Find, correct to three significant figures, the value of \(\sqrt{41830}\).
Answer
(A)
205
2
Write down the number 0.0052048 correct to three significant figures
Answer
(C)
0.00520
3
Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)
Answer
(C)
\(\frac{9}{4}\)
4
Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?
Answer
(D)
49
5
Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{\sqrt{1 + a} + \sqrt{a}}\)
Answer
(A)
1 + 2a - 2\(\sqrt{a(1 + a)}\)
6
When a dealer sells a bicycle for N81 he makes a profit of 8%. What did he pay for the bicycle?
Answer
(C)
N75
7
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
Answer
(C)
\(\frac{19}{2}\)
8
List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
Answer
(B)
3, 4, 5
9
Find the roots of the equation 10x2 - 13x - 3 = 0
Answer
(E)
x = -\(\frac{1}{5}\) or \(\frac{3}{2}\)
10
A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height
Answer
(B)
3cm
11
The ratio of the areas of similar triangles is necessarily equal to
Answer
(B)
the ratio of the squares of corresponding sides
12
P and Q are fixed points and X is a variable point which moves so that angle PXQ = 45o. What is the locus of x?
Answer
(B)
The perpendicular bisector of PQ
13
A man and his wife went to buy an article costing N400. The woman had 10% of the cost and the man 40% of the remainder. How much did they have altogether?
Answer
(C)
N184
14
Simplify \(\frac{log_{10}8}{log_{10}4}\)
Answer
(C)
\(\frac{3}{2}\)
15
Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
Answer
(A)
[\(\frac{7}{3}\) + \(\frac{5}{a}\)(v - 1)] + b
16
What factor is common to all the expressions x2 - x, 2x2 + x - 1 and x2 - 1?
Answer
(D)
No common factor
17
Which of the formula below represents the general terms of the following set of numbers(-1, \(\frac{2}{3}\), -\(\frac{1}{2}\), \(\frac{2}{5}\)......) for n = 1, 2, 3, 4.......?
Answer
(C)
(-1)n \(\frac{2}{n + 1}\)
18
Three numbers, x, y and z are connected by the relationships y = \(\frac{4x}{9}\) + 1. If x = 99, Find z = \(\frac{4y}{9}\) + 1
Answer
(C)
21
19
In a school, there are 35 students in class 2A and 40 in class 2B. The mean score for class 2 in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes
Answer
(B)
56.0
20
A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items, then the sector representing this group on the pie chart contains an angle xo at the centre of the circle where x is
Answer
(D)
72o
21
In triangle FGH, < G = 90º, < H = 60º, while in triangle XYZ, < X = 60º and < Y = 30º. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)
Answer
(D)
\(\frac{YZ}{XY}\)
22
A pentagon has four of its angles equal. If the size of the fifth angle is 60o, Find the size of each of the four equal angles.
Answer
(C)
120o
23
Find the product of (2\(\sqrt{y} - 3y\)) and (3y + 2\(\sqrt{y}\))
Answer
(C)
4y - 9y2
24
(\(\frac{x^a}{x^b}\))a + b = (\(\frac{x^{a + b}}{x^{a - b}}\))\(\frac{a^2}{b}\)
Answer
(D)
\(\frac{1}{x^{a2 + b2}}\)
25
What will be the value of k so that the quadratic equation kx2 - 4x + 1 = 0 has two equal roots?
Answer
(C)
4
26
Find the solution of the equation x + 2\(\sqrt{x} - 8\) = 0
Answer
(A)
(4, 16)
27
If it is given that \(5^{x + 1} + 5^x = 150\), then the value of x is equal to
Answer
(D)
2
28
Solve the system of equation 2\(^{x + y}\) = 32, \(3^{3y - x}\) = 27
Answer
(A)
(3, 2)
29
Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
Answer
(A)
\(\frac{1 - cos x}{sin x}\)
30
Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (take \(\pi\) = \(\frac{22}{7}\))
Answer
(A)
188.57cm2
31
Solve the equation for the positive values of \(\theta\) less than 360o. 3 tan \(\theta\) + 2 = -1
Answer
(A)
135o or 315o
32
Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.
The expression x\(^3\) - 4x\(^2\) + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.
Answer
(C)
c = -20 and d = -15
36
If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).
Answer
(D)
8
37
A cylindrical motor of height 12cm has uniform thickness of 2cm. If the diameter of its outer cross section is 10cm, Find the volume of the constituent material. (take \(\pi\) = \(\frac{22}{7}\)
Answer
(D)
\(\frac{4224}{7}\)cm3
38
If x varies inversely as y, and y varies directly as the square root of z, and z varies directly \(\frac{1}{w^2}\) write down in words how x varies with w
Answer
(B)
x varies directly as w2
39
Write the decimal number 39 to base 2
Answer
(A)
100111 base 2
40
If PN is perpendicular to QR, find the value of tan x.
Answer
(B)
\(\frac{3}{5}\)
41
In the figure, PQ\\SR, ST\\, ST\\RQ, PS = 7cm, PT = 7cm, SR = 4cm. Find the ratio of the area QRST to the area of PQRS.
Answer
(B)
56.105
42
In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90o, Find x
Answer
(D)
70o
43
In the figure, PS bisects angle QPR. Find the ratio SR:QR.
Answer
(C)
1:4
44
fG is a given straight line and H is a fixed point. The construction marks shown in the diagram indicate the
Answer
(D)
perpendicular from H to the line FG
45
In the figure, FGHJ is a circle of radius 3cm centre O. FOH, GOJ are perpendicular diameters. With G as centre of an arc of a circle is drawn to pass through F and H. Find the length of the perimeter of the lunar portion shaded.
