JAMB UTME - Mathematics - 1981

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

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

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?

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

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

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

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?

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

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

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

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

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

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%?

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?

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

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

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

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

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

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

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?

In the figure, find the area of XYZW

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

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

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

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

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?

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

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

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

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

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

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?

Multiply x² + x + 1 by x² - x + 1

Evaluate correct to 4 decimal places 827.51 x 0.015

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

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

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

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

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

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?

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?

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

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

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

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