Find, correct to three significant figures, the value of \(\sqrt{41830}\).
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(A)
205
2
Write down the number 0.0052048 correct to three significant figures
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(C)
0.00520
3
Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)
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(C)
\(\frac{9}{4}\)
4
Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?
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(D)
49
5
Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{\sqrt{1 + a} + \sqrt{a}}\)
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(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?
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(C)
N75
7
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
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(C)
\(\frac{19}{2}\)
8
List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
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(B)
3, 4, 5
9
Find the roots of the equation 10x2 - 13x - 3 = 0
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(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
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(B)
3cm
11
The ratio of the areas of similar triangles is necessarily equal to
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(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?
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(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?
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(C)
N184
14
Simplify \(\frac{log_{10}8}{log_{10}4}\)
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(C)
\(\frac{3}{2}\)
15
Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
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(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?
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(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.......?
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(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
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(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
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(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
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(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 \(\frac{FG}{FH}\)
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(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.
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(C)
120o
23
Find the product of (2\(\sqrt{y} - 3y\)) and (3y + 2\(\sqrt{y}\))
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(C)
4y - 9y2
24
(\(\frac{x^a}{x^b}\))a + b = (\(\frac{x^{a + b}}{x^{a - b}}\))\(\frac{a^2}{b}\)
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(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?
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(C)
4
26
Find the solution of the equation x + 2\(\sqrt{x} - 8\) = 0
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(A)
(4, 16)
27
If it is given that \(5^{x + 1} + 5^x = 150\), then the value of x is equal to
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(D)
2
28
Solve the system of equation 2\(^{x + y}\) = 32, \(3^{3y - x}\) = 27
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(A)
(3, 2)
29
Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
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(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 \(\pi\) = \(\frac{22}{7}\))
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(A)
188.57cm2
31
Solve the equation for the positive values of \(\theta\) less than 360o. 3 tan \(\theta\) + 2 = -1
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(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.
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(C)
c = -20 and d = -15
36
If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).
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(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 \(\pi\) = \(\frac{22}{7}\)
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(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
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(B)
x varies directly as w2
39
Write the decimal number 39 to base 2
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(A)
100111 base 2
40
If PN is perpendicular to QR, find the value of tan x.
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(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.
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(B)
56.105
42
In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90o, Find x
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(D)
70o
43
In the figure, PS bisects angle QPR. Find the ratio SR:QR.
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(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
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(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.
