JAMB UTME - Mathematics - 1979
Question 1 Report
A ladder resting on a vertical wall makes an angles whose tangent is 2.4 with the ground. If the distance between the foot of the ladder and the wall is 50cm, What is the length of the ladder?
Question 2 Report
12 men complete a job in 9 days. How many men working t the same rate would be required to complete the job in 6 days?
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Question 7 Report
PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15o find < QRS
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Question 10 Report
A trader goes to Ghana for y days with y cedis. For the first x days, he spends X cedis per day. The amount he has to spend per day for the rest of his stay is
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Question 11 Report
A cylinder of height h and radius r is open at one end. Its surface area is
Question 12 Report
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
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Question 13 Report
In the figure, PQ and QR are chords of the circle PQR. QRS is a straight line and PR is equal to RS, < PSR is 20o. What is the size of
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Question 15 Report
On each market day Mrs. Bassey walks to the market from her home at a steady speed. This journey normally takes her 2 hours to complete. She finds, however, that by increasing her usual speed by 1 km/hr she can save 20 minutes. Find her usual speed in km/hr
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Question 17 Report
After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?
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Question 18 Report
The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)
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Question 19 Report
In base ten, the number 101101 (base 2) equals
Question 20 Report
If y = x2 - 2x - 3, Find the least value of y and corresponding value of x
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Question 21 Report
The area under the speed time graph given the total distance covered by car. What is the average velocity to two places of decimals?
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Question 22 Report
If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is
Question 23 Report
The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increases in size of the quantity?
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Question 24 Report
What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?
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Question 25 Report
Which of the following values of the variable x, (a)x = 0, (b)x = -3, (c)x = 9, satisfy the inequalities 0 < \(\frac{x + 3}{x - 1}\) < 2?
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Question 26 Report
If x3 - 12x - 16 = 0 has x = -2 as a solution then the equaion has
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Question 27 Report
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
Question 29 Report
A father is now three times as old as his son. Twelve years ago he was six times as old as his son. How old are the son and the father?
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Question 30 Report
If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
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Question 33 Report
In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to
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Question 34 Report
A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?
Question 35 Report
Make x the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0
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Question 36 Report
The annul profits of a transport business were divided between the partners A and B in the ratio 3 : 5. If B received N3000 more than A, the total profit was
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Question 37 Report
Find the value of log10\(\frac{1}{40}\), given that log104 = 0.6021
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Question 39 Report
A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?
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Question 40 Report
In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS
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Question 42 Report
A man is standing in the corridor of a 10-storey building and looking down at a tall tree in front of the building. He sees the top of the tree at angle of depression of 30o. If the tree is 200m tall and the man's eyes are 300m above the ground, calculate the angle of depression of the foot tree as seen by the man
Question 43 Report
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
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Question 44 Report
An arc of circle of radius 2cm subtends an angle of 60o at the centre. Find the area of the sector
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Question 46 Report
x is directly proportional to y and inversely proportional to z. If x = 9 when y = 24 and z = 8, what is the value of x when y = 5 and z = 6?
Question 47 Report
In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65o and < RPS is 20o. What is the size of < PRS?
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Question 48 Report
(Numbers indicate the lengths of the sides of the triangles) If the area of \(\bigtriangleup\) PQR is k2sq. units what is the area of the shades portion?
Question 49 Report
The mean of the numbers 1.2, 1.0, 0.9, 1.4, 0.8, 0.8, 1.2 and 1.1 is
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