JAMB UTME - Mathematics - 1979

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Duba Amsa

Tambaya 7 Rahoto

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

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

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

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

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

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

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Duba Amsa

Tambaya 8 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Sequence And Series (WAEC)

Sequence And Series

Duba Amsa

Tambaya 9 Rahoto

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

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

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

\(\frac{1 + x}{x}\) Amsar da ta dace

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

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

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Karanta bayanin darasi akan Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Duba Amsa

Tambaya 10 Rahoto

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

20^o

40^o Amsar da ta dace

60^o

80^o

100^o

Bayanin Amsa

Karanta bayanin darasi akan Indices (WAEC)

Indices

Duba Amsa

Tambaya 11 Rahoto

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

1.3979

2.3979

1.6021 Amsar da ta dace

2.6021

Bayanin Amsa

Karanta bayanin darasi akan Logarithms (WAEC)

Logarithms

Duba Amsa

Tambaya 12 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Duba Amsa

Tambaya 13 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Duba Amsa

Tambaya 14 Rahoto

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

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

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

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

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

\(\frac{1}{2}\) Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Surds (radicals)

Duba Amsa

Tambaya 15 Rahoto

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

2 x 10^-5

2 x 10^-1

2 x 10¹ Amsar da ta dace

2 x 10^-4

Bayanin Amsa

Karanta bayanin darasi akan Positive And Negative Integers, Rational Numbers (WAEC)

Karanta bayanin darasi akan Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Duba Amsa

Tambaya 16 Rahoto

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 Amsar da ta dace

2\(\pi\)rh + 2\(\pi\)r²

Bayanin Amsa

Karanta bayanin darasi akan Volumes (WAEC)

Karanta bayanin darasi akan Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

Duba Amsa

Tambaya 17 Rahoto

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

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

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

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

\(\frac{43}{5}\) Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Percentages (WAEC)

Karanta bayanin darasi akan Fractions, Decimals, Approximations And Percentage (JAMB)

Karanta bayanin darasi akan Surds (radicals) (WAEC)

Karanta bayanin darasi akan Financial Arithmetic (WAEC)

Percentages

Fractions, Decimals, Approximations And Percentage

Surds (radicals)

Financial Arithmetic

Duba Amsa

Tambaya 18 Rahoto

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 Amsar da ta dace

40^o

60^o

Bayanin Amsa

Karanta bayanin darasi akan Circles (WAEC)

Circles

Duba Amsa

Tambaya 19 Rahoto

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% Amsar da ta dace

+100%

Bayanin Amsa

Duba Amsa

Tambaya 20 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Circles (WAEC)

Circles

Duba Amsa

Tambaya 21 Rahoto

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 Amsar da ta dace

16sq.cm

36sq.cm

Bayanin Amsa

Karanta bayanin darasi akan Mensuration (JAMB)

Karanta bayanin darasi akan Measures Of Dispersion (JAMB)

Karanta bayanin darasi akan Lengths And Perimeters (WAEC)

Mensuration

Measures Of Dispersion

Lengths And Perimeters

Duba Amsa

Tambaya 22 Rahoto

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

6x² + xy - 15y² + 4z² + 11xz - 7yz Amsar da ta dace

6x² + 3xy - 15y² + 4z²

6x² + 3xy - y² + 4z²

6x² + 3xy - 15y + z²

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 23 Rahoto

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

60cm²

65cm²

72cm²

144cm² Amsar da ta dace

156cm²

Bayanin Amsa

Duba Amsa

Tambaya 24 Rahoto

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

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

\(\frac{2y^3} {y^2 - x^2}\) Amsar da ta dace

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

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

Bayanin Amsa

Karanta bayanin darasi akan Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 25 Rahoto

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 Amsar da ta dace

45^o

25^o

Bayanin Amsa

Karanta bayanin darasi akan Angles Of Elevation And Depression (WAEC)

Angles Of Elevation And Depression

Duba Amsa

Tambaya 26 Rahoto

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

70^o

75^o

105^o

140^o

150^o Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Circles (WAEC)

Karanta bayanin darasi akan Angles Of Elevation And Depression (WAEC)

Circles

Angles Of Elevation And Depression

Duba Amsa

Tambaya 27 Rahoto

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\(\frac{1}{2}\) Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Variation (WAEC)

Karanta bayanin darasi akan Variation (JAMB)

Variation

Duba Amsa

Tambaya 28 Rahoto

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 Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Triangles And Polygons (WAEC)

Triangles And Polygons

Duba Amsa

Tambaya 29 Rahoto

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 Amsar da ta dace

N293.25

N360

Bayanin Amsa

Karanta bayanin darasi akan Percentages (WAEC)

Karanta bayanin darasi akan Positive And Negative Integers, Rational Numbers (WAEC)

Karanta bayanin darasi akan Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

Duba Amsa

Tambaya 30 Rahoto

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

5^{2x + 1}

5^{x + 1}

5^-5 Amsar da ta dace

5²

5³

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Duba Amsa

Tambaya 31 Rahoto

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

x = 0 or 2

x = -2 or 4 Amsar da ta dace

x = 2

x = -4

x = 2 or 4

Bayanin Amsa

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Quadratic Equations

Duba Amsa

Tambaya 32 Rahoto

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 Amsar da ta dace

12\(\pi\)cm³

\(\frac{38}{3}\)\(\pi\)cm³

\(\frac{40}{3}\)\(\pi\)cm³

\(\frac{32}{33}\)\(\pi\)cm³

Bayanin Amsa

Karanta bayanin darasi akan Volumes (WAEC)

Karanta bayanin darasi akan Areas (WAEC)

Volumes

Areas

Duba Amsa

Tambaya 33 Rahoto

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 Amsar da ta dace

3 roots with two equal and the third different

3 roots all equal

only one root

Bayanin Amsa

Karanta bayanin darasi akan Progression (JAMB)

Karanta bayanin darasi akan Quadratic Equations (WAEC)

Progression

Quadratic Equations

Duba Amsa

Tambaya 34 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Coordinate Geometry (WAEC)

Karanta bayanin darasi akan Angles (WAEC)

Coordinate Geometry

Angles

Duba Amsa

Tambaya 35 Rahoto

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 Amsar da ta dace

10^o

Bayanin Amsa

Duba Amsa

Tambaya 36 Rahoto

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

x = -8, y = 1

x = -2, y = 4

x = \(\frac{-34}{27}\), y = \(\frac{73}{27}\) Amsar da ta dace

x = 7, y = -9

Bayanin Amsa

Karanta bayanin darasi akan Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Duba Amsa

Tambaya 37 Rahoto

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 Amsar da ta dace

N24000

N8000

Bayanin Amsa

Karanta bayanin darasi akan Ratio, Proportions And Rates (WAEC)

Karanta bayanin darasi akan Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Duba Amsa

Tambaya 38 Rahoto

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 Amsar da ta dace

Bayanin Amsa

Duba Amsa

Tambaya 39 Rahoto

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

45 Amsar da ta dace

Bayanin Amsa

Karanta bayanin darasi akan Number Bases (WAEC)

Karanta bayanin darasi akan Number Bases (JAMB)

Number Bases

Duba Amsa

Tambaya 40 Rahoto

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2 Amsar da ta dace

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

Bayanin Amsa

Karanta bayanin darasi akan Logarithms (WAEC)

Logarithms

Duba Amsa

Tambaya 41 Rahoto

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 Amsar da ta dace

4478cm

Bayanin Amsa

Karanta bayanin darasi akan Euclidean Geometry (JAMB)

Euclidean Geometry

Duba Amsa

Tambaya 42 Rahoto

(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 Amsar da ta dace

\(\frac{1}{3}\)k² sq. units

\(\frac{8}{9}\)k² sq. units

\(\frac{7}{9}\)k² sq. units

\(\frac{2}{3}\)k² sq. u

Bayanin Amsa

Karanta bayanin darasi akan Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

Duba Amsa

Tambaya 43 Rahoto

In the figure, \(\bigtriangleup\) ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to

3\(\sqrt{2}\)