What is the different between 0.007685 correct to three significant figures and 0.007685 correct to four places of decimal?
Răspuns
(A)
10-5
7
If a : b = 5 : 8, x : y = 25 : 16; evaluate \(\frac{a}{x}\) : \(\frac{b}{y}\)
Răspuns
(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?
Răspuns
(B)
4
9
If the surface area of a sphere increased by 44%, find the percentage increase in diameter
Răspuns
(D)
20
10
Simplify \(4 - \frac{1}{2 - \sqrt{3}}\)
Răspuns
(D)
2 - \(\sqrt{3}\)
11
Find p in terms of q if \(\log_{3} p + 3\log_{3} q = 3\)
Răspuns
(A)
(\(\frac{3}{q}\))3
12
What are the values of y which satisfy the equation \(9^{y} - 4 \times 3^{y} + 3 = 0\) ?
Răspuns
(D)
0 and 1
13
Make R the subject of the formula S = \(\sqrt{\frac{2R + T}{2RT}}\)
Răspuns
(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
Răspuns
(B)
N63.00
15
If \(f(x) = 2x^2 - 5x + 3\), find f(x + 1).
Răspuns
(A)
2x2 - x
16
Solve for a positive number x such that \(2^{(x^3 - x^2 - 2x)} = 1\)
Răspuns
(C)
2
17
Simplify \(\frac{324 - 4x^2}{2x + 18}\)
Răspuns
(D)
-2(x - 9)
18
Factorize completely \(y^3 -4xy + xy^3 - 4y\)
Răspuns
(C)
y(1 + x)(y + 2)(y -2)
19
Factorize 4a2 - 12ab - C2 + 9b2
Răspuns
(C)
(2a - 3b + c)(2a - 3b - c)
20
What are K and L respectively if \(\frac{1}{2}\)(3y - 4x)2 = (8x2 + kxy + Ly2)
Răspuns
(A)
-12, \(\frac{9}{2}\)
21
Solve the pair of equation for x and y respectively \(2x^{-1} - 3y^{-1} = 4; 4x^{-1} + y^{-1} = 1\)
Răspuns
(D)
2, -1
22
What value of Q will make the expression 4x2 + 5x + Q a complete square?
Răspuns
(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
Răspuns
(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
Răspuns
(D)
(\(\frac{y}{x}\))\(\frac{1}{n - 2}\)
27
If -8, m, n, 19 are in arithmetic progression, find (m, n)
Răspuns
(A)
1, 10
28
A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k
Răspuns
(A)
4
29
PQRS is a rhombus. If PR\(^2\) + QS\(^2\) = kPQ\(^2\), determine k.
Răspuns
(D)
4
30
In XYZ, y = z = 30° and XZ = 3cm. Find YZ
Răspuns
(C)
3\(\sqrt{3}\) cm
31
if x : y = 5 : 12 and z = 52cm, find the perimeter of the triangle.
Răspuns
(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
Răspuns
(D)
10(cot35o - cot55o)
33
4sin2 x - 3 = 0, find x if 0 \(\geq\) x \(\geq\) 90o
Răspuns
(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?
Răspuns
(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
Răspuns
(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
Răspuns
(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
Răspuns
(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?
Răspuns
(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
Răspuns
(B)
(2.5, 2.6)
40
On the curve, the points at which the gradient of the curve is equal to zero are
