Mathematics questions and answers

Mathematics Questions and Answers

How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.

3,951.

X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.

A.

0.30

B.

0.50

C.

0.57

D.

1.80

Correct answer is A

P (X or Y) = P(X) + P(Y), when they are independent as given.
0.7 = 0.4 + P(Y)
P(Y) = 0.7 - 0.4 = 0.30

3,952.

If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?

A.

2.50m/s

B.

2.00 m/s

C.

0.25 m/s

D.

0.20 m/s

Correct answer is C

\(V = \frac{2}{3} \pi r^{3}\)

Given: \(\frac{\mathrm d V}{\mathrm d t} = 18\pi m^{3} s^{-1}\)

\(\frac{\mathrm d V}{\mathrm d t} = \frac{\mathrm d V}{\mathrm d r} \times \frac{\mathrm d r}{\mathrm d t}\)

\(\frac{\mathrm d V}{\mathrm d r} = 2\pi r^{2}\)

\(18\pi = 2\pi r^{2} \times \frac{\mathrm d r}{\mathrm d t}\)

\(\frac{\mathrm d r}{\mathrm d t} = \frac{18\pi}{2\pi r^{2}} = \frac{9}{r^{2}}\)

The rate of change of the radius when r = 6m,

\(\frac{\mathrm d r}{\mathrm d t} = \frac{9}{6^{2}} = \frac{1}{4}\)

= \(0.25 ms^{-1}\)

3,953.

A bowl is designed by revolving completely the area enclosed by y = x2 - 1, y = 3 and x ≥ 0 around the axis. What is the volume of this bowl?

A.

7π cubic units

B.

15π/2 cubic units

C.

8π cubic units

D.

17π/2 cubic units

Correct answer is B

30 π(y+1) dy = π[y2 + y30
= π(9/2 + 3) = 15π/2

3,954.

If y = 2x - sin2x, find dy/dx when x = π/4

A.

π

B.

C.

π/2

D.

-π/2

Correct answer is D

y = 2x cos2x - sin2x
dy/dx = 2 cos2x +(-2x sin2x) - 2 cos2x
= 2 cos2x - 2x sin2x - cos2x
= -2x sin2x
= -2 x (π/4) sin2 x (π/4)
= -(π/2) x 1 = -(π/2)

3,955.

Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)

A.

π

B.

π/2

C.

-π/2

D.

Correct answer is D

\(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta = \int^{\pi}_{0}\frac{-sin^{2}\theta}{sin^{2}\theta}\\ = \int^{\pi}_{0}d\theta = -\pi\)