WAEC - Mathematics (1990)

1
Simplify 125\(^{\frac{-1}{3}}\) x 49\(^{\frac{-1}{2}}\) x 10\(^0\)
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(C)
1/35
2
If 3\(^{2x}\) = 27, what is x?
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(B)
1.5
3
Express 0.00562 in standard form
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(A)
5.62 x 10^-3
4
Given that 1/3log₁₀ P = 1, find the value of P
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(E)
1000
5
Simplify \(\frac{\log \sqrt{8}}{\log 8}\)
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(B)
1/2
6
Evaluate using the logarithm table, log(0.65)²
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(D)
3.6258
7
If log x = \(\bar{2}.3675\) and log y = 0.9750, what is the value of x + y? Correct to three significant figures
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(E)
9.46
8
While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error
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(C)
7.44%
9
Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5
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(C)
3.5
10

From the graph determine the roots of the equation y = 2x\(^2\) + x - 6
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(C)
-2, 1.5
11

Find the values of x for which y = 5
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(B)
-2.6, 2.1
12
An arc of length 22cm subtends an angle of θ at the center of the circle. What is the value of θ if the radius of the circle is 15cm?[Take π = 22/7]
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(B)
84^o
13
Find the sum of the first five terms of the G.P 2,6, 18 ....
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(C)
242
14
Let J be the set of positive integers, If H = {x: x∈J, x\(^2\) < 3 and x ≠ 0}, then
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(A)
H = {1}
15
In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?
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(C)
35
16
The area shaded with horizontal lines is the solution set of the inequalities;
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(B)
y ≤ x, y + 2x ≥ -3, x ≤ 3
17

the area shaded with vertical lines is the solution set of the inequalities;
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(C)
y ≤ x, y ≤ 2x - 3, x ≤ 3
18

In the diagram above, O is the center of the circle with radius 10cm, and ∠ABC = 30°. Calculate, correct to 1 decimal place, the length of arc AC [Take π = 22/7]
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(B)
10.5cm
19
Factorize x\(^2\) + 4x - 192
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(C)
(x-12) (x+16)
20
Factorize 2e\(^2\) - 3e + 1
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(A)
(2e-1) (e-1)
21
Solve the equation 7y\(^2\) = 3y
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(C)
y = 0 or 3/7
22
Find the value of m which makes x\(^2\) + 8 + m a perfect square
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(E)
16
23
Solve the equation 2a\(^2\) - 3a - 27 = 0
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(E)
-3, 9/2
24
A sector of a circle of radius 7cm has an area of 44cm². Calculate the angle of the sector correct to the nearest degree [Take π = 22/7]
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(D)
103^o
25
calculate the surface area of a sphere of radius 7cm [Take π = 22/7]
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(C)
616cm²
26
If the radius of the parallel of latitude 30°N is equal to the radius of the parallel of latitude θ°S, what is the value of θ?
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(D)
30^o
27
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
Find the total surface area of the container
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(D)
528cm²
28
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]. What is the volume of the container?
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(E)
770cm³
29

In the diagram above, |PQ| = |PR| = |RS| and ∠RPS = 32°. Find the value of ∠QPR
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(C)
52^o
30

In the diagram above, WXYZ is a rhombus and ∠WYX = 20°. What is the value of ∠XZY
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(E)
70^o
31

In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR
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(C)
10.24cm²
32

Which angle is equal to ∠VWZ?
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(A)
∠VXZ
33

Which triangle is equal in area to ΔVWZ
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(B)
ΔVYZ
34
In the diagram above, PQRS s a cyclic quadrilateral, ∠PSR = 86^o and ∠QPR = 38^o. Calculate PRQ
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(C)
48^o
35
In the diagram below, O is the center of the circle if ∠QOR = 290^o, find the size ∠QPR
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(D)
35^o
36

In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTO. Find x.
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(E)
50^o
37
Which of the sketches above gives a correct method for constructed an angle of 120^o at the point P?
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(D)
I and II only
38
Use mathematical table to evaluate (cos40° - sin30°)
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(D)
0.2660
39
If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?
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(B)
63^o
40
From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69^o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building
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(B)
3.8m
41
The bearing of a point X from a point Y is 074°. What is the bearing of Y from X?
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(D)
254^o
42

The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart

How much money did he invest in agriculture?
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(E)
N4,000.00
43

The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school. What is the mode?
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(D)
N12
44

The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school.
What is the median of distribution
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(C)
N12.00
45
Two groups of male students cast their votes on a particular proposal. The result are as follows:

In favor Against

Group A 128 32

Group B 96 48

If a student in favor of the proposal is selected for a post, what is the probability that he is from group A?
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(A)
8/19

	In favor	Against
Group A	128	32
Group B	96	48