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.

501.

Find the length of the chord |AB| in the diagram shown above.

A.

4.2 cm

B.

4.3 cm

C.

3.2 cm

D.

3.4 cm

Correct answer is D

Length of chord = \(2r \sin (\frac{\theta}{2})\)

= \(2(3) \sin (\frac{68}{2})\)

= \(6 \sin 34\)

= \(6 \times 0.559\)

= 3.354 cm \(\approxeq\)  3.4 cm

502.

Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)

A.

\(-5 - 2\sqrt{6}\)

B.

\(-5 + 3\sqrt{2}\)

C.

\(5 - 2\sqrt{3}\)

D.

\(5 + 2\sqrt{6}\)

Correct answer is A

\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)

= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\)

= \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\)

= \(\frac{5 + 2\sqrt{6}}{-1}\)

= \(- 5 - 2\sqrt{6}\)

503.

In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology?

A.

42

B.

20

C.

70

D.

54

Correct answer is B

n(Total) = 50

n(Physics) = 40

n(Biology) = 30

Let n(Physics and Biology) = x

n(Physics only) = 40 -x

n(Biology only) = 30 - x

40 - x + 30 - x + x = 50

70 - x = 50

x = 20

504.

A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).

A.

6

B.

25

C.

15

D.

18

Correct answer is C

\(m \otimes n = mn + m - n\)

3 \(\otimes\) (2 \(\otimes\) 4)

2 \(\otimes\) 4 = 2(4) + 2 - 4 = 6

3 \(otimes\) 6 = 3(6) + 3 - 6  = 15

505.

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.

A.

148m

B.

382m

C.

282m

D.

248m

Correct answer is C

\(\tan 78 = \frac{h}{60}\)

\(h = 60 \tan 78\)

\(h = 60 \times 4.705 = 282.27m\)

\(\approxeq\) 282m to the nearest whole number.