JAMB UTME - Mathematics - 1980

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

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

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.

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

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

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

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

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 \(\pi\) = \(\frac{22}{7}\)

Find the area of the shades segments in the figure

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

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

Write down the number 0.0052048 correct to three significant figures

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.

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

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.

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

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

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?

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.......?

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

Simplify 10² + log₁₀5

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

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

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

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

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

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

Write the decimal number 39 to base 2