JAMB UTME - Mathematics - 1979

Question 1 Report

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

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

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

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

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

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

Answer Details

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Number Bases

Surds (radicals)

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Question 2 Report

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

6x² + xy - 15y² + 4z² + 11xz - 7yz Correct answer

6x² + 3xy - 15y² + 4z²

6x² + 3xy - y² + 4z²

6x² + 3xy - 15y + z²

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Algebraic Expressions

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Question 3 Report

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

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

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

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

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

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

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Surds (radicals)

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Question 4 Report

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Answer Details

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Modular Arithmetic

Surds (radicals)

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Question 5 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 Correct answer

Answer Details

Read lesson note on Coordinate Geometry (WAEC)

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Coordinate Geometry

Angles

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Question 6 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 Correct answer

40^o

60^o

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Circles

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Question 7 Report

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

20^o

40^o Correct answer

60^o

80^o

100^o

Answer Details

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Indices

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Question 8 Report

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

45 Correct answer

Answer Details

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Number Bases

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Question 9 Report

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

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

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

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

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

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 10 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 Correct answer

\(\frac{1}{3}\)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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Question 11 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 Correct answer

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Solution Of Linear Equations

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Question 12 Report

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 Correct answer

4478cm

Answer Details

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Euclidean Geometry

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Question 13 Report

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

2 x 10^-5

2 x 10^-1

2 x 10¹ Correct answer

2 x 10^-4

Answer Details

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Read lesson note on Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

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Question 14 Report

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 Correct answer

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

Answer Details

Read lesson note on Triangles And Polygons (WAEC)

Triangles And Polygons

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Question 15 Report

(3.2)² - (1.8)² equals

7.0 Correct answer

2.56

13.48

2.0

0.07

Answer Details

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Indices

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Question 16 Report

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

8 Correct answer

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Indices

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Question 17 Report

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

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

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

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

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

Answer Details

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Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

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Question 18 Report

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

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

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

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

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

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

Answer Details

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Algebraic Expressions

Algebraic Fractions

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Question 19 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 Correct answer

10^o

Answer Details

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Question 20 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 Correct answer

x = 2, y = -3

Answer Details

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Quadratic Equations

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Question 21 Report

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

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

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

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

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

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

Answer Details

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Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

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Question 22 Report

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

60cm²

65cm²

72cm²

144cm² Correct answer

156cm²

Answer Details

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Question 23 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 Correct answer

3 roots with two equal and the third different

3 roots all equal

only one root

Answer Details

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Progression

Quadratic Equations

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Question 24 Report

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

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

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

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

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

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

Answer Details

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Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

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Question 25 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 Correct answer

12\(\pi\)cm³

\(\frac{38}{3}\)\(\pi\)cm³

\(\frac{40}{3}\)\(\pi\)cm³

\(\frac{32}{33}\)\(\pi\)cm³

Answer Details

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Volumes

Areas

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Question 26 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 Correct answer

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Circles

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Question 27 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?

18 Correct answer

Answer Details

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Fractions, Decimals And Approximations

Ratio, Proportions And Rates

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Question 28 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 Correct answer

Answer Details

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Question 29 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\(\frac{2}{3}\)

5 Correct answer

Answer Details

Read lesson note on Sequence And Series (WAEC)

Sequence And Series

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Question 30 Report

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

x = 0 or 2

x = -2 or 4 Correct answer

x = 2

x = -4

x = 2 or 4

Answer Details

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Quadratic Equations

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Question 31 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 Correct answer

All of the above

Answer Details

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Linear Inequalities

Inequalities

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Question 32 Report

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2 Correct answer

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

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Read lesson note on Logarithms (WAEC)

Logarithms

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Question 33 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\(\frac{1}{2}\) Correct answer

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

Answer Details

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Variation

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Question 34 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. Correct answer

13.33 meter/sec.

Answer Details

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Integration

Simple Operations On Algebraic Expressions

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Question 35 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 = \(\frac{73}{27}\) Correct answer

x = 7, y = -9

Answer Details

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Solution Of Linear Equations

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Question 36 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 Correct answer

N293.25

N360

Answer Details

Read lesson note on Percentages (WAEC)

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Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

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Question 37 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\(\sqrt{3}\) Correct answer

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

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

Answer Details

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Question 38 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 Correct answer

Answer Details

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Solution Of Linear Equations

Quadratic Equations

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Question 39 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 Correct answer

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 40 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 Correct answer

16sq.cm

36sq.cm

Answer Details

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Mensuration

Measures Of Dispersion

Lengths And Perimeters

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Question 41 Report

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

5^{2x + 1}

5^{x + 1}

5^-5 Correct answer

5²

5³

Answer Details

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Number Bases

Modular Arithmetic

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Question 42 Report

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 Correct answer

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Probability

Linear Inequalities

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Question 43 Report

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

1.3979

2.3979

1.6021 Correct answer

2.6021

Answer Details

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Logarithms

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Question 44 Report

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

70^o

75^o

105^o

140^o

150^o Correct answer

Answer Details

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Circles

Angles Of Elevation And Depression

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Question 45 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 Correct answer

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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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Question 46 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 Correct answer

N24000

N8000

Answer Details

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Ratio, Proportions And Rates

Financial Arithmetic

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Question 47 Report