WAEC - Mathematics (1998)

1
Find the root of the equation 2x\(^2\) - 3x - 2 = 0
Хариулт
(E)
x = -1/2 or 2
2
What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0
Хариулт
(D)
16
3
If log\(_{10}\) q = 2.7078, what is q?
Хариулт
(C)
510.2
4
Cos x is negative and sin x is negative.Which of the following is true of x?
Хариулт
(C)
180^o < x < 270^o
5
Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures
Хариулт
(D)
210
6
If log\(_{10}\) a = 4; what is a?
Хариулт
(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?
Хариулт
(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?
Хариулт
(D)
1600m
9
Convert 35 to a number in base two
Хариулт
(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
Хариулт
(B)
6, 3, ³/₂
11
Find the number whose logarithm to base 10 is 2.6025
Хариулт
(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
Хариулт
(B)
3.95%
13
Simplify \(\frac{8^{\frac{2}{3}}*27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)
Хариулт
(C)
\(\frac{1}{3}\)
14
Solve the equation 5x² - 4x - 1 = 0
Хариулт
(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?
Хариулт
(B)
-p > -2q
16
For what value of x is the expression
x - 5/x² - 2x - 3
not defined?
Хариулт
(C)
-1, 3
17
Make S the subject of the formula: \(V = \frac{K}{\sqrt{T-S}}\)
Хариулт
(A)
\(T-\frac{K^2}{V^2} = S\)
18
Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
Хариулт
(A)
\(12x^2-5x+2=0\)
19
Find (X-Y) if 4x - 3y = 7 and 3x - 2y = 5
Хариулт
(C)
2
20
solve the inequality \((Y-2)<\frac{y}{3}\)
Хариулт
(B)
y < 3
21
If h(m+n) = m(h+r) find h in terms of m, n and r
Хариулт
(E)
\(h=\frac{mr}{n}\)
22
Given that \(\frac{6x-y}{x+2y}=2\), find the value of \(\frac{x}{y}\)
Хариулт
(D)
\(\frac{5}{4}\)
23
The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60^oN
Хариулт
(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
Хариулт
(D)
\(23\pi cm^2\)
25
Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3}\)
Хариулт
(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?
Хариулт
(D)
38%
27
A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 4?
Хариулт
(B)
\(\frac{1}{6}\)
28

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

The graph is that of the quadratic expression
Хариулт
(C)
\(y=x^2 - x - 2\)
30
The values of x when y = -1 are approximately
Хариулт
(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?
Хариулт
(C)
\(\frac{3}{5}\)
32

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

In the diagram, PQ||SR. Find the value of Z
Хариулт
(D)
90^o
34
In \(sin(X+30)^o=cos40^o\),find X
Хариулт
(B)
20^o
35
Find the value of X if \(cos x = \frac{5}{8}\) for \(0^o\le X\le 180^o\)
Хариулт
(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?
Хариулт
(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
Хариулт
(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
Хариулт
(C)
55^o
39
In the diagram, O is the center of the circle and the reflex angle ROS is 264^o. Find ∠RTS
Хариулт
(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
Хариулт
(E)
80^o
41

In the diagram PQ is a diameter of circle PMQN center O, if ∠PQM = 63o, find ∠MNQ
Хариулт
(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.
Хариулт
(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
Хариулт
(B)
5.350cm²
44

Calculate the perimeter of the trapezium PQRS
Хариулт
(C)
48cm
45
The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector
Хариулт
(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
Хариулт
(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?
Хариулт
(A)
24%
48
The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle
Хариулт
(B)
\(65m^2\)
49
In \(\triangle PQR\). T is a point on QR such that \(\angle QPT = 39^o and \angle PTR = 83^o. Calculate \angle PQT\)
Хариулт
(B)
\(44^o\)
50

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

Find the angle x in the diagram above
Хариулт
(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
Хариулт
(B)
\(y\frac{x}{\sqrt{2}}\)
53
Find the curved surface area of a cone of radius 3cm and slant height 7cm (\(take \pi = \frac{22}{7}\)
Хариулт
(C)
\(66cm^2\)
54

In the diagram above, |PQ| = |PR| = |RS| and ∠RSP = 35°. Find ∠QPR
Хариулт
(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?
Хариулт
(D)
16
56
Three of the angles of a hexagon are each X^o. The others are each 3X^o. Find X
Хариулт
(C)
60^o
57
Evaluate \(\sqrt{20}\times (\sqrt{5})^3\)
Хариулт
(D)
50
58
If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct
Хариулт
(D)
\(P\cap Q = \emptyset\)
59
It is observed that \(1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2. \\If \hspace{1mm}1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P^2 find\hspace{1mm}P\)
Хариулт
(C)
8
60
Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form
Хариулт
(C)
\(2.972 \times 10^{1}\)