JAMB Mathematics Past Questions & Answers

876.

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

$\frac{1}{9}$

$\frac{1}{27}$

$\frac{1}{81}$

View answer & explanation

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)

$x = \frac{d}{t^{2}}$

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

$\therefore x = \frac{9}{t^{2}}$

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

= $9 \div \frac{1}{9} = 9 \times 9 = 81$

877.

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?

30 years

6 years

9 years

3 years

1 year

View answer & explanation

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

878.

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

10:3

1:100

3:1

5:2

View answer & explanation

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

879.

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

100

0.4

0.1

View answer & explanation

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