# 1993 - WAEC Mathematics Past Questions and Answers - page 1

1

S = {1, 2, 3, 4, 5, 6}, T = {2,4,5,7} and R = {1,4, 5}, and (S∩T) ∪ R

A
{1, 4, 5}
B
{2, 4, 5}
C
{1, 2, 4, 5}
D
{2, 3, 4, 5}
correct option: c

S = {1, 2, 3, 4, 5, 6};  T = {2, 4, 5, 7}; R = {1, 4, 5}

(S∩T) ∪ R = {2, 4, 5}  ∪ {1, 4, 5}

= {1, 2, 4, 5}

2

Simplify: $$\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})$$

A
7/30
B
7/24
C
9/25
D
1/2
correct option: d

$$\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})$$

$$\frac{3}{4} \div \frac{5}{4} \times (\frac{9 - 4}{6})$$

= $$\frac{3}{4} \times \frac{4}{5} \times \frac{5}{6}$$

= $$\frac{1}{2}$$

3

Solve the inequality: 3m + 3 > 9

A
m > 2
B
m > 3
C
m>4
D
m>6
correct option: a

3m + 3 > 9

3m > 9 - 3

3m > 6

m > 2

4

Convert 89$$_{10}$$ to a number in base two.

A
1101001
B
1011001
C
1001101
D
101101
correct option: b

$$89_{10}$$

 2 89 2 44 r 1 2 22 r 0 2 11 r 0 2 5 r 1 2 2 r 1 2 1 r 0 0 r 1

$$89_{10} = 1011001_{2}$$

5
A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement
A
27/9%
B
26/7%
C
5%
D
277/9%
correct option: b
% Error =
Error /Actual measurement x
100/1

=
0.05/1.80 x
100/1 = 27/9%
6

The nth term of a sequence is given by (-1)$$^{n-2}$$ x 2$$^{n+1}$$. Find the sum of the second and third terms.

A
-2
B
1
C
2
D
6
correct option: a

when n = 2

(-1)$$^{n-2}$$ 2$$^{n+1}$$ = 2

When n = 3

(-1)$$^{n-2}$$ 2$$^{n+1}$$ = -4

Sum = 2 - 4 = -2

7

Simplify: $$\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}$$

A
1/4
B
0
C
1
D
2
correct option: d

$$\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}$$

= $$\frac{16^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}$$

= $$\frac{(2^4)^{\frac{3}{4}}}{4^{\frac{1}{2}} \times 4^{\frac{1}{2}}}$$

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

= 2

8

Simplify: $$\frac{\log \sqrt{27}}{\log \sqrt{81}}$$

A
1/6
B
3/8
C
1/2
D
3/4
correct option: b

$$\frac{\log \sqrt{27}}{\log 81}$$

= $$\frac{\log \sqrt{3^3}}{\log 3^4}$$

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

= $$\frac{\frac{3}{2} \log 3}{4 \log 3}$$

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

= $$\frac{3}{8}$$

9

Factorize the expression 2s$$^2$$ - 3st - 2t$$^2$$.

A
(2s - t)(s + 2t)
B
(2s + t)(s - 2t)
C
(s + t)(2s - 1)
D
(2s + t)(s -t)
correct option: b

2s$$^2$$ - 3st - 2t$$^2$$

= 2s$$^2$$ - 4st + st - 2t$$^2$$

= 2s(s - 2t) + t(s - 2t)

= (2s + t)(s - 2t)

10

Solve the equation x$$^2$$ - 2x - 3 = 0

A
(-3, 1)
B
(-1, -3)
C
(3,1)
D
(43, 0)
correct option: e

x$$^2$$ - 2x - 3 = 0

x$$^2$$ - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = (-1, 3)