The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?
Answer
(B)
38cm ≤ P < 42cm
2
Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.
Answer
(D)
\(4log_7 2\)
3
If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.
Answer
(B)
-1
4
From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number
Answer
(B)
\(\frac{2}{5}\)
5
The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
Find the value of K
Answer
(B)
30o
6
The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week
Answer
(D)
12 hours
7
A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?
Answer
(A)
\(\frac{2}{11}\)
8
The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?
Answer
(B)
6
9
Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite
Answer
(C)
I and III only
10
In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ
Answer
(D)
115o
11
Calculate the value of Y in the diagram
Answer
(C)
48o
12
In the diagram, POR is a circle with center O. ∠QPR = 50°, ∠PQO = 30° and ∠ORP = m. Find m.
Answer
(A)
20o
13
Given that m = -3 and n = 2 find the value of \(\frac{3n^2 - 2m^3}{m}\)
Answer
(A)
-22
14
Simplify \(\frac{2-18m^2}{1+3m}\)
Answer
(C)
\(2(1-3m)\)
15
If \(y = \sqrt{ax-b}\) express x in terms of y, a and b
Answer
(D)
\(x = \frac{y^2 + b}{a}\)
16
Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)
Answer
(C)
\(9\times 2^{n-1}\)
17
Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)
Answer
(C)
\(\frac{x-7}{x^2 - 1}\)
18
If y varies inversely as x\(^2\), how does x vary with y?
Answer
(B)
x varies inversely as √y
19
If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)
Answer
(C)
\(\frac{\sqrt{3}-1}{2}\)
20
From the top of a cliff 20m high, a boat can be sighted at sea 75m from the foot of the cliff. Calculate the angle of depression of the boat from the top of the cliff
Answer
(A)
14.9 o
21
From the diagram above. ABC is a triangle inscribed in a circle center O. ∠ACB = 40º and |AB| = x cm. Calculate the radius of the circle.
Answer
(C)
\(\frac{x}{2 sin 40^o}\)
22
The diagram shows the position of three ships A, B and C at sea. B is due north of C such that |AB| = |BC| and the bearing of B from A = 040°. What is the bearing of A from C
Answer
(D)
290o
23
A pole of length L leans against a vertical wall so that it makes an angle of 60o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.
Answer
(D)
\(\frac{16\sqrt{3}}{3}\)
24
In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.
Answer
(D)
30cm2
25
The height of a pyramid on square base is 15cm. If the volume is 80cm\(^3\), find the length of the side of the base
Answer
(C)
4.0cm
26
Simplify 3.72 x 0.025 and express your answer in the standard form
Answer
(C)
\(9.3\times 10^{-2}\)
27
Two numbers 24\(_{x}\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y
Answer
(A)
2x = 3(y - 1)
28
A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed
Answer
(C)
\(\frac{x + 2y}{3}kmh^{-1}\)
29
The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.
Answer
(B)
36cm
30
Water flows from a tap into cylindrical container at the rate 5πcm\(^3\) per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.
Answer
(B)
5cm
31
Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.
Answer
(C)
\(\frac{m-3}{2}\ge10\)
32
Which of the following pairs of inequalities is represented on the number line?
Answer
(C)
\(x\le -2 and x\ge1\)
33
If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?
Answer
(D)
bc = 750
34
The root of a quadratic equation in x, are -m and 2n. Find the equation
Answer
(A)
\(x^2 + x(m - 2n)-2mn=0\)
35
A survey shows that 28% of all the men in a village wear size 9 shoes. What is the probability that a man selected at random in the village wears size 9 shoes?
Answer
(A)
\(\frac{7}{25}\)
36
Solve the inequality 2x + 3 < 5x
Answer
(A)
\(x>1\)
37
In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y
Answer
(D)
\(\frac{y^2}{x}\)
38
Describe the locus L shown in the diagram below
Answer
(C)
Locus of points equidistant from \(\bar{ZX}\) and \(\bar{ZY}\)
39
Which of the following statements is true from the diagram above?
Answer
(A)
m + n = 90o
40
In the diagram, O is the centre of the circle ∠PQR = 75o, ∠OPS = yo and \(\bar{OR}\) is parallel to \(\bar{PS}\). Find y
