Evaluate \(\frac{81.81+99.44}{20.09+36.16}\) correct to 3 significant figures.
Answer
(B)
3.22
4
A man bought a second-hand photocopying machine for N34,000. He serviced it at a cost of N2,000 and then sold it at a profit of 15%. What was the selling price?
Answer
(C)
N41,400
5
A student spent 1/5 of his allowance on books, 1/2 of remainder on food and kept the rest for contingencies. What fraction was kept?
Answer
(C)
2/5
6
If log\(_{10}\)2 = 0.3010 and log\(_{10}\)7 = 0.8451, evaluate log\(_{10}\)280
Answer
(B)
2.4471
7
Simplify \(\frac{5+\sqrt{7}}{3+\sqrt{7}}\)
Answer
(B)
4-√7
8
If x = {n\(^2\)+1:n is a positive integer and 1 \(\leq\) n \(\leq\) 5},
Y = {5n:n is a positive integer and 1 \(\leq\) n \(\leq\) 5}, find x \(\cap\) y.
Answer
(A)
{5,10}
9
I.S∩T∩W=S II. S ∪ T ∪ W = W
III. T ∩ W = S
If S⊂T⊂W, which of the above statements are true?
Answer
(A)
I and II
10
If \(p=\sqrt{\frac{rs^3}{t}}\), express r in terms of p, s and t?
Answer
(A)
\(\frac{p^2 t}{s^3}\)
11
A polynomial in x whose roots are 4/3 and -3/5 is?
Answer
(A)
15x2 - 11x – 12
12
Which of the following equations represent the graph above?
Answer
(D)
y = 2-7x-4x2
13
W is directly proportional to U. If W = 5 when U = 3, find U when W = 2/7
Answer
(A)
6/35
14
Determine the value of x for which (x\(^2\) - 1) > 0?
Answer
(A)
x < -1 or x > 1
15
Find the range of values of x for which 3x - 7 \(\leq\) 0 and x + 5 > 0?
Answer
(C)
-5 < x \(\leq\) \(\frac{7}{3}\)
16
The sum of the first n terms of the arithmetic progression 5, 11, 17, 23, 29, 35, ... is?
Answer
(B)
n(3n + 2)
17
Find to infinity, the sum of the sequence \(1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3,.....\)
Answer
(A)
10
18
If m * n = n - (m+2) for any real number m and n find the value of 3*(-5)?
Answer
(C)
-10
19
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?
Answer
(A)
-5/4
20
If Q is\( \left[ \begin{array}{cc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\) , then |Q| is?
Answer
(C)
22
21
If P \(=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
Answer
(D)
5
22
Find the acute angle between the straight lines y = x and y = √3x
Answer
(A)
15o
23
A regular polygon has 150º as the size of each interior angle. How many sides does it have?
Answer
(A)
12
24
In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n?
Answer
(B)
52o
25
If the hypotenuse of a right-angled isosceles triangle is 2cm. What is the area of the triangle?
Answer
(B)
1 cm2
26
A chord drawn 5 cm away from the center of a circle of radius 13 cm. Calculate the length of the chord?
Answer
(D)
24cm
27
Find the radius of a sphere whose surface area is 154 cm\(^2\)?
Answer
(B)
3.50 cm
28
Find the locus of a particle which moves in the first quadrant so that it is equidistant from the lines x = 0 and y = 0 (where k is a constant)?
Answer
(B)
x - y = 0
29
What is the locus of the mid-point of all the chords of length 6cm with circle of radius 5cm and with center O?
Answer
(A)
A circle of radius 4 cm and the center 0
30
What is the value of p if the gradient of the line joining (-1,p) and (p, 4) is
2
3
?
Answer
(D)
2
31
What is the value of r if the distance between the point (4,2) and (1,r) is 3 units?
Answer
(B)
2
32
If y = 3 cos 4x, dy/dx equals?
Answer
(D)
-12 sin 4x
33
Find the value of sin 45° - cos 30°
Answer
(D)
\(\frac{\sqrt{2}-\sqrt{3}}{2}\)
34
A cliff on the bank of a river is 300 meter high. if the angle of depression of a point on the opposite side of the river is 60º, find the width of the river?
Answer
(C)
100√3m
35
If s = (2 + 3t)(5t - 4), find ds/dt when t = \(\frac{4}{5}\) secs
Answer
(C)
22 unit per sec
36
The distance traveled by a particle from a fixed point is given as s = (t\(^3\) - t\(^2\) - t + 5)cm. Find the minimum distance that the particle can cover from the fixed point?
Answer
(B)
4.0 cm
37
Evaluate ∫sec\(^2\)θ dθ?
Answer
(B)
tan θ + k
38
No. of Days
1
2
3
4
5
6
No. of students
20
2x
60
40
x
50
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term?
Answer
(B)
120
39
The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?
Answer
(B)
50
40
The probability of a student passing any examination is 2/3. If the students takes three examination, what is the probability that he will not pass any of them?
Answer
(D)
1/27
41
5, 8, 6 and k occur with frequency 3, 2, 4, and 1 respectively and have a mean of 5.7. Find the value of k?
Answer
(C)
2
42
What is the mean deviation of x, 2x, x+1 and 3x. If their mean is 2?
Answer
(A)
0.5
43
In how many ways can a delegation of 3 be chosen from 5 men and 3 women. If at least 1 man and 1 woman must be included?
Answer
(D)
45
44
In how many ways can 9 people be seated if 3 chairs are available?
Answer
(B)
504
45
Marks
2
3
4
5
6
7
8
9
No. of students
3
4
1
0
4
5
2
1
The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5?
