JAMB UTME - Mathematics - 1979

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 11 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

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Read lesson note on Euclidean Geometry (JAMB)

Euclidean Geometry

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Question 12 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

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Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

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Question 13 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 14 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\(\frac{1}{5}\)

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Read lesson note on Variation (WAEC)

Read lesson note on Variation (JAMB)

Variation

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Question 15 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

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Read lesson note on Sequence And Series (WAEC)

Sequence And Series

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Question 16 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

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Read lesson note on Number Bases (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

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Question 17 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

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

Angles Of Elevation And Depression

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Question 18 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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Read lesson note on Surds (radicals) (WAEC)

Surds (radicals)

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Question 19 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

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Read lesson note on Progression (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Progression

Quadratic Equations

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Question 20 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

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Read lesson note on Circles (WAEC)

Circles

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Question 21 Report

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

60cm²

65cm²

72cm²

144cm² Correct answer

156cm²

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Question 22 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.

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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 23 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

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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

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Question 24 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%

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Question 25 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

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

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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

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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 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 27 Report

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

5^{2x + 1}

5^{x + 1}

5^-5 Correct answer

5²

5³

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Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

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Question 28 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

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Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

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Question 29 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

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Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles

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Question 30 Report

(3.2)² - (1.8)² equals

7.0 Correct answer

2.56

13.48

2.0

0.07

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Read lesson note on Indices (WAEC)

Indices

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Question 31 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

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Read lesson note on Volumes (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

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Question 32 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

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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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Question 33 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 34 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

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Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

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Question 35 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 36 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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Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

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Question 37 Report

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

45 Correct answer

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Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

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Question 38 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 39 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 40 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

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

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

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Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

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Question 41 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

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Question 42 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 43 Report

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If < PQS = 15^o find < QRS

75^o