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

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

JAMB UTME - Mathematics - 1979

Vraag 1 Verslag

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

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

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Vraag 2 Verslag

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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Vraag 3 Verslag

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

70^o

75^o

105^o

140^o

150^o

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Vraag 4 Verslag

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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Fractions, Decimals, Approximations And Percentage

Surds (radicals)

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Vraag 5 Verslag

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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Vraag 6 Verslag

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

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

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

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

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

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

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Algebraic Expressions

Ratio, Proportions And Rates

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Vraag 7 Verslag

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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Vraag 8 Verslag

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

60cm²

65cm²

72cm²

144cm²

156cm²

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Vraag 9 Verslag

One of the following statements is wrong. Which is it?

If a triangle is equiangular then it is also equilateral

If a triangle is equilateral then it is also then it is also equiangular

If two triangles are similar then they are also congurent

The sum of the interior angles of any triangle is 180 degrees

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Triangles And Polygons

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Vraag 10 Verslag

If the value of \(\pi\) is taken to be \(\frac{22}{7}\), the area of a semi-circle of diameter 42m is

5544m²

1386m²

132m²

264m²

693m²

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Coordinate Geometry

Angles

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Vraag 11 Verslag

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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Vraag 12 Verslag

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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Vraag 13 Verslag

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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Vraag 14 Verslag

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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Vraag 15 Verslag

In this figure, PQRS is a parallelogram, PS = PT and < PST = 55\(^o\). The size of <PQR is

125^o

120^o

115^o

110^o

10^o

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Vraag 16 Verslag

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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Vraag 17 Verslag

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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Vraag 18 Verslag

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

1.3979

2.3979

1.6021

2.6021

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Logarithms

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Vraag 19 Verslag

(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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Vraag 20 Verslag

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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Vraag 21 Verslag

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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Vraag 22 Verslag

After getting a rise of 15%, a man's new monthly salary is N345. How much per month did he earn before the increase?

N330

n396.75

N300

N293.25

N360

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Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

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Vraag 23 Verslag

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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Vraag 24 Verslag

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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Vraag 25 Verslag

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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Vraag 26 Verslag

What is the greatest straight line distance between two vertices (corners) of a cube whose sides are 2239cm long?

\(\sqrt{2239cm}\)

\(\sqrt{2}\) x 2239cm

\(\frac{\sqrt{3}}{2}\) 2239cm

\(\sqrt{3}\) x 2239cm

4478cm

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Euclidean Geometry

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Vraag 27 Verslag

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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Vraag 28 Verslag

(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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Vraag 29 Verslag

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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Vraag 30 Verslag

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

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Sine, Cosine And Tangent Of An Angle

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Vraag 31 Verslag

If y = x² - 2x - 3, Find the least value of y and corresponding value of x

x = 3, y = 3

x = 1, y = -3

x = 4, y = 1

x = 1, y = -4

x = 2, y = -3

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Quadratic Equations

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Vraag 32 Verslag

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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Vraag 33 Verslag

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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Vraag 34 Verslag

In \(\bigtriangleup\)PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS

4cm

32cm

\(\frac{30}{7}\)

\(\frac{40}{7}\)

4.8cm

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Vraag 35 Verslag

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

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Solution Of Linear Equations

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Vraag 36 Verslag

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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Vraag 37 Verslag

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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Vraag 38 Verslag

The mean of the numbers 1.2, 1.0, 0.9, 1.4, 0.8, 0.8, 1.2 and 1.1 is

1.5

0.8

1.0

1.02

1.05

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Probability

Linear Inequalities

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Vraag 39 Verslag

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

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

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

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

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

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Algebraic Expressions

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Vraag 40 Verslag

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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Vraag 41 Verslag

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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Vraag 42 Verslag

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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Vraag 43 Verslag

Find the value of (4^{\(\frac{1}{2}\)})⁶

Antwoorddetails

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Indices

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Vraag 44 Verslag

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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Vraag 45 Verslag

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

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Ratio, Proportions And Rates

Financial Arithmetic

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Vraag 46 Verslag