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.

726.

If U = {x : x is an integer and 1 ≤ x ≤ 20 }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2

A.

\(\frac{3}{4}\)

B.

\(\frac{3}{10}\)

C.

\(\frac{1}{4}\)

D.

\(\frac{1}{20}\)

Correct answer is A

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

E1 = {3, 6, 9, 12, 15, 18}

E2 = {4, 8, 12, 16, 20}

Probability of E2 = \(\frac{5}{20}\) i.e \(\frac{\text{Total number in}E_2}{\text{Entire number in set}}\)

Probability of set E2 = 1 − \(\frac{5}{20}\)

= \(\frac{15}{20}\)

= \(\frac{3}{4}\)

727.

What is the next number in the series 2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\)...

A.

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

B.

\(\frac{2}{8}\)

C.

\(\frac{3}{7}\)

D.

\(\frac{1}{8}\)

Correct answer is D

2, 1, \(\frac{1}{2}\), \(\frac{1}{4}\).....

There are 4 terms in the series
Therefore the next number will be the 5th term

Tn = ar\(^{n − 1}\) (formular for geometric series)

a = first term = 2

r = common rate = \(\frac{\text{next term}}{\text{previous term}}\) = \(\frac{1}{2}\)

n = number of terms

T5 = 5th term = ?

T5 = ar\(^{5 - 1}\)

= ar\(^4\)

= 2 × (ar\(^{n − 1}\))4

= 2 × \(\frac{1}{16}\)

= \(\frac{1}{8}\)

728.

Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N

A.

{2, 3}

B.

{2, 3, 4}

C.

{3, 4, 6}

D.

{2}

Correct answer is D

T = {evenn numbers from 1 to 12} N = {common factors of 6,8 and 12} Find T ∩ N T = {2, 4, 6, 8, 10, 12} N = {2} T ∩ N = {2} i.e value common to T & N

729.

From the diagram, which of the following is true?

A.

m + n + p = 180o

B.

m + n = 180o

C.

m = p + n

D.

n = m + p

Correct answer is D

In the diagram, \(\beta\) = p(vertically opposite angles)

m + \(\beta\) = n(sum of interior opp. angles)

m + p = n

730.

An object is 6m away from the base of a mast. If the angle of depression of the object from the top of the mast is 50o, find, correct to 2 decimal places, the height of the mast.

A.

8.60m

B.

7.83m

C.

7.51m

D.

7.15m

Correct answer is D

In the diagram give, \(\alpha\) 50o(alternative angles)

tan\(\alpha\) = \(\frac{h}{6}\)

h = 6tan\(\alpha\)

= 6tan 50o

= 6 x 1.1918

= 7.1508

= 7.15m (2d.p)