JAMB UTME - Mathematics - 1980
Question 1 Report
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.
Question 2 Report
If \(\theta\) = \(\frac{3}{2}\) and \(\theta\) is less than 90o, calculate tan \(\frac{(90 - \theta)}{cos^2\theta}\)
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Question 3 Report
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 4 Report
Simplify \(\frac{log_{10}8}{log_{10}4}\)
Question 6 Report
A solid cylinder of radius 3cm has a total surface area of 36\(\pi\)cm2. Find its height
Question 7 Report
Make c the subject of formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
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Question 8 Report
Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)
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Question 10 Report
List all integer values of x satisfying the inequality -1 < 2x - 5 \(\leq\) 5
Question 11 Report
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 12 Report
In the figure, If PT is parallel to RS, PQ = PT, and angle SQT = 90o, Find x
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Question 14 Report
Solve the system of equation 2x + y = 32, 33y - x = 27
Question 15 Report
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?
Question 17 Report
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 18 Report
Find, correct to three significant figures, the value of \(\sqrt{41830}\).
Question 19 Report
Write down the number 0.0052048 correct to three significant figures
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Question 20 Report
(\(\frac{x^a}{x^b}\))a + b by (\(\frac{x^{a + b}}{x^{a - b}}\))\(\frac{a^2}{b}\)
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Question 21 Report
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 23 Report
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 25 Report
Solve the equation for the positive values of \(\theta\) less than 360o. 3 tan \(\theta\) + 2 = -1
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Question 26 Report
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 27 Report
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 30 Report
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 31 Report
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 32 Report
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
Question 33 Report
The median of the set of numbers 4, 9, 4, 13, 7, 14, 10, 17 is
Question 34 Report
Evaluate \((2^{0} + 4^{-\frac{1}{2}})^{2}\)
Question 35 Report
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 39 Report
If it is given that 5x + 1 + 5x = 150, then the value of x is equal to
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Question 40 Report
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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Question 41 Report
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 42 Report
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 43 Report
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 44 Report
Rationalize the denominator of the given expression \(\frac{\sqrt{1 + a} - \sqrt{a}}{1 + a + \sqrt{a}}\)
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Question 45 Report
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 46 Report
The ratio of the areas of similar triangles is necessarily equal to
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Question 47 Report
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 48 Report
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 49 Report
What factor is common to all the expressions x2 - x, 2x2 + x - 1 and x2 - 1?
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