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.

The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81

A.

12

B.

27

C.

9

D.

4

E.

36

Correct answer is C

1st term a = 3, 5th term = 9, sum of n = 81

nth term = a + (n - 1)d, 5th term a + (5 - 1)d = 9

3 + 4d = 9

4d = 9 - 3

d = \(\frac{6}{4}\)

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

= 6

Sn = \(\frac{n}{2}\)(6 + \(\frac{3}{4}\)n - \(\frac{3}{2}\))

81 = \(\frac{12n + 3n^2}{4}\) - 3n

= \(\frac{3n^2 + 9n}{4}\)

3n2 + 9n = 324

3n2 + 9n - 324 = 0

By almighty formula positive no. n = 9
= 3

1,892.

Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 - cos x}\) is

A.

sin x

B.

cos2x

C.

2

D.

3

Correct answer is C

\(\frac{\sin^{2} x}{1 + \cos x} + \frac{\sin^{2} x}{1 - \cos x}\)

\(\frac{\sin^{2} x (1 - \cos x) + \sin^{2} x (1 + \cos x)}{1 - \cos^{2} x}\)

= \(\frac{\sin^{2} x - \cos x \sin^{2} x + \sin^{2} x + \sin^{2} x \cos x}{\sin^{2} x}\)

(Note: \(\sin^{2} x + \cos^{2} x = 1\)).

= \(\frac{2 \sin^{2} x}{\sin^{2} x}\)

= 2.

1,893.

The area of a circular plate is one-sixteenth the surface area of a ball. If the area of the plate is given as P cm², then the radius of the ball is

A.

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

B.

\(\frac{P}{\sqrt{\pi}}\)

C.

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

D.

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

Correct answer is D

Surface area of a sphere = 4\(\pi\)r2

\(\frac{1}{16}\) of 4\(\pi\)r2

= \(\frac{\pi r^2}{4}\)

P = \(\frac{\pi r^2}{4}\)

r = 2\(\frac{P}{\pi}\)

1,894.

The difference between the length and width of a rectangle is 6cm and the area is 135cm². What is the length?

A.

25cm

B.

18cm

C.

15cm

D.

24cm

E.

27cm

Correct answer is C

Area = L x B

L - B = 6

L = 6 + B

area = 135

B(6 + B) = B2 + 6B - 135 = 0

B = 9

L = 6 + 9

= 15

1,895.

The positive root of t in the following equation, 4t2 + 7t - 1 = 0, correct to 4 places of decimal, is

A.

1.0622

B.

10.6225

C.

0.1328

D.

0.3218

E.

2.0132

Correct answer is C

\(4t^{2} + 7t - 1 = 0\)

Using a = 4, b = 7, c = -1.

\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

= \(\frac{-7 \pm \sqrt{7^{2} - 4(4)(-1)}}{2(4)}\)

= \(\frac{-7 \pm \sqrt{49 + 16}}{8}\)

= \(\frac{-7 \pm \sqrt{65}}{8}\)

= \(\frac{-7 \pm 8.0623}{8}\)

The positive answer = \(\frac{-7 + 8.0623}{8} = \frac{1.0623}{8}\)

\(\approxeq 0.1328\) (4 decimal place)