JAMB UTME - Mathematics - 1981

Find a two-digit number such that three times the tens digit is 2 less than twice the units digit and twice the number is 20 greater than the number obtained by reversing the digits

Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 - cos x}\) is

If sine x equals cosine x, what is x in radians?

If b = a + cp and r = ab + \(\frac{1}{2}\)cp², express b² in terms of a, c, r.

The difference between 4\(\frac{5}{7}\) and 2\(\frac{1}{4}\) greater by

The weights of 30 new-born babies are given as follow: 6, 9, 5, 7, 6, 7, 5, 8, 9, 5, 7, 5, 8, 7, 8, 7, 5, 6, 5, 7, 6, 9, 9, 7, 8, 8, 7, 8, 9, 8. The mode is

Find the value of x satisfying \(\frac{x}{2}\) - \(\frac{1}{3}\) < \(\frac{2x}{5}\) + \(\frac{1}{6}\)

Solve \(\frac{1}{x + 1}\) - \(\frac{1}{x + 3}\) = \(\frac{1}{4}\)

What is the area between two concentric circles of diameters 26cm and 20cm?

In the figure, find the area of XYZW

Multiply x² + x + 1 by x² - x + 1

In the figure, the chords XY and ZW are produced to meet at T such that YT = WT, ZYW = 40o and YTW = 30o. What is YXW?

The positive root of t in the following equation, 4t2 + 7t - 1 = 0, correct to 4 places of decimal, is

If \(\sin x° = \frac{a}{b}\), what is \(\sin (90 - x)°\)?

The number 25 when converted from the tens and units base to the binary base (base two) is one of the following

A baking recipe calls for 2.5kg of sugar and 4.5kg of flour. With this recipe some cakes were baked using 24.5kg of a mixture of sugar and flour. How much sugar was used?

By selling an article for N45.00 a man makes a profit of 80%. For how much should he have sold it in order to make a profit of 32%?

The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r : t. In 1980, the price of a loaf went up by 25% and that of a packet of sugar went up by 10%. Their new ratio is now

simplify \(\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}\)

Evaluate correct to 4 decimal places 827.51 x 0.015

Marks scored by some children in an arithmetic test are:5, 3, 6, 9, 4, 7, 8, 6, 2, 7, 8, 4, 5, 2, 1, 0, 6, 9, 0, 8.
The arithmetic mean of the marks is

The sum of the root of a quadratic equation is \(\frac{5}{2}\) and the product of its root is 4. The quadratic equation is

Given that 10x = 0.2 and log102 = 0.3010, find x

In one and a half hours, the minute hand of a clock rotates through an angle of

Suppose x varies inversely as y, y varies directly as the square of t and x = 1, when t = 3. Find x when t = \(\frac{1}{3}\).

Two cars X and Y start at the same point and travel towards a point P which is 150km away. If the average speed of Y is 60km per hour and x arrives at P 25 minutes earlier than Y. What is the average speed of X?

Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)

An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?

In the figure, WU//YZ, WY//YZ = 12cm, VZ = 6cm, XU = 8cm. Determine the length of WU.

The area of a circular plate is one-sixteenth the surface area of a ball of a ball, If the area of the plate is given as P cm², then the radius of the ball is

Simplify T = \(\frac{4R_2}{R_1^{-1} + R_2^{-1} + 4R_3^{-1}}\)

In the figure, find x in terms of a, b and c.

Simplify \(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)

A micrometer is defined as one millionth of a millimeter. A length of 12,000 micrometres may be represented as

A sum of money invested at 5% per annum simple interest amounts to $285.20 after 3 years. How long will it take the same sum to amount to $434.00 at 7\(\frac{1}{2}\)% per annum simple interest?

In the diagram, XZ is the diameter of a circle's radius \(\frac{5}{2}\). If XY is 4cm, then the area of the triangle XYZ is

What is the length of an arc of a circle that substends 2\(\frac{1}{2}\) radians at the centre when the raduis of the circle = \(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\) then

A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?

If \(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\), find y when x = 4.

In \(\bigtriangleup\)XYZ, XY = 3cm, XZ = 5cm and YZ = 7cm. If the bisector of XYZ meets XZ at W, what is the length of XW?

Evaluate \(\frac{6.3 \times 10^5}{8.1 \times 10^3}\) to 3 significant fiqures

What is the size of an exterior angle of a regular pentagon?

The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81

Which of the following fractions is less than one-third?

The difference between the length and width of a rectangle is 6cm and the area is 135cm2. What is the length?

7 pupils of average age 12 years leave a class of 25 pupils of average age 14 years. If 6 new pupils of average age 11years join the class, what is the average age of the pupils now in the class?

A group of 14 children children received the following scores in a reading test: 35, 35, 26, 26, 26, 29, 29, 29, 12, 25, 25, 25, 25, 17. What was the median score?