# 2000 - WAEC Mathematics Past Questions and Answers - page 1

1
Express $$\frac{7}{19}$$ as a percentage, correct to one decimal place
A
2.7%
B
3.7%
C
27.1%
D
36.8%
correct option: d
$$\frac{7}{19}$$ as a percentage will be
$$\frac{7}{19}\times \frac{100}{1}\% = 36.8\%$$
2

Express 398753 correct to three significant figures

A
398000
B
398700
C
398800
D
399000
correct option: d

398753 $$\approxeq$$ 399000 (to 3 s.f)

3
simplify $$\frac{10}{\sqrt{32}}$$
A
$$\frac{5}{4}\sqrt{2}$$
B
$$\frac{4}{5}\sqrt{2}$$
C
$$\frac{5}{16}\sqrt{2}$$
D
$$\frac{16}{5}\sqrt{2}$$
correct option: a
$$\frac{10}{\sqrt{32}}=\frac{10}{\sqrt{16\times 2}} = \frac{10}{4\sqrt{2}}\ \frac{10\times \sqrt{2}}{4\sqrt{2}\times\sqrt{2}}=\frac{10\sqrt{2}}{4\times 2}= \frac{5}{4}\sqrt{2}$$
4

Find the missing number in the addition of the following numbers, in base seven
$$\begin{matrix} 4 & 3 & 2 & 1\ 1 & 2 & 3 & 4\ * & * & * & *\ 1&2&3&4&1 \end{matrix}$$

A
3453
B
5556
C
6016
D
13453
correct option: a

4321$$_7$$ + 1234$$_7$$ = 5555$$_7$$

Missing number = 12341$$_7$$ - 5555$$_7$$

= 3453$$_7$$

5

What fraction must be subtracted from the sum of $$2\frac{1}{6}$$ and $$2\frac{7}{12}$$ to give $$3\frac{1}{4}$$?

A
$$\frac{1}{3}$$
B
$$\frac{1}{2}$$
C
$$1\frac{1}{6}$$
D
$$1\frac{1}{2}$$
correct option: d

$$2\frac{1}{6} + 2\frac{7}{12}$$

= $$\frac{13}{6} + \frac{31}{12}$$

= $$\frac{26 + 31}{12}$$

= $$\frac{57}{12} = \frac{19}{4}$$

$$\frac{19}{4} - 3\frac{1}{4}$$

= $$\frac{19}{4} - \frac{13}{4}$$

= $$\frac{6}{4}$$

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

6
Simplify $$\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}$$
A
$$\frac{80}{243}$$
B
$$\frac{1}{64}$$
C
$$\frac{25}{6}$$
D
$$\frac{15}{4}$$
correct option: d
$$\left(\frac{16}{81}\right)^{-\frac{3}{4}}\times \sqrt{\frac{100}{81}}\ \frac{1}{\left(\sqrt[4]{\frac{16}{81}}\right)^3}\times \frac{10}{9}=\frac{1}{\left(\frac{2}{3}\right)^3}\times\frac{10}{9}\ =\frac{27}{8}\times \frac{10}{9}=\frac{15}{4}$$
7
Which of the following numbers is perfect cube?
A
350
B
504
C
950
D
1728
correct option: d
8

If $$104_x = 68$$, find the value of x

A
5
B
7
C
8
D
9
correct option: c

$$104_x = 68\ 1 \times x^2 + 0 \times x + 4 \times x^0 = 68\ x^2 = 68 - 4; x^2 = 64\ x = \sqrt{64}=8$$

9

The ages of three men are in the ratio 3:4:5. If the difference between the ages of the oldest and youngest is 18 years, find the sum of the ages of the three men

A
45 years
B
72 years
C
108 years
D
216 years
correct option: c

Given that the ages are in the ratio 3: 4: 5.

Let the sum of their ages be t.

$$\therefore$$ The youngest age = $$\frac{3}{12} t$$

The eldest age = $$\frac{5}{12} t$$

$$\implies \frac{5}{12} t - \frac{3}{12} t = 18$$

$$\frac{2t}{12} = 18 \implies t = \frac{18 \times 12}{2}$$

t = 108 years.

The sum of their ages = 108 years.

10

Given that $$log_4 x = -3$$, find x.

A
$$\frac{1}{81}$$
B
$$\frac{1}{64}$$
C
64
D
81
correct option: b

$$\log_4 x = -3$$

$$x = 4^{-3}$$

= $$\frac{1}{64}$$