WAEC - Mathematics (1998)

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

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

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

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

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

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

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

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

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

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