JAMB UTME - Mathematics - 1982

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

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

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

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?

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

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

If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\)

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

The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are

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

A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participant is

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

The arithmetic mean of the ages of 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl?

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

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?

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

A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60^o to the vertical?

The solution to the simultaneous equations 3x + 5y = 4, 4x + 3y = 5 is

A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.

Express 37.05 x 0.0042 in standard form

The solution to the quadratic equation 5 + 3x - 2x² = 0 is

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

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

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

If the function y = 5x is graphed, what would be its intercept on the y-axis?

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

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

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

Simplify \(\frac{3}{2x - 1}\) + \(\frac{2 - x}{x - 2}\)

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

Express 130 kilometers per second in meters per hour

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

The factors of 6x - 5 - x2 are

If f(x - 2) = 3x² + 4x + 1. Find the area of the sector

Simplify f^{\(\frac{1}{2}\)}g²h^{\(\frac{1}{2}\)} \(\div\) f^{\(\frac{5}{2}\)}g^oh^{\(\frac{7}{3}\)}

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

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

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

The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement?

Two distinct sectors i the same circle substend 100^o and 30^o respectively at the centre of the circle. Their corresponding arcs are in ratio

A variable y is inversely proportional to x², when y = 10, x = 2. What is y when x = 10?

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

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

A side of a rhombus is 2cm in length. An angle of the rhombus is 60^o. What is the length of the diagonal facing this angle?

The area of the curved surface of the cone generated by the sector of a circle radius 6cm and are length 22cm is (\(\pi\) = \(\frac{22}{7}\))

Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)

Determine the mean monthly salary of 50 employees of a company from the following frequency distribution.
\(\begin{array}{c|c} \text{Monthly salary} & \text{Frequency}\\\hline N200.00 & 10\\ N325.00 & 5\\N100.00 & 20\\N120.00 & 2\\ N60.00 & 10\\ N80.00 & 3\end{array}\)

A housewife bought 3 kilograms of garri at N13.00 per kg. She deposited N160. 00 for half a cow and bought 24 oranges at 10k each. She came back home with N20.60. She therefore left home with