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

JAMB UTME - Mathematics - 1979

Tambaya 1 Rahoto

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

Bayanin Amsa

Read lesson note on Circles (WAEC)

Circles

Duba Amsa

Tambaya 2 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

\(\frac{1}{3}\)k² sq. units

\(\frac{8}{9}\)k² sq. units

\(\frac{7}{9}\)k² sq. units

\(\frac{2}{3}\)k² sq. u

Bayanin Amsa

Read lesson note on Simple Operations On Algebraic Expressions (WAEC)

Simple Operations On Algebraic Expressions

Duba Amsa

Tambaya 3 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

16sq.cm

36sq.cm

Bayanin Amsa

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

Duba Amsa

Tambaya 4 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

N293.25

N360

Bayanin Amsa

Read lesson note on Percentages (WAEC)

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Percentages

Positive And Negative Integers, Rational Numbers

Financial Arithmetic

Duba Amsa

Tambaya 5 Rahoto

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.

Bayanin Amsa

Read lesson note on Integration (JAMB)

Read lesson note on Simple Operations On Algebraic Expressions (WAEC)

Integration

Simple Operations On Algebraic Expressions

Duba Amsa

Tambaya 6 Rahoto

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

Bayanin Amsa

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Inequalities (JAMB)

Linear Inequalities

Inequalities

Duba Amsa

Tambaya 7 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

45^o

25^o

Bayanin Amsa

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

Angles Of Elevation And Depression

Duba Amsa

Tambaya 8 Rahoto

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

2 x 10^-5

2 x 10^-1

2 x 10¹

2 x 10^-4

Bayanin Amsa

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Number Bases (WAEC)

Positive And Negative Integers, Rational Numbers

Number Bases

Duba Amsa

Tambaya 9 Rahoto

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

Bayanin Amsa

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 10 Rahoto

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

Bayanin Amsa

Read lesson note on Indices (WAEC)

Indices

Duba Amsa

Tambaya 11 Rahoto

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

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

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

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

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

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

Bayanin Amsa

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Algebraic Fractions (WAEC)

Algebraic Expressions

Algebraic Fractions

Duba Amsa

Tambaya 12 Rahoto

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

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

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

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

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

Bayanin Amsa

Read lesson note on Algebraic Expressions (WAEC)

Algebraic Expressions

Duba Amsa

Tambaya 13 Rahoto

What is log₇(49^a) - log₁₀(0.01)?

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

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

7^2a + 2

2a + 2

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

Bayanin Amsa

Read lesson note on Logarithms (WAEC)

Logarithms

Duba Amsa

Tambaya 14 Rahoto

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

Bayanin Amsa

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

Duba Amsa

Tambaya 15 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

12\(\pi\)cm³

\(\frac{38}{3}\)\(\pi\)cm³

\(\frac{40}{3}\)\(\pi\)cm³

\(\frac{32}{33}\)\(\pi\)cm³

Bayanin Amsa

Read lesson note on Volumes (WAEC)

Read lesson note on Areas (WAEC)

Volumes

Areas

Duba Amsa

Tambaya 16 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

4478cm

Bayanin Amsa

Read lesson note on Euclidean Geometry (JAMB)

Euclidean Geometry

Duba Amsa

Tambaya 17 Rahoto

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

5^{2x + 1}

5^{x + 1}

5^-5

5²

5³

Bayanin Amsa

Read lesson note on Number Bases (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Number Bases

Modular Arithmetic

Duba Amsa

Tambaya 18 Rahoto

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

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

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

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

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

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

Bayanin Amsa

Read lesson note on Fractions, Decimals And Approximations (WAEC)

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Algebraic Expressions

Ratio, Proportions And Rates

Duba Amsa

Tambaya 19 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

Bayanin Amsa

Read lesson note on Coordinate Geometry (WAEC)

Read lesson note on Angles (WAEC)

Coordinate Geometry

Angles

Duba Amsa

Tambaya 20 Rahoto

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

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

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

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

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

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

Bayanin Amsa

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

Duba Amsa

Tambaya 21 Rahoto

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

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

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

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

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

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

Bayanin Amsa

Read lesson note on Number Bases (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Number Bases

Surds (radicals)

Duba Amsa

Tambaya 22 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

Bayanin Amsa

Duba Amsa

Tambaya 23 Rahoto

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

60cm²

65cm²

72cm²

144cm²

156cm²

Bayanin Amsa

Duba Amsa

Tambaya 24 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

Bayanin Amsa

Read lesson note on Circles (WAEC)

Circles

Duba Amsa

Tambaya 25 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 = \(\frac{73}{27}\)

x = 7, y = -9

Bayanin Amsa

Read lesson note on Solution Of Linear Equations (WAEC)

Solution Of Linear Equations

Duba Amsa

Tambaya 26 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\(\frac{1}{2}\)

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

Bayanin Amsa

Read lesson note on Variation (WAEC)

Read lesson note on Variation (JAMB)

Variation

Duba Amsa

Tambaya 27 Rahoto

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

Bayanin Amsa

Duba Amsa

Tambaya 28 Rahoto

Find x in the diagram below.

3\(\sqrt{3}\)

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

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

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

Bayanin Amsa

Read lesson note on Modular Arithmetic (WAEC)

Read lesson note on Surds (radicals) (WAEC)

Modular Arithmetic

Surds (radicals)

Duba Amsa

Tambaya 29 Rahoto

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

Bayanin Amsa

Read lesson note on Change Of Subject Of A Formula/Relation (WAEC)

Read lesson note on Solution Of Linear Equations (WAEC)

Change Of Subject Of A Formula/Relation

Solution Of Linear Equations

Duba Amsa

Tambaya 30 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

Bayanin Amsa

Duba Amsa

Tambaya 31 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%

+100%

Bayanin Amsa

Duba Amsa

Tambaya 32 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

2\(\pi\)rh + 2\(\pi\)r²

Bayanin Amsa

Read lesson note on Volumes (WAEC)

Read lesson note on Lengths And Perimeters (WAEC)

Volumes

Lengths And Perimeters

Duba Amsa

Tambaya 33 Rahoto

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

3\(\sqrt{2}\)

2\(\sqrt{3}\)

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

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

Bayanin Amsa

Duba Amsa

Tambaya 34 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

N24000

N8000

Bayanin Amsa

Read lesson note on Ratio, Proportions And Rates (WAEC)

Read lesson note on Financial Arithmetic (WAEC)

Ratio, Proportions And Rates

Financial Arithmetic

Duba Amsa

Tambaya 35 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

3 roots with two equal and the third different

3 roots all equal

only one root

Bayanin Amsa

Read lesson note on Progression (JAMB)

Read lesson note on Quadratic Equations (WAEC)

Progression

Quadratic Equations

Duba Amsa

Tambaya 36 Rahoto

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

Bayanin Amsa

Read lesson note on Number Bases (WAEC)

Read lesson note on Number Bases (JAMB)

Number Bases

Duba Amsa

Tambaya 37 Rahoto

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

70^o

75^o

105^o

140^o

150^o

Bayanin Amsa

Read lesson note on Circles (WAEC)

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

Circles

Angles Of Elevation And Depression

Duba Amsa

Tambaya 38 Rahoto

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

Bayanin Amsa

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

Duba Amsa

Tambaya 39 Rahoto

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

Bayanin Amsa

Read lesson note on Quadratic Equations (WAEC)

Quadratic Equations

Duba Amsa

Tambaya 40 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

Bayanin Amsa

Read lesson note on Sine, Cosine And Tangent Of An Angle (WAEC)

Sine, Cosine And Tangent Of An Angle

Duba Amsa

Tambaya 41 Rahoto

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

Bayanin Amsa

Read lesson note on Probability (WAEC)

Read lesson note on Linear Inequalities (WAEC)

Probability

Linear Inequalities

Duba Amsa

Tambaya 42 Rahoto

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

20^o

40^o

60^o

80^o

100^o

Bayanin Amsa

Read lesson note on Indices (WAEC)

Indices

Duba Amsa

Tambaya 43 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\(\frac{2}{3}\)