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.

81.

Find the volume of the cylinder above
[Take \(\pi= ^{22}/_7\)]

A.

9,856 cm\(^3\)

B.

14,784 cm\(^3\)

C.

4,928 cm\(^3\)

D.

19,712 cm\(^3\)

Correct answer is B

Volume of the cylinder = \(\frac{θ}{360} \times \pi r^2h\)

θ = 360\(^o\) - 90\(^o\) = 270\(^o\)

∴ Volume of the cylinder = \(\frac{270}{360} \times \frac{22}{7} \times \frac{14^2}{1} \times \frac{32}{1} = \frac{37,255,680}{2520} = 14,784cm^3\)

82.

Find the compound interest (CI) on ₦15,700 for 2 years at 8% per annum compounded annually.

A.

₦6,212.48

B.

₦2,834.48

C.

₦18,312.48

D.

₦2,612.48

Correct answer is D

Principal (P) = ₦15,700

Rate (R) = 8

Number of years (t) = 2

A = P \((1+\frac{R}{100})^t\)

⇒ A = 15700 \((1+\frac{8}{100})^2\)

⇒ A = 15700 (1 + 0.08)\(^2\)

⇒ A = 15700 (1.08)\(^2\)

⇒ A = 15700 x 1.1664

⇒ A = ₦18,312.48

Total amount, A = ₦18,312.48

A = P + CI

⇒ CI = A - P

⇒ CI = 18,312.48 - 15,700

∴ CI = ₦2,612.48

83.

Find the area, to the nearest cm\(^2\), of the triangle whose sides are in the ratio 2 : 3 : 4 and whose perimeter is 180 cm.

A.

1162 cm\(^2\)

B.

1163 cm\(^2\)

C.

1160 cm\(^2\)

D.

1161 cm\(^2\)

Correct answer is A

Let the length of the sides of triangle be 2x, 3x and 4x.

Perimeter of triangle = 180cm

⇒ \(2x +3x + 4x = 180\)

⇒ \(9x = 180\)

⇒ \(x = \frac{180}{9}\) = 20cm

Then the sides of the triangle are:

\(2x = 2\times20 = 40cm; 3x = 3\times20\) = 60cm and \(4x\) = 4\(\times20 \)= 80cm

Using Heron's formula

Area of triangle = \(\sqrt s(s-a)(s-b)(s-c)\)

Where s = \(\frac{a + b + c}{2}\)

Let a = 40cm, b = 60cm, c = 80cm and s = \(\frac{40 + 60 + 80}{2} = \frac{180}{2}\) = 90cm

⇒ A = \(\sqrt90 (90 - 40) (90 - 60) (90 - 80) = \sqrt90 \times 50 \times 30 \times 10 = \sqrt1350000\)

∴ A =1162cm\(^2\) (to the nearest cm\(^2)\)

84.

A man sells different brands of an items. \(^1/_9\) of the items he has in his shop are from Brand A, \(^5/_8\) of the remainder are from Brand B and the rest are from Brand C. If the total number of Brand C items in the man's shop is 81, how many more Brand B items than Brand C does the shop has?

A.

243

B.

108

C.

54

D.

135

Correct answer is C

Let the total number of items in the man's shop = \(y\)

Number of Brand A's items in the man's shop = \(\frac {1}{9} y\)

Remaining items = 1 - \(\frac {1}{9} y = \frac {8}{9} y\)

Number of Brand B's items in The man's shop = \(\frac{5}{8} of \frac{8}{9}y = \frac{5}{9}y\)

Total of Brand A and Brand B's items = \(\frac{1}{9}y + \frac{5}{9}y = \frac{2}{3}y\)

Number of Brand C's items in the man's shop = 1 - \(\frac{2}{3}y = \frac{1}{3}y\)

\(\implies\frac{1}{3}y\) = 81 (Given)

\(\implies y\) = 81 x 3 = 243

∴ The total number of items in the man's shop = 243

∴ Number of Brand B's items in the man's shop = \(\frac{5}{9}\) x 243 = 135

∴ The number of more Brand B items than Brand C = 135 - 81 =54

85.

A rectangular plot of land has sides with lengths of 38 m and 52 m corrected to the nearest m. Find the range of the possible values of the area of the rectangle

A.

1931.25 m\(^2\) ≤ A < 2021.25 m\(^2\)

B.

1950 m\(^2\) ≤ A < 2002 m\(^2\)

C.

1957 m\(^2\) ≤ A < 1995 m\(^2\)

D.

1931.25 m\(^2\) ≥ A > 2021.25 m\(^2\)

Correct answer is A

The sides have been given to the nearest meter, so

51.5 m ≤ length < 52.5

37.5 m ≤ width < 38.5

Minimum area = 37.5 x 51.5 = 1931.25 m\(^2\)

Maximum area = 38.5 x 52.5 = 2021.25 m\(^2\)

∴ The range of the area = 1931.25 m\(^2\) ≤ A < 2021.25 m\(^2\)