1989 - WAEC Mathematics Past Questions & Answers - page 1

1
If 3loga + 5loga - 6loga = log64, what is a?
A
4
B
6
C
8
D
16
CORRECT OPTION: c
loga3 + loga5 - loga6
log(
a3 * a5/a6) = loga64

a2 = 64 a = 8
2
If the second and fourth term of a G.P are 8 and 32 respectively,what is the sum of the first four terms?
A
28
B
40
C
48
D
60
CORRECT OPTION: d

ar = 8 .....(1)


ar3 = 32 .....(2)


divide (2) by (1)

r2 = 4 r = 2 ∴ a = 4



S =
a(rn - 1)/r - 1

S =
4(24 - 1)/2 - 1 = 60
3

In the diagram above, TPS is a straight line, PQRS is a parallelogram with base QR and height 8cm. |QR| = 6cm and the area of triangle QST is 52cm2. Find the area of ΔQPT

A
39cm2
B
28cm2
C
24cm2
D
21cm2
CORRECT OPTION: b

Area of \(\Delta\)QST = 52cm\(^2\); height = 8cm
b=base length; but A = 1/2 b x h
=52=1/2 x b x 8cm = 104 =8b
b=104/8 = 13cm; ST= 13cm; PS = 6cm
TP = 13 - 6 = 7cm;
area of \(\Delta\)QST = 1/2 b x h
= 1/2 x 7 x 8/1 = 28cm\(^2\)

4

In the diagram O is the center of the circle, if ∠QRS = 62o, find the value of ∠SQR.

A
14o
B
28o
C
31o
D
45o
CORRECT OPTION: b

< QSR = 90° (angle in a semi-circle)

\(\therefore\) < SQR = 180° - (90° + 62°)

= 28°

5

Evaluate, using logarithm tables \(\frac{5.34 \times 67.4}{2.7}\)

A
1.332
B
13.32
C
133.2
D
1332
CORRECT OPTION: c
No Log
5.34 0.7275 +
67.4 1.8287
  2.5562 -
2.7 0.4314
Antilog = 133.2 2.1248

\(\therefore \frac{5.34 \times 67.4}{2.7} = 133.2\)

6
Factorize 35 - 2b - b2
A
(35-2b)(b-1)
B
(7+b)(5-b)
C
(3+7b)(5-b)
D
(35-b)(3b+7)
CORRECT OPTION: b
35 - 2b - b 2;
35 - 7b + 5b - b 2

7(5 - b) + 5(5 - b)

(7 + b)(5 - b)
7

Evaluate \(\frac{0.009}{0.012}\), leaving your answer in standard form.

A
7.5 x 102
B
7.5 x 101
C
7.5 x 10-1
D
7.5 x 10-2
CORRECT OPTION: c

\(\frac{0.009}{0.012}\)

=\(\frac{0.009}{0.012}\) = \(\frac{9}{12}\) = 0.75

=\(7.5 \times 10^{-1}\)

8
The graph above is that of a quadratic function y = 2x2 - x - 6
The roots of the equation are
A
1.5, 2
B
-1.5, 2
C
1, -6
D
1, 6
CORRECT OPTION: b
The roots are; x = -1.5 and 2
9
Factorize the following expression; 2x2 + x - 15
A
(2x+5)(x-3)
B
(2x-5)(x+3)
C
(2x-5)(x-3)
D
(2x-3)(x+5)
CORRECT OPTION: b
2x 2 + x - 15; 2x 2 + 6x - 5x - 15

(2x 2 + 6x) - ( 5x + 15)

2x(x + 3) - 5(x + 3)

(2x - 5)(x + 3)
10
The angle of elevation of X from Y is 30o. If XY = 40m, how high is X above the level of Y?
A
10m
B
20m
C
20√3m
D
40m
CORRECT OPTION: b
XZ = 40 x sin30o
= 20m
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