JAMB UTME - Mathematics - 1979

Ajụjụ 1 Ripọtì

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\(\sqrt{3}\) Azịza ziri ezi

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

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

Akọwa Nkọwa

Lee Azịza

Ajụjụ 2 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Probability (WAEC)

Gụọ akwụkwọ nkuzi na Linear Inequalities (WAEC)

Probability

Linear Inequalities

Lee Azịza

Ajụjụ 3 Ripọtì

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

20^o

40^o Azịza ziri ezi

60^o

80^o

100^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Indices (WAEC)

Indices

Lee Azịza

Ajụjụ 4 Ripọtì

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

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

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

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

\(\frac{43}{5}\) Azịza ziri ezi

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Percentages (WAEC)

Gụọ akwụkwọ nkuzi na Fractions, Decimals, Approximations And Percentage (JAMB)

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Gụọ akwụkwọ nkuzi na Financial Arithmetic (WAEC)

Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

Lee Azịza

Ajụjụ 5 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Coordinate Geometry (WAEC)

Gụọ akwụkwọ nkuzi na Angles (WAEC)

Coordinate Geometry

Angles

Lee Azịza

Ajụjụ 6 Ripọtì

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

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

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

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

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Lee Azịza

Ajụjụ 7 Ripọtì

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

6x² + xy - 15y² + 4z² + 11xz - 7yz Azịza ziri ezi

6x² + 3xy - 15y² + 4z²

6x² + 3xy - y² + 4z²

6x² + 3xy - 15y + z²

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Algebraic Expressions

Lee Azịza

Ajụjụ 8 Ripọtì

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 Azịza ziri ezi

3 roots with two equal and the third different

3 roots all equal

only one root

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Progression (JAMB)

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Progression

Quadratic Equations

Lee Azịza

Ajụjụ 9 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Sequence And Series (WAEC)

Sequence And Series

Lee Azịza

Ajụjụ 10 Ripọtì

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

2 x 10^-5

2 x 10^-1

2 x 10¹ Azịza ziri ezi

2 x 10^-4

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Positive And Negative Integers, Rational Numbers (WAEC)

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Lee Azịza

Ajụjụ 11 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 12 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Solution Of Linear Equations (WAEC)

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

Lee Azịza

Ajụjụ 13 Ripọtì

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 Azịza ziri ezi

N24000

N8000

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Ratio, Proportions And Rates (WAEC)

Gụọ akwụkwọ nkuzi na Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Lee Azịza

Ajụjụ 14 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Lee Azịza

Ajụjụ 15 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Lee Azịza

Ajụjụ 16 Ripọtì

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\(\frac{1}{2}\) Azịza ziri ezi

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Variation (WAEC)

Gụọ akwụkwọ nkuzi na Variation (JAMB)

Variation

Lee Azịza

Ajụjụ 17 Ripọtì

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 Azịza ziri ezi

x = 2, y = -3

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Quadratic Equations

Lee Azịza

Ajụjụ 18 Ripọtì

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

60cm²

65cm²

72cm²

144cm² Azịza ziri ezi

156cm²

Akọwa Nkọwa

Lee Azịza

Ajụjụ 19 Ripọtì

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 Azịza ziri ezi

2\(\pi\)rh + 2\(\pi\)r²

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Volumes (WAEC)

Gụọ akwụkwọ nkuzi na Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

Lee Azịza

Ajụjụ 20 Ripọtì

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 Azịza ziri ezi

10^o

Akọwa Nkọwa

Lee Azịza

Ajụjụ 21 Ripọtì

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

45 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Number Bases (JAMB)

Number Bases

Lee Azịza

Ajụjụ 22 Ripọtì

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

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

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

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

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

\(\frac{1}{2}\) Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Surds (radicals)

Lee Azịza

Ajụjụ 23 Ripọtì

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

5^{2x + 1}

5^{x + 1}

5^-5 Azịza ziri ezi

5²

5³

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Number Bases (WAEC)

Gụọ akwụkwọ nkuzi na Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Lee Azịza

Ajụjụ 24 Ripọtì

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 Azịza ziri ezi

4478cm

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Euclidean Geometry (JAMB)

Euclidean Geometry

Lee Azịza

Ajụjụ 25 Ripọtì

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 Azịza ziri ezi

40^o

60^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 26 Ripọtì

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 Azịza ziri ezi

12\(\pi\)cm³

\(\frac{38}{3}\)\(\pi\)cm³

\(\frac{40}{3}\)\(\pi\)cm³

\(\frac{32}{33}\)\(\pi\)cm³

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Volumes (WAEC)

Gụọ akwụkwọ nkuzi na Areas (WAEC)

Volumes

Areas

Lee Azịza

Ajụjụ 27 Ripọtì

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 Azịza ziri ezi

16sq.cm

36sq.cm

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Mensuration (JAMB)

Gụọ akwụkwọ nkuzi na Measures Of Dispersion (JAMB)

Gụọ akwụkwọ nkuzi na Lengths And Perimeters (WAEC)

Mensuration

Measures Of Dispersion

Lengths And Perimeters

Lee Azịza

Ajụjụ 28 Ripọtì

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

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

c = \(\frac{2d - 5 - abd}{ad}\) Azịza ziri ezi

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Change Of Subject Of A Formula/Relation (WAEC)

Gụọ akwụkwọ nkuzi na Solution Of Linear Equations (WAEC)

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Lee Azịza

Ajụjụ 29 Ripọtì

Find x in the diagram below.

3\(\sqrt{3}\)

\(\frac{3(\sqrt{3} - 1)}{\sqrt{3} + 1}\) Azịza ziri ezi

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Modular Arithmetic (WAEC)

Gụọ akwụkwọ nkuzi na Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

Lee Azịza

Ajụjụ 30 Ripọtì

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

x = 0 or 2

x = -2 or 4 Azịza ziri ezi

x = 2

x = -4

x = 2 or 4

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Quadratic Equations (WAEC)

Quadratic Equations

Lee Azịza

Ajụjụ 31 Ripọtì

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 Azịza ziri ezi

All of the above

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Linear Inequalities (WAEC)

Gụọ akwụkwọ nkuzi na Inequalities (JAMB)

Linear Inequalities

Inequalities

Lee Azịza

Ajụjụ 32 Ripọtì

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

\(\frac{1}{6}\) Azịza ziri ezi

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

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

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Fractions, Decimals And Approximations (WAEC)

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Gụọ akwụkwọ nkuzi na Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

Lee Azịza

Ajụjụ 33 Ripọtì

(3.2)² - (1.8)² equals

7.0 Azịza ziri ezi

2.56

13.48

2.0

0.07

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Indices (WAEC)

Indices

Lee Azịza

Ajụjụ 34 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Lee Azịza

Ajụjụ 35 Ripọtì

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 Azịza ziri ezi

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Triangles And Polygons (WAEC)

Triangles And Polygons

Lee Azịza

Ajụjụ 36 Ripọtì

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. Azịza ziri ezi

13.33 meter/sec.

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Integration (JAMB)

Gụọ akwụkwọ nkuzi na Simple Operations On Algebraic Expressions (WAEC)

Integration

Simple Operations On Algebraic Expressions

Lee Azịza

Ajụjụ 37 Ripọtì

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

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

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

\(\frac{1 + x}{x}\) Azịza ziri ezi

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Gụọ akwụkwọ nkuzi na Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Lee Azịza

Ajụjụ 38 Ripọtì

Solve the simultaneous linear equations: 2x + 5y = 11, 7x + 4y = 2

x = -8, y = 1

x = -2, y = 4

x = \(\frac{-34}{27}\), y = \(\frac{73}{27}\) Azịza ziri ezi

x = 7, y = -9

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Lee Azịza

Ajụjụ 39 Ripọtì

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2 Azịza ziri ezi

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Logarithms (WAEC)

Logarithms

Lee Azịza

Ajụjụ 40 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Lee Azịza

Ajụjụ 41 Ripọtì

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

70^o

75^o

105^o

140^o

150^o Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Gụọ akwụkwọ nkuzi na Angles Of Elevation And Depression (WAEC)

Circles

Angles Of Elevation And Depression

Lee Azịza

Ajụjụ 42 Ripọtì

(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 Azịza ziri ezi

\(\frac{1}{3}\)k² sq. units

\(\frac{8}{9}\)k² sq. units

\(\frac{7}{9}\)k² sq. units

\(\frac{2}{3}\)k² sq. u

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

Lee Azịza

Ajụjụ 43 Ripọtì

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 Azịza ziri ezi

\(\frac{\pi}{2}\)cm²

\(\frac{\pi}{3}\)cm²

\(\pi\)cm²

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Circles (WAEC)

Circles

Lee Azịza

Ajụjụ 44 Ripọtì

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

1.3979

2.3979

1.6021 Azịza ziri ezi

2.6021

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Logarithms (WAEC)

Logarithms

Lee Azịza

Ajụjụ 45 Ripọtì

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 Azịza ziri ezi

N293.25

N360

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Percentages (WAEC)

Gụọ akwụkwọ nkuzi na Positive And Negative Integers, Rational Numbers (WAEC)

Gụọ akwụkwọ nkuzi na Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

Lee Azịza

Ajụjụ 46 Ripọtì

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 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Fractions, Decimals And Approximations (WAEC)

Gụọ akwụkwọ nkuzi na Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Ratio, Proportions And Rates

Lee Azịza

Ajụjụ 47 Ripọtì

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

8 Azịza ziri ezi

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Indices (WAEC)

Indices

Lee Azịza

Ajụjụ 48 Ripọtì

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 Azịza ziri ezi

42^o

Akọwa Nkọwa

Lee Azịza

Ajụjụ 49 Ripọtì

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

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

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

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

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

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Algebraic Expressions (WAEC)

Algebraic Expressions

Lee Azịza

Ajụjụ 50 Ripọtì

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 Azịza ziri ezi

45^o

25^o

Akọwa Nkọwa

Gụọ akwụkwọ nkuzi na Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Lee Azịza






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