JAMB UTME - Mathematics - 1980

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.

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

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Find the area of the shades segments in the figure

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

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

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

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Write the decimal number 39 to base 2

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

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

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

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

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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.

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

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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.

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

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

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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.......?

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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

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

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

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

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

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

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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?

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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.

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

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

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

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

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

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

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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

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

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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.

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

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Write down the number 0.0052048 correct to three significant figures

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Simplify 10² + log₁₀5

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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

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

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

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

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

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

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

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

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

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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?

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

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

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