JAMB Mathematics 1978 Past Questions

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A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame

A.15sq.cm
B.20sq.cm
C.13sq.cm
D.16sq.cm
E.17sq.cm

the sum of 3\(\frac{7}{8}\) and 1\(\frac{1}{3}\) is less than the difference between \(\frac{3}{8}\) and 1\(\frac{2}{3}\) by:

A.3\(\frac{2}{3}\)
B.5\(\frac{1}{4}\)
C.6\(\frac{1}{2}\)
D.8
E.8\(\frac{1}{8}\)

Multiply (x + 3y + 5) by (2x² + 5y)

A.2x² + 3yx² + 10xy + 15y² + 13y + 10x² + 2x + 10
B.2x³ + 6yx² + 5xy + 5y² + 31y + 5x² + 2x + 10
C.2x³ + 6xy² + 5xy + 15y² + 12y + 10x² + 2x = 10
D.2x² + 6xy² + 5xy + 15y² + 13y + 10x² + 2x + 10
E.2x³ + 2yx² + 10xy + 10y² + 31y + 5x² + 10

Arrange and \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude.

A.\(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{71}{97}\)
B.\(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{3}{5}\) , \(\frac{71}{97}\)
C.\(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{71}{97}\), \(\frac{34}{59}\)
D.\(\frac{9}{16}\), \(\frac{3}{5}\), \(\frac{71}{97}\), \(\frac{34}{59}\)
E.

The sum of the progression is 1 + x + x² + x³ + ......

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

The number of telephone calls N between two cities A and B varies directly as the population P_A, P_B respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?

A.N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\)
B.N = \(\frac{kp_AP_B}{D^2}\)
C.N = \(\frac{kD_AP_D}{B^2}\)
D.N = \(\frac{kD^2_AP_D}{B}\)
E.

Find the square root of 170 - 20\(\sqrt{30}\)

A.2 \(\sqrt{10}\) - 5\(\sqrt{3}\)
B.2 \(\sqrt{5}\) - 5\(\sqrt{6}\)
C.5 \(\sqrt{10}\) - 2\(\sqrt{3}\)
D.3 \(\sqrt{5}\) - 8\(\sqrt{6}\)
E.

If x² + 4 = 0, then x ?

A.4
B.-4
C.2
D.-2
E.None of the above

What is the number whose logarithm to base 10 is 2.3482?

A.223
B.2228
C.2.235
D.22.37
E.0.2229

Five years ago, a father was 3 times as old as his son, now their combined ages amount to 110years. thus, the present age of the father is

A.75 years
B.60 years
C.98 years
D.80 years
E.105 years

If y = 2x² + 9x - 35. Find the range of values for which y < 0.

A.7 < x < \(\frac{5}{2}\)
B.-5 < 7 < x
C.-7 < x < 5
D.-7 < x < \(\frac{5}{2}\)
E.

Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased 15%. Thus the fractional increase in the family food bill is now

A.\(\frac{1}{12}\)
B.\(\frac{6}{35}\)
C.\(\frac{19}{300}\)
D.\(\frac{7}{200}\)
E.\(\frac{5}{100}\)

Given that a*b = ab + a + b and that a0b = a + b = 1. Find an expression (not involving * or 0) for (a*b) 0 (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers

A.ac + ab + bc + b + c + 1
B.ac + ab + a + c + 2
C.ab + ac + a + b + 1
D.ac + bc + ab + b + c + 2
E.ab + ac + 2a + b + c + 1

If a circular paper disc is trimmed in such a way that its circumference is reduced in the ratio 2:5, In what ratio is the surface reduced?

A.8 : 125
B.2 : 5
C.8 : 25
D.4 : 25
E.4 : 10

If the four interior angles of a quadrilateral are (p + 10)^o, (p - 30)^o, (2p - 450^o, and (p + 15)^o, then p is

A.125^o
B.82^o
C.135^o
D.105^o
E.60^o

Simplify \(\frac{a - b}{a + b}\) - \(\frac{a + b}{a - b}\)

A.\(\frac{4ab}{a - b}\)
B.\(\frac{-4ab}{a^2 - b^2}\)
C.\(\frac{-4ab}{a^{-2} - b}\)
D.\(\frac{4ab}{a^{-2} - b^{-2}}\)
E.

A force of 5 units acts on a particle in the direction to the east and another force of 4 units acts on the particle in the direction north-east. The resultants of the two forces is

A.\(\sqrt{3}\) units
B.3 units
C.\(\sqrt{41 + 20 \sqrt{2}}\) units
D.\(\sqrt{41 - 20 \sqrt{2}}\) units
E.

The minimum point on the curve y = x² - 6x + 5 is at

A.(1, 5)
B.(2, 3)
C.(-3, -4)
D.(3, -4)
E.

If 3x - \(\frac{1}{4}\)^{-\(\frac{1}{2}\)} > \(\frac{1}{4}\) - x, then the interval of values of x is

A.x > \(\frac{1}{3}\)
B.x < \(\frac{1}{3}\)
C.x < \(\frac{1}{4}\)
D.x < \(\frac{9}{16}\)
E.x > \(\frac{9}{16}\)

A canal has rectangular cross section of width10cm and breadth 1m. If water of uniform density 1 gm cm^-3 flows through it at a constant speed of1000mm per minute, the adjacent sea is

A.100000
B.1000000
C.120000
D.30000
E.350000

a man runs a distance of 9km at a constant speed for the first 4 km and then 2 km\h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4 km is

A.6 km/h
B.8 km/h
C.9 km\h
D.11 km\h
E.13 km\h

A pyramid is constructed on a cuboid. The figure has

A.twelve faces
B.thirteen vertices
C.fourteen edges
D.fifteen edges
E.sixteen edges

In a geometric progression, the first term is 153 and the sixth term is \(\frac{17}{27}\). The sum of the first four terms is

A.\(\frac{860}{3}\)
B.\(\frac{680}{3}\)
C.\(\frac{608}{3}\)
D.\(\frac{680}{3}\)
E.

An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is

A.351
B.531
C.135
D.153
E.

A triangle has angles 30^o, 15^o and 135^o. The side opposite to the angle 30^o is length 6cm. The side opposite to the angle 135^o is equal to

A.12cm
B.6cm
C.6\(\sqrt{2}\)cm
D.12\(\sqrt{2}\)cm
E.

A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is

A.36\(\pi\)cm²
B.54\(\sqrt{3}\)cm²
C.\(\sqrt{3}\)cm²
D.\(\frac{1}{x - 1}\)
E.

In a soccer competition in one season, a club had scored the following goals: 2, 0, 3, 3, 2, 1, 4, 0, 0, 5, 1, 0, 2, 2, 1, 3, 1, 4, 1 and 1. The mean, median and mode are respectively

A.1, 1.8 and 1.5
B.1.8, 1.5 and 1
C.1.8, 1 and 1.5
D.1.51, 1 and 1.8
E.1.5, 1.8 and 1

If sec² \(\theta\) + tan² \(\theta\) = 3, then the angle \(\theta\) is equal to

A.30^o
B.45^o
C.60^o
D.90^o
E.105^o

A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is

A.1cm
B.\(\sqrt{\frac{3\pi}{24}}\)
C.\(\frac{\pi}{24\sqrt{3}}\)
D.24\(\sqrt{3}\)
E.

The set of value of x and y which satisfies the equations x² - y - 1 = 0 and y - 2x + 2 = 0 is

A.1, 0
B.1, 1
C.2, 2
D.0, 2
E.1, 2

A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cycular of radius 3cm and height 4cm.Which of the following statements is true?

A.the volume of the sphere is greater than the volume of the cone
B.the volume of the cone is less than the volume of the cylinder
C.the total surface area of the cone is greater than that of the sphere
D.The total surface area of the cylinder is less than that of the sphere
E.the total sufeac area of the cone is equal to that of the cylinder

The quantity (x + y) is a factor of

A.x² + y²
B.x³ - y³
C.2x² - 3xy + y² - x + 1
D.2x³ + 2x²y - xy + 3x - y² + 3y
E.x⁵ - y⁵

Two triangles have the same areas if

A.two sides in one triangle are equal to two sides in the other
B.three sides in one triangle are equal to three sides in the other
C.two angles in the triangle are equal to two angles in the other
D.three angles in one triangle are equal to three angles in the other
E.one side and the opposite angle in one triangle are equal to one side and the opposite angle in the other

If (25)^{x - 1} = 64(\(\frac{5}{2}\))⁶, then x has the value

A.7
B.4
C.32
D.64
E.5

Assuming log_e 4.4 = 1.4816 and log_e 7.7 = 2.0142, then the value of log_e \(\frac{7}{4}\) is

A.0.5326
B.3.4958
C.0.4816
D.0.0142
E.1.3594

The locus of all points having a distance of 1 unit from each of the two fixed points a and b is

A.a line parallel to the line ab
B.a line perpendicular to the line ab through the mid-point of ab
C.a circle through a and b with centre at the mid-point of ab
D.a circle with centre at a and passes through b
E.a circle in a plane perpendicular to ab and centre at the mid-point of the line ab

Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)

A.-3
B.3
C.\(\frac{3}{5}\)
D.\(\frac{-3}{2}\)
E.1n 6 - 2 1n 5

Simplify \(\frac{(a^2 - \frac{1}{a}) + (a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 \frac{1}{a}^2}\)

A.a^{\(\frac{2}{3}\)}
B.a^{-\(\frac{1}{3}\)}
C.a2 + 1
D.a
E.a^{\(\frac{1}{3}\)}

If x⁴ - kx³ + 10x² + 1x - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1

A.k = -7, 1 = -15
B.k = -15, 1 = -7
C.k = \(\frac{15}{3}\) , 1 = -7
D.k = \(\frac{7}{3}\) , 1 = -17
E.

Evaluate without using tables sin(-1290^o)

A.\(\frac{3}{2}\)
B.-\(\frac{3}{2}\)
C.\(\frac{2}{2}\)
D.1
E.\(\frac{1}{2}\)

The angle of elevation of the top of a vertical tower from a point A on the ground is 60^o. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the tower is 45^o. Find the distance of A from the foot of the tower

A.3 + \(\sqrt{3}\)
B.5 + \(\sqrt{3}\)
C.3 - \(\sqrt{3}\)
D.1
E.\(\sqrt{3}\) - 1

The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b

A.2
B.4
C.\(\sqrt{10}\)
D.35
E.2.2

Add the same number to the numerator and denominator of \(\frac{3}{18}\). If the resulting fraction is \(\frac{1}{2}\), then the number added is

A.13
B.14
C.15
D.12
E.11

The smallest number such that when it is divided by 3 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is

A.387
B.493
C.502
D.441
E.634

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In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.

A.4cm
B.6cm
C.3cm
D.2cm
E.1cm

Question image

In the figure, AB is parallel to CD then x + y + z is

A.185^o
B.200^o
C.270^o
D.360^o
E.195^o

Question image

In the Figure FD\\AC, the area of AEF = 6sq.cm. AE = 3cm, BC = 3cm, CD = 5cm, < BCD is an obtuse angle. Find the length of BD.

A.\(\sqrt{33}\)
B.6
C.4
D.2\(\sqrt{13}\)
E.4\(\sqrt{5}\)

Question image

In the figure, 0 is the centre of the circle ABC, < CED = 30^o, < EDA = 40^o. What is the size of < ABC?

A.70^o
B.110^o
C.130^o
D.125^o
E.145^o