Which of the following correctly expresses 48 as a product of prime factors?
答え
(D)
2 x 2 x 2 x 2 x 3
2
Evaluate \((20_{three})^2 - (11_{three})^2\) in base three
答え
(C)
202
3
Evaluate \(log_{10}5 + log_{10}20\)
答え
(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?
答え
(C)
35
5
If N varies directly as M and N = 8 when M = 20 find M when N = 7
答え
(C)
\(17\frac{1}{2}\)
6
Express 0.0462 in standard form
答え
(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?
答え
(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
答え
(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.
答え
(B)
p = 1, q = 2
14
Evaluate \(\frac{x^2 + x - 2}{2x^2 + x -3}\) when x = -1
答え
(D)
1
15
Factorize \(6x^2 + 7x - 20\)
答え
(D)
(3x-4)(2x+5)
16
Simplify \(\frac{2x-1}{3}-\frac{x+3}{2}\)
答え
(C)
\(\frac{x-11}{6}\)
17
If \(\frac{y-3}{2}<\frac{2y-1}{3}\), which of the following is true?
答え
(C)
y > -7
18
if \(\frac{4m+3n}{4m-3n}=\frac{5}{2}\), find the ratio m:n
答え
(A)
7:4
19
If \(2x^2 + kx - 14 = (x+2)(2x-7)\), find the value of K
答え
(A)
-3
20
which of the following is not quadratic expression?
答え
(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?
答え
(D)
y = -3
22
Subtract (-y + 3x + 5z) from (4y - x - 2z)
答え
(A)
5y - 4x - 7z
23
If \(y \propto \frac{1}{\sqrt{x}}\) and x = 16 when y = 2, find x when y = 24
答え
(A)
\(\frac{1}{9}\)
24
If 2x : (x +1) = 3:2, what is the value of x?
答え
(D)
3
25
The bearing S40°E is the same as
答え
(D)
140o
26
Given that sin \(P = \frac{5}{13}\), where p is acute, find the value of cos p - tan p
答え
(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|
答え
(D)
8.7km
28
Express 25° 45' in decimal (Hint: 1° = 60')
答え
(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?
答え
(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?
答え
(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?
答え
(C)
p+q=1
32
What is the range of their age?
答え
(B)
20 years
33
What is the mode?
答え
(C)
24.0 years
34
How many students are there in the group?
答え
(C)
52
35
Which of the following is not the the size of an exterior angle of a regular polygon?
答え
(D)
21o
36
In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50°. What is the size of ∠PSQ?
答え
(B)
80o
37
PQRS is a rhombus of side 16cm. The diagonal |QS| = 20cm. Calculate, correct to the nearest degree, ∠PQR
答え
(D)
103o
38
In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.
答え
(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 \(\pi =\frac{22}{7}\)
答え
(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 \(\pi = \frac{22}{7}\)
答え
(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
答え
(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?
答え
(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?
答え
(B)
42cm2
44
A solid cylinder of radius 7cm is 10 cm long. Find its total surface area.
答え
(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
