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.

36.

Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)

A.

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

B.

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

C.

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

D.

\(\frac{5}{3}\)

Correct answer is B

\(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)

applying the laws of indices

\(2^{5x - x} = 2^{10(1/5)}\)

\(2^{4x} = 2^{10(1/5)}\)

\(2^{4x} = 2^2\)
Equating the powers
then 4x = 2

therefore, x = \(\frac{2}{4}\) = \(\frac{1}{2}\) 

37.

The interior angle of a regular polygon is 6 times its exterior angle find the number of sides of the polygon.

A.

12

B.

15

C.

10

D.

14

Correct answer is D

each interior angle of a polygon = \(\frac{(n - 2)\times 180}{n}\) where n = no of side of a polygon

each exterior angle of a polygon = \(\frac{360}{n}\)

then  \(\frac{(n - 2)\times 180}{n}\) = 6\(\times\) \(\frac{360}{n}\)

= (n - 2) 180 = 2160

= 180n - 360 = 2160

= 180n = 2160 + 360

= 180n = 2520

therefore, n = \(\frac{2520}{180}\) = 14.

38.

Evaluate, correct to three decimal place \(\frac{4.314 × 0.000056}{0.0067}\)

A.

0.037

B.

0.004

C.

0.361

D.

0.036

Correct answer is D

\(\frac{4.314 × 0.000056}{0.0067}\)

\(\frac{0.000242}{0.0067}\)

= 0.036 ( to 3 decimal places)

39.

Express \(413_7\) to base 5

A.

\(2311_5\)

B.

\(1131_5\)

C.

\(1311_5\)

D.

\(2132_5\)

Correct answer is C

\(413_7\) to base 5 

convert first to base 10

\(417_7 = 4 × 7^2 + 1 × 7^1 + 3 × 7^0\)
= 4 × 49 + 1 × 7 + 3 × 1
= 196 + 7 + 3

= \(206_{10}\)

convert this result to base 5

5 206
5 41R1
5 8R1
5 1R3
  0R1

\(∴ 413_7 = 1311_5\)

40.

For what value of x is  \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\)  is undefined?

A.

\(\frac{1}{5}, \frac{3}{2}\)

B.

\(\frac{-1}{5}, \frac{3}{2}\)

C.

\(\frac{1}{5}, \frac{-3}{2}\)

D.

\(\frac{-1}{5}, \frac{-3}{2}\)

Correct answer is B

The fraction  \(\frac{ x^2 + 2 }{ 10x^2 - 13x - 3}\)  is undefined when the denominator is equal to zero

\(then  10x^2 - 13x - 3 = 0\)

by factorisation,  \(10x^2 - 13x - 3\) = 0 becomes \( 10x^2 - 15x +2x -3\) = 0

\(5x(2x - 3) + 1(2x - 3) = 0\)

\((5x + 1)(2x - 3) = 0\)

\(then, x = \frac{-1}{5}\) or \(\frac{3}{2}\)