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.

1,741.

A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is

A.

1cm

B.

\(\sqrt{\frac{3\pi}{24}}\)

C.

\(\frac{\pi}{24\sqrt{3}}\)

D.

24\(\sqrt{3}\)

Correct answer is C

The rise of water is equivalent to the volume of the sphere of radius \(\frac{1}{2}\)cm immersed x \(\frac{1}{\text{No. of sides sq. root 3}}\)

Vol. of sphere of radius = 4\(\pi\) x \(\frac{1}{8}\) x \(\frac{1}{3}\) - (\(\frac{1}{2}\))3

= \(\frac{1}{8}\)

= \(\frac{\pi}{6}\) x \(\frac{1}{4\sqrt{3}}\)

= \(\frac{\pi}{24\sqrt{3}}\)

1,742.

If sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3, then the angle \(\theta\) is equal to

A.

30o

B.

45o

C.

60o

D.

90o

E.

105o

Correct answer is B

sec\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3

Where 1 + tan\(^2\) \(\theta\) = sec\(^2\) \(\theta\)

1 + tan\(^2\) \(\theta\) + tan\(^2\) \(\theta\) = 3

2 tan\(^2\) \(\theta\) = 2

tan\(^2\) \(\theta\) = 1

tan\(\theta\) = √1

where √1 = 1

tan\(\theta\) = 1

And  tan 45°  = 1 

∴ \(\theta\) = 45°

1,743.

In a soccer competition in one season, a club had scored the following goals: 2, 0, 3, 3, 2, 1, 4, 0, 0, 5, 1, 0, 2, 2, 1, 3, 1, 4, 1 and 1. The mean, median and mode are respectively

A.

1, 1.8 and 1.5

B.

1.8, 1.5 and 1

C.

1.8, 1 and 1.5

D.

1.51, 1 and 1.8

E.

1.5, 1.8 and 1

Correct answer is B

By re-arranging the goals in ascending order 0. 0. 0. 0. 0, 1. 1. 1. 1. 1. 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5.

Mean = \(\frac{36}{20}\) = 1.8

Median = \(\frac{1 + 2}{2}\)

= \(\frac{3}{2}\)

= 1.5

Mode = 1

= 1.8, 1.5 and 1

1,744.

A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is

A.

36\(\pi\)cm2

B.

54\(\sqrt{3}\)cm2

C.

\(\sqrt{3}\)cm2

D.

\(\frac{1}{x - 1}\)

Correct answer is B

Sum of interior angle of hexagon = [2(6) - 4]90°

= 720°

sum of central angle = 360°

Each central angle = \(\frac{360}{6}\)

= 60°

Area of Hexagon = \(\frac{1}{2}\) x 6 x 6 sin 60°

\(\frac{36 \times 6\sqrt{3}}{2 \times 2}\)

= \(54 \sqrt{3}\)cm2

1,745.

A triangle has angles 30°, 15° and 135°. The side opposite to the angle 30° is length 6cm. The side opposite to the angle 135° is equal to

A.

12cm

B.

6cm

C.

6\(\sqrt{2}\)cm

D.

12\(\sqrt{2}\)cm

Correct answer is C

\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 135}\)

\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 45}\)

x = \(\frac{6 \times \sin 45}{\sin 30}\)

= \(6 \sqrt{2}\)cm