Find (101\(_2\))\(^2\), expressing the answer in base 2.
Answer
(B)
11001
2
If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?
Answer
(C)
N4.00
3
Express 0.000834 in standard form
Answer
(A)
8.34 x 10-4
4
Given that log2a = log84, find a
Answer
(D)
22/3
5
By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?
Answer
(D)
N400.00
6
Find the nth term Un of the A.P., 11, 4, -3,....... .
Answer
(D)
Un= 18-7n
7
lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.
Answer
(C)
1
8
If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal
Answer
(A)
[1,2,4,6,7,8]
9
Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
Answer
(B)
-5 or +1
10
Which of the following could be the inequality illustrated in the sketch graph above?
Answer
(B)
y≤-3x+3
11
Solve the inequality: \(\frac{1}{3}(2x - 1) < 5\)
Answer
(D)
x <8
12
What is the smaller value of x for which x\(^2\) - 3x + 2= 0?
Answer
(A)
1
13
Factorize the expression x(a - c) + y(c - a)
Answer
(B)
(a - c)(x - y)
14
If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
Answer
(C)
9
15
Solve the equation 3x\(^2\) + 25x -18 = 0
Answer
(D)
-9,2/3
16
Solve the equation (x +2)(x - 7) = 0
Answer
(B)
x = -2 or 7
17
Solve the following simultaneous equations: x+ y = 3/2; x - y = 5/2 and use your result to find the value of 2y + x
Answer
(D)
1
18
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
What is the minimum value of y?
Answer
(B)
-7
19
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
Find the roots of the equation y=3x\(^2\) + x - 7
Answer
(C)
1.4and-1.7
20
In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|
Answer
(E)
6cm
21
The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.
Answer
(E)
96cm2
22
A water tank of height \(\frac{1}{2}\) m has a square base of side \(1\frac{1}{2}\) m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m\(^3\)]
Answer
(B)
375 litres
23
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
Find the total surface area of the container
Answer
(D)
528cm2
24
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
What is the volume of the container?
Answer
(E)
770cm3
25
Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take π = 22/7]
Answer
(B)
66cm2
26
A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.
Answer
(B)
6cm
27
The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
Answer
(D)
24cm
28
The positions of two countries P and Q are (15°N, 12°E) and (65°N, 12°E) respectively. What is the difference in latitude?
Answer
(D)
50o
29
A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?
Answer
(B)
7cm
30
The angle of a sector of a circle is 108°. If the radius of the circle is 31/2cm, find the perimeter of the sector
Answer
(E)
13 3/5cm,
31
In the diagram above; O is the centre of the circle and |BD| = |DC|. If ∠DCB = 35°, find ∠BAO.
Answer
(A)
20o
32
In the diagram above, AO is perpendicular to OB. Find x
Answer
(D)
30o
33
In the diagram above, PQ is parallel to TU, ∠PQR = 50°, ∠QRS = 86° and ∠STU = 64°. Calculate the value of x.
Answer
(D)
100o
34
If log\(_{10}\) x = \(\bar{2}.3675\) and log\(_{10}\) y = \(\bar{2}.9738\), what is the value of x + y, correct lo three significant figures?
Answer
(A)
O.117
35
In the diagram above, AB//CD, the bisector of ∠BAC and ∠ACD meet at E. Find the value of ∠AEC
Answer
(E)
90o
36
In the diagram above, AB//CD. What is the size of the angle marked x?
Answer
(B)
93o
37
The locus of a point which is equidistant from two given fixed points is the
Answer
(A)
perpendicular bisector of the straight line joining them
38
In the diagram above, the value of angles b + c is
Answer
(A)
180o
39
Which of the following angles is an exterior angle of a regular polygon?
Answer
(E)
72o
40
In ΔABC above, BC is produced to D, /AB/ = /AC/ and ∠BAC = 50o. Find ∠ACD
Answer
(E)
115o
41
Without using tables, find the value of \(\frac{\sin 20°}{\cos 70°} + \frac{\cos 25°}{\sin 65°}\)
Answer
(A)
2
42
In the diagram above, ∠PRQ = 90°, ∠QPR = 30° and /PQ/ = 10 cm. Find y.
Answer
(B)
5cm
43
The bearing of two points Q and R from a point P are 030° and 120° respectively, lf /PQ/ = 12 m and /PR/ = 5 m, find the distance QR.
Answer
(A)
13m
44
What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14?
Answer
(A)
8
45
The mean of 20 observations in an experiment is 4, lf the observed largest value is 23, find the mean of the remaining observations.
