WAEC - Mathematics (2004)

1
1. Evaluate \( 202^2_{three} - 112^2_{three}\)
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(A)
21120
2
If \(y = 23_{five} + 101_{three}\), find y, leaving your answer in base two
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(B)
10111
3
Given that sin (5x - 28)^o = cos (3x - 50)^o,0 < x < 90^o, find the value of x
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(B)
21^o
4
Solve for t in the equation \(\frac{3}{4}t+\frac{1}{3}(21-t)\) = 11,
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(D)
\(9\frac{3}{5}\)
5
A school girl spends \(\frac{1}{4}\) of her pocket money on books and \(\frac{1}{3}\) on dress. What fraction remains?
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(C)
\(\frac{5}{12}\)
6

In the diagram, \(R\hat{P}Q = Q\hat{R}Y, \hspace{1mm} P\hat{Q}R = R\hat{Y}Q, \\ \hspace{1mm}|QP| = 3cm \hspace{1mm}|QY| = 4cm \hspace{1mm}and \hspace{1mm}|RY | = 5cm. \hspace{1mm} Find \hspace{1mm}|QR|\)
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(C)
6.4cm
7
Find the value of x in the diagram
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(B)
28^o
8
There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?
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(C)
\(\frac{12}{m+12}\)
9
Simplify \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}\)and correct your answer to the nearest whole number
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(C)
7
10
The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30^o. Calculate the height of the tower.
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(B)
20.78m
11
Find the area of a rectangle of length 4cm and whose diagonal is 8cm, (Leave your answer in surd form)
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(D)
16√3cm²
12
Given that x + y = 7 and 3x-y = 5, evaluate \(\frac{y}{2}-3\).
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(A)
-1
13

In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS
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(D)
125^o
14
If \(\left(\frac{1}{4}\right)^{(2-y)} = 1\), find y.
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(D)
2
15
Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm
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(B)
592cm²
16
If \(\frac{x}{a+1}+\frac{y}{b}\) 1. Make y the subject of the relation
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(A)
\(\frac{b(a-x+1)}{a+1}\)
17
lf \(log_q p= r\), express p in terms of q and r
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(D)
p=q^r
18
Find the next two terms of the sequence
1, 5, 14, 30, 55, ...
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(D)
91, 140
19
Each interior angle of a regular polygon is 108°. How many sides has it?
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(A)
5
20
Solve the equation 10-3x-x² = 0
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(A)
x=2 or-5
21
Find, correct to two decimal places, the mean of 9, 13, 16, 17, 19, 23, 24.
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(B)
17.29
22

In the diagram, ∆XYZ is similar to ∆PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|
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(A)
5.6 cm
23
Factorise 27p²x² - 48y².
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(D)
3(3px -4y)(3px +4y)
24
What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take \(\pi = \frac{22}{7}\))
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(C)
269.5cm³
25
Find the sum of the roots of the equation 2x² + 3x - 9 = 0
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(D)
\(-\frac{3}{2}\)
26
Given that ξ = {1, 2, 3, . . . . . . ,10}, P= (x : x is prime) and Q = {y : y is odd}, find P'∩Q
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(B)
{1,9}
27

In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80º. Find ∠QRS.
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(D)
40^o
28
Find the mean deviation of 6, 7, 8, 9, 10
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(A)
1.2
29
A point X is on the bearing 342^o from a point Y. What is the bearing of Y from X?
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(D)
162^o
30

In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of ∠QPR.
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(C)
55^o
31
Find the average of the first four prime numbers greater than10
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(D)
15
32
Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K,
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(C)
32
33
In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ∠WMR = 30^o and |WM| = |MR| Find the value of x
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(B)
25^o
34
The table above gives the marks scored by a group of students in a test Use the table to answer the Question below
What is the median mark?
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(C)
3
35
The table above gives the marks scored by a group of students in a test Use the table to answer the Question below
What is the probability of selecting a student from the group that scored 2 or 3?
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(D)
\(\frac{6}{11}\)
36
Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
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(D)
x < -4
37
A boy walks 800m in 20 minutes. Calculate his average speed in km per hour
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(A)
2.4
38
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
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(B)
\(\frac{a-3b}{a^2-b^2}\)
39

The diagram is a circle centre O. Find the value of x
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(E)
65.5\(^{\circ}\)
40
Use the graph to answer the Question below
What are the roots of the equation x² + 3x - 4 = 0?
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(D)
-4, 1
41
The values of x when y = 3 are approximately
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(B)
-4.6 and 1.5
42
Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?
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(D)
8x² - 2x – 3 = 0
43
The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is
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(A)
the perpendicular bisector of the line segment X Y
44
Given that \(P\propto \frac{1}{\sqrt{r}}\) and p = 3 when r = 16, find the value of r when p = \(\frac{3}{2}\)
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(B)
64
45
Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.
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(C)
III only