JAMB UTME - Mathematics - 1979

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

\(\frac{y(y - x)}{y - x}\) cedis

\(\frac{Yy - Xx)}{y - x}\) cedis

\(\frac{Y - Xy)}{y - x}\) cedis

\(\frac{Y - X}{y - x}\) cedis

\(\frac{Y - Xx}{y - x}\) cedis

Answer Details

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Solution Of Linear Equations

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Question 10 Report

(3.2)² - (1.8)² equals

7.0

2.56

13.48

2.0

0.07

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Indices

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Question 11 Report

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15^o find < QRS

75^o

37\(\frac{1}{2}\)^o

127\(\frac{1}{2}\)^o

105^o

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Circles

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Question 12 Report

The solution of the equation x² - 2x = 8 is

x = 0 or 2

x = -2 or 4

x = 2

x = -4

x = 2 or 4

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Quadratic Equations

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Question 13 Report

In the figure, PQ is parallel to SQ ; QS bisets < PSQ, < PQS is 65^o and < RPS is 20^o. What is the size of < PRS?

45^o

35^o

40^o

30^o

42^o

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Question 14 Report

In the parallelogram PQRS, PE is perpendicular to QR. Find the area of the parallelogram.

60cm²

65cm²

72cm²

144cm²

156cm²

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Question 15 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

N5000

N1800

N12000

N24000

N8000

Answer Details

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Ratio, Proportions And Rates

Financial Arithmetic

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Question 16 Report

In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to

3\(\sqrt{2}\)

2\(\sqrt{3}\)

\(\frac{\sqrt{3}}{2}\)

\(\frac{2}{\sqrt{3}}\)

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Question 17 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?

(a), (b), (c)

(c)

None of the choices

All of the above

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Linear Inequalities

Inequalities

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Question 18 Report

For the set of numbers 2, 3, 5, 6, 7, 7, 8

The median is greater than the mode

the mean is greater than the mode

the mean is greater than the median

the median is equal to the mean

the mean is less than the median

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Question 19 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?

\(\frac{5}{6}\)

3\(\frac{3}{5}\)

2\(\frac{1}{2}\)

1\(\frac{1}{5}\)

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Variation

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Question 20 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?

20 and 45

100 and 150

45 and 65

35 and 75

20 and 60

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Solution Of Linear Equations

Quadratic Equations

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Question 21 Report

If O is the centre of the circle, < POS equls

70^o

75^o

105^o

140^o

150^o

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Circles

Angles Of Elevation And Depression

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Question 22 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?

\(\frac{59300}{625}\)

\(\frac{50900}{625}\)

200%

+100%

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Question 23 Report

Simplify \(\frac{1 - x^2}{x - x^2}\), where x \(\neq\) 0

\(\frac{1}{x}\)

\(\frac{1 - x}{x}\)

\(\frac{1 + x}{x}\)

\(\frac{1}{x - 1}\)

\(\frac{-x - 1}{1}\)

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Algebraic Expressions

Algebraic Fractions

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Question 24 Report

PQ is parallel to RS. Calculate the value of x.

20^o

40^o

60^o

80^o

100^o

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Indices

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Question 25 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?

17.72 meter/sec.

21.67 meters/sec

2.5 meter/sec.

20.45 meters/sec.

13.33 meter/sec.

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Integration

Simple Operations On Algebraic Expressions

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Question 26 Report

The following table relates the number of objects f corresponding to a certain size x. What is the average size of an object?
\(\begin{array}{c|c} f & 1 & 2 & 3 & 4 & 5 \\ \hline x & 1 & 2 & 4 & 8 & 16\end{array}\)

\(\frac{31}{15}\)

\(\frac{31}{5}\)

\(\frac{129}{5}\)

\(\frac{43}{5}\)

\(\frac{16}{5}\)

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Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

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Question 27 Report

A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?

20sq.cm

100sq.cm

25sq.cm

16sq.cm

36sq.cm

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Mensuration

Measures Of Dispersion

Lengths And Perimeters

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Question 28 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?

\(\frac{5}{9}\)k² sq. units

\(\frac{1}{3}\)k² sq. units

\(\frac{8}{9}\)k² sq. units

\(\frac{7}{9}\)k² sq. units

\(\frac{2}{3}\)k² sq. u

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Simple Operations On Algebraic Expressions

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Question 29 Report

Make x the subject of the equation a(b + c) + \(\frac{5}{d}\) - 2 = 0

c = \(\frac{2d - 5 - b}{ad}\)

c = \(\frac{2d - 5 - abd}{ad}\)

c = \(\frac{2d - 5 - ab}{ad}\)

c = \(\frac{5 - 2d - b}{ad}\)

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Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

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Question 30 Report

Find x in the diagram below.

3\(\sqrt{3}\)

\(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\)

\(\frac{(\sqrt{3} - 1)}{\sqrt{3} + 1}\)

\(\frac{3 - 1}{\sqrt{3} + 1}\)

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Modular Arithmetic

Surds (radicals)

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Question 31 Report

Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2

x = -8, y = 1

x = -2, y = 4

x = \(\frac{-34}{27}\), y = \(\frac{73}{27}\)

x = 7, y = -9

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Solution Of Linear Equations

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Question 32 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 20^o. What is the size of

70^o

90^o

80^o

40^o

60^o

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Circles

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Question 33 Report

Rationalize the denominator of the expression \(\frac{6 + 2\sqrt{5}}{4 - 3\sqrt{6}}\)

\(\frac{12+ 4\sqrt{5 + 7} 5 + 6\sqrt{3}}{39}\)

\(\frac{-(24 + 18\sqrt{6} + 8\sqrt{5} + 6\sqrt{30})}{39}\)

\(\frac{24 + 3\sqrt{6 + 8} 5 + 6\sqrt{30}}{19}\)

\(\frac{-15 + 3\sqrt{5 + 18} 5 + 6\sqrt{30}}{36}\)

\(\frac{-(12 + 4\sqrt{5} +9\sqrt{6} + 3\sqrt{30})}{19}\)

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Number Bases

Surds (radicals)

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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?

\(\frac{44}{3}\)\(\pi\)cm³

12\(\pi\)cm³

\(\frac{38}{3}\)\(\pi\)cm³

\(\frac{40}{3}\)\(\pi\)cm³

\(\frac{32}{33}\)\(\pi\)cm³

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Volumes

Areas

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Question 35 Report

An arc of circle of radius 2cm subtends an angle of 60^o at the centre. Find the area of the sector

\(\frac{2 \pi}{3}\)cm²

\(\frac{\pi}{2}\)cm²

\(\frac{\pi}{3}\)cm²

\(\pi\)cm²

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Circles

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Question 36 Report

A cylinder of height h and radius r is open at one end. Its surface area is

2\(\pi\)rh

\(\pi\)r²h

2\(\pi\)rh + \(\pi\)r²

2\(\pi\)rh + 2\(\pi\)r²

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Volumes

Lengths And Perimeters

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Question 37 Report

Simplify 2\(\frac{5}{12}\) - 1\(\frac{7}{8}\) x \(\frac{6}{5}\)

\(\frac{1}{6}\)

\(\frac{13}{20}\)

\(\frac{11}{30}\)

\(\frac{9}{4}\)

\(\frac{5}{3}\)

Answer Details

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Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

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Question 38 Report

If \(\sqrt{3^{\frac{1}{x}}}\) = \(\sqrt{9}\) then the value of x is:

\(\frac{3}{4}\)

\(\frac{4}{3}\)

\(\frac{1}{3}\)

\(\frac{2}{3}\)

\(\frac{1}{2}\)

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Surds (radicals)

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Question 39 Report

\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) equals

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

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Positive And Negative Integers, Rational Numbers

Number Bases

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Question 40 Report

Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x - 1}}\)

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

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Number Bases

Modular Arithmetic

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Question 41 Report

If x³ - 12x - 16 = 0 has x = -2 as a solution then the equaion has

x = -4 as a solution also

3 roots all different

3 roots with two equal and the third different

3 roots all equal

only one root

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Progression

Quadratic Equations

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Question 42 Report

Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)

\(\frac{x^2 + y^2} {(x - y)^2}\)

\(\frac{2y^3} {y^2 - x^2}\)

\(\frac{3x^2 + y^2} {(2x - y)^2}\)

\(\frac{x^2 + y^2} {(x^2 - y)}\)

Answer Details

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Algebraic Expressions

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Question 43 Report

What is log₇(49^a) - log₁₀(0.01)?

\(\frac{49^a}{100}\)

\(\frac{a}{2}\) + 2

7^2a + 2

2a + 2

\(\frac{2a}{2}\)

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Logarithms

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Question 44 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 30^o. 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

30^o

60^o

45^o

25^o

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Angles Of Elevation And Depression

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Question 45 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

1\(\frac{2}{3}\)

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Sequence And Series

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Question 46 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?

1.1m

1.2m

0.9m

1.3m

Answer Details

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Sine, Cosine And Tangent Of An Angle

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Question 47 Report

Find the value of log₁₀\(\frac{1}{40}\), given that log₁₀4 = 0.6021

1.3979

2.3979