JAMB UTME - Mathematics - 1979

Ibeere 1 Ìròyìn

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

60cm²

65cm²

72cm²

144cm²

156cm²

Awọn alaye Idahun

Wo Idahun

Ibeere 2 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\(\sqrt{3}\)

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

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

Awọn alaye Idahun

Wo Idahun

Ibeere 3 Ìròyìn

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

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

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

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Percentages (WAEC)

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals, Approximations And Percentage (JAMB)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

Wo Idahun

Ibeere 4 Ìròyìn

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

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

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

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Wo Idahun

Ibeere 5 Ìròyìn

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

Awọn alaye Idahun

Wo Idahun

Ibeere 6 Ìròyìn

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Probability (WAEC)

Ka ìwé ẹ̀kọ́ nípa Linear Inequalities (WAEC)

Probability

Linear Inequalities

Wo Idahun

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Progression (JAMB)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Progression

Quadratic Equations

Wo Idahun

Ibeere 8 Ìròyìn

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (JAMB)

Number Bases

Wo Idahun

Ibeere 9 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Wo Idahun

Ibeere 10 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?

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Ratio, Proportions And Rates

Wo Idahun

Ibeere 11 Ìròyìn

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

70^o

75^o

105^o

140^o

150^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Ka ìwé ẹ̀kọ́ nípa Angles Of Elevation And Depression (WAEC)

Circles

Angles Of Elevation And Depression

Wo Idahun

Ibeere 12 Ìròyìn

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 13 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

Wo Idahun

Ibeere 14 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

Awọn alaye Idahun

Wo Idahun

Ibeere 15 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Percentages (WAEC)

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

Wo Idahun

Ibeere 16 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Volumes (WAEC)

Ka ìwé ẹ̀kọ́ nípa Areas (WAEC)

Volumes

Areas

Wo Idahun

Ibeere 17 Ìròyìn

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

1.3979

2.3979

1.6021

2.6021

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Logarithms (WAEC)

Logarithms

Wo Idahun

Ibeere 18 Ìròyìn

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

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

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

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Fractions, Decimals And Approximations (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

Wo Idahun

Ibeere 19 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 20 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Mensuration (JAMB)

Ka ìwé ẹ̀kọ́ nípa Measures Of Dispersion (JAMB)

Ka ìwé ẹ̀kọ́ nípa Lengths And Perimeters (WAEC)

Mensuration

Measures Of Dispersion

Lengths And Perimeters

Wo Idahun

Ibeere 21 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Linear Inequalities (WAEC)

Ka ìwé ẹ̀kọ́ nípa Inequalities (JAMB)

Linear Inequalities

Inequalities

Wo Idahun

Ibeere 22 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Positive And Negative Integers, Rational Numbers (WAEC)

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Wo Idahun

Ibeere 23 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Euclidean Geometry (JAMB)

Euclidean Geometry

Wo Idahun

Ibeere 24 Ìròyìn

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Indices (WAEC)

Indices

Wo Idahun

Ibeere 25 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Quadratic Equations (WAEC)

Quadratic Equations

Wo Idahun

Ibeere 26 Ìròyìn

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Triangles And Polygons (WAEC)

Triangles And Polygons

Wo Idahun

Ibeere 27 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\(\frac{1}{5}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Variation (WAEC)

Ka ìwé ẹ̀kọ́ nípa Variation (JAMB)

Variation

Wo Idahun

Ibeere 28 Ìròyìn

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.

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Integration (JAMB)

Ka ìwé ẹ̀kọ́ nípa Simple Operations On Algebraic Expressions (WAEC)

Integration

Simple Operations On Algebraic Expressions

Wo Idahun

Ibeere 29 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 = \(\frac{5 - 2d - b}{ad}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Change Of Subject Of A Formula/Relation (WAEC)

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Wo Idahun

Ibeere 30 Ìròyìn

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

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Number Bases (WAEC)

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Wo Idahun

Ibeere 31 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

Wo Idahun

Ibeere 32 Ìròyìn

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

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

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

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Surds (radicals)

Wo Idahun

Ibeere 33 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Coordinate Geometry (WAEC)

Ka ìwé ẹ̀kọ́ nípa Angles (WAEC)

Coordinate Geometry

Angles

Wo Idahun

Ibeere 34 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

Awọn alaye Idahun

Wo Idahun

Ibeere 35 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Circles (WAEC)

Circles

Wo Idahun

Ibeere 36 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

Awọn alaye Idahun

Wo Idahun

Ibeere 37 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Ratio, Proportions And Rates (WAEC)

Ka ìwé ẹ̀kọ́ nípa Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Wo Idahun

Ibeere 38 Ìròyìn

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

20^o

40^o

60^o

80^o

100^o

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Indices (WAEC)

Indices

Wo Idahun

Ibeere 39 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\(\frac{2}{3}\)

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Sequence And Series (WAEC)

Sequence And Series

Wo Idahun

Ibeere 40 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Wo Idahun

Ibeere 41 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%

Awọn alaye Idahun

Wo Idahun

Ibeere 42 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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Wo Idahun

Ibeere 43 Ìròyìn

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

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

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

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Algebraic Expressions (WAEC)

Ka ìwé ẹ̀kọ́ nípa Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Wo Idahun

Ibeere 44 Ìròyìn

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Awọn alaye Idahun

Ka ìwé ẹ̀kọ́ nípa Modular Arithmetic (WAEC)

Ka ìwé ẹ̀kọ́ nípa Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

Wo Idahun

Ibeere 45 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?