# 2004 - WAEC Mathematics Past Questions & Answers - page 1

1
1. Evaluate $$202^2_{three} - 112^2_{three}$$
A
21120
B
21121
C
21112
D
21011
CORRECT OPTION: a
$$202^2_{three}$$when converted to base ten $$=(202_3)^2\ 202_3 = 2 \times 3^2 + 0 \times 3^1 + 2\times 3^0 = 18 + 0 + 2\ =20_{ten}; (202_3)^2 = (20)^2_{ten} = 400\ 112^2_{three}$$when converted to base ten $$= (112_3)^2\ 112_3 = 1 \times 3^2 + 1 \times 3^1 + 2\times 3^0 = 9+3+2=14_{ten}\ (112_3)^2 = (14)^2_{ten} = 196_{ten}\ Evaluate \Longrightarrow 400-196 = 204$$
Reconvert to base three
$$\begin{matrix} 3 & 204\ 3 & 69 &R0\ 3 & 22 & R2\ 3 & 7 & R1\ 2 & 2 & R1\ & 0& R2 \uparrow\ \end{matrix} \ =21120_3$$
2
If $$y = 23_{five} + 101_{three}$$, find y, leaving your answer in base two
A
1110
B
10111
C
11101
D
111100
CORRECT OPTION: b
$$23_{five} = X_{ten}; X_{ten} = 2\times 5^1 + 3\times 5^0 = 10 + 3 = 13\ 101_{three}=P_{ten}; P_{ten} = 1\times 3^2 + 0\times 3^1 + 1\times 3^0=9+0+1=10_{ten}\ Y = 13+10=23_{ten}$$;
Converting to base two
$$\begin{matrix} 2 & 23\ 2 & 11 &R1\ 2 & 5 & R1\ 2 & 2 & R1\ 2 & 1 & R0\ & 0& R1 \uparrow\ \end{matrix} \ =y=10111_2$$
3
Given that sin (5x - 28)o = cos (3x - 50)o,0 < x < 90o, find the value of x
A
14o
B
21o
C
32o
D
39o
CORRECT OPTION: b
Sin (5x – 28)o = cos (3x - 50)o
Since by the trigonometry relation
Sin(5x – 28)o = cos[90 – (5x – 28)]o
Hence cos(3x – 50)o = cos[90 – (5x – 28)]o
3x – 50 = 90 - (5x-28)
3x – 50 = 90 – 5x + 28
3x + 5x = 90 + 28 + 50
8x = 168
$$x = \frac{168}{8}=21^{\circ}$$
4
Solve for t in the equation $$\frac{3}{4}t+\frac{1}{3}(21-t)$$ = 11,
A
$$\frac{9}{13}$$
B
$$\frac{9}{5}$$
C
5
D
$$9\frac{3}{5}$$
CORRECT OPTION: d
$$\frac{3}{4}t+\frac{1}{3}(21-t) = 11; \frac{3t}{4} + \frac{7}{1} - \frac{t}{3} = \frac{11}{1}\ \frac{3 \times 3t + 7\times 12 – 4 \times t = 11 \times 12}{12}\ 9t + 84 – 4t = 132; 5t = 132 – 84\ 5t = 48; t = \frac{48}{5} = 9\frac{3}{5}$$
5
A school girl spends $$\frac{1}{4}$$ of her pocket money on books and $$\frac{1}{3}$$ on dress. What fraction remains?
A
$$\frac{5}{6}$$
B
$$\frac{7}{12}$$
C
$$\frac{5}{12}$$
D
$$\frac{1}{6}$$
CORRECT OPTION: c
Let the girls pocket money be rep. by x. The amount spent on books = $$\frac{1}{4}of\hspace{1mm}x = \frac{x}{4}$$
The amount spent on dress $$=\frac{1}{3} of \hspace{1mm}x=\frac{x}{3}$$
∴The fraction that remains = $$\frac{x}{1}-\left(\frac{x}{4}+\frac{x}{3}\right)\ \frac{3x+4x}{12}; = \frac{12x-7x}{12} = \frac{5x}{12} = \frac{5}{12}$$
6

In the diagram, $$R\hat{P}Q = Q\hat{R}Y, \hspace{1mm} P\hat{Q}R = R\hat{Y}Q, \ \hspace{1mm}|QP| = 3cm \hspace{1mm}|QY| = 4cm \hspace{1mm}and \hspace{1mm}|RY | = 5cm. \hspace{1mm} Find \hspace{1mm}|QR|$$

A
2.0cm
B
2.5cm
C
6.4cm
D
10.0cm
CORRECT OPTION: c

$$\frac{PR}{QR} = \frac{QR}{QY} = \frac{QP}{YR}$$ (SSS Congruence)

$$\frac{QR}{4} = \frac{8}{5}$$

$$QR = \frac{4 \times 8}{5}$$

= 6.4 cm

7
Find the value of x in the diagram
A
10o
B
28o
C
36o
D
44o
CORRECT OPTION: b
The sum of angles at point = 360o
(x+10)o + (4x+50)o + 20o + 3xo + 2xo = 360o
10x + 80o = 360o
10x = 360o - 80o = 280o
$$\frac{280}{10}=28^{\circ}$$
8
There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?
A
$$\frac{m}{12}$$
B
$$\frac{12}{m}$$
C
$$\frac{12}{m+12}$$
D
$$\frac{12}{m-12}$$
CORRECT OPTION: c
Prob. (a girl) $$=\frac{Number\hspace{1mm} of\hspace{1mm} girls}{Number \hspace{1mm} of \hspace{1mm} boys \hspace{1mm} and \hspace{1mm} girls\hspace{1mm} in \hspace{1mm} class}\ = \frac{12}{m+12}$$
9

Simplify $$7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}$$and correct your answer to the nearest whole number

A
33
B
8
C
7
D
0
CORRECT OPTION: d

$$7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}; \frac{15}{2} - \left(\frac{5}{2}+\frac{3}{1}\right)\div \frac{33}{2}\ \frac{15}{2} - \left(\frac{5+6}{2}\right)\div \frac{33}{2}; \frac{15}{2} - \frac{11}{2} \div \frac{33}{2}\ \frac{15-11}{2}\div \frac{33}{2}; \frac{4}{2} \times \frac{2}{33} = \frac{4}{33} = 0.1212$$
The nearest whole number is 0

10
The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30o. Calculate the height of the tower.
A
62.35m
B
20.78m
C
18.00m
D
10.39m
CORRECT OPTION: b
Where H is the height of the tower H = ?
$$Tan 30^{\circ} = \frac{H}{36} \Rightarrow H = 36 \times tan30^{\circ}\ H = 36 \times 0.5774 = 20.79$$
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