JAMB UTME - Mathematics - 1978

Swali 1 Ripoti

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 2 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Triangles And Polygons

Tazama Jibu

Swali 3 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Areas (WAEC)

Soma maelezo ya somo kwenye Angles (WAEC)

Areas

Angles

Tazama Jibu

Swali 4 Ripoti

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\(\sqrt{6}\)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

Tazama Jibu

Swali 5 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 6 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Integration (JAMB)

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Integration

Linear Inequalities

Tazama Jibu

Swali 7 Ripoti

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sequence And Series (WAEC)

Sequence And Series

Tazama Jibu

Swali 8 Ripoti

Evaluate without using tables sin(-1290^o)

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sine, Cosine And Tangent Of An Angle (WAEC)

Soma maelezo ya somo kwenye Trigonometry (JAMB)

Sine, Cosine And Tangent Of An Angle

Trigonometry

Tazama Jibu

Swali 9 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 10 Ripoti

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

(1, 5)

(2, 3)

(-3, -4)

(3, -4)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Quadratic Equations

Tazama Jibu

Swali 11 Ripoti

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

351

531

135

153

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sequence And Series (WAEC)

Sequence And Series

Tazama Jibu

Swali 12 Ripoti

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Positive And Negative Integers, Rational Numbers (WAEC)

Fractions, Decimals And Approximations

Positive And Negative Integers, Rational Numbers

Tazama Jibu

Swali 13 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 14 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Volumes (WAEC)

Volumes

Tazama Jibu

Swali 15 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Number Bases (WAEC)

Number Bases

Tazama Jibu

Swali 16 Ripoti

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

4cm

6cm

3cm

2cm

1cm

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles And Intercepts On Parallel Lines (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles And Intercepts On Parallel Lines

Triangles And Polygons

Tazama Jibu

Swali 17 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Indices (WAEC)

Indices

Tazama Jibu

Swali 18 Ripoti

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

\(\sqrt{10}\)

2.2

Maelezo ya Majibu

Soma maelezo ya somo kwenye Introductory Calculus (WAEC)

Soma maelezo ya somo kwenye Vectors In A Plane (WAEC)

Introductory Calculus

Vectors In A Plane

Tazama Jibu

Swali 19 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Lengths And Perimeters

Areas

Tazama Jibu

Swali 20 Ripoti

If a circular paper disc is trimmed in such a way that its circumference is reduced in the ratio 2:5, In what ratio is the surface area reduced?

8 : 125

2 : 5

8 : 25

4 : 25

4 : 10

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Soma maelezo ya somo kwenye Areas (WAEC)

Circles

Areas

Tazama Jibu

Swali 21 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Algebraic Expressions

Tazama Jibu

Swali 22 Ripoti

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

185^o

200^o

270^o

360^o

195^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Euclidean Geometry (JAMB)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Euclidean Geometry

Triangles And Polygons

Tazama Jibu

Swali 23 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Circles (WAEC)

Circles

Tazama Jibu

Swali 24 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Graphs Of Linear And Quadratic Functions (WAEC)

Graphs Of Linear And Quadratic Functions

Tazama Jibu

Swali 25 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Fractions (WAEC)

Soma maelezo ya somo kwenye Binary Operations (JAMB)

Soma maelezo ya somo kwenye Progression (JAMB)

Algebraic Fractions

Binary Operations

Progression

Tazama Jibu

Swali 26 Ripoti

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

223

2228

2.235

22.37

0.2229

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Logarithms

Tazama Jibu

Swali 27 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Number Bases (WAEC)

Fractions, Decimals And Approximations

Number Bases

Tazama Jibu

Swali 28 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Surds (radicals) (WAEC)

Surds (radicals)

Tazama Jibu

Swali 29 Ripoti

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\(\sqrt{3}\)

Maelezo ya Majibu

Soma maelezo ya somo kwenye Mensuration (JAMB)

Mensuration

Tazama Jibu

Swali 30 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Linear Inequalities (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Linear Inequalities

Quadratic Equations

Tazama Jibu

Swali 31 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 32 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 33 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Angles (WAEC)

Soma maelezo ya somo kwenye Triangles And Polygons (WAEC)

Angles

Triangles And Polygons

Tazama Jibu

Swali 34 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Algebraic Expressions (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Algebraic Expressions

Quadratic Equations

Tazama Jibu

Swali 35 Ripoti

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Sequence And Series (WAEC)

Soma maelezo ya somo kwenye Progression (JAMB)

Sequence And Series

Progression

Tazama Jibu

Swali 36 Ripoti

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

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

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

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

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

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Ratio, Proportions And Rates (WAEC)

Fractions, Decimals And Approximations

Ratio, Proportions And Rates

Tazama Jibu

Swali 37 Ripoti

If sec² \(\theta\) + tan² \(\theta\) = 3, then the angle \(\theta\) is equal to

30^o

45^o

60^o

90^o

105^o

Maelezo ya Majibu

Soma maelezo ya somo kwenye Logarithms (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Logarithms

Quadratic Equations

Tazama Jibu

Swali 38 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Solution Of Linear Equations (WAEC)

Soma maelezo ya somo kwenye Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

Tazama Jibu

Swali 39 Ripoti

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

Maelezo ya Majibu

Tazama Jibu

Swali 40 Ripoti

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

Maelezo ya Majibu

Soma maelezo ya somo kwenye Fractions, Decimals And Approximations (WAEC)

Soma maelezo ya somo kwenye Lengths And Perimeters (WAEC)

Fractions, Decimals And Approximations

Lengths And Perimeters

Tazama Jibu

Swali 41 Ripoti

A pyramid is constructed on a cuboid. The figure has

twelve faces

thirteen vertices

fourteen edges

fifteen edges

sixteen edges

Maelezo ya Majibu

Soma maelezo ya somo kwenye Polynomials (JAMB)

Polynomials

Tazama Jibu

Swali 42 Ripoti

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 - \(\sqrt{3}\)