TMUA Applied Mathematics 3

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?

Accepted Answer

25 m

Answer

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)?

Accepted Answer

0.7

Answer

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?

Accepted Answer

2400 N

Answer

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?

Accepted Answer

x = 1 and x = 2

Answer

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)

Accepted Answer

24.5 N

Answer

By symmetry each string bears half the weight: T = ½ × 5 × 9.8 = 24.5 N.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Applied Mathematics 3