JAMB UTME - Mathematics - 1978
Question 1 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 2 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 4 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 5 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 6 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 8 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 10 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 11 Report
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
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Question 13 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 14 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 16 Report
A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame
Question 20 Report
If sec2 \(\theta\) + tan2 \(\theta\) = 3, then the angle \(\theta\) is equal to
Question 21 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 22 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 23 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 25 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 27 Report
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
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Question 28 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 29 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 30 Report
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
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Question 33 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 34 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 36 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 37 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 38 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 39 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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Question 40 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 41 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 42 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 43 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 44 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 46 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 47 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 48 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
