Which of the following correctly expresses 48 as a product of prime factors?
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(D)
2 x 2 x 2 x 2 x 3
2
Evaluate \((20_{three})^2 - (11_{three})^2\) in base three
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(C)
202
3
Evaluate \(log_{10}5 + log_{10}20\)
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(A)
2
4
In a class of 80 students, every students studies Economics or Geography or both. If 65 students study Economics and 50 study Geography, how many study both subjects?
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(C)
35
5
If N varies directly as M and N = 8 when M = 20 find M when N = 7
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(C)
\(17\frac{1}{2}\)
6
Express 0.0462 in standard form
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(D)
4.62 x 10-2
7
In a bag of oranges, the ratio of the good ones to the bad ones is 5:4. If the number of bad oranges in the bag is 36, how many oranges are there in the altogether?
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(A)
81
8
A boy estimated his transport fare for a journey as N190 instead of N200. Find the percentage error in his estimate
A man is four times as old as his son. The difference between their ages is 36 years Find the sum of their ages
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(C)
60 years
13
Given that y = px + q and y = 5 when x = 3, while y = 4 when x = 2, find the value of p and q.
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(B)
p = 1, q = 2
14
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
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(D)
1
15
Factorize \(6x^2 + 7x - 20\)
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(D)
(3x-4)(2x+5)
16
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\)
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(C)
\(\frac{x-11}{6}\)
17
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true?
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(C)
y > -7
18
if \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n
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(A)
7:4
19
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K
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(A)
-3
20
which of the following is not quadratic expression?
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(D)
y = 5(x-1)
21
The graph of the curve \(y = 2x^2 - 5x - 1\) and a straight line PQ were drawn to solve the equation \(2x^2 - 5x + 2 = 0\)
What is the equation of the straight line PQ?
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(D)
y = -3
22
Subtract (-y + 3x + 5z) from (4y - x - 2z)
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(A)
5y - 4x - 7z
23
If \(y \propto \frac{1}{\sqrt{x}}\) and x = 16 when y = 2, find x when y = 24
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(A)
\(\frac{1}{9}\)
24
If 2x : (x +1) = 3:2, what is the value of x?
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(D)
3
25
The bearing S40°E is the same as
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(D)
140o
26
Given that sin \(P = \frac{5}{13}\), where p is acute, find the value of cos p - tan p
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(A)
\(\frac{79}{156}\)
27
Three observation posts P,Q and R are such that Q is due east of P and R is due north of Q. If |PQ| = 5km and |PR| = 10km, find |QR|
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(D)
8.7km
28
Express 25° 45' in decimal (Hint: 1° = 60')
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(A)
25.75o
29
A box contains 5 red, 3 green and 4 blue balls. A boy is allowed to take away two balls from the box. What is the probability that the two balls are red?
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(A)
\(\frac{5}{33}\)
30
A box contains 5 red, 3 green and 4 blue balls. A boy is allowed to take away two balls from the box.What is the probability that one is green and the other is blue?
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(A)
\(\frac{2}{11}\)
31
If the probability that an event will occur is p and the probability that it will not occur is q, which of the following is true?
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(C)
p+q=1
32
What is the range of their age?
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(B)
20 years
33
What is the mode?
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(C)
24.0 years
34
How many students are there in the group?
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(C)
52
35
Which of the following is not the the size of an exterior angle of a regular polygon?
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(D)
21o
36
In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50°. What is the size of ∠PSQ?
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(B)
80o
37
PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ∠PQR
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(D)
103o
38
In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.
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(B)
32o
39
A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle? Take \(\pi =\frac{22}{7}\)
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(B)
17cm
40
A sector of a circle radius 14 cm subtends an angle 135° at the center of the circle. What is the perimeter of the sector? Take \(\pi = \frac{22}{7}\)
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(B)
61cm
41
In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ∆LMN is 18cm2, find the area of the quadrilateral MPQN
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(C)
14cm2
42
The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the area of the cross-section?
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(B)
6cm2
43
The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the volume of the prism?
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(B)
42cm2
44
A solid cylinder of radius 7cm is 10 cm long. Find its total surface area.
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(D)
\(238\pi cm^2\)
45
PQRS is a trapezium in which |PS| = 9cm, |QR| = 15cm, |PQ| = \(2\sqrt{3}, \angle PQR = 90^o and \angle QRS = 30^o\). Calculate the area of the trapezium
