The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?
پاسخ دهید
(B)
38cm ≤ P < 42cm
2
Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.
پاسخ دهید
(D)
\(4log_7 2\)
3
If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.
پاسخ دهید
(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
پاسخ دهید
(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
پاسخ دهید
(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
پاسخ دهید
(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?
پاسخ دهید
(A)
\(\frac{2}{11}\)
8
The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?
پاسخ دهید
(B)
6
9
Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite
پاسخ دهید
(C)
I and III only
10
In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ
پاسخ دهید
(D)
115o
11
Calculate the value of Y in the diagram
پاسخ دهید
(C)
48o
12
In the diagram, POR is a circle with center O. ∠QPR = 50°, ∠PQO = 30° and ∠ORP = m. Find m.
پاسخ دهید
(A)
20o
13
Given that m = -3 and n = 2 find the value of \(\frac{3n^2 - 2m^3}{m}\)
پاسخ دهید
(A)
-22
14
Simplify \(\frac{2-18m^2}{1+3m}\)
پاسخ دهید
(C)
\(2(1-3m)\)
15
If \(y = \sqrt{ax-b}\) express x in terms of y, a and b
پاسخ دهید
(D)
\(x = \frac{y^2 + b}{a}\)
16
Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)
پاسخ دهید
(C)
\(9\times 2^{n-1}\)
17
Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)
پاسخ دهید
(C)
\(\frac{x-7}{x^2 - 1}\)
18
If y varies inversely as x\(^2\), how does x vary with y?
پاسخ دهید
(B)
x varies inversely as √y
19
If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)
پاسخ دهید
(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
پاسخ دهید
(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.
پاسخ دهید
(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
پاسخ دهید
(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.
پاسخ دهید
(D)
\(\frac{16\sqrt{3}}{3}\)
24
In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.
پاسخ دهید
(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
پاسخ دهید
(C)
4.0cm
26
Simplify 3.72 x 0.025 and express your answer in the standard form
پاسخ دهید
(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
پاسخ دهید
(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
پاسخ دهید
(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.
پاسخ دهید
(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.
پاسخ دهید
(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.
پاسخ دهید
(C)
\(\frac{m-3}{2}\ge10\)
32
Which of the following pairs of inequalities is represented on the number line?
پاسخ دهید
(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?
پاسخ دهید
(D)
bc = 750
34
The root of a quadratic equation in x, are -m and 2n. Find the equation
پاسخ دهید
(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?
پاسخ دهید
(A)
\(\frac{7}{25}\)
36
Solve the inequality 2x + 3 < 5x
پاسخ دهید
(A)
\(x>1\)
37
In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y
پاسخ دهید
(D)
\(\frac{y^2}{x}\)
38
Describe the locus L shown in the diagram below
پاسخ دهید
(C)
Locus of points equidistant from \(\bar{ZX}\) and \(\bar{ZY}\)
39
Which of the following statements is true from the diagram above?
پاسخ دهید
(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
