If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)
Răspuns
(B)
\(\frac{2}{3}\)
2
Arrange the following numbers in ascending order of magnitude \(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
Răspuns
(A)
\(\frac{6}{7}\) < 0.865 < \(\frac{13}{15}\)
3
A sum of money was invested at 8% per annum simple interest. If after 4 years the money amounts to N330.00. Find the amount originally invested
Răspuns
(D)
N250.00
4
In the equation below, Solve for x if all the numbers are in base 2: \(\frac{11}{x}\) = \(\frac{1000}{x + 101}\)
Răspuns
(B)
11
5
List all integers satisfying the inequality -2 \(\leq\) 2 x -6 < 4
Răspuns
(B)
2, 3, 4
6
Find correct to two decimals places 100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
Răspuns
(A)
100.02
7
John gives one-third of his money to Janet who has N105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find how much money john has at first
Răspuns
(A)
N45.00
8
Find x if log\(_9\)x = 1.5
Răspuns
(B)
27.0
9
Write h in terms of a, b, c, d if a = \(\frac{b(1 - ch)}{1 - dh}\)
Răspuns
(D)
h = \(\frac{a - b}{ad - bc}\)
10
22\(\frac{1}{2}\)% of the Nigerian Naira is equal to 17\(\frac{1}{10}\)% of a foreign currency M. What is the conversion rate of the M to the Naira?
Răspuns
(C)
1M = 1\(\frac{18}{57}\)N
11
Find the values of p for which the equation x\(^2\) - (p - 2)x + 2p + 1 = 0
Răspuns
(B)
(0, 12)
12
If \(e^{x} = 1 + x + \frac{x^{2}}{1.2} + \frac{x^{3}}{1.2.3} + ... \), find \(\frac{1}{e^{\frac{1}{2}}}\)
\((\sqrt[4]{3} + \sqrt[4]{2})(\sqrt[4]{3} - \sqrt[4]{2})(\sqrt{3} + \sqrt{2})\) is equal to
Răspuns
(A)
1
14
In a restaurant, the cost of providing a particular type of food is partly constant and partially inversely proportional to the number of people. If cost per head for 100 people is 30k and the cost for 40 people is 60k, Find the cost for 50 people?
Răspuns
(C)
50k
15
The factors of 9 - (x2 - 3x - 1)2 are
Răspuns
(A)
-(x - 4)(x + 1) (x - 1)(x - 2)
16
If 32y + 6(3y) = 27. Find y
Răspuns
(E)
1
17
Factorize abx2 + 8y - 4bx - 2axy
Răspuns
(A)
(ax - 4)(bx - 2y)
18
At what real value of x do the curves whose equations are y = x3 + x and y = x2 + 1 intersect?
Răspuns
(E)
1
19
If the quadratic function 3x2 - 7x + R is a perfect square, find R
Răspuns
(B)
\(\frac{49}{12}\)
20
Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12
Răspuns
(A)
(6, -8): (-2, 8)
21
Solve the following equation \(\frac{2}{2r - 1}\) - \(\frac{5}{3}\) = \(\frac{1}{r + 2}\)
In \(\bigtriangleup\) XYZ, XY = 13cm, YZ = 9cm, XZ = 11cm and XYZ = \(\theta\). Find cos\(\theta\)o
Răspuns
(D)
\(\frac{43}{78}\)
25
Find the missing value in the table below
\(\begin{array}{c|c} x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y = 4 - 3x - x^3 & 80 & & 18 & 8 & 4 & 0 & -10 & -32 \end{array}\)
Răspuns
(C)
40
26
The number of goals scored by a football team in 20 matches is shown below
\(\begin{array}{c|c} \text{No. of goals} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \text{No. of matches} & 3 & 5 & 7 & 4 & 1 & 0 \end{array}\)
What are the values of the mean and the mode respectively?
Răspuns
(B)
(1.75, 2)
27
If the hypotenuse of right angled isosceles triangle is 2, what is the length of each of the other sides?
Răspuns
(A)
\(\sqrt{2}\)
28
If two fair coins are tossed, what is the probability of getting at least one head?
Răspuns
(E)
\(\frac{3}{4}\)
29
The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is?
Răspuns
(A)
234.00 cm3
30
The bearing of a bird on a tree from a hunter on the ground is N72oE. What is the bearing of the hunter from the birds?
Răspuns
(B)
S 72o W
31
Without using table, calculate the value of 1 + sec2 30o
Răspuns
(A)
2\(\frac{1}{3}\)
32
What is the probability that a number chosen at random from the intergers between 1 and 10 inclusive is either a prime or a multiple of 3?
Răspuns
(B)
\(\frac{3}{5}\)
33
Find the area of a regular hexagon inscribed in a circle of radius 8cm
Răspuns
(B)
96\(\sqrt{3}\) cm3
34
If cos \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90o. Calculate \(\frac{\cot(90 - \theta)}{sin^2\theta}\)
Răspuns
(A)
\(\frac{4}{\sqrt{3}}\)
35
A solid sphere of radius 4cm has a mass of 64kg. What will be the mass of a shell of the same metal whose internal and external radii are 2cm and 3cm respectively?
Răspuns
(C)
19kg
36
PRSQ is a trapezium of area 14cm2 in which PQ||RS. If PQ = 4cm and SR = 3cm, Find the area of SQR in cm2
Răspuns
(B)
6.0
37
A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?
Răspuns
(D)
\(\frac{1}{3}\)
38
Two points X and Y both on latitude 60oS have longitude147oE and 153oW respectively. Find to the nearest kilometer the distance between X and Y measured along the parallel of latitude(Take 2\(\pi\)R = 4 x 104km, where R is the radius of the earth)
Răspuns
(A)
16667km
39
In a class of 120 students, 18 of them scored an A grade in mathematics. If the section representing the A grade students on a pie chart has angle Zo at the centre of the circle, what is Z?
Răspuns
(E)
54
40
If a{\(\frac{x + 1}{x - 2} - \frac{x - 1}{x + 2}\)} = 6x. Find a in its simplest form
Răspuns
(D)
x2 - 4
41
In \(\bigtriangleup\) XYZ, XKZ = 90O, XK = 15cm, XZ = 25cm and YK = 8cm. Find the area of \(\bigtriangleup\)XYZ
Răspuns
(C)
210 sq.cm
42
In the figure, MNQP is a cyclic quadrilateral. MN and Pq are produced to meet at X and NQ and MP are produced to meet at Y. If MNQ = 86o and NQP = 122o find (xo, yo)
Răspuns
(A)
28o, 36o
43
In the figure POQ is the diameter of the circle PQR. If PSR = 145o, find xo
Răspuns
(E)
55o
44
In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
Răspuns
(E)
a\(\sqrt{3}\)
45
In the figure, PQ is the tangent from P to the circle QRS with SR as its diameter. If QPR = \(\theta\)o and RQP = \(\phi\)o, which of the following relationships between \(\theta\)o and \(\phi\)o is correct
