JAMB UTME - Mathematics - 1981

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

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

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

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

Evaluate correct to 4 decimal places 827.51 x 0.015

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?

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

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

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

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 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

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

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

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

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

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

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

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

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 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?

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?

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.

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

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

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

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

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

Multiply x² + x + 1 by x² - x + 1

In the figure, find the area of XYZW

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

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

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

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

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?

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

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

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

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

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?

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 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

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

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?

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