JAMB UTME - Mathematics - 1979

A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?

A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30^o. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man

In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to

For the set of numbers 2, 3, 5, 6, 7, 7, 8

If x³ - 12x - 16 = 0 has x = -2 as a solution then the equaion has

Find x in the diagram below.

Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0

(3.2)² - (1.8)² equals

PQ is parallel to RS. Calculate the value of x.

A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?

The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)

Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)

Find the value of (4^{\(\frac{1}{2}\)})⁶

Make x the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0

The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was

After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?

If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is

If y = x² - 2x - 3, Find the least value of y and corresponding value of x

On each market day Mrs. Bassey walks to the market from her home at a steady speed. This journey normally takes her 2 hours to complete. She finds, however, that by increasing her usual speed by 1 km/hr she can save 20 minutes. Find her usual speed in km/hr

In base ten, the number 101101 (base 2) equals

(Numbers indicate the lengths of the sides of the triangles) If the area of \(\bigtriangleup\) PQR is k2sq. units what is the area of the shades portion?

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15^o find < QRS

The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity?

In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS

Multiply (3x + 5y + 4z) by (2x - 3y + z)

In the figure, PQ and QR are chords of the circle PQR. QRS is a straight line and PR is equal to RS, < PSR is 20^o. What is the size of

Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x - 1}}\)

Which of the following values of the variable x, (a)x = 0, (b)x = -3, (c)x = 9, satisfy the inequalities 0 < \(\frac{x + 3}{x - 1}\) < 2?

A cylinder of height h and radius r is open at one end. Its surface area is

x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?

One of the following statements is wrong. Which is it?

The solution of the equation x² - 2x = 8 is

12 men complete a job in 9 days. How many men working t the same rate would be required to complete the job in 6 days?

In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is

Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2

If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:

A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?

The area under the speed time graph given the total distance covered by car. What is the average velocity to two places of decimals?

\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) equals

A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?

Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)

The mean of the numbers 1.2, 1.0, 0.9, 1.4, 0.8, 0.8, 1.2 and 1.1 is

An arc of circle of radius 2cm subtends an angle of 60^o at the centre. Find the area of the sector

What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?

Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)

A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is

In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65^o and < RPS is 20^o. What is the size of < PRS?

In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.

If O is the centre of the circle, < POS equls

What is log₇(49^a) - log₁₀(0.01)?