Given that x = 2 and y = -\(\frac{1}{4}\), evaluate \(\frac{x^2y - 2xy}{5}\)
Answer
(A)
zero
10
Factorize 5y2 + 2ay - 3a2
Answer
(D)
(y + a)(5y - 3a)
11
If 4y is 9 greater than the sum of y and 3x, by how much is y greater than x?
Answer
(A)
3
12
If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r
Answer
(C)
\(\frac{25}{9} p^2r\)
13
Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)
Answer
(D)
\(\frac{x - 4}{2x - 3}\)
14
PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]
Answer
(A)
4.19cm2
15
If the volume of a cube is 343cm3, find the length of its side
Answer
(C)
7cm
16
The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x
Answer
(C)
y = 160 - x
17
If xo is obtuse, which of the following is true?
Answer
(D)
90 < x < 180
18
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
Answer
(C)
\(\sqrt{2}\)
19
If cos (x + 25)o = sin 45o, find the value of x
Answer
(A)
20
20
If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
Answer
(D)
2(105)
21
If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?
A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M
Answer
(D)
9
24
An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)]
Answer
(D)
75o
25
What is the length of an edge of a cube whose total surface area is X cm2 and whose total surface area is \(\frac{X}{2}\)cm3?
Answer
(A)
3
26
XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]
Answer
(B)
22.67cm
27
If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x
Answer
(B)
-1\(\frac{1}{2}\)
28
Find the quadratic equation whose roots are c and -c
Answer
(A)
x2 - c2 = 0
29
Solve the inequality 1 - 2x < - \(\frac{1}{3}\)
Answer
(C)
x > \(\frac{2}{3}\)
30
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime?
Answer
(B)
\(\frac{3}{4}\)
31
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their product is odd?
Answer
(D)
zero
32
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7?
Answer
(C)
\(\frac{1}{8}\)
33
Find the mean deviation of these numbers 10, 12, 14, 15, 17, 19.
Answer
(A)
2.5
34
In the diagram, < QPR = 90o. If q2 = 25 - r2. Find the value of p
Answer
(C)
5
35
In the diagram, /PQ/ = /QR/ and /PR/ = /RS/ = /SP/, calculate the side of < QRS
Answer
(C)
90o
36
In the diagram above, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus.
Answer
(B)
52cm
37
In the figure shown, PQs is a straight line. What is the value of < PRQ?
Answer
(D)
78o
38
In the diagram, PQ//RS, QU//PT and < PSR = 42o. Find angle x.
Answer
(C)
42o
39
In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to the area of \(\bigtriangleup\)YZR?
Answer
(B)
2:1
40
In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.
