WAEC - Mathematics (1998)

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

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

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

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

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

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

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

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

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

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