WAEC Mathematics Past Questions & Answers - Page 98

486.

An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))

A.

8800cm2

B.

8448cm2

C.

4400cm2

D.

4224cm2

Correct answer is A

L2 = 962 + 282

= 9216 + 784

= 10000

L = \(\sqrt{10000}\)

= 100cm

curved surface area = \(\pi r l\)

= \(\frac{22}{7} \times 28 \times 100\)

= 8800cm2

area of cone = area of sector

area of sector = 8800cm2

487.

Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M

A.

(x + 2)2

B.

x(x + 2)

C.

xv + 2

D.

x2 - x

Correct answer is D

(x = 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2)m

(m + 2)[(x2 - 3x + 2) + 2(x - 1)] = (x + 2)M

divide both side by (x + 2)

(x2 - 3x + 2) + 2(x - 1) = M

x2 - 3x + 2 + 2x - 2 = M

x2 - 3x + 2 + 2x - 2 = M

x2 - 3x + 2x = M

x2 - x = M

M = x2 - x

488.

The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used

A.

1: 1,000,000

B.

1: 500,000

C.

1: 100,000

D.

1: 10,000

Correct answer is A

1km = 100,000cm

on the map 1 cm represent every 10 km which is equal to (10 x 100,000cm)

= 1,000,000cm

the scale is 1:1,000,000

489.

The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))

A.

48cm3

B.

47cm3

C.

38cm3

D.

12cm3

Correct answer is C

Volume of a cone = \(\frac{1}{3} \pi r^2h\)

h2 = 52 = 32

= 25 - 9 = 16

h = \(\sqrt{16}\)

h = 4cm

v = \(\frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4\)

\(\frac{1}{3} \times \frac{22}{7} \times 9 \times 4\)

= \(\frac{22 \times 3 \times 4}{7}\)

= 37.7cm3

= 38cm3

490.

A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume

A.

322m3

B.

448m3

C.

632m2

D.

840m2

Correct answer is B

Volume of pyramid = \(\frac{1}{3}\) x base area x height

= \(\frac{1}{3} \times 12^4 \times 8 \times 14\)

= 4 x 8 x 14 = 448m3