JAMB UTME - Mathematics - 1979
Pergunta 1 Relatório
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
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Pergunta 2 Relatório
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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Pergunta 3 Relatório
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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Pergunta 5 Relatório
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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Pergunta 7 Relatório
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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Pergunta 8 Relatório
If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
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Pergunta 10 Relatório
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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Pergunta 12 Relatório
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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Pergunta 13 Relatório
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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Pergunta 14 Relatório
What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?
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Pergunta 15 Relatório
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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Pergunta 18 Relatório
If x3 - 12x - 16 = 0 has x = -2 as a solution then the equaion has
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Pergunta 19 Relatório
A cylinder of height h and radius r is open at one end. Its surface area is
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Pergunta 20 Relatório
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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Pergunta 21 Relatório
Make x the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0
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Pergunta 23 Relatório
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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Pergunta 24 Relatório
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?
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Pergunta 25 Relatório
PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15o find < QRS
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Pergunta 26 Relatório
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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Pergunta 27 Relatório
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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Pergunta 28 Relatório
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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Pergunta 29 Relatório
If y = x2 - 2x - 3, Find the least value of y and corresponding value of x
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Pergunta 30 Relatório
Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
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Pergunta 31 Relatório
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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Pergunta 32 Relatório
Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2
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Pergunta 34 Relatório
If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is
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Pergunta 35 Relatório
Find the value of log10\(\frac{1}{40}\), given that log104 = 0.6021
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Pergunta 37 Relatório
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
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Pergunta 38 Relatório
In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.
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Pergunta 40 Relatório
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?
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Pergunta 43 Relatório
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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Pergunta 44 Relatório
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
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Pergunta 46 Relatório
(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?
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Pergunta 48 Relatório
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
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Pergunta 49 Relatório
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?
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Pergunta 50 Relatório
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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