JAMB Mathematics 1991 Past Questions

Question 0

Simplify 3\(\frac{1}{3}\) - 1\(\frac{1}{4}\) x \(\frac{2}{3}\) + 1\(\frac{2}{5}\)

A.2
B.3
C.4
D.5
E.

Objective

Question 0

If 2257 is the result of subtracting 4577 from 7056 in base n, find n

A.8\(\frac{17}{30}\)
B.9\(\frac{9}{10}\)
C.10\(\frac{1}{10}\)
D.11\(\frac{11}{36}\)
E.

Objective

Question 0

Find correct to 3 decimal places (\(\frac{1}{0.05}\) + \(\frac{1}{5.005}\)) - (0.05 x 2.05)

A.99.998
B.98.999
C.89.899
D.9.998
E.

Objective

Question 0

express 62 \(\div\) 3 as a decimal correct to 3 significant figures

A.20.6
B.20.667
C.20.67
D.20.7
E.

Objective

Question 0

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

A.250
B.750
C.1000
D.1250
E.

Objective

Question 0

Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe

A.N10.80
B.N10.67
C.N2.80
D.N2.67
E.

Objective

Question 0

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?

A.2\(\frac{4}{5}\)%
B.16\(\frac{7}{8}\)%
C.18\(\frac{1}{8}\)%
D.18\(\frac{7}{8}\)%
E.

Objective

Question 0

What is the product of \(\frac{27}{5^1}\)(3)^-3 and \(\frac{(1)^{-1}}{5}\)?

A.5
B.3
C.1
D.\(\frac{1}{25}\)
E.

Objective

Question 0

Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9

A.1 - 4 log3
B.-1 + 2 log 3
C.-1 + 5 log2
D.1 - 2log 2
E.

Objective

Question 0

Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)

A.- \(\frac{1}{2}\sqrt{5}\)
B.\(\frac{1}{2}\sqrt{5}\)
C.-- \(\frac{1}{4}\sqrt{5}\)
D.5
E.

Objective

Question 0

Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)

A.5 - 2\(\sqrt{6}\)
B.5 + 2\(\sqrt{6}\)
C.5\(\sqrt{6}\)
D.5
E.

Objective

Question 0

Multiply (x² - 3x + 1) by (x - a)

A.x³ - (3 + a) x² + (1 + 3a)x - a
B.x³ - (3 - a)x² + 3ax - a
C.x³ - (3 - a)x² - (1 = 3a) - a
D.x³ + (3 - a)x² + (1 + 3a) - a
E.

Objective

Question 0

Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 2

A.3
B.-\(\frac{3}{5}\)
C.\(\frac{3}{5}\)
D.-3
E.

Objective

Question 0

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

A.\(\frac{(p + q)}{pw + qu}\)
B.\(\frac{uw(p + q)}{pw + qu}\)
C.\(\frac{uw(p + q)}{pw}\)
D.\(\frac{uw}{pw + qu}\)
E.

Objective

Question 0

If w varies inversely as \(\frac{ur}{u + r}\) and is equal to 8 when

u = 2 and r = 6, find a relationship between u, v, w.

A.urw = 16(u + v)
B.16ur = 3w(u + v)
C.urw = 12(u + v)
D.12urw = u + v
E.

Objective

Question 0

If g(x) = x² + 3x + 4, find g(x + 1) - g(x)

A.(x + 2)
B.2(x + 2)
C.(2x + 1)
D.(x² + 4)
E.

Objective

Question 0

Factorize m³ - 2m² - m + 2

A.(m² + 1)(m - 2)
B.(m - 1)(m + 1)(m + 2)
C.(m - 2)(m + 1)(m - 1)
D.(m² + 2)(m - 1)
E.

Objective

Question 0

Factorize 1 - (a - b)²

A.(1 - a - b)(1 - a + b)
B.(1 + a - b)(1 - a + b)
C.(1 - a + b)(1 - a + b)
D.(1 + a + b)(1 + a + b)
E.

Objective

Question 0

Which of the following is a factor of rs + tr - pt - ps?

A.(p - s)
B.(s - p)
C.r - p)
D.r + p)
E.

Objective

Question 0

Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x² + xy = 6

A.-1 and 5
B.-5 and 1
C.1 and 5
D.1 and 1
E.

Objective

Question 0

Find the range of values of x which satisfy the inequality \(\frac{x}{2}\) + \(\frac{x}{3}\) + \(\frac{x}{4}\) < 1

A.x < \(\frac{12}{13}\)
B.x < 13
C.x < 9
D.\(\frac{13}{12}\)
E.

Objective

Question 0

Find the positive number n, such that thrice its square is equal to twelve times the number

A.1
B.2
C.3
D.4
E.

Objective

Question 0

What is the nth term of the progression 27, 9, 3,......?

A.27\(\frac{1}{3}\) ^{n - 1}
B.3^{n + 2}
C.27 + 18(n - 1)
D.27 + 6(n - 1)
E.

Objective

Question 0

Solve the equation (x - 2) (x - 3) = 12

A.2, 3
B.3, 6
C.-1, 6
D.1, -6
E.

Objective

Question 0

Simplify \(\frac{\sqrt{1 + x} + \sqrt{x}}{\sqrt{1 + x} - \sqrt{x}}\)

A.-2x - 2\(\sqrt{x (1 + x)}\)
B.1 + 2x + 2\(\sqrt{x (1 + x)}\)
C.\(\sqrt{x (1 + x)}\)
D.1 + 2x - 2\(\sqrt{x (1 + x)}\)
E.

Objective

Question 0

Evaluate x²(x² - 1)^{-\(\frac{1}{2}\)} - (x² - 1)^{\(\frac{1}{2}\)}

A.(x² - 1)^{-\(\frac{1}{2}\)}
B.(x² - 1)¹
C.(x² - 1)
D.(x² - 1)^-1
E.

Objective

Question 0

Find the gradient of the line passing through the points (-2, 0) and (0, -4)

A.2
B.-4
C.-2
D.4
E.

Objective

Question 0

At what value of x is the function y = x² - 2x - 3 minimum?

A.1
B.-1
C.-4
D.4
E.

Objective

Question 0

Find the sum of the 20 term in an arithmetic progression whose first term is 7 and last term is 117

A.2480
B.1240
C.620
D.124
E.

Objective

Question 0

The area of a square is 144 sq cm. Find the length of its diagonal

A.11\(\sqrt{3cm}\)
B.12cm
C.12\(\sqrt{2cm}\)
D.13cm
E.

Objective

Question 0

One angle of a rhombus is 60^o. The shorter of the two diagonals is 8cm long. Find the length of the longer one.

A.8\(\sqrt{3}\)
B.\(\frac{16}{\sqrt{3}}\)
C.\(\sqrt{3}\)
D.\(\frac{10}{\sqrt{3}}\)
E.

Objective

Question 0

If the exterior angles of a pentagon are x^o, (x + 5)^o, (x + 10), (x + 15)^o and (x + 20)^o, find x

A.118^o
B.72^o
C.62^o
D.36^o
E.

Objective

Question 0

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.

A.60 (tan 62^o - tan 64^o)
B.60 (cot 64^o - cot 62^o)
C.60 (cot 62^o - cot 64^o)
D.60 (tan 64^o - tan 62^o)
E.

Objective

Question 0

Simplify cos² x (sec²x + sec² x tan²x)

A.tan x
B.tanx secx
C.\(\frac{1 + tan^2x}{sec^2x}\)
D.cosec²x
E.

Objective

Question 0

If cos x = \(\sqrt{\frac{a}{b}}\) find coses x

A.\(\frac{b}{\sqrt{b - a}}\)
B.\(\sqrt{\frac{b}{a}}\)
C.\(\sqrt{\frac{b}{b - a}}\)
D.\(\sqrt{\frac{b - a}{a}}\)
E.

Objective

Question 0

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.

A.0.30^o
B.045^o
C.060^o
D.090^o
E.

Objective

Question 0

Find the total area of the surface of a solid cylinder whose base radius is 4cm and height is 5cm

A.56\(\pi\) cm²
B.72\(\pi\) cm²
C.96\(\pi\) cm²
D.192\(\pi\) cm²
E.

Objective

Question 0

3% of a family's income is spent on electricity, 58% 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

A.76.8^o and 25.2^o
B.10.8^o and 224.6^o
C.112.4^o and 72.0^o
D.39.6^o and 212.4^o
E.

Objective

Question 0

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

A.6.7, 6
B.7.6, 5
C.5.7, 87
D.34, 6
E.

Objective

Question 0

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

A.96
B.94
C.92
D.90
E.

Objective

Question 0

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?

A.\(\frac{5}{12}\)
B.\(\frac{1}{3}\)
C.\(\frac{3}{4}\)
D.\(\frac{7}{24}\)
E.

Objective

Question 0

In the figure above, Find the value of x

A.130^o
B.110^o
C.100^o
D.90^o
E.

Objective

Question 0

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

A.7.3, 5.9
B.7.7, 12.5
C.12.5, 7.7
D.5.9, 7.3
E.

Objective

Question 0

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

A.40^o
B.30^o
C.25^o
D.15^o
E.

Objective

Question 0

In the figure above, find the value of y

A.28^o
B.122^o
C.150^o
D.152^o
E.

Objective

Question 0

In this figure, PQ = PR = PS and SRT = 68^o. Find QPS

A.136^o
B.124^o
C.12^o
D.68^o
E.

Objective

Question 0

In the figure, PQRS is a square of sides 8cm. What is the area of \(\bigtriangleup\)UVW?

A.64 sq. cm
B.40 sq.cm
C.50 sq.cm
D.10 sq.cm
E.

Objective

Question 0

Find the volume of the figure

A.\(\frac{a \pi^2}{3} (x + 3y) \)
B.a\(\pi ^2\)y
C.\(\frac{a \pi ^2}{3}\)(y + x)
D.(\(\frac{1}{3} a \pi ^2 x + y\))
E.

Objective