If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)
Answer
(B)
\(\frac{2}{3}\)
2
Arrange the following numbers in ascending order of magnitude \(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
Answer
(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
Answer
(D)
N250.00
4
In the equation below, Solve for x if all the numbers are in base 2: \(\frac{11}{x}\) = \(\frac{1000}{x + 101}\)
Answer
(B)
11
5
List all integers satisfying the inequality -2 \(\leq\) 2 x -6 < 4
Answer
(B)
2, 3, 4
6
Find correct to two decimals places 100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
Answer
(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
Answer
(A)
N45.00
8
Find x if log\(_9\)x = 1.5
Answer
(B)
27.0
9
Write h in terms of a, b, c, d if a = \(\frac{b(1 - ch)}{1 - dh}\)
Answer
(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?
Answer
(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
Answer
(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
Answer
(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?
Answer
(C)
50k
15
The factors of 9 - (x2 - 3x - 1)2 are
Answer
(A)
-(x - 4)(x + 1) (x - 1)(x - 2)
16
If 32y + 6(3y) = 27. Find y
Answer
(E)
1
17
Factorize abx2 + 8y - 4bx - 2axy
Answer
(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?
Answer
(E)
1
19
If the quadratic function 3x2 - 7x + R is a perfect square, find R
Answer
(B)
\(\frac{49}{12}\)
20
Solve for (x, y) in the equation 2x + y = 4: x^2 + xy = -12
Answer
(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
Answer
(D)
\(\frac{43}{78}\)
25
Find the missing value in the table below
\(\begin{array}{c|c} x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y = 4 - 3x - x^3 & 80 & & 18 & 8 & 4 & 0 & -10 & -32 \end{array}\)
Answer
(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?
Answer
(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?
Answer
(A)
\(\sqrt{2}\)
28
If two fair coins are tossed, what is the probability of getting at least one head?
Answer
(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?
Answer
(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?
Answer
(B)
S 72o W
31
Without using table, calculate the value of 1 + sec2 30o
Answer
(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?
Answer
(B)
\(\frac{3}{5}\)
33
Find the area of a regular hexagon inscribed in a circle of radius 8cm
Answer
(B)
96\(\sqrt{3}\) cm3
34
If cos \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90o. Calculate \(\frac{\cot(90 - \theta)}{sin^2\theta}\)
Answer
(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?
Answer
(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
Answer
(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?
Answer
(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)
Answer
(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?
Answer
(E)
54
40
If a{\(\frac{x + 1}{x - 2} - \frac{x - 1}{x + 2}\)} = 6x. Find a in its simplest form
Answer
(D)
x2 - 4
41
In \(\bigtriangleup\) XYZ, XKZ = 90O, XK = 15cm, XZ = 25cm and YK = 8cm. Find the area of \(\bigtriangleup\)XYZ
Answer
(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)
Answer
(A)
28o, 36o
43
In the figure POQ is the diameter of the circle PQR. If PSR = 145o, find xo
Answer
(E)
55o
44
In the figure, GHIJKLMN is a cube of side a. Find the length of HN.
Answer
(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
