JAMB UTME - Mathematics - 1978
Frage 1 Bericht
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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Frage 3 Bericht
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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Frage 4 Bericht
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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Frage 5 Bericht
If sec2 \(\theta\) + tan2 \(\theta\) = 3, then the angle \(\theta\) is equal to
Frage 6 Bericht
A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is
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Frage 7 Bericht
If \(3x - \frac{1}{4})^{\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is
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Frage 10 Bericht
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
Frage 11 Bericht
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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Frage 12 Bericht
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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Frage 13 Bericht
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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Frage 15 Bericht
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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Frage 16 Bericht
In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.
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Frage 18 Bericht
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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Frage 23 Bericht
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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Frage 24 Bericht
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
Frage 25 Bericht
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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Frage 27 Bericht
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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Frage 28 Bericht
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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Frage 29 Bericht
Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)
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Frage 30 Bericht
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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Frage 33 Bericht
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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Frage 34 Bericht
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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Frage 35 Bericht
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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Frage 36 Bericht
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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Frage 37 Bericht
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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Frage 38 Bericht
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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Frage 40 Bericht
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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Frage 41 Bericht
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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Frage 42 Bericht
Arrange \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude.
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Frage 43 Bericht
A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame
Frage 44 Bericht
An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is
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Frage 45 Bericht
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?
Frage 46 Bericht
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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Frage 48 Bericht
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
