JAMB UTME - Mathematics - 1979

Question 1 Rapport

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

Détails de la réponse

Read lesson note on Ratio, Proportions And Rates (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

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Question 2 Rapport

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

20^o

40^o

60^o

80^o

100^o

Détails de la réponse

Read lesson note on Indices (WAEC)

Indices

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Question 3 Rapport

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

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

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

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

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

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

Détails de la réponse

Read lesson note on Number Bases (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

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Question 4 Rapport

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

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

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

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

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

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

Détails de la réponse

Read lesson note on Fractions, Decimals And Approximations (WAEC)

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

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Question 5 Rapport

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Détails de la réponse

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

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Question 6 Rapport

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

Détails de la réponse

Read lesson note on Variation (WAEC)

Read lesson note on Variation (JAMB)

Variation

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Question 7 Rapport

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

Détails de la réponse

Read lesson note on Mensuration (JAMB)

Read lesson note on Measures Of Dispersion (JAMB)

Read lesson note on Lengths And Perimeters (WAEC)

Mensuration

Measures Of Dispersion

Lengths And Perimeters

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Question 8 Rapport

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

60cm²

65cm²

72cm²

144cm²

156cm²

Détails de la réponse

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Question 9 Rapport

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

Détails de la réponse

Read lesson note on Volumes (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

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Question 10 Rapport

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

Détails de la réponse

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 11 Rapport

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

Détails de la réponse

Read lesson note on Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

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Question 12 Rapport

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

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

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

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

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

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

Détails de la réponse

Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

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Question 13 Rapport

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

Détails de la réponse

Read lesson note on Sequence And Series (WAEC)

Sequence And Series

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Question 14 Rapport

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

Détails de la réponse

Read lesson note on Progression (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Progression

Quadratic Equations

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Question 15 Rapport

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

Détails de la réponse

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Question 16 Rapport

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

Détails de la réponse

Read lesson note on Change Of Subject Of A Formula/Relation (WAEC)

Read lesson note on Solution Of Linear Equations (WAEC)

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

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Question 17 Rapport

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

Détails de la réponse

Read lesson note on Indices (WAEC)

Indices

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Question 18 Rapport

(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

Détails de la réponse

Read lesson note on Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

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Question 19 Rapport

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.

Détails de la réponse

Read lesson note on Integration (JAMB)

Read lesson note on Simple Operations On Algebraic Expressions (WAEC)

Integration

Simple Operations On Algebraic Expressions

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Question 20 Rapport

Multiply (3x + 5y + 4z) by (2x - 3y + z)

6x² + xy - 15y² + 4z² + 11xz - 7yz

6x² + 3xy - 15y² + 4z²

6x² + 3xy - y² + 4z²

6x² + 3xy - 15y + z²

Détails de la réponse

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 21 Rapport

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

Détails de la réponse

Read lesson note on Circles (WAEC)

Circles

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Question 22 Rapport

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?

Détails de la réponse

Read lesson note on Fractions, Decimals And Approximations (WAEC)

Read lesson note on Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Ratio, Proportions And Rates

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Question 23 Rapport

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

Détails de la réponse

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

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Question 24 Rapport

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

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

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

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

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

Détails de la réponse

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 25 Rapport

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

Détails de la réponse

Voir la réponse

Question 26 Rapport

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

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

Détails de la réponse

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

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Question 27 Rapport

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

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

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

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

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

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

Détails de la réponse

Read lesson note on Percentages (WAEC)

Read lesson note on Fractions, Decimals, Approximations And Percentage (JAMB)

Read lesson note on Surds (radicals) (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

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Question 28 Rapport

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

Détails de la réponse

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Question 29 Rapport

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

Détails de la réponse

Voir la réponse

Question 30 Rapport

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

Détails de la réponse

Read lesson note on Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

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Question 31 Rapport

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2

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

Détails de la réponse

Read lesson note on Logarithms (WAEC)

Logarithms

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Question 32 Rapport

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

Détails de la réponse

Read lesson note on Circles (WAEC)

Circles

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Question 33 Rapport

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

Détails de la réponse

Read lesson note on Triangles And Polygons (WAEC)

Triangles And Polygons

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Question 34 Rapport

(3.2)² - (1.8)² equals

7.0

2.56

13.48

2.0

0.07

Détails de la réponse

Read lesson note on Indices (WAEC)

Indices

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Question 35 Rapport

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

Détails de la réponse

Read lesson note on Probability (WAEC)

Read lesson note on Linear Inequalities (WAEC)

Probability

Linear Inequalities

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Question 36 Rapport

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

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

Détails de la réponse

Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

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Question 37 Rapport

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

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

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

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

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

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

Détails de la réponse

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

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Question 38 Rapport

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

1.3979

2.3979

1.6021

2.6021

Détails de la réponse

Read lesson note on Logarithms (WAEC)

Logarithms

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Question 39 Rapport

In base ten, the number 101101 (base 2) equals

Détails de la réponse

Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

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Question 40 Rapport

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

Détails de la réponse

Voir la réponse

Question 41 Rapport

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

Détails de la réponse

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 42 Rapport

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\(\sqrt{3}\)

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

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

Détails de la réponse

Voir la réponse

Question 43 Rapport

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

Détails de la réponse

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 44 Rapport

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

Détails de la réponse

Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

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Question 45 Rapport

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

Détails de la réponse

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 46 Rapport

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

Détails de la réponse

Read lesson note on Percentages (WAEC)

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

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Question 47 Rapport

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

70^o

75^o

105^o

140^o

150^o

Détails de la réponse

Read lesson note on Circles (WAEC)

Read lesson note on Angles Of Elevation And Depression (WAEC)

Circles

Angles Of Elevation And Depression

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Question 48 Rapport

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%

Détails de la réponse

Voir la réponse

Question 49 Rapport

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