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.

1,891.

Suppose x varies inversely as y, y varies directly as the square of t and x = 1, when t = 3. Find x when t = \(\frac{1}{3}\).

A.

81

B.

27

C.

\(\frac{1}{9}\)

D.

\(\frac{1}{27}\)

E.

\(\frac{1}{81}\)

Correct answer is A

\(x \propto \frac{1}{y}\)

\(x = \frac{k}{y}\)

\(y \propto t^{2}\)

\(y = ct^{2}\) 

k and c are constants.

\(x = \frac{k}{ct^{2}}\)

Let \(\frac{k}{c} = d\) (a constant)

\(x = \frac{d}{t^{2}}\)

\(1 = \frac{d}{3^{2}} \implies d = 9\)

\(\therefore x = \frac{9}{t^{2}}\)

\(x = 9 \div (\frac{1}{3})^{2} \)

= \( 9 \div \frac{1}{9} = 9 \times 9 = 81\)

1,892.

The arithmetic mean of the ages of 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl?

A.

30 years

B.

6 years

C.

9 years

D.

3 years

E.

1 year

Correct answer is D

1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs 2nd group of 30 pupils at average age of 15.2 yrs give total age of 15.2 x 30 = 456yrs Difference in age = 459 - 456 = 3 yrs

1,893.

Two distinct sectors in the same circle substend 100° and 30° respectively at the centre of the circle. Their corresponding arcs are in ratio

A.

10:3

B.

1:100

C.

3:1

D.

5:2

Correct answer is A

The distinct sectors in the same circle substend 100o and 30o respectively at the centre of the circle. Their corresponding arcs are in ratio 100:30 = 10:3

1,894.

A variable y is inversely proportional to x2, when y = 10, x = 2. What is y when x = 10?

A.

2

B.

4

C.

100

D.

0.4

E.

0.1

Correct answer is D

y \(\alpha\) \(\frac{1}{x^2}\)

y = \(\frac{k}{x^2}\)

k = x2y

= (2)2 x 10

= 40

y = \(\frac{40}{x^2}\)

= \(\frac{40}{(10)^2}\)

= \(\frac{40}{100}\)

= 0.4

1,895.

A side of a rhombus is 2cm in length. An angle of the rhombus is 60°. What is the length of the diagonal facing this angle?

A.

2cm

B.

8cm

C.

4cm

D.

2\(\sqrt{3}\)cm

E.

16cm

Correct answer is D

\(\frac{x}{2}\) = sin60° = cos30°

x = 2 sino

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

= \(\sqrt{3}\)

length of the diagonal = 2 x \(\sqrt{2}\)

= 2\(\sqrt{3}\)