JAMB UTME - Mathematics - 1980

Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\)

If \(\theta\) = \(\frac{3}{2}\) and \(\theta\) is less than 90^o, calculate tan \(\frac{(90 - \theta)}{cos^2\theta}\)

(\(\frac{x^a}{x^b}\))^{a + b} by (\(\frac{x^{a + b}}{x^{a - b}}\))^{\(\frac{a^2}{b}\)}

In the figure, FGHJ is a circle of radius 3cm centre O. FOH, GOJ are perpendicular diameters. With G as centre of an arc of a circle is drawn to pass through F and H. Find the length of the perimeter of the lunar portion shaded.

Find the missing numerator \(\frac{5}{x + 1}\) - \(\frac{3}{1 - x}\) - \(\frac{7x - 1}{x^2 - 1}\) = \(\frac{?}{x + 1}\).

Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.

Find the roots of the equation 10x² - 13x - 3 = 0

Find, correct to three significant figures, the value of \(\sqrt{41830}\).

In a school, there are 35 students in class 2A and 40 in class 2B. The mean score for class 2 in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes

The ratio of the areas of similar triangles is necessarily equal to

In the figure, PS bisects angle QPR. Find the ratio SR:QR.

If PN is perpendicular to QR, find the value of tan x.

Solve the equation for the positive values of \(\theta\) less than 360^o. 3 tan \(\theta\) + 2 = -1

If it is given that 5^{x + 1} + 5^x = 150, then the value of x is equal to

What will be the value of k so that the quadratic equation kx² - 4x + 1 = 0 has two equal roots?

Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)

If x varies inversely as y, and y varies directly as the square root of z, and z varies directly \(\frac{1}{w^2}\) write down in words how x varies with w

Find the solution of the equation x + 2\(\sqrt{x - 8}\) = 0

Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)

When a dealer sells a bicycle for N81 he makes a profit of 80%. What did he pay for the bicycle?

A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items, then the sector representing this group on the pie chart contains an angle x^o at the centre of the circle where x is

Find the product of (2\(\sqrt{y - 3y}\)) and (3y = 2y)

A cylindrical motor of height 12cm has uniform thickness of 2cm. If the diameter of its outer cross section is 10cm, Find the volume of the constituent material. (take \(\pi\) = \(\frac{22}{7}\)

A man and his wife went to buy an article costing N400. The woman had 10% of the cost and the man 40% of the remainder. How much did they have altogether?

Write the decimal number 39 to base 2

In triangle FGB, < G = 90^o, < H = 60^o, while in triangle XYZ, < X = 60^o and < Y = 30^o. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)

Solve the system of equation 2^{x + y} = 32, 3^{3y - x} = 27

Find the area of the shades segments in the figure

Write down the number 0.0052048 correct to three significant figures

Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?

The expression x3 - 4x2 + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.

In the figure, PQ\\SR, ST\\, ST\\RQ, PS = 7cm, PT = 7cm, SR = 4cm. Find the ratio of the area QRST to the area of PQRS.

In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90^o, Find x

fG is a given straight line and H is a fixed point. The construction marks shown in the diagram indicate the

Three numbers, x, y and z are connected by the relationships y = \(\frac{4x}{9}\) + 1. If x = 99, find z

Simplify 10² + log₁₀5

In the figure, PS = SR and Rx is a tangent to the circle at R, < QRX is equal to 72^o. Find

What factor is common to all the expressions x² - x, 2x² + x - 1 and x² - 1?

List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5

A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height

A pentagon has four of its angles equal. If the size of the fifth angle is 60^o, Find the size of each of the four equal angles.

Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (take \(\pi\) = \(\frac{22}{7}\))

P and Q are fixed points and X is a variable point which moves so that angle PXQ = 45o. What is the locus of x?

The angles marked in the figure are measured in degrees. Find x.

The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is

If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).

Simplify \(\frac{log_{10}8}{log_{10}4}\)

Which of the formula below represents the general terms of the following set of numbers(-1, \(\frac{2}{3}\), -\(\frac{1}{2}\), \(\frac{2}{5}\)......) for n = 1, 2, 3, 4.......?

Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))