JAMB UTME - Mathematics - 1980
Question 1 Rapport
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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Question 2 Rapport
The ratio of the areas of similar triangles is necessarily equal to
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Question 3 Rapport
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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Question 4 Rapport
Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\)
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Question 6 Rapport
Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
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Question 7 Rapport
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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Question 8 Rapport
If \(\theta\) = \(\frac{3}{2}\) and \(\theta\) is less than 90o, calculate tan \(\frac{(90 - \theta)}{cos^2\theta}\)
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Question 9 Rapport
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 xo at the centre of the circle where x is
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Question 10 Rapport
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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Question 11 Rapport
The angles marked in the figure are measured in degrees. Find x.
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Question 12 Rapport
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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Question 13 Rapport
Solve the equation for the positive values of \(\theta\) less than 360o. 3 tan \(\theta\) + 2 = -1
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Question 14 Rapport
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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Question 15 Rapport
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
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Question 16 Rapport
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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Question 17 Rapport
In the figure, PS = SR and Rx is a tangent to the circle at R, < QRX is equal to 72o. Find
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Question 18 Rapport
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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Question 19 Rapport
List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
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Question 20 Rapport
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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Question 21 Rapport
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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Question 22 Rapport
In the figure, PS bisects angle QPR. Find the ratio SR:QR.
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Question 23 Rapport
Find the solution of the equation x + 2\(\sqrt{x - 8}\) = 0
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Question 24 Rapport
What will be the value of k so that the quadratic equation kx2 - 4x + 1 = 0 has two equal roots?
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Question 25 Rapport
A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height
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Question 26 Rapport
In triangle FGB, < G = 90o, < H = 60o, while in triangle XYZ, < X = 60o and < Y = 30o. Form XYZ write down the ratio equal to \(\frac{FG}{FH}\)
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Question 28 Rapport
Which of the following is NOT a factor of 12\(^{4}\) - 5\(^{4}\)?
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Question 30 Rapport
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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Question 32 Rapport
What factor is common to all the expressions x2 - x, 2x2 + x - 1 and x2 - 1?
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Question 33 Rapport
If it is given that 5x + 1 + 5x = 150, then the value of x is equal to
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Question 35 Rapport
A pentagon has four of its angles equal. If the size of the fifth angle is 60o, Find the size of each of the four equal angles.
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Question 37 Rapport
(\(\frac{x^a}{x^b}\))a + b by (\(\frac{x^{a + b}}{x^{a - b}}\))\(\frac{a^2}{b}\)
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Question 38 Rapport
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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Question 41 Rapport
In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90o, Find x
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Question 42 Rapport
Write down the number 0.0052048 correct to three significant figures
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Question 43 Rapport
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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Question 44 Rapport
If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).
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Question 45 Rapport
Find, correct to three significant figures, the value of \(\sqrt{41830}\).
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Question 46 Rapport
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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Question 47 Rapport
Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
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Question 49 Rapport
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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