JAMB UTME - Mathematics - 1978

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

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

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

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 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 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 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 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

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.

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

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

Two triangles have the same areas if

If x2 + 4 = 0, then x ?

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?

The quantity (x + y) is a factor of

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

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

Multiply (x + 3y + 5) by (2x2 + 5y + 2)

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

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

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

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

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

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

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

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

A pyramid is constructed on a cuboid. The figure has

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

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

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:

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

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

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

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

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

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

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

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

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

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

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

Evaluate without using tables sin(-1290^o)

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

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

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

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

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

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?