JAMB UTME - Mathematics - 1978
Question 1 Report
Simplify \(\frac{(a^2 - \frac{1}{a}) (a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 - \frac{1}{a}^2}\)
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Question 2 Report
The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is
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Question 3 Report
If \(3x - \frac{1}{4})^{\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is
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Question 4 Report
An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is
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Question 5 Report
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
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Question 8 Report
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.
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Question 10 Report
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
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Question 12 Report
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
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Question 15 Report
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:
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Question 16 Report
If sec2 \(\theta\) + tan2 \(\theta\) = 3, then the angle \(\theta\) is equal to
Question 17 Report
Given that \(a*b = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving * or ♦) for (a*b) ♦ (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers
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Question 18 Report
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
Question 20 Report
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
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Question 21 Report
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
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Question 22 Report
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
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Question 23 Report
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
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Question 24 Report
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 area reduced?
Question 27 Report
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
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Question 29 Report
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
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Question 30 Report
A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame
Question 31 Report
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
Question 32 Report
The set of value of x and y which satisfies the equations x2 - y - 1 = 0 and y - 2x + 2 = 0 is
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Question 33 Report
In the figure, 0 is the centre of the circle ABC, < CED = 30o, < EDA = 40o. What is the size of < ABC?
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Question 34 Report
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?
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Question 35 Report
A triangle has angles 30o, 15o and 135o. The side opposite to the angle 30o is length 6cm. The side opposite to the angle 135o is equal to
Question 36 Report
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
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Question 37 Report
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?
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Question 38 Report
Arrange \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude.
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Question 39 Report
The locus of all points having a distance of 1 unit from each of the two fixed points a and b is
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Question 40 Report
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
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Question 41 Report
If the four interior angles of a quadrilateral are (p + 10)o, (p - 30)o, (2p - 450o, and (p + 15)o, then p is
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Question 42 Report
The angle of elevation of the top of a vertical tower from a point A on the ground is 60o. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the tower is 45o. Find the distance of A from the foot of the tower
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Question 43 Report
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
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Question 46 Report
Assuming loge 4.4 = 1.4816 and loge 7.7 = 2.0142, then the value of loge \(\frac{7}{4}\) is
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