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.

3,821.

What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?

A.

B.

16π

C.

D.

Correct answer is A

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

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

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

= \(8\pi\)

3,822.

Find the derivatives of (2 + 3x)(1 - x) with respect to x

A.

6

B.

-3

C.

1 - 6x

D.

6x - 1

Correct answer is C

y = (2 + 3x)(1 - x)
y = 2 - 2x + 3x - 3x2
y = 2 + x - 3x2
dy/dx = 1 - 6x

3,823.

If y = 3 cos(x/3), find dy/dx when x = (3π/2)

A.

1

B.

-3

C.

2

D.

-1

Correct answer is D

y = 3cos(x/3)
dy/dx = 3x(1/3)x - sin (x/3)
= - sin x/3
But x = 3π/2 ∴ -sin(x/3) = -sin(3π/6)
= -sin (3 * 180)/6
= - sin 90
= -1

3,824.

The locus of a point which is 5 cm from the line LM is a

A.

line distance 10 cm from LM and parallel to LM

B.

pair of line on opposite sides of LM and parallel to it, each distance 5 cm from LM

C.

line parallel to LM and 5 cm from LM

D.

pair of parallel lines on one side of LM and parallel to LM

Correct answer is B

The locus of a point which is 5cm from the line LM is a pair of lines on opposite sides of LM and parallel to it, each distance 5cm from LM.

3,825.

P, R and S lie on a circle center as shown above while Q lies outside the circle. Find ∠PSO

A.

45o

B.

55o

C.

35o

D.

40o

Correct answer is C

xo = 35 + 29 (Exterior angle = sum of two interior opposite angles)
x = 55o (∠ at the center twice ∠ at circumference) y = 110o
∠PSO = ∠SPO (base ∠S of 1sc Δ b/c PO = SO)
∴ ∠PSO = (180 - 110)/2
= 35o