied Mathematics 5
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)