JAMB UTME - Mathematics - 1979

Swali 1 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Volumes

Areas

Tazama Jibu

Swali 2 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Tazama Jibu

Swali 3 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Tazama Jibu

Swali 4 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 5 Ripoti

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

70^o

75^o

105^o

140^o

150^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Angles Of Elevation And Depression (WAEC)

Circles

Angles Of Elevation And Depression

Tazama Jibu

Swali 6 Ripoti

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 7 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 8 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Soma maelezo ya somo kwenye Inequalities (JAMB)

Linear Inequalities

Inequalities

Tazama Jibu

Swali 9 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Euclidean Geometry

Tazama Jibu

Swali 10 Ripoti

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%

Maelezo ya Majibu

Tazama Jibu

Swali 11 Ripoti

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.

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Integration

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 12 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 13 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Tazama Jibu

Swali 14 Ripoti

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

1.3979

2.3979

1.6021

2.6021

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 15 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

Tazama Jibu

Swali 16 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 17 Ripoti

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 18 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Tazama Jibu

Swali 19 Ripoti

(3.2)² - (1.8)² equals

7.0

2.56

13.48

2.0

0.07

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 20 Ripoti

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Triangles And Polygons

Tazama Jibu

Swali 21 Ripoti

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

Tazama Jibu

Swali 22 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

Tazama Jibu

Swali 23 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Coordinate Geometry (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Coordinate Geometry

Angles

Tazama Jibu

Swali 24 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Progression (JAMB)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Progression

Quadratic Equations

Tazama Jibu

Swali 25 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Tazama Jibu

Swali 26 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 27 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 28 Ripoti

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

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Tazama Jibu

Swali 29 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 30 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Change Of Subject Of A Formula/Relation (WAEC)

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Tazama Jibu

Swali 31 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Soma maelezo ya somo kwenye Number Bases (JAMB)

Number Bases

Tazama Jibu

Swali 32 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Tazama Jibu

Swali 33 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

Tazama Jibu

Swali 34 Ripoti

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\(\sqrt{3}\)

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

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

Maelezo ya Majibu

Tazama Jibu

Swali 35 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Variation (WAEC)

Soma maelezo ya somo kwenye Variation (JAMB)

Variation

Tazama Jibu

Swali 36 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sequence And Series (WAEC)

Sequence And Series

Tazama Jibu

Swali 37 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 38 Ripoti

(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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

Tazama Jibu

Swali 39 Ripoti

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

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

Maelezo ya Majibu

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Tazama Jibu

Swali 40 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 41 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Probability (WAEC)

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Probability

Linear Inequalities

Tazama Jibu

Swali 42 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Percentages (WAEC)

Soma maelezo ya somo kwenye Fractions, Decimals, Approximations And Percentage (JAMB)

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Soma maelezo ya somo kwenye Financial Arithmetic (WAEC)

Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

Tazama Jibu

Swali 43 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Tazama Jibu

Swali 44 Ripoti

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

60cm²