Mathematics

Published by :

WITH COMPLETE SOLUTIONSQUESTION BANK

OSWAAL

OSWAAL BOOKS0562-2857671, 25277811/11, Sahitya Kunj, M.G. Road, Agra -282002 (UP) India

0562-2854582 contact@oswaalbooks.com www.OswaalBooks.com

Class

8

( iii )

CONTENTS

l Syllabus vii - viii

1. Rational Numbers 1 - 11

2. Linear Equations in One Variable 12 - 25

3. Understanding Quadrilaterals 26 - 37

4. Practical Geometry 38 - 48

5. Data Handling 49 - 61

6. Squares and Square Roots 62 - 71

7. Cubes and Cube Roots 72 - 84

8. Comparing Quantities 85 - 99

9. Algebraic Expressions and Identities 100 - 109

10. Visualising Solid Shapes 110 - 117

11. Mensuration 118 - 131

12. Exponents and Powers 132 - 142

13. Direct and Inverse Proportions 143 - 154

14. Factorisation 155 - 162

15. Introduction to Graphs 163 - 176

16. Playing with Numbers 177 - 184

ll

PREFACE

Year after year CBSE has been introducing changes in the curriculum of

various classes. We, at Oswaal Books, closely follow every change made by the

Board and endeavor to equip students with the latest study material to prepare

for the Examinations.

The latest offering from us are these Question Banks. These will provide

comprehensive practice material for every chapter. These are prepared by

experienced teachers who have translated their expertise into making

important questions from every chapter in order to facilitate wholesome

learning of every concept.

Highlights of our Question banks:

• Question Bank strictly as per the NCERT Curriculum

• Variety of Questions from NCERT Textbooks

• A synopsis of the important points from every chapter

• Value Based Questions as specified by CBSE Board

• Answers follow the marking scheme and the prescribed word limit

We feel extremely happy to offer our Question Banks and hope that with them,

every student will discover a more thorough way of preparing and thereby

excelling in their examinations. Though we have taken enough care to ensure

our products to be error free, yet we welcome any feedback or suggestions that

come our way for improvisation.

We wish you good luck for the forthcoming academic year!!

–Publisher

EARN WHILE YOU LEARNGive us Feedback and make money for it!

We at Oswaal Books try our best to make sure that our publications are error free. At the same time we also acknowledge that it is humane to make errors. It is this understanding that makes us strive to improve our publications on an on going basis.

So in case if you have any suggestions/comments or ideas, we will be excited to hear from you. You can either email us at contact@oswaalbooks.com or fill out the form below.

For each minor error, we will pay you Rs. 5 and for every major error we will pay you Rs. 10. These errors will be approved by our panel of authors and errors which have already been brought to our notice by some other reader will not be valid.

IMPORTANT NOTE : This is not a competition. This is an effort to make our books better for many more readers to come.

FEEDBACK - FORM

Date :

QUESTION BANK

Mathematics, Class-VIII

Your name with complete address & telephone number :__________________________________________

____________________________________________________________________________________________

First Name ______________________________ Last Name________________________________________

Date of Birth___________________________________________________________ Sex M/F______________

Address__________________________________________________________Pincode ___________________

Tel : Mobile E-mail _________________________________________________________________________

Name of your School / College _________________________________________________________________

___________________________________________________________________________________________

Name of the teacher or coaching class with address where you are studying :____________________

___________________________________________________________________________________________

Name and Address of the book-seller from where you have purchased this book :_________________

___________________________________________________________________________________________

Who recommended you this book :____________________________________________________________

___________________________________________________________________________________________

What else needs to be incorporated in the book according to your considered view :_______________

___________________________________________________________________________________________

Any error (s)/irrelevent matter : ______________________________________________________________

___________________________________________________________________________________________

Any suggestions you may be pleased to offer :___________________________________________________

___________________________________________________________________________________________

Fill in Hindi or English and send this Feedback Form to

SWAATI JAIN, Oswaal Books 'Oswaal House' 1/11 Sahitya Kunj, M.G. Road, AGRA-282 002.

Receiving Dt.:___________(Office use only)

Mathematics Syllabus

Number System (50 hrs)

(i) Rational Numbers:

w Properties of rational numbers. (including identities).

w Using general form of expression to describe properties

w Consolidation of operations on rational numbers.

w Representation of rational numbers on the number line

w Between any two rational numbers there lies another rational number (Making children see that if we take two rational numbers then unlike for whole numbers, in this case you can keep finding more and more numbers that lie between them.)

w Word problem (higher logic, two operations, including ideas like area)

(ii) Powers

w Integers as exponents.

w Laws of exponents with integral powers

(iii) Squares, Square roots, Cubes, Cube roots.

w Square and Square roots

w Square roots using factor method and division method for numbers containing (a) no more than total 4 digits and (b) no more than 2 decimal places

w Cubes and cubes roots (only factor method for numbers containing at most 3 digits)

w Estimating square roots and cube roots. Learning the process of moving nearer to the required number.

(iv) Playing with numbers

w Writing and understanding a 2 and 3 digit number in generalized form (100a + 10b + c , where a, b, c can be only digit 0-9) and engaging with various puzzles concerning this. (Like finding the missing numerals represented by alphabets in sums involving any of the four operations.) Children to solve and create problems and puzzles.

w Number puzzles and games

w Deducing the divisibility test rules of 2, 3, 5, 9, 10 for a two or three-digit number expressed in the general form.

Algebra (20 hrs)

(i) Algebraic Expressions

w Multiplication and division of algebraic exp.(Coefficient should be integers)

w Some common errors (e.g. 2 + x ≠ 2x, 7x + y ≠ 7xy )2 2 2 2 2

w Identities (a ± b) = a ± 2ab + b , a – b = (a – b) (a + b)

w Factorisation (simple cases only) as examples the following types 2 2 2

w a(x + y), (x ± y) , a – b , (x + a).(x + b)

w Solving linear equations in one variable in contextual problems involving multiplication and division (word problems) (avoid complex coefficient in the equations)

Ratio and Proportion (25 hrs)

w Slightly advanced problems involving applications on percentages, profit & loss, overhead expenses, Discount, tax.

w Difference between simple and compound interest (compounded yearly up to 3 years or half-yearly up to 3 steps only), Arriving at the formula for compound interest through patterns and using it for simple problems. Direct variation – Simple and direct word problems Inverse variation – Simple and direct word problems.

w Time & work problems– Simple and direct word problems

( vii )

w Geometry (40 hrs)

(i) Understanding shapes:

• Properties of quadrilaterals – Sum of angles of a quadrilateral is equal to 3600 (By verification)

• Properties of parallelogram (By verification)

(i) Opposite sides of a parallelogram are equal,

(ii) Opposite angles of a parallelogram are equal,

(iii) Diagonals of a parallelogram bisect each other. [Why (iv), (v) and (vi) follow from (ii)]

(iv) Diagonals of a rectangle are equal and bisect each other.

(v) Diagonals of a rhombus bisect each other at right angles.

(vi) Diagonals of a square are equal and bisect each other at right angles.

(ii) Representing 3-D in 2-D

w Identify and Match pictures with objects [more complicated e.g. nested, joint 2-D and 3-D shapes (not more than 2)].

w Drawing 2-D representation of 3-D objects (Continued and extended)

w Counting vertices, edges & faces & verifying Euler's relation for 3-D figures with flat faces (cubes, cuboids, tetrahedrons, prisms and pyramids)

(iii) Construction:

Construction of Quadrilaterals:

w Given four sides and one diagonal

w Three sides and two diagonals. Three sides and two included angles. Two adjacent sides and three angles.

Mensuration (15 hrs)

(i) Area of a trapezium and a polygon.

(ii) Concept of volume, measurement of volume using a basic unit, volume of a cube, cuboid and cylinder

(iii) Volume and capacity (measurement of capacity)

(iv) Surface area of a cube, cuboid, cylinder.

Data handling (15 hrs)

(i) Reading bar-graphs, ungrouped data, arranging it into groups, representation of grouped data through bar-graphs, constructing and interpreting bar-graphs.

(ii) Simple Pie charts with reasonable data numbers

(iii) Consolidating and generalising the notion of chance in events like tossing coins, dice etc. Relating it to chance in life events. Visual representation of frequency outcomes of repeated throws of the same kind of coins or dice. Throwing a large number of identical dice/coins together and aggregating the result of the throws to get large number of individual events. Observing the aggregating numbers over a large number of repeated events. Comparing with the data for a coin. Observing strings of throws, notion of randomness

Introduction to graphs (15 hrs)

PRELIMINARIES:

(i) Axes (Same units), Cartesian Plane

(ii) Plotting points for different kind of situations (perimeter vs length for squares, area as a function of side of a square, plotting of multiples of different numbers, simple interest vs number of years etc.)

(iii) Reading off from the graphs Reading of linear graphs Reading of distance vs time graph

________________

( viii )

LET’S REVISE Natural Numbers : Counting numbers starting from 1 are known as natural numbers and denoted

by N.i.e., N = {1, 2, 3, 4, 5...............}

Whole Numbers : All natural numbers together with 0 are called whole numbers and denotedby W.i.e., W = {0, 1, 2, 3, 4, 5..............}

Integers : All natural numbers and negatives of natural numbers included with 0 are calledintegers.i.e., ............. – 5, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5...................etc. are all integersWe can represent the integers on the number line as shown below :

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6XX'

Rational Number : A number is called rational if we can write the number in the form of ,pq

where p and q are integers and q 0

i.e.,

31 2 0 5 71 , 2 , 0 and , , are all rational numbers.

1 1 1 8 14 15

Between two rational numbers x and y, there exists a Rational number 2

·x y

The idea of ‘mean’ helps us to find rational numbers between two given rational numbers. We can find countless rational numbers between two rational numbers.

– xy is called the additive inverse of

xy and vice-versa.

yx

is called the multiplicative inverse or reciprocal of ·xy

The rational number 0 is the additive identity for all rational numbers because a number doesnot change when 0 is added to it.

The rational number 1 is the multiplicative identity for all rational numbers because on multiplyinga rational number with 1, its value does not change.

Rational numbers can be represented on a number line. The denominator of the rational number indicates the number of equal parts into which the first

unit has been divided whereas the numerator indicates as to how many of these parts are to betaken into consideration.

Rational Numbers

1CHAPTERUnit I

Number System

OSWAAL CBSE Question Bank, Mathematics - VIII2 ]

[A] Objective Type Questions [1 mark each]

(i) Multiple Choice Questions

1. Which of the following numbers is the additive inverse of 7

29 :

(A) 297 (B) –

297 (C) –

729 (D)

729

2. Which of the following numbers is the multiplicative inverse of 1531

:

(A) 3115 (B) –

3115 (C) –

1531 (D)

1531

3. Which of the following numbers has no multiplicative inverse :(A) 0 (B) 1 (C) – 1 (D) none of these

4. Which of the following numbers is the product of 6

13 and –

263

:

(A) 1 (B) – 4 (C) –266133 (D)

266133

5. Which of the following numbers is its own reciprocal :

(A) 10 (B) zero (C) 15 (D) 1

6. Which of the following numbers is the decimal form of 14

:

(A) – 0·25 (B) 2·5 (C) 0·25 (D) – 2·5

7. Which of the following numbers lies in the middle of 34

and 74

:

(A) 5·0 (B) 3·0 (C) 2·5 (D) 1·258. Which pair of following numbers are respectively the additive and multiplicative

identities :(A) 2 and 0 (B) 1 and – 1 (C) – 1 and 0 (D) 0 and 1

9. Which of the following numbers is the simplest form of 3 1 5 :4 4 4

(A) 94

(B) –34

(C) –94

(D) 74

10. Which of the following properties indicates the given operation

1 3 1 1 3 15 5 7 5 5 7

(A) commutative (B) associative (C) distributive (D) none of these

11. What should be added to 34

to get ‘– 1’ ?

(A) 14

(B) 14

(C) 1 (D) 34

12. For rational numbers, multiplicative identity is :(A) 0 (B) – 1 (C) 2 (D) 1

13. The value of 3 4 15 145 7 16 9

is equal to :

(A) 14

(B) 12

(C) 18

(D) 16

14. The reciprocal of

45

is :

(A) 45 (B)

54

(C) 54

(D) 45

15. Which of the following numbers has no reciprocal ?(A) – 3 (B) – 2 (C) – 1 (D) 0

16. Which of the following is the product of 7

8 and

2?

21

(A) 1

12 (B) 12 (C)

6316

(D) 16147

17. What should be subtracted from 35

to get – 2 ?

(A) 75

(B) 13

5(C)

135

(D) 75

18. Additive inverse of 59

is :

(A) 95

(B) 34

(C) 59

(D) 95

19. A rational number between 23

and 14

is :

(A) 5

12(B)

512

(C) 5

24(D)

524

20.

4 112 7?

3 5 15 20

(A) 15

(B) 415

(C) 1360

(D) 730

(ii) Fill in the Blanks : [NCERT]1. Zero has .................... reciprocal.2. The numbers .................... and ................ are their reciprocals.3. The reciprocal of –5 is ....................

4. Reciprocal of 1,

x wherex 0 is ...................

5. The product of two rational numbers is always a ....................

(iii) True/False :

1. The additive inverse of 2 2

is ·3 3

2.12

is a natural number.

3. The multiplicative inverse of 12

is 2.

RATIONAL NUMBERS [ 3

OSWAAL CBSE Question Bank, Mathematics - VIII4 ]

4. The negative of 2 is 1

.2

5. If a and b are two consecutive rational numbers, then

.2

a bb [NCERT]

ANSWERS

[A] Objective Type Questions

(i) Multiple Choice Questions :

1. (C) 729

2. (A) 3115

3. (B) 1 4. (B) – 4

5. (D) 1 6. (C) 0·25 7. (D) 1·25 8. (B) 1 and – 1

9. (B) 34

10. (B) associative 11. (B) 14 12. (D) 1

13. (B) 12

14. (C) 54

15. (D) 0 16. (A) 1

12

17. (D) 75 18. (C)

59 19. (D)

524

20. (C) 13

·60

(ii) Fill in the Blanks :1. no 2. 1 and – 1 3. 1

5 4. x5. rational number.

(iii) True/False :1. True 2. False 3. True 4. False5. True

[B] Very Short Answer Type Questions [1 mark each]

Q. 1. Is 1 the multiplicative identity for integers ? Also for whole numbers.Ans. Yes, 1 is the multiplicative identity for integers as well as for whole numbers. 1

Q. 2. Write the additive inverse of 5

·9 [NCERT]

Ans. Additive inverse of 5 5

is ·9 91

Q. 3. Write the multiplicative inverse of 13

·19[NCERT]

Ans. The multiplicative inverse of 1319

is 19

·131

Q 4. Write the rational number that does not have a reciprocal.Ans. The rational number ‘0’ does not have a reciprocal. 1Q 5. Use sign < or > to fill in the box :

10 5

7 7

Ans. 10 5

7 7 1

Q. 6. Is 0·7 the multiplicative inverse of 3

1 ?7

Give reasons. [NCERT]

Ans. Yes, since 0·7 = 7

10½

Multiplicative inverse of 7

10 =

107

= 3

1 ·7

½

Q. 7. The rational numbers that are equal to their reciprocals.Ans. The rational numbers 1 and (– 1) are equal to their reciprocals respectively. 1Q. 8. The rational number that is equal to its negative.Ans. The rational number 0 is equal to its negative. 1Q. 9. How many integers are there between – 1 and 1 ?Ans. There is only one integer between – 1 and 1. It is 0. 1Q. 10. How many integers are there between – 9 and – 10 ?Ans. There is no integer between – 9 and – 10. 1

[C] Short Answer Type Questions [2 marks each]

Q. 1. Find using distributivity :

37 7 55 12 5 12

Sol.

37 7 55 12 5 12 =

37 55 12 12

1

=3 57

5 12

= 7 2 7 1 7

·5 12 5 6 301

Q. 2. Multiply 6

13 by the reciprocal of 7

·16

Sol. Reciprocal of 7 16

is ·16 7 1

Now,6 16

13 7 =

6 ( 16) 96·13 7 91

1

Q. 3. Simplify : 16 939 26

Sol. We have

16 939 ( 26) =

91639 26

½

Now, the LCM of 39 and 26 is 78.

Rewriting 1639

and 926

in such a manner they have the same denominator 78.

1639

=

16 239 2

= 3278

½

926

=

9 3

26 3 =

2778

16 939 26

=

32 ( 27)78 78

½

= 32 ( 27)78

=32 27

78 =

578

. ½

RATIONAL NUMBERS [ 5

OSWAAL CBSE Question Bank, Mathematics - VIII6 ]

Q. 4. Verify the following :

5 38 5

=53

5 8

Sol. Verification : L.H.S. = 5 38 5

1

= 5 5 3 8

40

=

25 24 1

40 40

R.H.S. =53

5 8

1

= 3 8 ( 5) 5

40

=

24 25 1

40 40 L.H.S. = R.H.S. Verified.

Q. 5. Subtract 3 5

from ·8 7

Sol. The additive inverse of 3 3 is ·8 8

1

5 37 8

= 5 37 8

= ( 5) 8 3 756

= 40 2156

=19

56

. 1

Q. 6. What should be subtract from – 34 , so as to get

56 ? [NCERT]

Sol. Suppose x is the rational number to be subtracted from 34

to get 5

.6

Then ½

34

x =56

3 54 6

= x

x =3 54 6

x =( 3) 3 ( 5) 2

12

1½{ LCM of 4 and 6 is 12}

x =9 ( 10)

12

x =19

12

. ½

Oswaal CBSE Question BanksMathemaitcs For Class 8

Publisher : Oswaal Books ISBN : 9789386681607 Author : Panel Of Experts

Type the URL : http://www.kopykitab.com/product/11512

Get this eBook

25%OFF