WAEC - Mathematics (1998)

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

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

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

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

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

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

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

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

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

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