JAMB UTME - Mathematics - 1982

If N560.70 is shared in the ratio 7 : 2 : 1, what is the smallest share?

The diagram is the distance time graph of a vehicle. Find its average speed in kilometers per hour during the journey

Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)

In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52^o. Find the angle marked m

The graphical method of solving the equation x3 + 3x2 + 4x - 28 = 0 is by drawing the graphs of the curves

Express 130 kilometers per second in meters per hour

If K is a constant, which of the following equations best describes the parabola?

In the diagram, angle QPR = 90^o, angle PSR = 90^o and PR = 5 units. Find the length of QS.

In a regular polygon of n sides, each interior angle is 144o. Find n

The solution of the quadratic equation bx2 + cx + a = 0 is given by

TP and TQ are tangents to a circle centre 0 and r is a point on the circumference of the circle as shown in the figure. If angle PTQ = 45^o, what is the magnitude of the angle PRO?

Simplify 3 - 2 \(\div\) \(\frac{4}{5}\) + \(\frac{1}{2}\)

Solve for x, If \(\frac{\frac{2}{x}}{\frac{p^2 + p^2}{p^2 + p^2}}\) = m

What is the least possible value of \(\frac{9}{1 + 2x^2}\) if 0 \(\geq\) x \(\geq\) 2?

Which of the following lines is not parallel to the line 3y + 2x + 7 = 0?

If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)

Seven years ago, the age of a father was three times that of his son, but in six years time the age of the son will be half that of his father, representing the present ages of the father and son by x and y, respectively, the two equations relating x and y are

The currency used in a country is called 'Matimalik'(M) and is of base seven. A lady in that country bought 4 bags of rice at M56 per bag and and 3 tins of milk at M4 per tin. What is the total cost of the item she bought?

Write the equation 2 log2x - x log2(1 + y) = 3 in a form not involving logarithms

The factors of 6x - 5 - x2 are

Find the median of the set set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113

A man bought wrist watch for N150 but was only able to sell it for N120. Find the loss per cent on the transaction

In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR

PQRS is a parallelogram with area 50 square cm and the side PQ is 10cm long. T is a point on RS and TF is the altitude of the triangle TPQ. Find TF

Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\)

The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is

Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r