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