JAMB Mathematics Past Questions & Answers - Page 381

1,901.

Find the curved surface area of a cone with circular base diameter 10 cm and height 12 cm

25 πcm²

65 πcm²

120 πcm²

156 πcm²

View answer & explanation

Correct answer is B

L² = 12² + 5²
= 144 + 25
= 169
L = √169
= 13
Curved surface Area = πrL
= ⁵/₁ * ¹³/₁ * π
= 65πcm²

1,902.

A sector of a circle has an area of 55 cm². If the radius of the circle is 10 cm, calculate the angle of the sector
[π = 22/7]

45^o

63^o

75^o

90^o

View answer & explanation

Correct answer is B

Area of a sector = \(\frac{\theta}{360}\times \pi r^2\\55=\frac{\theta}{360}\times \frac{22}{7}\times \frac{10\times 10}{1}\\\theta=\frac{360 \times 55 \times 7}{22 \times 10 \times 10}\\\theta = 63^{\circ}\)

1,903.

The sum of the interior angle of a regular polygon is 1800^o. Calculate the size of one exterior angle of the polygon

30^o

24^o

18^o

12^o

View answer & explanation

Correct answer is A

Sum of interior ∠s = 1800^o
∴(n - 2) 180^o = 1800^o
180n -360^o = 1800^o
180n = 1800^o + 360^o
180n = 2160^o
n = 2160^o/180^o
n = 12 sides
Each exterior ∠ = 360^o/n
= 360^o/12
= 30^o

1,904.

An operation * is defined on the set of real numbers by a * b = ab + 2(a + b + 1). find the identity element

-1

-2

View answer & explanation

Correct answer is C

a * b = ab + 2(a + b + 1)
let e be the identity element
∴ a * e = e * a = a
∴ a * e = a
ae + 2(a + e + 1) = a
ae + 2a + 2e + 2 = a
ae + 2e = a - 2a = 2
(a + 2)e = -a - 2
e = -a-2 / (a+2)
e = -(a+2) / (a+2)
e = -1