Simplify 3\(\frac{1}{3}\) - 1\(\frac{1}{4}\) x \(\frac{2}{3}\) + 1\(\frac{2}{5}\)
Answer
(C)
4
2
If 2257 is the result of subtracting 4577 from 7056 in base n, find n
Answer
(A)
8
3
Find correct to 3 decimal places (\(\frac{1}{0.05} \div\frac{1}{5.005}\)) - (0.05 x 2.05)
Answer
(A)
99.998
4
express 62 \(\div\) 3 as a decimal correct to 3 significant figures
Answer
(D)
20.7
5
Factory P produces 20,000 bags of cement per day while factory Q produces 15,000 bags per day. If P reduces production by 5% and Q increases production by 5%, determine the effective loss in the number of bags produced per day by the two factories
Answer
(A)
250
6
Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?
Answer
(C)
N2.80
7
If 3 gallons of spirit containing 20% water are added to 5 gallons of another spirit containing 15% water, what percentage of the mixture is water?
Answer
(B)
16\(\frac{7}{8}\)%
8
What is the product of \(\frac{27}{5^1}\)(3)-3 and \(\frac{(1)^{-1}}{5}\)?
Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy}\) When x = -2 and y = 3
Answer
(D)
-3
14
A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin
Answer
(B)
\(\frac{uw(p + q)}{pw + qu}\)
15
If w varies inversely as \(\frac{uv}{u + v}\) and is equal to 8 when
u = 2 and v = 6, find a relationship between u, v, w.
Answer
(C)
uvw = 12(u + v)
16
If g(x) = x2 + 3x + 4, find g(x + 1) - g(x)
Answer
(B)
2(x + 2)
17
Factorize \(m^3 - 2m^2\) - m + 2
Answer
(C)
(m - 2)(m + 1)(m - 1)
18
Factorize 1 - (a - b)2
Answer
(B)
(1 + a - b)(1 - a + b)
19
Which of the following is a factor of rs + tr - pt - ps?
Answer
(C)
r - p)
20
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x\(^2\) + xy = 6.
Answer
(A)
-1 and 5
21
Find the range of values of x which satisfy the inequality \(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{x}{4}\) < 1
Answer
(A)
x < \(\frac{12}{13}\)
22
Find the positive number n, such that thrice its square is equal to twelve times the number
Answer
(D)
4
23
What is the nth term of the progression 27, 9, 3,......?
Find the gradient of the line passing through the points (-2, 0) and (0, -4)
Answer
(C)
-2
28
At what value of x is the function y = x2 - 2x - 3 minimum?
Answer
(A)
1
29
Find the sum of the first 20 terms in an arithmetic progression whose first term is 7 and last term is 117.
Answer
(B)
1240
30
The area of a square is 144 sq cm. Find the length of its diagonal
Answer
(C)
12\(\sqrt{2cm}\)
31
One angle of a rhombus is 60o. The shorter of the two diagonals is 8cm long. Find the length of the longer one.
Answer
(A)
8\(\sqrt{3}\)
32
If the exterior angles of a pentagon are x°, (x + 5)°, (x + 10)°, (x + 15)° and (x + 20)°, find x
Answer
(C)
62o
33
A flagstaff stands on the top of a vertical tower. A man standing 60 m away from the tower observes that the angles of elevation of the top and bottom of the flagstaff are 64o and 62o respectively. Find the length of the flagstaff.
Answer
(D)
60 (tan 64o - tan 62o)
34
Simplify \(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
Answer
(C)
\(\sec^2 x\)
35
If cos x = \(\sqrt{\frac{a}{b}}\) find cosec x
Answer
(C)
\(\sqrt{\frac{b}{b - a}}\)
36
From a point Z, 60 m north of X, a man walks 60√3m eastwards to another point Y. Find the bearing of Y from X.
Answer
(C)
060o
37
Find the total area of the surface of a solid cylinder whose base radius is 4cm and height is 5cm
Answer
(B)
72\(\pi\) cm2
38
3% of a family's income is spent on electricity, 59% on food, 20% on transport, 11% on education and 7% on extended family. The angles subtended at the centre of the pie chart under education and food are respectively
Answer
(D)
39.6o and 212.4o
39
Fifty boxes each of 50 bolts were inspected for the number which were defective. The following was the result
\(\begin{array}{c|c} \text{No. defective per box} & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No. of boxes} & 2 & 7 & 17 & 10 & 8 & 6\end{array}\)
The mean and the median of the distribution are respectively
Answer
(A)
6.7, 6
40
Fifty boxes each of 50 bolts were inspected for the number which were defective. The following was the result
\(\begin{array}{c|c} \text{No. defective per box} & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No. of boxes} & 2 & 7 & 17 & 10 & 8 & 6\end{array}\)
Find the percentage of boxes containing at least 5 defective bolts each
Answer
(A)
96
41
A crate of soft drinks contains 10 bottles of Coca-cola, 8 of Fanta and 6 of sprite. If one bottle is selected at random, what is the probability that it is NOT a Cocacola bottle?
Answer
(D)
\(\frac{7}{12}\)
42
In the figure above, Find the value of x
Answer
(A)
130o
43
PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PM = 5cm, PN = 12cm and PQ = 4.8cm, calculate the respective lengths of PR and PT in centimeters
Answer
(C)
12.5, 7.7
44
PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PNR = 110o and PMQ = 55o, find MPQ
