WAEC - Mathematics (1998)

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

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

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

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

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

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

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

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

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

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