WAEC Further Mathematics Past Questions & Answers - Page 82

406.

A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Calculate the distance covered in the first 2 seconds.

A.

2m

B.

4m

C.

6m

D.

8m

Correct answer is B

\(v(t) = (3t^{2} - 2t) ms^{-1}\)

\(s(t) = \int v(t) \mathrm {d} t\)

= \(\int (3t^{2} - 2t) \mathrm {d} t = t^{3} - t^{2}\)

\(s(2) = 2^{3} - 2^{2} = 8 - 4 = 4m\)

407.

A body of mass 25kg changes its speed from 15m/s to 35m/s in 5 seconds by the action of an applied force F. Find the value of F.

A.

100N

B.

375N

C.

500N

D.

600N

Correct answer is A

\(F = ma = m(\frac{v - u}{t})\)

\(F = 25(\frac{35 - 15}{5}) = 25 \times 4 = 100N\)

408.

Two forces 10N and 15N act on an object at an angle of 120° to each other. Find the magnitude of the resultant.

A.

\(5\sqrt{5}N\)

B.

\(5\sqrt{7}N\)

C.

\(7\sqrt{5}N\)

D.

\(7\sqrt{7}N\)

Correct answer is B

No explanation has been provided for this answer.

409.

A force of 200N acting on a body of mass 20kg initially at rest causes it to move a distance of 320m along a straight line for t secs. Find the value of t.

A.

4s

B.

6s

C.

8s

D.

10s

Correct answer is C

F = ma

\(200 = 20a \implies a = 10m/s^{2}\)

\(s = ut + \frac{1}{2}at^{2}\)

\(320 = (0 \times t) + \frac{1}{2} 10t^{2}\)

\(320 = 5t^{2} \implies t^{2} = 64\)

\(t = 8secs\)

410.

A basket contains 3 red and 1 white identical balls. A ball is drawn from the basket at random. Calculate the probability that it is either white or red.

A.

\(\frac{1}{3}\)

B.

\(\frac{1}{2}\)

C.

\(\frac{3}{4}\)

D.

1

Correct answer is D

P(white or red) = P(white) + P(red)

= \(\frac{3}{4} + \frac{1}{4}\)

= 1