Solve the inequality: \(\frac{2x - 5}{2} < (2 - x)\)
Answer
(D)
x < 2\(\frac{1}{4}\)
11
If x = 64 and y = 27, evaluate: \(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)
Answer
(C)
\(\frac{5}{11}\)
12
If \(\frac{1}{2}\)x + 2y = 3 and \(\frac{3}{2}\)x - 2y = 1, find (x + y)
Answer
(A)
3
13
Given that \(p^{\frac{1}{3}}\) = \(\frac{\sqrt[3]{q}}{r}\), make q the subject of the equation
Answer
(C)
q = pr3
14
A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord
Answer
(A)
2\(\sqrt{21}\)cm
15
A cube and cuboid have the same base area. The volume of the cube is 64cm\(^3\) while that of the cuboid is 80cm\(^3\). Find the height of the cuboid
Answer
(C)
5cm
16
If sin x = \(\frac{5}{13}\) and 0o \(\leq\) x \(\leq\) 90o, find the value of (cos x - tan x)
Answer
(C)
\(\frac{79}{156}\)
17
An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50o, Find, correct to 2 decimal places, the height of the mast
Answer
(C)
7.15m
18
The bearing of Y from X is 060º and the bearing of Z from Y = 060º. Find the bearing of X from Z
Answer
(B)
240o
19
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
Answer
(D)
1.01
20
If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
Answer
(A)
\(\frac{3}{2}\)
21
If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\leq\) 4), where y is an integer, find p\(\cap\)Q
Answer
(C)
{3, 4, 5, 6, 7}
22
Find the values of k in the equation 6k2 = 5k + 6
Answer
(B)
{\(\frac{-2}{3}, \frac{3}{2}\)}
23
If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
Answer
(A)
8
24
The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k
Answer
(D)
-8
25
What is the locus of the point X which moves relative to two fixed points P and M on a plane such that < PXM = 30o
Answer
(B)
an arc of a circle with PM as a chord
26
When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number
Answer
(C)
5
27
Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction
Answer
(A)
\(\frac{x - 7}{x^2 + x - 6}\)
28
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
Answer
(B)
12
29
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
Answer
(B)
-1
30
A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume
Answer
(B)
448m3
31
The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))
Answer
(C)
38cm3
32
The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used
Answer
(A)
1: 1,000,000
33
Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M
Answer
(D)
x2 - x
34
An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))
Answer
(A)
8800cm2
35
In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.
Answer
(A)
112cm
36
in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L
Answer
(B)
10K units
37
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
Answer
(D)
\(\bigtriangleup\) XYZ= \(\bigtriangleup\) NOM
38
In the diagram, PQRS is a rhombus and < PSQ = 35º. Calculate the size of < PRQ
Answer
(B)
55o
39
Find the value of m in the diagram
Answer
(D)
17o
40
In the diagram, O is the centre of the circle. OM||XZ and < ZOM = 25º. Calculate ∠XYZ
Answer
(D)
65o
41
Using the histogram, estimate the mode of distribution
Answer
(C)
53.5
42
Using the histogram, what is the median class?
Answer
(C)
40.5 - 50.5
43
The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. How many textbooks are for the technical class?
Answer
(D)
250
44
The pie chart shows the distribution of 600 mathematics textbooks for Arts, Business, Science and Technical Classes. What percentage of the total number of textbooks belongs to science?
Answer
(A)
12\(\frac{1}{2}\)%
45
In the diagram, PQRST is a regular polygon with sides QR and TS produced to meet at V. Find the size of < RVS
