JAMB UTME - Mathematics - 1979

Question 1 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

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 2 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

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 3 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 Correct answer

2\(\pi\)rh + 2\(\pi\)r²

Answer Details

Read lesson note on Volumes (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

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Question 4 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

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 5 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

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 6 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

Answer Details

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 7 Report

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

45 Correct answer

Answer Details

Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

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Question 8 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

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

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Question 9 Report

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2 Correct answer

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

Answer Details

Read lesson note on Logarithms (WAEC)

Logarithms

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Question 10 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

Answer Details

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 11 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

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 12 Report

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 Correct answer

Answer Details

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Question 13 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

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 14 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 15 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

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

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Question 16 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

Read lesson note on Logarithms (WAEC)

Logarithms

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Question 17 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

Answer Details

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

Simple Operations On Algebraic Expressions

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Question 18 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

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 19 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 20 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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Read lesson note on Circles (WAEC)

Circles

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Question 21 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

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 22 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 Correct answer

42^o

Answer Details

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Question 23 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

Read lesson note on Indices (WAEC)

Indices

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Question 24 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)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles

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Question 25 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

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 26 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

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 27 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

Read lesson note on Variation (WAEC)

Read lesson note on Variation (JAMB)

Variation

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Question 28 Report

(3.2)² - (1.8)² equals

7.0 Correct answer

2.56

13.48

2.0

0.07

Answer Details

Read lesson note on Indices (WAEC)

Indices

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Question 29 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 30 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 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

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Question 32 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

Read lesson note on Number Bases (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

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Question 33 Report

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

8 Correct answer

Answer Details

Read lesson note on Indices (WAEC)

Indices

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Question 34 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% Correct answer

+100%

Answer Details

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Question 35 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)

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 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 Correct answer

3 roots with two equal and the third different

3 roots all equal

only one root

Answer Details

Read lesson note on Progression (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Progression

Quadratic Equations

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Question 37 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

Answer Details

Read lesson note on Probability (WAEC)

Read lesson note on Linear Inequalities (WAEC)

Probability

Linear Inequalities

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Question 38 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 39 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

Answer Details

Read lesson note on Circles (WAEC)

Circles

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Question 40 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 Correct answer

\(\frac{\pi}{2}\)cm²

\(\frac{\pi}{3}\)cm²

\(\pi\)cm²

Answer Details

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Circles

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Question 41 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

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 42 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

Answer Details

Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

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Question 43 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

Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

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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

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 45 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

Read lesson note on Euclidean Geometry (JAMB)

Euclidean Geometry

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Question 46 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\(\frac{2}{3}\)