# 2002 - WAEC Mathematics Past Questions and Answers - page 1

1

In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.

A
8m
B
9m
C
10m
D
13m
correct option: a

Given, Length of minor arc = 5.5m

Angle subtended by minor arc = 360° - 210° = 150°

$$\therefore 5.5 = \frac{150}{360} \times 2 \times \frac{22}{7} \times r$$

$$\frac{55r}{21} = 5.5$$

$$r = \frac{5.5 \times 21}{55}$$

r = 2.1m

Length of major arc = $$\frac{210}{360} \times 2 \times \frac{22}{7} \times 2.1$$

= $$7.7m \approxeq 8m$$ (to the nearest metre)

2

A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is $$2\sqrt{3}$$ cm. Calculate the volume of the pyramid

A
$$5\frac{1}{3}cm^3$$
B
$$10\frac{2}{3}cm^3$$
C
$$16cm^3$$
D
$$32cm^3$$
correct option: b

$$BD^2 = 4^2 + 4^2$$

$$BD = \sqrt{16 + 16} = \sqrt{32}$$

$$BD = 4\sqrt{2} cm$$

$$(2\sqrt{3})^2 = (2\sqrt{2})^2 + h^2$$

$$h^2 = 12 - 8 = 4$$

$$h = \sqrt{4} = 2 cm$$

Volume of pyramid = $$\frac{a^2 h}{3}$$

= $$\frac{4^2 \times 2}{3}$$

= $$\frac{32}{3} = 10\frac{2}{3} cm^3$$

3

The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area

A
$$9\pi cm^2$$
B
$$15\pi cm^2$$
C
$$16\pi cm^2$$
D
$$20\pi cm^2$$
correct option: b

Curved surface area or a cone $$=\pi rl$$
from the information $$l^2 = 4^2 + 3^2 = 16+9\ l = \sqrt{25} = 5; ∴ C.S.A\hspace{1mm} = \frac{22}{7}\times 3 \times 5\ Since \frac{22}{7}=\pi ∴ C.S.A\hspace{1mm} =\hspace{1mm}15\pi$$

4

In the diagram above, ∠PQU=36°, ∠QRT = 29°, PQ||RT. Find ∠PQR

A
94o
B
65o
C
61o
D
54o
correct option: b

< UQR = 29° (alternate angles)

< PQR = < PQU + < UQR

= 36° + 29°

= 65°

5

Simplify $$5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)$$

A
$$1\frac{3}{4}$$
B
$$3\frac{1}{2}$$
C
$$4\frac{1}{2}$$
D
$$8\frac{1}{2}$$
correct option: c

$$5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\ \frac{21}{4}\div \left(1\frac{4-3}{6}\right)\ \frac{21}{4}\div \left(1\frac{1}{6}\right)\ \frac{21}{4} \times \frac{6}{7}= 4\frac{1}{2}$$

6
Find the value of x in 0.5x + 2.6 = 5x + 0.35
A
0.5
B
2
C
2.6
D
5
correct option: a
$$0.5x + 2.6 = 5x + 0.35\ 0.5x - 5x = 0.35-2.6\ -4.5x = -2.25\ x = \frac{-2.25}{-4.5}\ 0.5$$
7
Find the value of x in the diagram
A
31o
B
35o
C
37o
D
41o
correct option: b
Sum of exterior angle of any polygon is 360o
(2x+5)o + 2xo + (x-20)o + xo + (3x+10)o + (x + 15)o = 360o; 10x = 350
x = 35
8
If $$M5_{ten} = 1001011_{two}$$ find the value of M
A
5
B
6
C
7
D
8
correct option: c
$$M5_{ten} = 1001011_{two}\ =1 \times 2^6 + 0\times 2^5 + 0\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 \ =64+8+2+1=75_{ten}\ ∴ m = 7$$
9

The diagram is the graph of $$y = 6 + x - x^2$$. The graph intercepts the x- axis at P and R and the y- axis at Q.

What is the value of y at Q?

A
$$6\frac{1}{3}$$
B
6
C
3
D
zero
correct option: a
10

The diagram is the graph of $$y = 6 + x - x^2$$. The graph intercepts the x- axis at P and R and the y- axis at Q.

When $$y = 3\frac{1}{3}$$, what is the positive value of x?

A
$$2\frac{1}{2}$$
B
$$2\frac{1}{5}$$
C
$$1\frac{1}{5}$$
D
zero
correct option: b