2002 - WAEC Mathematics Past Questions & 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
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