JAMB Mathematics 1987 Past Questions

Convert 241 in base 5 to base 8,

Find the least length of a rod which can be cut into exactly equal strips, each of either 40cm or 48cm in length

A rectangular lawn has an area of 1815 square yards. if its length is 50 meters, find its width in meters given that 1 metre equals 1.1 yards

Reduce each number to two significant figures and then evaluate \(\frac{0.021741 \times 1.2047}{0.023789}\)

A train moves from P to Q at an average speed of 90km/h and immediately returns from Q to P through the same route at an average speed of 45km/h. Find the average speed for the entire journey

If the length of a square is increased by 20% while while its width is decreased by 20% to form a rectangle, what is the ratio of the area of the rectangle to the area of the square?

Two brothers invested a total of N5,000.00 on a farm project, the farm yield was sold for N 15,000.00 at the end of the season. If the profit was shared in the ratio 2 : 3, what is the difference in the amount to profit received by the brothers?

A man invests a sum of money at 4% per annum simple invest. After 3 years, the principal amounts to N7,000.00. Find the sum invested

By selling 20 oranges for N1.35 a trader makes a profit of 8%. What is his percentage gain or loss if he sells the same 20 oranges for N1.10?

Four boys and ten girls can cut a field in 5 hours if the boys work at \(\frac{5}{4}\) the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?

Evaluate without using tables (0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\)

Simplify without using tables \(\frac{log_26}{log_28}\) - \(\frac{log_23}{log_2\frac{1}{2}}\)

Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)

If P = \(\frac{2}{3}\) (\(\frac{1 - r^2}{n^2}\)), find n when r = \(\frac{1}{3}\) and p = 1

If a u² - 3v² and b = 2uv + v² evaluate (2a - b)(a - b²), when u = 1 and v = -1

The formula Q = 1.5 + 0.5n gives the cost Q(in Naira)of feeding n people one additional person

If P varies inversely as V and V varies directly as R², find the relationship between P and R given that R = 7 when P = 2

Make y the subject of the formula Z = x² + \(\frac{1}{y^3}\)

Find the values of m which make the following quadratic function a perfect square. x² + 2(m + 1)x + m + 3

Factorize 6^{2x + 1} + 7(6^x) - 5

Find the values of y which satisfy the simultaneous equations x + y = 5, x² - 2y² = 1

An (n - 2)² sided figure has n diagonals. Find the number n diagonals for 25-sided figure

Solve the inequality x - 1 > 4(x + 2)

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

The minimum value of y in the equation y = x² - 6x + 8 is

Find the eleventh term of the progression 4, 8, 16.....

Three angles of a nonagon are equal and the sum of six other angles is 110^o. Calculate the sixe of one of the equal angles

Two chords QR and NP of a circle intersect inside the circle at x. If RQP = 37^o, RQN = 49^o and QPN = 35^o, find PRQ

The sine, cosine and tangent of 210^o are respectively

If tan \(\theta\) = \(\frac{m^2 - n^2}{2mn}\) find sec\(\theta\)

From two points x and y, 8m apart, and in line with a pole, the angle of elevation of the top of the pole are 30^o and 60^o respectively. Fins the height of the pole assuming that x, y and the foot of the pole are the same horizontal plane and x and y are on the same side of the pole.

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

What is the circumference of latitude 0^oS if R is the radius of the earth?

The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4.3cm

What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre 0

Taking the period of day light on a certain day to be from 5.30a.m to 7.00p.m. Calculate the angle of a pie chart designed to show the periods of the day light and of darkness on that day

The goals scored by 40 football teams from three league divisions are recorded below
\(\begin{array}{c|c} \text{Number of goals} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline frequency & 4 & 3 & 15 & 16 & 1 & 0 & 1\end{array}\)
What is the total number of goals scored by all the terms?

The numbers 3, 2, 8, 5, 7, 12, 9 and 14 are the marks scored by a group of students in a class test. If P is scored by an group of students in a class test. If P is the mean and Q the median, the P + Q is

Below are the scores of group of students in a music test
\(\begin{array}{c|c}scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No, of students} & 3 & 6 & 10 & 8 & 6 & 5 & 2 & 4 & 12\end{array}\)
If CF(x) is the number of students with scores less than or equal to x, find CF(6)

Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium

An (n - 2)² sided figure has n diagonals. Find the number n diagonals for a 25-sided figure

In the diagram, POQ is a diameter, 0 is the centre of the circle and TP is a tangent. Find the value of x

In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.

Three angles of a nonagon are equal and the sum of six other angles is 1110^o. Calculate the size of one of the equal angles.

In the figure, find the value of x

In the figure, PQRS is a rectangle. If the shaded area is 72 sq. cm, find h

The figure is an example of the construction of a