WAEC - Mathematics (1998)

1
Find the root of the equation 2x\(^2\) - 3x - 2 = 0
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(E)
x = -1/2 or 2
2
What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0
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(D)
16
3
If log\(_{10}\) q = 2.7078, what is q?
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(C)
510.2
4
Cos x is negative and sin x is negative.Which of the following is true of x?
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(C)
180^o < x < 270^o
5
Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures
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(D)
210
6
If log\(_{10}\) a = 4; what is a?
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(E)
10000
7
A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room?
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(D)
4.20m
8
When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight?
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(D)
1600m
9
Convert 35 to a number in base two
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(C)
100011_two
10
The nth term of a sequence is represented by 3 x 2^(2-n). Write down the first three terms of the sequence
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(B)
6, 3, ³/₂
11
Find the number whose logarithm to base 10 is 2.6025
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(D)
400.4
12
A piece of cloth was measured as 6.10m. If the actual length of the cloth is 6.35, find the percentage error, correct to 2 decimal places
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(B)
3.95%
13
Simplify \(\frac{8^{\frac{2}{3}}*27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)
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(C)
\(\frac{1}{3}\)
14
Solve the equation 5x² - 4x - 1 = 0
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(D)
1, -1/5
15
p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?
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(B)
-p > -2q
16
For what value of x is the expression
x - 5/x² - 2x - 3
not defined?
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(C)
-1, 3
17
Make S the subject of the formula: \(V = \frac{K}{\sqrt{T-S}}\)
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(A)
\(T-\frac{K^2}{V^2} = S\)
18
Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
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(A)
\(12x^2-5x+2=0\)
19
Find (X-Y) if 4x - 3y = 7 and 3x - 2y = 5
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(C)
2
20
solve the inequality \((Y-2)<\frac{y}{3}\)
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(B)
y < 3
21
If h(m+n) = m(h+r) find h in terms of m, n and r
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(E)
\(h=\frac{mr}{n}\)
22
Given that \(\frac{6x-y}{x+2y}=2\), find the value of \(\frac{x}{y}\)
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(D)
\(\frac{5}{4}\)
23
The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60^oN
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(B)
\(60\pi cm\)
24

In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 120° at the center
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(D)
\(23\pi cm^2\)
25
Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3}\)
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(D)
\(\frac{ 3x + 4}{(x-2)(x+3)}\)
26
The following numbers represent at a set of scores for a class of 32 students, where the maximum score possible was 12, 6, 5, 9, 4, 4, 8, 7, 5, 6, 3, 2, 5, 4, 6, 9, 10, 4, 3, 2, 3, 4, 6, 8, 7, 4, 2, 1, 8, 7, 7, 6, 11. What is the percentage of the class, correct to the nearest whole number, scored above 6?
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(D)
38%
27
A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 4?
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(B)
\(\frac{1}{6}\)
28

In the diagram above, the area of triangle ABC is 35cm\(^2\). Find the value of y
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(B)
10cm
29

The graph is that of the quadratic expression
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(C)
\(y=x^2 - x - 2\)
30
The values of x when y = -1 are approximately
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(D)
-0.6 and 1.6
31
A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?
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(C)
\(\frac{3}{5}\)
32

In ∆PQR. ∠PQR is a right angle. |QR| = 2cm and ∠PRQ = 60o. Find |PR|
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(B)
4cm
33

In the diagram, PQ||SR. Find the value of Z
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(D)
90^o
34
In \(sin(X+30)^o=cos40^o\),find X
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(B)
20^o
35
Find the value of X if \(cos x = \frac{5}{8}\) for \(0^o\le X\le 180^o\)
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(C)
51.3^o
36
A ladder 5cm long long rest against a wall such that its foot makes an angle 30o with the horizontal. How far is the foot of the ladder from the wall?
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(C)
\(\frac{5\sqrt{3}}{2}m\)
37
A chord of circle of radius 26cm is 10cm from the center of the circle. calculate the length of the chord
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(D)
48cm
38
Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35^o,find ∠PQS
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(C)
55^o
39
In the diagram, O is the center of the circle and the reflex angle ROS is 264^o. Find ∠RTS
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(A)
48^o
40
If the exterior angles of quadrilateral are y^o, (y + 5)^o, (y + 10)^o and (y + 25)^o, find y
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(E)
80^o
41

In the diagram PQ is a diameter of circle PMQN center O, if ∠PQM = 63o, find ∠MNQ
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(E)
27^o
42
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50^o. Use the diagram to answer question below. (take π = 3.142)
Calculate correct to one decimal place, the length of arc PQ.
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(E)
3.1cm
43
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50^o. Use the diagram to answer question below. (take π = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ
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(B)
5.350cm²
44

Calculate the perimeter of the trapezium PQRS
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(C)
48cm
45
The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector
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(D)
10cm²
46

The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
If a hundred students travelled by bus, find the total number of students in the school
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(B)
400
47
The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
What percentage, to the nearest whole number, of tghe students travelled to school on foot?
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(A)
24%
48
The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle
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(B)
\(65m^2\)
49
In \(\triangle PQR\). T is a point on QR such that \(\angle QPT = 39^o and \angle PTR = 83^o. Calculate \angle PQT\)
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(B)
\(44^o\)
50

Find the value of x in the diagram above
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(E)
5.6cm
51

Find the angle x in the diagram above
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(D)
130^o
52
The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x
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(B)
\(y\frac{x}{\sqrt{2}}\)
53
Find the curved surface area of a cone of radius 3cm and slant height 7cm (\(take \pi = \frac{22}{7}\)
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(C)
\(66cm^2\)
54

In the diagram above, |PQ| = |PR| = |RS| and ∠RSP = 35°. Find ∠QPR
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(D)
40^o
55

P varies inversely as Q. The table above shows the value of Q for some selected values of P
What is the missing value of Q in the table?
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(D)
16
56
Three of the angles of a hexagon are each X^o. The others are each 3X^o. Find X
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(C)
60^o
57
Evaluate \(\sqrt{20}\times (\sqrt{5})^3\)
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(D)
50
58
If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct
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(D)
\(P\cap Q = \emptyset\)
59
It is observed that \(1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2. \\If \hspace{1mm}1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P^2 find\hspace{1mm}P\)
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(C)
8
60
Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form
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(C)
\(2.972 \times 10^{1}\)