There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?
Answer
(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
Answer
(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 30o. Calculate the height of the tower.
Answer
(B)
20.78m
11
Find the area of a rectangle of length 4cm and whose diagonal is 8cm, (Leave your answer in surd form)
Answer
(D)
16√3cm2
12
Given that x + y = 7 and 3x-y = 5, evaluate \(\frac{y}{2}-3\).
Answer
(A)
-1
13
In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS
Answer
(D)
125o
14
If \(\left(\frac{1}{4}\right)^{(2-y)} = 1\), find y.
Answer
(D)
2
15
Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm
Answer
(B)
592cm2
16
If \(\frac{x}{a+1}+\frac{y}{b}\) 1. Make y the subject of the relation
Answer
(A)
\(\frac{b(a-x+1)}{a+1}\)
17
lf \(log_q p= r\), express p in terms of q and r
Answer
(D)
p=qr
18
Find the next two terms of the sequence
1, 5, 14, 30, 55, ...
Answer
(D)
91, 140
19
Each interior angle of a regular polygon is 108°. How many sides has it?
Answer
(A)
5
20
Solve the equation 10-3x-x2 = 0
Answer
(A)
x=2 or-5
21
Find, correct to two decimal places, the mean of 9, 13, 16, 17, 19, 23, 24.
Answer
(B)
17.29
22
In the diagram, ∆XYZ is similar to ∆PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|
Answer
(A)
5.6 cm
23
Factorise 27p2x2 - 48y2.
Answer
(D)
3(3px -4y)(3px +4y)
24
What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take \(\pi = \frac{22}{7}\))
Answer
(C)
269.5cm3
25
Find the sum of the roots of the equation 2x2 + 3x - 9 = 0
Answer
(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
Answer
(B)
{1,9}
27
In the diagram, KS is a tangent to the circle centre O at R and ∠ROQ = 80º. Find ∠QRS.
Answer
(D)
40o
28
Find the mean deviation of 6, 7, 8, 9, 10
Answer
(A)
1.2
29
A point X is on the bearing 342o from a point Y. What is the bearing of Y from X?
Answer
(D)
162o
30
In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of ∠QPR.
Answer
(C)
55o
31
Find the average of the first four prime numbers greater than10
Answer
(D)
15
32
Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K,
Answer
(C)
32
33
In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ∠WMR = 30o and |WM| = |MR| Find the value of x
Answer
(B)
25o
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?
Answer
(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?
Answer
(D)
\(\frac{6}{11}\)
36
Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
Answer
(D)
x < -4
37
A boy walks 800m in 20 minutes. Calculate his average speed in km per hour
Answer
(A)
2.4
38
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
Answer
(B)
\(\frac{a-3b}{a^2-b^2}\)
39
The diagram is a circle centre O. Find the value of x
Answer
(E)
65.5\(^{\circ}\)
40
Use the graph to answer the Question below
What are the roots of the equation x2 + 3x - 4 = 0?
Answer
(D)
-4, 1
41
The values of x when y = 3 are approximately
Answer
(B)
-4.6 and 1.5
42
Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?
Answer
(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
Answer
(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 = \(\frac{3}{2}\)
Answer
(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.
