TMUA Applied Mathematics 5

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)

Accepted Answer

57.7 N

Answer

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?

Accepted Answer

340

Answer

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?

Accepted Answer

2 m/s²

Answer

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?

Accepted Answer

e^(−1)

Answer

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?

Accepted Answer

9e^(−3)/2

Answer

P(X=2) = e^(−3) × 3²/2! = 9e^(−3)/2.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Applied Mathematics 5