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.

2,196.

If a = -3, b = 2, c = 4, evaluate \(\frac{a^3 - b^3 - c^{\frac{1}{2}}}{b - a - c}\)

A.

37

B.

\(\frac{-37}{5}\)

C.

\(\frac{37}{5}\)

D.

-37

Correct answer is D

\(\frac{a^{3} - b^{3} - c^{\frac{1}{2}}}{b - a - c} = \frac{(-3)^{3} - (2)^{3} - 4^{\frac{1}{2}}}{2 - (-3) - 4}\)

= \(\frac{-37}{1} = -37\)

2,197.

If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3

A.

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

B.

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

C.

\(\frac{8}{27}\)

D.

\(\frac{4}{9}\)

Correct answer is C

\(x \propto \frac{1}{\sqrt[3]{y}} \implies x = \frac{k}{\sqrt[3]{y}}\)

When y = 8, x = 1

\(1 = \frac{k}{\sqrt[3]{8}} \implies 1 = \frac{k}{2}\)

\(k = 2\)

\(\therefore x = \frac{2}{\sqrt[3]{y}}\)

When x = 3,

\(3 = \frac{2}{\sqrt[3]{y}} \implies \sqrt[3]{y} = \frac{2}{3}\)

\(y = (\frac{2}{3})^{3} = \frac{8}{27}\)

2,198.

If \(\frac{1}{p}\) = \(\frac{a^2 + 2ab + b^2}{a - b}\) and \(\frac{1}{q}\) = \(\frac{a + b}{a^2 - 2ab + b^2}\) Find \(\frac{p}{q}\)

A.

\(\frac{a + b}{a - b}\)

B.

\(\frac{1}{a^2 - b^2}\)

C.

\(\frac{a - b}{a + b}\)

D.

a2 - b2

Correct answer is B

\(\frac{1}{p} = \frac{a^{2} + 2ab + b^{2}}{a - b}\)

\(\frac{1}{q} = \frac{a + b}{a^{2} - 2ab + b^{2}}\)

\(\frac{1}{p} = \frac{(a + b)^{2}}{a - b}\)

\(\frac{1}{q} = \frac{a + b}{(a - b)^{2}}\)

\(\therefore p = \frac{a - b}{(a + b)^{2}}\)

\(\frac{p}{q} = p \times \frac{1}{q} = \frac{a - b}{(a + b)^{2}} \times \frac{a + b}{(a - b)^{2}}\)

= \(\frac{1}{(a + b)(a - b)}\)

= \(\frac{1}{a^{2} - b^{2}}\)

2,199.

If n is the median and m is the mode of the following set of numbers, 2.4, 2.1, 1.6, 2.6, 2.6, 3.7, 2.1, 2.6, then (n, m) is

A.

(2.6, 2.6)

B.

(2.5, 2.6)

C.

(2.6, 2.5)

D.

(2.5, 2.1)

Correct answer is B

Arrange the numbers in order, 1.6, 2.1, 2.1| 2.4, 2.6| 2.6, 2.6, 3.7

n = median = \(\frac{2.4 + 2.6}{2}\)

= 2.5

m = mode = 2.6

∴ (n, m) = (2.5, 2.6)

2,200.

In a family of 21 people, the average age is 14years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather?

A.

35 years

B.

40 years

C.

42 years

D.

54 years

Correct answer is C

Total age of the whole family = 21 x 14 = 294

Total age without the grandfather = 21 x 12 = 252

Age of grandfather = 294 - 252

= 42 years