JAMB UTME - Mathematics - 1982

Question 1 Report

Write the equation 2 log2x - x log2(1 + y) = 3 in a form not involving logarithms

2^x(1 + y) = 3

2^x - x(1 + y) = 8

x² = 8(1 + y)^x

x² - x(1 + y) = 8

x² - (1 + y)² = 8

Answer Details

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Logarithms

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Question 2 Report

A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participant is

150^o

67\(\frac{1}{2}\)^o

67^o

135^o

68^o

Answer Details

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Representation Of Data

Measures Of Location

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Question 3 Report

If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\)

\(\frac{5}{2}\)

\(\frac{26}{7}\)

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

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Algebraic Fractions

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Question 4 Report

The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement?

0.05cm

0.5cm

0.045cm

0.005cm

0.004cm

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Quadratic Equations

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Question 5 Report

In a regular polygon of n sides, each interior angle is 144o. Find n

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Triangles And Polygons

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Question 6 Report

The graphical method of solving the equation x3 + 3x2 + 4x - 28 = 0 is by drawing the graphs of the curves

y = x³ and y = 3x² + x - 28

y = x³ + 3x² + 4x + 4 and the line y = \(\frac{28}{x}\)

y = x³ + 3x² + 4x and y

y = x² + 3x + 4 and y = \(\frac{28}{x}\)

y = x² + 3x + 4 and line y = 28x

Answer Details

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Variation

Algebraic Expressions

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Question 7 Report

A side of a rhombus is 2cm in length. An angle of the rhombus is 60^o. What is the length of the diagonal facing this angle?

2cm

8cm

4cm

2\(\sqrt{3}\)cm

16cm

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Question 8 Report

A housewife bought 3 kilograms of garri at N13.00 per kg. She deposited N160. 00 for half a cow and bought 24 oranges at 10k each. She came back home with N20.60. She therefore left home with

N220.00

N222.00

N201.40

N202.00

N180.80

Answer Details

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Percentages

Modular Arithmetic

Areas

Financial Arithmetic

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Question 9 Report

If f(x - 2) = 3x² + 4x + 1. Find the area of the sector

Answer Details

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Coordinate Geometry

Quadratic Equations

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Question 10 Report

Express 37.05 x 0.0042 in standard form

15.561 x 10²

1.5561 x 10^-4

1.556 x 10^-1

1.5561 x 10¹

1.55 x 10¹

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Fractions, Decimals And Approximations

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Question 11 Report

The currency used in a country is called 'Matimalik'(M) and is of base seven. A lady in that country bought 4 bags of rice at M56 per bag and and 3 tins of milk at M4 per tin. What is the total cost of the item she bought?

M246₇

M242₇

M236₇

M341₇

M338₇

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Number Bases

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Question 12 Report

A man bought wrist watch for N150 but was only able to sell it for N120. Find the loss per cent on the transaction

25%

11%

20%

80%

30%

Answer Details

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Percentages

Ratio, Proportions And Rates

Financial Arithmetic

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Question 13 Report

The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is

y = Q + \(\frac{P}{x^2}\)

y = Q + px

y = \(\frac{PQ}{x^2}\)

y = Q - \(\frac{P}{x^2}\)

Answer Details

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Variation

Progression

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Question 14 Report

Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\)

\(\alpha\) = 1, \(\beta\) = \(\frac{5}{7}\)

\(\alpha\)= 1, \(\beta\) = -\(\frac{5}{7}\)

\(\alpha\)= \(\frac{3}{5}\), \(\beta\) = -6

\(\alpha\)= 1, \(\beta\) = -\(\frac{3}{5}\)

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Algebraic Fractions

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Question 15 Report

In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR

150^o

30^o

60^o

120^o

90^o

Answer Details

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Polynomials

Loci

Simple Operations On Algebraic Expressions

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Question 16 Report

Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)

1, -2

-1, 2

2, 3

-1. -2

-2, -3

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Polynomials

Algebraic Fractions

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Question 17 Report

TP and TQ are tangents to a circle centre 0 and r is a point on the circumference of the circle as shown in the figure. If angle PTQ = 45^o, what is the magnitude of the angle PRO?

135

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

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

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Circles

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Question 18 Report

Rationalize the expression \(\frac{1}{\sqrt{2} + \sqrt{5}}\)

\(\frac{1}{3}\)(\(\sqrt{5} - \sqrt{2}\)

\(\frac{\sqrt{2}}{3}\) + \(\frac{\sqrt{5}}{5}\)

\(\sqrt{2} - \sqrt{5}\)

5(\(\sqrt{2} - \sqrt{5}\)

\(\frac{1}{3}\)(\(\sqrt{2} - \sqrt{5}\)

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Surds (radicals)

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Question 19 Report

The solution of the quadratic equation bx2 + cx + a = 0 is given by

x = b \(\pm\) \(\frac{\sqrt{b^2 - 4ac}}{2a}\)

x = c \(\pm\) \(\frac{\sqrt{b^2 - 4ab}}{2b}\)

x = -c \(\pm\) \(\frac{\sqrt{c^2 - 4ab}}{2b}\)

x = -b \(\pm\) \(\frac{\sqrt{b^2 - 4ac}}{2b}\)

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Quadratic Equations

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Question 20 Report

If the function y = 5x is graphed, what would be its intercept on the y-axis?

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

zero

Answer Details

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Solution Of Linear Equations

Simple Operations On Algebraic Expressions

Graphs Of Linear And Quadratic Functions

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Question 21 Report

Solve for x, If \(\frac{\frac{2}{x}}{\frac{p^2 + p^2}{p^2 + p^2}}\) = m

\(\frac{4pq}{m(p + q)}\)

\(\frac{2p^2q^2}{m(q^2 + p^2)}\)

\(\frac{2pq}{m(q^2 + p^2)}\)

\(\frac{2p^2q^2}{m(p^2)}\)

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Algebraic Fractions

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Question 22 Report

In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52^o. Find the angle marked m

128^o

52^o

104^o

64^o

116^o

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Circles

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Question 23 Report

What is the least possible value of \(\frac{9}{1 + 2x^2}\) if 0 \(\geq\) x \(\geq\) 2?

Answer Details

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Fractions, Decimals And Approximations

Number Bases

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Question 24 Report

A variable y is inversely proportional to x², when y = 10, x = 2. What is y when x = 10?

100

0.4

0.1

Answer Details

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Indices

Ratio, Proportions And Rates

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Question 25 Report

Find the median of the set set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113

117.5

118

117

116

113

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Linear Inequalities

Measures Of Location

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Question 26 Report

PQRS is a parallelogram with area 50 square cm and the side PQ is 10cm long. T is a point on RS and TF is the altitude of the triangle TPQ. Find TF

10cm

12.5cm

8cm

6cm

5cm

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Volumes

Loci

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Question 27 Report

The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are

(21cm³, 3cm³)

(24cm³, 3cm³)

(24cm³, 21cm³)

(72cm³, 9cm³)

(63cm³, 9cm³)

Answer Details

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Volumes

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Question 28 Report

A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60^o to the vertical?

It does not rise

2\(\sqrt{3}\) meters

3 meters

1 meters

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Circles

Angles Of Elevation And Depression

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Question 29 Report

In the diagram, angle QPR = 90^o, angle PSR = 90^o and PR = 5 units. Find the length of QS.

5 tan 25^o sin 65^o

5 cos 25^o sin 65^o

5 tan 25^o cos 65^o

cos 25^o cos 65^o

5 cosec 25^o

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Linear Inequalities

Areas

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Question 30 Report

Two distinct sectors i the same circle substend 100^o and 30^o respectively at the centre of the circle. Their corresponding arcs are in ratio

10:3

1:100

3:1

5:2

Answer Details

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Circles

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Question 31 Report

Which of the following lines is not parallel to the line 3y + 2x + 7 = 0?

3y + 2x - 7 = 0

9y + 6x + 17 = 0

24y + 16x + 19 = 0

3y - 2x + 7 = 0

15y + 10x - 13 = 0

Answer Details

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Linear Inequalities

Coordinate Geometry

Triangles And Polygons

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Question 32 Report

Seven years ago, the age of a father was three times that of his son, but in six years time the age of the son will be half that of his father, representing the present ages of the father and son by x and y, respectively, the two equations relating x and y are

3y - x = 0; 2y - x = 0

3y - x = 14; x - 2y = 6

3y - x =7; x - 2y = 6

3y - x = 14; y - 2x = 6

x + 3y = 7; x = 2y = 12

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Solution Of Linear Equations

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Question 33 Report

The arithmetic mean of the ages of 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl?

30 years

6 years

9 years

3 years

1 year

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Logical Reasoning

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Question 34 Report

The solution to the quadratic equation 5 + 3x - 2x² = 0 is

(\(\frac{5}{2}\), 1)

(5, 3)

-(\(\frac{5}{2}\), -1)

(\(\frac{5}{2}\), -1)

Answer Details

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Quadratic Equations

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Question 35 Report

A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.

42cm²

3cm²

21cm²

24cm²

12cm²

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Circles

Triangles And Polygons

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Question 36 Report

The area of the curved surface of the cone generated by the sector of a circle radius 6cm and are length 22cm is (\(\pi\) = \(\frac{22}{7}\))

58 sq.cm

34 sq.cm

132 sq.cm

77 sq.cm

66 sq.cm

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Coordinate Geometry

Areas

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Question 37 Report

Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r

4:105

7:15

20:21

2:35

3:20

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Sine, Cosine And Tangent Of An Angle

Surds (radicals)

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Question 38 Report

Determine the mean monthly salary of 50 employees of a company from the following frequency distribution.
\(\begin{array}{c|c} \text{Monthly salary} & \text{Frequency}\\\hline N200.00 & 10\\ N325.00 & 5\\N100.00 & 20\\N120.00 & 2\\ N60.00 & 10\\ N80.00 & 3\end{array}\)

N215.30

N134.10

N143.10

N80.00

N50.30

Answer Details

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Representation Of Data

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