JAMB - Mathematics (1991)

1
Simplify 3\(\frac{1}{3}\) - 1\(\frac{1}{4}\) x \(\frac{2}{3}\) + 1\(\frac{2}{5}\)
Хариулт
(C)
4
2
If 2257 is the result of subtracting 4577 from 7056 in base n, find n
Хариулт
(A)
8
3
Find correct to 3 decimal places (\(\frac{1}{0.05} \div\frac{1}{5.005}\)) - (0.05 x 2.05)
Хариулт
(A)
99.998
4
express 62 \(\div\) 3 as a decimal correct to 3 significant figures
Хариулт
(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
Хариулт
(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?
Хариулт
(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?
Хариулт
(B)
16\(\frac{7}{8}\)%
8
What is the product of \(\frac{27}{5^1}\)(3)-3 and \(\frac{(1)^{-1}}{5}\)?
Хариулт
(D)
\(\frac{1}{25}\)
9
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
Хариулт
(D)
1 - 2log 2
10
Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
Хариулт
(B)
\(\frac{1}{2}\sqrt{5}\)
11
Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
Хариулт
(B)
5 + 2\(\sqrt{6}\)
12
Multiply (x² - 3x + 1) by (x - a)
Хариулт
(A)
x³ - (3 + a) x² + (1 + 3a)x - a
13
Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy}\) When x = -2 and y = 3
Хариулт
(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
Хариулт
(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.
Хариулт
(C)
uvw = 12(u + v)
16
If g(x) = x² + 3x + 4, find g(x + 1) - g(x)
Хариулт
(B)
2(x + 2)
17
Factorize \(m^3 - 2m^2\) - m + 2
Хариулт
(C)
(m - 2)(m + 1)(m - 1)
18
Factorize 1 - (a - b)²
Хариулт
(B)
(1 + a - b)(1 - a + b)
19
Which of the following is a factor of rs + tr - pt - ps?
Хариулт
(C)
r - p)
20
Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x\(^2\) + xy = 6.
Хариулт
(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
Хариулт
(A)
x < \(\frac{12}{13}\)
22
Find the positive number n, such that thrice its square is equal to twelve times the number
Хариулт
(D)
4
23
What is the nth term of the progression 27, 9, 3,......?
Хариулт
(A)
27\(\frac{1}{3}\) ^{n - 1}
24
Solve the equation (x - 2) (x - 3) = 12
Хариулт
(C)
-1, 6
25
Simplify \(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)
Хариулт
(B)
1 + 2x + 2\(\sqrt{x (1 + x)}\)
26
Evaluate x²(x² - 1)^{-\(\frac{1}{2}\)} - (x² - 1)^{\(\frac{1}{2}\)}
Хариулт
(A)
(x² - 1)^{-\(\frac{1}{2}\)}
27
Find the gradient of the line passing through the points (-2, 0) and (0, -4)
Хариулт
(C)
-2
28
At what value of x is the function y = x² - 2x - 3 minimum?
Хариулт
(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.
Хариулт
(B)
1240
30
The area of a square is 144 sq cm. Find the length of its diagonal
Хариулт
(C)
12\(\sqrt{2cm}\)
31
One angle of a rhombus is 60^o. The shorter of the two diagonals is 8cm long. Find the length of the longer one.
Хариулт
(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
Хариулт
(C)
62^o
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 64^o and 62^o respectively. Find the length of the flagstaff.
Хариулт
(D)
60 (tan 64^o - tan 62^o)
34
Simplify \(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
Хариулт
(C)
\(\sec^2 x\)
35
If cos x = \(\sqrt{\frac{a}{b}}\) find cosec x
Хариулт
(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.
Хариулт
(C)
060^o
37
Find the total area of the surface of a solid cylinder whose base radius is 4cm and height is 5cm
Хариулт
(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
Хариулт
(D)
39.6^o and 212.4^o
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
Хариулт
(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
Хариулт
(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?
Хариулт
(D)
\(\frac{7}{12}\)
42
In the figure above, Find the value of x
Хариулт
(A)
130^o
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
Хариулт
(C)
12.5, 7.7
44
PMN and PQR are two secants of the circle MQTRN and PT is a tangent. If PNR = 110^o and PMQ = 55^o, find MPQ
Хариулт
(D)
15^o
45
In the figure above, find the value of y
Хариулт
(B)
122^o