What is the different between 0.007685 correct to three significant figures and 0.007685 correct to four places of decimal?
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(A)
10-5
7
If a : b = 5 : 8, x : y = 25 : 16; evaluate \(\frac{a}{x}\) : \(\frac{b}{y}\)
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(D)
2 : 5
8
Oke deposited N800.00 in the bank at the rate of 12\(\frac{1}{2}\)% simple interest. After some time the total amount was one and half times the principal. For how many years was the money left in the bank?
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(B)
4
9
If the surface area of a sphere increased by 44%, find the percentage increase in diameter
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(D)
20
10
Simplify \(4 - \frac{1}{2 - \sqrt{3}}\)
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(D)
2 - \(\sqrt{3}\)
11
Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)
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(A)
(\(\frac{3}{q}\))3
12
What are the values of y which satisfy the equation \(9^{y} - 4 \times 3^{y} + 3 = 0\) ?
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(D)
0 and 1
13
Make R the subject of the formula S = \(\sqrt{\frac{2R + T}{2RT}}\)
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(B)
R = \(\frac{T}{2(TS^2 - 1)}\)
14
The cost of dinner for a group of students is partly constant and partly varies directly as the number of students. If the cost is N74.00 when the number of students is 20 and N96.00 when the number of students is 30, find the cost when there are 15 students
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(B)
N63.00
15
If \(f(x) = 2x^2 - 5x + 3\), find f(x + 1).
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(A)
2x2 - x
16
Solve for a positive number x such that \(2^{(x^3 - x^2 - 2x)} = 1\)
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(C)
2
17
Simplify \(\frac{324 - 4x^2}{2x + 18}\)
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(D)
-2(x - 9)
18
Factorize completely \(y^3 -4xy + xy^3 - 4y\)
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(C)
y(1 + x)(y + 2)(y -2)
19
Factorize 4a2 - 12ab - C2 + 9b2
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(C)
(2a - 3b + c)(2a - 3b - c)
20
What are K and L respectively if \(\frac{1}{2}\)(3y - 4x)2 = (8x2 + kxy + Ly2)
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(A)
-12, \(\frac{9}{2}\)
21
Solve the pair of equation for x and y respectively \(2x^{-1} - 3y^{-1} = 4; 4x^{-1} + y^{-1} = 1\)
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(D)
2, -1
22
What value of Q will make the expression 4x2 + 5x + Q a complete square?
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(A)
\(\frac{25}{16}\)
23
find the range of values of values of r which satisfies the following inequality, where a, b and c are positive \(\frac{r}{a}\) + \(\frac{r}{b}\) + \(\frac{r}{c}\) > 1
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(A)
r > \(\frac{abc}{bc + ac + ab}\)
24
Express \(\frac{1}{x + 1}\) - \(\frac{1}{x - 2}\) as a single algebraic fraction
The sum of the first two terms of a geometric progression is x and sum of the last terms is y. If there are n terms in all, then the common ratio is
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(D)
(\(\frac{y}{x}\))\(\frac{1}{n - 2}\)
27
If -8, m, n, 19 are in arithmetic progression, find (m, n)
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(A)
1, 10
28
A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k
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(A)
4
29
PQRS is a rhombus. If PR\(^2\) + QS\(^2\) = kPQ\(^2\), determine k.
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(D)
4
30
In XYZ, y = z = 30° and XZ = 3cm. Find YZ
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(C)
3\(\sqrt{3}\) cm
31
if x : y = 5 : 12 and z = 52cm, find the perimeter of the triangle.
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(D)
120cm
32
The pilot of an aeroplane, flying 10km above the ground in the direction of a landmark, views the landmark to have angles of depression of 35o and 55o. Find the distance between the two points of observation
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(D)
10(cot35o - cot55o)
33
4sin2 x - 3 = 0, find x if 0 \(\geq\) x \(\geq\) 90o
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(C)
60o
34
A square tile has side 30cm. How many of these tiles will cover a rectangular floor of length 7.2m and width 4.2m?
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(A)
336
35
A cylindrical metal pipe 1m long has an outer diameter of 7.2cm and an inner diameter of 2.8cm. Find the volume of metal used for the cylinder
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(B)
1100\(\pi\)cm3
36
OXYZW is a pyramid with a square base such that OX = OY= OZ = OW = 5cm and XY = XW = YZ = WZ = 6cm. Find the height OT
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(D)
4\(\sqrt{3}\)
37
In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represents meat in pie chart
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(D)
157.5o
38
In a family of 21 people, the average age is 14years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather?
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(D)
54 years
39
If n is the median and m is the mode of the following set of numbers, 2.4, 2.1, 1.6, 2.6, 2.6, 3.7, 2.1, 2.6, then (n, m) is
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(B)
(2.5, 2.6)
40
On the curve, the points at which the gradient of the curve is equal to zero are
