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.

206.

A rectangular pyramid has an area 24cm\(^2\) and height 7.5cm. Find its volume?

A.

65.0cm\(^3\)

B.

70.5cm\(^3\)

C.

56.5cm\(^3\)

D.

60.0cm\(^3\)

Correct answer is D

Volume of a rectangular pyramid = \(\frac{length * width * height}{3}\) or \(\frac{area * height}{3}\)

= \(\frac{24 * 7.5}{3}\) → \(\frac{180}{3}\)

Volume of the rectangular pyramid = 60cm\(^3\)

208.

Find the length of a chord 3cm from the centre of a circle of radius 5cm

A.

8cm

B.

5.6cm

C.

7cm

D.

6.5cm

Correct answer is A

Using pythagoras formula:

Hyp\(^2\) = adj\(^2\) + opp\(^2\)

5\(^2\) = opp\(^2\) + 3\(^2\) 

5\(^2\) - 3\(^2\) = adj\(^2\)

4 = adj

length of the chord = 2 * 4 = 8cm

209.

Simplify \(\frac{1}{3-√2}\) in the form of p + q√2

A.

\(\frac{7}{3}\) - \(\frac{1}{7√2}\)

B.

\(\frac{7}{3}\) + \(\frac{1}{7√2}\)

C.

\(\frac{3}{7}\) - \(\frac{1}{7√2}\)

D.

\(\frac{3}{7}\) + \(\frac{√2}{7}\)

Correct answer is D

Rationalization with conjugate \({3+√2}\)

 \(\frac{1}{3-√2}\)

→ \(\frac{1 * [3+√2]}{[3-√2][3+√2]}\)

=  \(\frac{3+√2}{9 -3√2 + 3√2 + √4}\)

=  \(\frac{3+√2}{9 - 2}\) →  \(\frac{3+√2}{7}\)

= \(\frac{3}{7}\) +  \(\frac{√2}{7}\)

210.

If sin θ = -  \(\frac{3}{5}\) and θ lies in the third quadrant, find cos θ

A.

\(\frac{4}{5}\)

B.

- \(\frac{5}{4}\)

C.

\(\frac{5}{4}\)

D.

- \(\frac{4}{5}\)

Correct answer is D

Where sin θ = \(\frac{opp}{hyp}\) → \(\frac{-3}{5}\)

opp = -3, hyp = 5

using pythagoras formula 

hyp\(^2\) = adj\(^2\) + opp\(^2\)

adj\(^2\) = hyp\(^2\) - opp\(^2\)

adj\(^2\) = 5\(^2\) - 3\(^2\) → 25 - 9

adj\(^2\) = 16

adj = 4

cos θ = \(\frac{adj}{hyp}\) → \(\frac{4}{5}\)

In third quadrant: cos θ is negative → - \(\frac{4}{5}\)