TMUA Applied Mathematics 2

Question 1

A particle moves in a straight line with velocity v = 3t² − 12t + 9 m/s. At what time(s) is the particle momentarily at rest?

Accepted Answer

t = 1 s and t = 3 s

Answer

Setting v = 0 gives 3t² − 12t + 9 = 0, factoring to 3(t−1)(t−3) = 0, so t = 1 s and t = 3 s.

Question 2

A ball is projected vertically upward with speed 20 m/s from ground level. Taking g = 10 m/s², what is the maximum height reached?

Accepted Answer

20 m

Answer

Using v² = u² − 2gs with v = 0 gives s = u²/(2g) = 400/20 = 20 m.

Question 3

A force of 12 N acts on a mass of 3 kg starting from rest. What is the speed after 4 seconds?

Accepted Answer

16 m/s

Answer

Acceleration a = F/m = 12/3 = 4 m/s², then v = u + at = 0 + 4(4) = 16 m/s.

Question 4

A discrete random variable X has P(X = 1) = 0.3, P(X = 2) = 0.5, P(X = 3) = 0.2. What is E(X)?

Accepted Answer

1.9

Answer

E(X) = 1(0.3) + 2(0.5) + 3(0.2) = 0.3 + 1.0 + 0.6 = 1.9.

Question 5

A uniform beam of length 4 m and weight 200 N is supported at both ends. A 100 N load is placed 1 m from the left end. What is the reaction at the left support?

Accepted Answer

175 N

Answer

Taking moments about the right support: R_L × 4 = 200 × 2 + 100 × 3 = 700, so R_L = 175 N.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Applied Mathematics 2