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