TMUA Applied Mathematics 4

Question 1

A stone is thrown horizontally at 15 m/s from a cliff 80 m high. Taking g = 10 m/s², how far from the base does it land?

Accepted Answer

60 m

Answer

Time of flight: 80 = ½(10)t² → t = 4 s; horizontal distance = 15 × 4 = 60 m.

Question 2

A 2 kg object rests on a horizontal surface with μ = 0.3. A horizontal force of 8 N is applied. What is the net force? (g = 10 m/s²)

Accepted Answer

2 N

Answer

Friction = μmg = 0.3 × 2 × 10 = 6 N; net force = 8 − 6 = 2 N.

Question 3

The displacement of a particle is s(t) = t³ − 6t² + 9t. What is the total distance travelled between t = 0 and t = 3?

Accepted Answer

8 m

Answer

v = 0 at t=1 and t=3; s(0)=0, s(1)=4, s(3)=0; total distance = |4−0| + |0−4| = 8 m.

Question 4

Two independent events A and B have P(A) = 0.3 and P(B) = 0.4. What is P(A' ∩ B')?

Accepted Answer

0.42

Answer

P(A' ∩ B') = P(A')P(B') = 0.7 × 0.6 = 0.42.

Question 5

A trapezium rule estimate for ∫₀⁴ x² dx uses 4 equal strips of width 1. What is the estimate?

Accepted Answer

22

Answer

Ordinates: y₀=0, y₁=1, y₂=4, y₃=9, y₄=16; estimate = ½(1)[0 + 2(1+4+9) + 16] = ½(44) = 22.

(TMUA) Test of Mathematics for University Admission Practice Test