JAMB UTME - Mathematics - 1981
Question 1 Report
A baking recipe calls for 2.5kg of sugar and 4.5kg of flour. With this recipe some cakes were baked using 24.5kg of a mixture of sugar and flour. How much sugar was used?
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Question 2 Report
Simplify \(\frac{\sqrt{2}}{\sqrt{3} - \sqrt{2}}\) - \(\frac{3 - 2}{\sqrt{3} + \sqrt{2}}\)
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Question 3 Report
The positive root of t in the following equation, 4t2 + 7t - 1 = 0, correct to 4 places of decimal, is
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Question 4 Report
If sine x equals cosine x, what is x in radians?
Question 5 Report
The area of a circular plate is one-sixteenth the surface area of a ball of a ball, If the area of the plate is given as P cm2, then the radius of the ball is
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Question 6 Report
The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r : t. In 1980, the price of a loaf went up by 25% and that of a packet of sugar went up by 10%. Their new ratio is now
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Question 7 Report
Suppose x varies inversely as y, y varies directly as the square of t and x = 1, when t = 3. Find x when t = \(\frac{1}{3}\).
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Question 8 Report
Two cars X and Y start at the same point and travel towards a point P which is 150km away. If the average speed of Y is 60km per hour and x arrives at P 25 minutes earlier than Y. What is the average speed of X?
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Question 10 Report
In the figure, WU//YZ, WY//YZ = 12cm, VZ = 6cm, XU = 8cm. Determine the length of WU.
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Question 11 Report
The first term of an Arithmetic progression is 3 and the fifth term is 9. Find the number of terms in the progression if the sum is 81
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Question 12 Report
A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?
Question 14 Report
The number 25 when converted from the tens and units base to the binary base (base two) is one of the following
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Question 15 Report
Evaluate \(\frac{6.3 \times 10^5}{8.1 \times 10^3}\) to 3 significant fiqures
Question 16 Report
The weights of 30 new-born babies are given as follow: 6, 9, 5, 7, 6, 7, 5, 8, 9, 5, 7, 5, 8, 7, 8, 7, 5, 6, 5, 7, 6, 9, 9, 7, 8, 8, 7, 8, 9, 8. The mode is
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Question 17 Report
If b = a + cp and r = ab + \(\frac{1}{2}\)cp2, express b2 in terms of a, c, r.
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Question 18 Report
In the figure, find x in terms of a, b and c.
Question 19 Report
simplify \(\frac{6^{2n + 1} \times 9^n \times 4^{2n}}{18^n \times 2^n \times 12^{2n}}\)
Question 20 Report
Solve the given equation \((\log_{3} x)^{2} - 6(\log_{3} x) + 9 = 0\)
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Question 22 Report
The difference between the length and width of a rectangle is 6cm and the area is 135cm2. What is the length?
Question 23 Report
Evaluate correct to 4 decimal places 827.51 x 0.015
Question 24 Report
A micrometer is defined as one millionth of a millimeter. A length of 12,000 micrometres may be represented as
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Question 25 Report
In the figure, the chords XY and ZW are produced to meet at T such that YT = WT, ZYW = 40o and YTW = 30o. What is YXW?
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Question 26 Report
What is the length of an arc of a circle that substends 2\(\frac{1}{2}\) radians at the centre when the raduis of the circle = \(\frac{k}{k + 1}\) + \(\frac{k + 1}{k}\) then
Question 27 Report
7 pupils of average age 12 years leave a class of 25 pupils of average age 14 years. If 6 new pupils of average age 11years join the class, what is the average age of the pupils now in the class?
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Question 28 Report
What is the area between two concentric circles of diameters 26cm and 20cm?
Question 29 Report
The sum of the root of a quadratic equation is \(\frac{5}{2}\) and the product of its root is 4. The quadratic equation is
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Question 30 Report
A sum of money invested at 5% per annum simple interest amounts to $285.20 after 3 years. How long will it take the same sum to amount to $434.00 at 7\(\frac{1}{2}\)% per annum simple interest?
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Question 31 Report
By selling an article for N45.00 a man makes a profit of 80%. For how much should he have sold it in order to make a profit of 32%?
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Question 32 Report
Given that 10x = 0.2 and log102 = 0.3010, find x
Question 33 Report
The difference between 4\(\frac{5}{7}\) and 2\(\frac{1}{4}\) greater by
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Question 35 Report
Show that \(\frac{\sin 2x}{1 + \cos x}\) + \(\frac{sin2 x}{1 - cos x}\) is
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Question 37 Report
Find the value of x satisfying \(\frac{x}{2}\) - \(\frac{1}{3}\) < \(\frac{2x}{5}\) + \(\frac{1}{6}\)
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Question 38 Report
In one and a half hours, the minute hand of a clock rotates through an angle of
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Question 39 Report
In \(\bigtriangleup\)XYZ, XY = 3cm, XZ = 5cm and YZ = 7cm. If the bisector of XYZ meets XZ at W, what is the length of XW?
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Question 40 Report
Find a two-digit number such that three times the tens digit is 2 less than twice the units digit and twice the number is 20 greater than the number obtained by reversing the digits
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Question 42 Report
If \(\log_{2} y = 3 - \log_{2} x^{\frac{3}{2}}\), find y when x = 4.
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Question 43 Report
A group of 14 children children received the following scores in a reading test: 35, 35, 26, 26, 26, 29, 29, 29, 12, 25, 25, 25, 25, 17. What was the median score?
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Question 44 Report
In the diagram, XZ is the diameter of a circle's radius \(\frac{5}{2}\). If XY is 4cm, then the area of the triangle XYZ is
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Question 46 Report
An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?
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Question 47 Report
Marks scored by some children in an arithmetic test are:5, 3, 6, 9, 4, 7, 8, 6, 2, 7, 8, 4, 5, 2, 1, 0, 6, 9, 0, 8.
The arithmetic mean of the marks is
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