JAMB UTME - Mathematics - 1980

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

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

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

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

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

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

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.

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

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

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

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

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.

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.

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

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

Simplify 10² + log₁₀5

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 \(\frac{FG}{FH}\)

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

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

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

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

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

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

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

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

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.......?

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

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?

Write down the number 0.0052048 correct to three significant figures

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

Find the area of the shades segments in the figure

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

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.

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

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

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

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

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

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

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

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

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

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

Write the decimal number 39 to base 2

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

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?