JAMB UTME - Mathematics - 1979
Pregunta 2 Informe
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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Pregunta 3 Informe
PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15o find < QRS
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Pregunta 4 Informe
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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Pregunta 5 Informe
(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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Pregunta 6 Informe
Find the value of log10\(\frac{1}{40}\), given that log104 = 0.6021
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Pregunta 7 Informe
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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Pregunta 8 Informe
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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Pregunta 9 Informe
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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Pregunta 11 Informe
Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
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Pregunta 12 Informe
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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Pregunta 13 Informe
If y = x2 - 2x - 3, Find the least value of y and corresponding value of x
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Pregunta 14 Informe
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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Pregunta 15 Informe
What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?
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Pregunta 16 Informe
If x3 - 12x - 16 = 0 has x = -2 as a solution then the equaion has
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Pregunta 17 Informe
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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Pregunta 18 Informe
A cylinder of height h and radius r is open at one end. Its surface area is
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Pregunta 19 Informe
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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Pregunta 21 Informe
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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Pregunta 23 Informe
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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Pregunta 24 Informe
Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)
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Pregunta 25 Informe
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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Pregunta 26 Informe
Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)
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Pregunta 27 Informe
In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.
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Pregunta 28 Informe
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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Pregunta 29 Informe
Make x the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0
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Pregunta 31 Informe
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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Pregunta 33 Informe
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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Pregunta 34 Informe
Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2
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Pregunta 36 Informe
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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Pregunta 38 Informe
Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0
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Pregunta 40 Informe
If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:
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Pregunta 42 Informe
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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Pregunta 43 Informe
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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Pregunta 44 Informe
In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is
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Pregunta 45 Informe
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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Pregunta 46 Informe
\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) equals
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Pregunta 47 Informe
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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Pregunta 48 Informe
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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Pregunta 49 Informe
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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