JAMB UTME - Mathematics - 1978

Ibeere 1 Ìròyìn

Assuming log_e 4.4 = 1.4816 and log_e 7.7 = 2.0142, then the value of log_e \(\frac{7}{4}\) is

0.5326

3.4958

0.4816

0.0142

1.3594

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Logarithms

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Ibeere 2 Ìròyìn

In a geometric progression, the first term is 153 and the sixth term is \(\frac{17}{27}\). The sum of the first four terms is

\(\frac{860}{3}\)

\(\frac{680}{3}\)

\(\frac{608}{3}\)

\(\frac{680}{3}\)

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Sequence And Series

Progression

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Ibeere 3 Ìròyìn

If y = 2x² + 9x - 35. Find the range of values for which y < 0.

7 < x < \(\frac{5}{2}\)

-5 < 7 < x

-7 < x < 5

-7 < x < \(\frac{5}{2}\)

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Linear Inequalities

Quadratic Equations

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Ibeere 4 Ìròyìn

Multiply (x + 3y + 5) by (2x2 + 5y + 2)

2x² + 3yx² + 10xy + 15y² + 13y + 10x² + 2x + 10

2x³ + 6yx² + 5xy + 15y² + 31y + 5x² + 2x + 10

2x³ + 6xy² + 5xy + 15y² + 12y + 10x² + 2x = 10

2x² + 6xy² + 5xy + 15y² + 13y + 10x² + 2x + 10

2x³ + 2yx² + 10xy + 10y² + 31y + 5x² + 10

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Algebraic Expressions

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Ibeere 5 Ìròyìn

Two triangles have the same areas if

two sides in one triangle are equal to two sides in the other

three sides in one triangle are equal to three sides in the other

two angles in the triangle are equal to two angles in the other

three angles in one triangle are equal to three angles in the other

one side and the opposite angle in one triangle are equal to one side and the opposite angle in the other

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Triangles And Polygons

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Ibeere 6 Ìròyìn

The minimum point on the curve y = x2 - 6x + 5 is at

(1, 5)

(2, 3)

(-3, -4)

(3, -4)

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Quadratic Equations

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Ibeere 7 Ìròyìn

In the figure, 0 is the centre of the circle ABC, < CED = 30^o, < EDA = 40^o. What is the size of < ABC?

70^o

110^o

130^o

125^o

145^o

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Circles

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Ibeere 8 Ìròyìn

An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is

351

531

135

153

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Sequence And Series

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Ibeere 9 Ìròyìn

The angle of elevation of the top of a vertical tower from a point A on the ground is 60^o. From a point B, 2 units of distance further away from the foot of the tower, the angle of elevation of the tower is 45^o. Find the distance of A from the foot of the tower

3 + \(\sqrt{3}\)

5 + \(\sqrt{3}\)

3 - \(\sqrt{3}\)

\(\sqrt{3}\) - 1

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Circles

Coordinate Geometry

Graphs Of Linear And Quadratic Functions

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Ibeere 10 Ìròyìn

If (25)^{x - 1} = 64(\(\frac{5}{2}\))⁶, then x has the value

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Indices

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Ibeere 11 Ìròyìn

A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is

36\(\pi\)cm²

54\(\sqrt{3}\)cm²

\(\sqrt{3}\)cm²

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

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Circles

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Ibeere 12 Ìròyìn

The smallest number such that when it is divided by 8 has a remainder of 6 and when it is divided by 9, has a remainder of 7 is

387

493

502

441

634

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Number Bases

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Ibeere 13 Ìròyìn

Simplify \(\frac{(a^2 - \frac{1}{a}) (a^{\frac{4}{3}} + a^{\frac{2}{3}})}{a^2 - \frac{1}{a}^2}\)

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

a^{-\(\frac{1}{3}\)}

\(a^{2}\) + 1

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

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Algebraic Expressions

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Ibeere 14 Ìròyìn

The quantity (x + y) is a factor of

x² + y²

x³ - y³

2x² - 3xy + y² - x + 1

2x³ + 2x²y - xy + 3x - y² + 3y

x⁵ - y⁵

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Algebraic Expressions

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Ibeere 15 Ìròyìn

The locus of all points having a distance of 1 unit from each of the two fixed points a and b is

a line parallel to the line ab

a line perpendicular to the line ab through the mid-point of ab

a circle through a and b with centre at the mid-point of ab

a circle with centre at a and passes through b

a circle in a plane perpendicular to ab and centre at the mid-point of the line ab

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Ibeere 16 Ìròyìn

Arrange \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude.

\(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{71}{97}\)

\(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{3}{5}\) , \(\frac{71}{97}\)

\(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{71}{97}\), \(\frac{34}{59}\)

\(\frac{9}{16}\), \(\frac{3}{5}\), \(\frac{71}{97}\), \(\frac{34}{59}\)

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Fractions, Decimals And Approximations

Positive And Negative Integers, Rational Numbers

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Ibeere 17 Ìròyìn

In a soccer competition in one season, a club had scored the following goals: 2, 0, 3, 3, 2, 1, 4, 0, 0, 5, 1, 0, 2, 2, 1, 3, 1, 4, 1 and 1. The mean, median and mode are respectively

1, 1.8 and 1.5

1.8, 1.5 and 1

1.8, 1 and 1.5

1.51, 1 and 1.8

1.5, 1.8 and 1

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Integration

Linear Inequalities

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Ibeere 18 Ìròyìn

The set of value of x and y which satisfies the equations x² - y - 1 = 0 and y - 2x + 2 = 0 is

1, 0

1, 1

2, 2

0, 2

1, 2

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Algebraic Expressions

Quadratic Equations

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Ibeere 19 Ìròyìn

In the figure, AB is parallel to CD then x + y + z is

185^o

200^o

270^o

360^o

195^o

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Euclidean Geometry

Triangles And Polygons

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Ibeere 20 Ìròyìn

Simplify \(\frac{a - b}{a + b}\) - \(\frac{a + b}{a - b}\)

\(\frac{4ab}{a - b}\)

\(\frac{-4ab}{a^2 - b^2}\)

\(\frac{-4ab}{a^{-2} - b}\)

\(\frac{4ab}{a^{-2} - b^{-2}}\)

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Algebraic Fractions

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Ibeere 21 Ìròyìn

If x⁴ - kx³ + 10x² + 1x - 3 is divisible by (x - 1), and if when it is divided by (x + 2) the remainder is 27, find the constants k and 1

k = -7, 1 = -15

k = -15, 1 = -7

k = \(\frac{15}{3}\) , 1 = -7

k = \(\frac{7}{3}\) , 1 = -17

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Solution Of Linear Equations

Algebraic Expressions

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Ibeere 22 Ìròyìn

If x2 + 4 = 0, then x ?

-4

-2

None of the above

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Quadratic Equations

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Ibeere 23 Ìròyìn

A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cycular of radius 3cm and height 4cm.Which of the following statements is true?

the volume of the sphere is greater than the volume of the cone

the volume of the cone is less than the volume of the cylinder

the total surface area of the cone is greater than that of the sphere

The total surface area of the cylinder is less than that of the sphere

the total sufeac area of the cone is equal to that of the cylinder

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Volumes

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Ibeere 24 Ìròyìn

A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame

15sq.cm

20sq.cm

13sq.cm

16sq.cm

17sq.cm

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Lengths And Perimeters

Areas

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Ibeere 25 Ìròyìn

In the figure, DE//BC: DB//FE: DE = 2cm, FC = 3cm, AE = 4cm. Determine the length of EC.

4cm

6cm

3cm

2cm

1cm

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Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Ibeere 26 Ìròyìn

Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased 15%. Thus the fractional increase in the family food bill is now

\(\frac{1}{12}\)

\(\frac{6}{35}\)

\(\frac{19}{300}\)

\(\frac{7}{200}\)

\(\frac{5}{100}\)

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Fractions, Decimals And Approximations

Ratio, Proportions And Rates

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Ibeere 27 Ìròyìn

The sum of \(3\frac{7}{8}\) and \(1\frac{1}{3}\) is less than the difference between \(\frac{3}{8}\) and \(1\frac{2}{3}\) by:

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

5\(\frac{1}{4}\)

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

8\(\frac{1}{8}\)

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Fractions, Decimals And Approximations

Lengths And Perimeters

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Ibeere 28 Ìròyìn

In the Figure FD\\AC, the area of AEF = 6sq.cm. AE = 3cm, BC = 3cm, CD = 5cm, < BCD is an obtuse angle. Find the length of BD.

\(\sqrt{33}\)

2\(\sqrt{13}\)

4\(\sqrt{5}\)

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Ibeere 29 Ìròyìn

Five years ago, a father was 3 times as old as his son, now their combined ages amount to 110years. thus, the present age of the father is

75 years

60 years

98 years

80 years

105 years

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Solution Of Linear Equations

Quadratic Equations

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Ibeere 30 Ìròyìn

A pyramid is constructed on a cuboid. The figure has

twelve faces

thirteen vertices

fourteen edges

fifteen edges

sixteen edges

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Polynomials

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Ibeere 31 Ìròyìn

The sum of the progression is 1 + x + x2 + x3 + ......

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

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

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

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

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Sequence And Series

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Ibeere 32 Ìròyìn

The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?

N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\)

N = \(\frac{k P_{A} P_{B} }{D^2}\)

N = \(\frac{kD_AP_D}{B^2}\)

N = \(\frac{kD^2_AP_D}{B}\)

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Ibeere 33 Ìròyìn

Without using tables, simplify \(\frac{1n \sqrt{216} - 1n \sqrt{125} - 1n\sqrt{8}}{2(1n3 - 1n5)}\)

-3

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

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

1n 6 - 2 1n 5

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Surds (radicals)

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Ibeere 34 Ìròyìn

Given that \(a*b = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving * or ♦) for (a*b) ♦ (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers

ac + ab + bc + b + c + 1

ac + ab + a + c + 2

ab + ac + a + b + 1

ac + bc + ab + b + c + 2

ab + ac + 2a + b + c + 1

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Algebraic Fractions

Binary Operations

Progression

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Ibeere 35 Ìròyìn

Add the same number to the numerator and denominator of \(\frac{3}{18}\). If the resulting fraction is \(\frac{1}{2}\), then the number added is

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Fractions, Decimals And Approximations

Number Bases

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Ibeere 36 Ìròyìn

A triangle has angles 30o, 15o and 135o. The side opposite to the angle 30o is length 6cm. The side opposite to the angle 135o is equal to

12cm

6cm

6\(\sqrt{2}\)cm

12\(\sqrt{2}\)cm

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Angles

Triangles And Polygons

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Ibeere 37 Ìròyìn

Find the square root of 170 - 20\(\sqrt{30}\)

2 \(\sqrt{10}\) - 5\(\sqrt{3}\)

2 \(\sqrt{5}\) - 5\(\sqrt{6}\)

5 \(\sqrt{10}\) - 2\(\sqrt{3}\)

3 \(\sqrt{5}\) - 8\(\sqrt{6}\)

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Surds (radicals)

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Ibeere 38 Ìròyìn

If \(3x - \frac{1}{4})^{\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is

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

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

x < \(\frac{1}{4}\)

x < \(\frac{9}{16}\)

x > \(\frac{9}{16}\)

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Ibeere 39 Ìròyìn

A hollow right prism of equilateral triangular base of side 4cm is filled with water up to a certain height. If a sphere of radius \(\frac{1}{2}\)cm is immersed in the water, then the rise of water is

1cm

\(\sqrt{\frac{3\pi}{24}}\)

\(\frac{\pi}{24\sqrt{3}}\)

24\(\sqrt{3}\)

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Mensuration

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Ibeere 40 Ìròyìn

Evaluate without using tables sin(-1290^o)

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

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

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

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

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Sine, Cosine And Tangent Of An Angle

Trigonometry

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Ibeere 41 Ìròyìn

If the four interior angles of a quadrilateral are (p + 10)o, (p - 30)o, (2p - 450o, and (p + 15)o, then p is

125^o

82^o

135^o

105^o

60^o

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Triangles And Polygons

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Ibeere 42 Ìròyìn

What is the number whose logarithm to base 10 is 2.3482?

223

2228

2.235

22.37

0.2229

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Logarithms

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Ibeere 43 Ìròyìn

A man runs a distance of 9km at a constant speed for the first 4 km and then 2 km\h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4 km is

6 km/h

8 km/h

9 km\h

11 km\h

13 km\h

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Ibeere 44 Ìròyìn

A force of 5 units acts on a particle in the direction to the east and another force of 4 units acts on the particle in the direction north-east. The resultants of the two forces is

\(\sqrt{3}\) units

3 units

\(\sqrt{41 + 20 \sqrt{2}}\) units

\(\sqrt{41 - 20 \sqrt{2}}\) units

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Graphs Of Linear And Quadratic Functions

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Ibeere 45 Ìròyìn

A canal has rectangular cross section of width10cm and breadth 1m. If water of uniform density 1 gm cm-3 flows through it at a constant speed of1000mm per minute, the adjacent sea is

100000

1000000

120000

30000

350000

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Areas

Angles

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Ibeere 46 Ìròyìn

The vectors a and b are given in terms of two perpendicular units vectors i and j on a plane by a = 2i - 3j, b = -i + 2j. Find the magnitude of the vector a + 3b