JAMB UTME - Mathematics - 1979

Question 1 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

Answer Details

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Question 2 Report

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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Question 3 Report

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

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 4 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

Answer Details

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Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

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Question 5 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

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

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Ratio, Proportions And Rates

Financial Arithmetic

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Question 6 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

Answer Details

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 7 Report

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

1.3979

2.3979

1.6021

2.6021

Answer Details

Read lesson note on Logarithms (WAEC)

Logarithms

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Question 8 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 9 Report

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

Answer Details

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 10 Report

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?

Answer Details

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 11 Report

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

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

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

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

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

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

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

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Question 12 Report

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

Answer Details

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Question 13 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

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 14 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

Answer Details

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 15 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

Answer Details

Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

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Question 16 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

Answer Details

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Question 17 Report

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Answer Details

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Read lesson note on Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

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Question 18 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

Answer Details

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

Angles Of Elevation And Depression

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Question 19 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

Answer Details

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 20 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

Answer Details

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

Simple Operations On Algebraic Expressions

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Question 21 Report

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

Answer Details

Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles

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Question 22 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

Answer Details

Read lesson note on Circles (WAEC)

Circles

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Question 23 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.

Answer Details

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 24 Report

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

Answer Details

Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

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Question 25 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 = \(\frac{5 - 2d - b}{ad}\)

Answer Details

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 26 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

Answer Details

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 27 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

Answer Details

Read lesson note on Circles (WAEC)

Circles

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Question 28 Report

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

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

Answer Details

Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

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Question 29 Report

(3.2)² - (1.8)² equals

7.0

2.56

13.48

2.0

0.07

Answer Details

Read lesson note on Indices (WAEC)

Indices

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Question 30 Report

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

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 31 Report

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

Answer Details

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 32 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

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

Sine, Cosine And Tangent Of An Angle

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Question 33 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\(\sqrt{3}\)

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

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

Answer Details

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Question 34 Report

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

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

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

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

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

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

Answer Details

Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

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Question 35 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\(\frac{1}{5}\)

Answer Details

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Variation

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Question 36 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

Answer Details

Read lesson note on Progression (JAMB)

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Progression

Quadratic Equations

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Question 37 Report

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

20^o

40^o

60^o

80^o

100^o

Answer Details

Read lesson note on Indices (WAEC)

Indices

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Question 38 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%

Answer Details

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Question 39 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

Answer Details

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 40 Report

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

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

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

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

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

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

Answer Details

Read lesson note on Percentages (WAEC)

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

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Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

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Question 41 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

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 42 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\(\frac{2}{3}\)