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.

1,921.

The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r : t. In 1980, the price of a loaf went up by 25% and that of a packet of sugar went up by 10%. Their new ratio is now

A.

40r:50t

B.

44r : 50t

C.

50r : 44t

D.

44r:55t

E.

55r:44t

Correct answer is C

Ratio of bread to sugar = r:t

25% increase in bread = \(\frac{125r}{100}\)

10% increase in sugar = \(\frac{100t}{100}\)

New ratio = \(\frac{125r}{100}\):\(\frac{110t}{100}\)

= 25r:22t

= 50r:44t

1,922.

If sine x equals cosine x, what is x in radians?

A.

\(\frac{\pi}{2}\)

B.

\(\frac{\pi}{3}\)

C.

\(\frac{\pi}{4}\)

D.

\(\frac{\pi}{6}\)

E.

\(\frac{\pi}{12}\)

Correct answer is C

\(\sin x = \cos x\)

\(\implies x = 45°\)

In radians, \(x = \frac{\pi}{4}\).

1,923.

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)

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

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

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

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

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

1,924.

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

1,925.

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