JAMB UTME - Mathematics - 1979

Ibeere 1 Ìròyìn

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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Wo Idahun

Ibeere 2 Ìròyìn

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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Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

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Ibeere 3 Ìròyìn

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

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Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

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Ibeere 4 Ìròyìn

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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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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Ibeere 5 Ìròyìn

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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Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Ibeere 6 Ìròyìn

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

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Read lesson note on Indices (WAEC)

Indices

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Ibeere 7 Ìròyìn

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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Read lesson note on Progression (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Progression

Quadratic Equations

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Ibeere 8 Ìròyìn

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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Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 9 Ìròyìn

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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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

Wo Idahun

Ibeere 10 Ìròyìn

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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Read lesson note on Volumes (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

Wo Idahun

Ibeere 11 Ìròyìn

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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Read lesson note on Euclidean Geometry (JAMB)

Euclidean Geometry

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Ibeere 12 Ìròyìn

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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Read lesson note on Circles (WAEC)

Circles

Wo Idahun

Ibeere 13 Ìròyìn

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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Read lesson note on Variation (WAEC)

Read lesson note on Variation (JAMB)

Variation

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Ibeere 14 Ìròyìn

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

60cm²

65cm²

72cm²

144cm²

156cm²

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Wo Idahun

Ibeere 15 Ìròyìn

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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Read lesson note on Circles (WAEC)

Circles

Wo Idahun

Ibeere 16 Ìròyìn

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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Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

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Ibeere 17 Ìròyìn

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

Simple Operations On Algebraic Expressions

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Ibeere 18 Ìròyìn

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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Wo Idahun

Ibeere 19 Ìròyìn

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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Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Wo Idahun

Ibeere 20 Ìròyìn

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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Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 21 Ìròyìn

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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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

Wo Idahun

Ibeere 22 Ìròyìn

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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Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Ibeere 23 Ìròyìn

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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Read lesson note on Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 24 Ìròyìn

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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Wo Idahun

Ibeere 25 Ìròyìn

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

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Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 26 Ìròyìn

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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Wo Idahun

Ibeere 27 Ìròyìn

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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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

Wo Idahun

Ibeere 28 Ìròyìn

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

Read lesson note on Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Wo Idahun

Ibeere 29 Ìròyìn

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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Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

Wo Idahun

Ibeere 30 Ìròyìn

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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Wo Idahun

Ibeere 31 Ìròyìn

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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Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Wo Idahun

Ibeere 32 Ìròyìn

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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Read lesson note on Sequence And Series (WAEC)

Sequence And Series

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Ibeere 33 Ìròyìn

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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Read lesson note on Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 34 Ìròyìn

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

Sine, Cosine And Tangent Of An Angle

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Ibeere 35 Ìròyìn

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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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

Wo Idahun

Ibeere 36 Ìròyìn

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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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

Wo Idahun

Ibeere 37 Ìròyìn

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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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

Wo Idahun

Ibeere 38 Ìròyìn

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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Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Wo Idahun

Ibeere 39 Ìròyìn

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

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

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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

Wo Idahun

Ibeere 40 Ìròyìn

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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Read lesson note on Circles (WAEC)

Circles

Wo Idahun

Ibeere 41 Ìròyìn

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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Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles

Wo Idahun

Ibeere 42 Ìròyìn

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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Read lesson note on Number Bases (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Wo Idahun

Ibeere 43 Ìròyìn

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

Angles Of Elevation And Depression

Wo Idahun

Ibeere 44 Ìròyìn

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

20^o

40^o