FOR TERM 1

SEP. 2015

EXAMS

CBSE Continuous and Comprehensive Evaluation (CCE)

Published by :

Class

9

MATHEMATICSSUMMATIVE ASSESSMENT

& FORMATIVE

QUESTION BANKwith complete solutions

OUR DISTRIBUTORS

© Publisher

Typeset by : R.N. GraphicsPrinted by : Upkar Printing Unit

02

15

CONTENTS

iii

Syllabus v - viii

_______________________________________

1. Real Numbers 1 - 28

lTopic 1. Rational Number

lTopic 2. Irrational NumberthlTopic 3. n Root of Real Number

lTopic 4. Laws of Exponents with Integral Powers

lTopic 5. Rationalisation of Real Numbers

2. Polynomials 29 - 52

lTopic 1. Polynomials

lTopic 2. Remainder Theorem

lTopic 3. Factor Theorem

lTopic 4. Algebraic Identities

3. Introduction to Euclid's Geometry 53 - 63

lTopic 1. Euclid's Geometry

lTopic 2. Euclid's Postulates

4. Lines and Angles 64 - 89

lTopic 1. Different Types of Angles

lTopic 2. Transversal Line

lTopic 3. Angle Sum Property of a Triangle

5. Triangles 90 - 114

lTopic 1. Criteria for Congruence of Triangles

lTopic 2. Some Properties of Triangles

lTopic 3. Inequalities of a Triangle

6. Co-ordinate Geometry 115- 131

lTopic 1. Cartesian System

lTopic 2. Plotting a Point in a Plane

lTopic 3. Graph of Linear Equation

7. Areas 132- 147

lTopic 1. Area of Triangle

lTopic 2. Heron's Formula

lTopic 3. Application of Heron's Formula in finding Area of Quadrilaterals

_________________________________ 148 -168

Unit I : Number System

Unit II : Algebra

Unit III : Geometry

Unit IV : Co-ordinate Geometry

Unit V : Mensuration

Summative Assessment

Formative Assessment

PREFACE

iv

CBSE always believes in Global Trends of Educational Transformation. The CBSE

curriculum gets its lead from National Curriculum Framework – 2005 and Right to Free and

Compulsory Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has

been started to improve the quality of Education and was meant to lessen the burden of

studies on Students. CCE stands for Continuous & Comprehensive Evaluation. The term

'Continuous' in CCE refers to periodicity and regularity in assessment and the term

'Comprehensive' refers to overall assessment of the learner, in both curricular & co curricular

scheme of things.

These Oswaal CCE Question Banks for Classes IX & X have been written so as to

supplement the need of the students to prepare for these progressive assessments at school

during the entire year.

CCE Question Bank has been divided into two parts: Formative assessment (FA) &

Summative Assessment (SA). Formative part of the book will assist the students to prepare for

the frequent class room based evaluation, both as an individual and as a group activity. The

various formative techniques include Quizzes, Chapter assignment, Work sheets, Projects,

Seminar, Symposium, Action Plans, etc. These activities have been elaborated by CBSE Board

on www.cbse.nic.in. The students can read through all these components while revising a

chapter to be always prepared for the surprise FA's in the class.

Question Bank is divided in 3 sections i.e. reading, writing & Grammar & Literature Reader

& Long Reading Text. Each section is updated and in line with CBSE guidelines and syllabus.

Our team has given special focus while writing for language based subjects, because this

subject is not only important from examination point of view but also improves day to day

communication through reading, writing and grammar skills. Solutions are always checked

twice and tried to make precise as per marking scheme. Practically, this book provides

students everything they need to learn. Since we believe in continuous improvement, hence

this book is updated, reviewed every year with new questions, changes in syllabus and

reader's suggestions.

At last we would like to thank our authors, editors, reviewers and specially students who

regularly send us suggestions which helps in continuous improvement of this book and

makes this book stand in the category of “One of the Best”. Wish you all Happy Learning.

For ENGLISH

CBSE always believes in Global Trends of Educational Transformation. The CBSE

curriculum gets its lead from National Curriculum Framework – 2005 and Right to Free and

Compulsory Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has

been started to improve the quality of Education and was meant to lessen the burden of

studies on Students. CCE stands for Continuous & Comprehensive Evaluation. The term

'Continuous' in CCE refers to periodicity and regularity in assessment and the term

'Comprehensive' refers to overall assessment of the learner, in both curricular & co curricular

scheme of things.

These Oswaal CCE Question Banks for Classes IX & X have been written so as to

supplement the need of the students to prepare for these progressive assessments at school

during the entire year.

CCE Question Bank has been divided into two parts: Formative assessment (FA) &

Summative Assessment (SA). Formative part of the book will assist the students to prepare for

the frequent class room based evaluation, both as an individual and as a group activity. The

various formative techniques include Quizzes, Chapter assignment, Work sheets, Projects,

Seminar, Symposium, Action Plans, etc. These activities have been elaborated by CBSE Board

on www.cbse.nic.in. The students can read through all these components while revising a

chapter to be always prepared for the surprise FA's in the class.

Each chapter includes brief description and covers all typologies of Questions specified by

CBSE, with well-labelled and high quality figures / diagrams for easy and fast learning.

Solutions are always checked twice and tried to make precise as per marking scheme.

Practically, this book provides students everything they need to learn. Since we believe in

continuous improvement, hence this book is updated, reviewed every year with new

questions, changes in syllabus and reader's suggestions.

At last we would like to thank our authors, editors, reviewers and specially students who

regularly send us suggestions which helps in continuous improvement of this book and

makes this book stand in the category of “One of the Best”. Wish you all Happy Learning.

CBSE always believes in Global Trends of Educational Transformation. The CBSE curriculum

gets its lead from National Curriculum Framework – 2005 and Right to Free and Compulsory

Education Act – 2009. CBSE introduced CCE in the later half of 2009. CCE has been started to

improve the quality of Education and was meant to lessen the burden of studies on Students. CCE

stands for Continuous & Comprehensive Evaluation. The term 'Continuous' in CCE refers to

periodicity and regularity in assessment and the term 'Comprehensive' refers to overall assessment

of the learner, in both curricular & co curricular scheme of things.

These Oswaal CCE Question Banks for Classes IX & X have been written so as to supplement

the need of the students to prepare for these progressive assessments at school during the entire

year.

CCE Question Bank has been divided into two parts: Formative assessment (FA) & Summative

Assessment (SA). Formative part of the book will assist the students to prepare for the frequent class

room based evaluation, both as an individual and as a group activity. The various formative

techniques include Quizzes, Chapter assignment, Work sheets, Projects, Seminar, Symposium,

Action Plans, etc. These activities have been elaborated by CBSE Board on www.cbse.nic.in. The

students can read through all these components while revising a chapter to be always prepared for

the surprise FA's in the class.

Each chapter includes brief description and covers all typologies of Questions specified by

CBSE, with well-labelled and high quality figures / diagrams for easy and fast learning. Solutions

are checked twice and made precise as per the CBSE marking scheme. Practically, this book

provides students everything they need to learn. Since we believe in continuous improvement,

hence this book is updated, reviewed every year with new questions, changes in syllabus and

reader's suggestions.

At last we would like to thank our authors, editors, reviewers and specially students who

regularly send us suggestions which helps in continuous improvement of this book and makes this

book stand in the category of “One of the Best”. Wish you all Happy Learning.

MATHEMATICS

Class - IXFor Term I (April - September 2015)

v

Course StructureFIRST TERMTime : 3 Hours

II. ALGEBRA (Contd.) 23

III. GEOMETRY (Contd.) 17

IV. TRIGONOMETRY (Contd.) 08

V. PROBABILITY 08

VI. COORDINATE GEOMETRY 11

VII. MENSURATION 23

TOTAL 90

2 1Standard form of a quadratic equation ax + bx + c = 0, (a 0). Solution of the quadratic

equations (only real roots) by factorization, by completing the square and by using

quadratic formula. Relationship discriminant and nature of roots.

Problems related to day to day activities to be incorporated.

Motivation for studying Arithmetic Progression Derivation of standard results of finding ththe n term and sum of first n terms and their application in solving daily life problems.

Tangents to a circle motivated by chords drawn from points coming closer and closer to the

point.

(i) (Prove) The tangent at any point of a circle is perpendicular to the radius through the

point of contact.

(ii) (Prove) The lengths of tangents drawn from an external point to circle are equal.

(i) Division of a line segment in a given ratio (internally).

(ii) Tangent to a circle from a point outside it.

(iii) Construction of a triangle similar to a given triangle.

UNIT II : ALGEBRA (Contd.)

UNIT III : GEOMETRY (Contd.)

3. QUADRATIC EQUATIONS (15) Periods

4. ARITHMETIC PROGRESSIONS (8) Periods

2. CIRCLES (8) Periods

3. CONSTRUCTIONS (8) Periods

SYLLABUS

Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such

Factors and multiples. Zeros of a polynomial. State and motivate the Remainder Theorem with examples.

vi

... contd. Syllabus

UNIT IV : TRIGONOMETRY

UNIT V : STATISTICS AND PROBABILITY

UNIT VI : COORDINATE GEOMETRY

UNIT VII : MENSURATION

PRESCRIBED BOOKS :

3. HEIGHTS AND DISTANCES (8) Periods

2. PROBABILITY (10) Periods

1. LINES (In two dimensions) (14) Periods

1. AREAS RELATED TO CIRCLES (12) Periods

2. SURFACE AREAS AND VOLUME (12) Periods

Simple and believable problems on heights and distances. Problems should not involve

more than two right triangles. Angles of elevation / depression should be only 30°, 45°,

60°.

Classical definition of probability. Connection with probability as given in Class IX.

Simple problems on single events, not using set notation. '

Review the concepts of coordinate geometry done earlier including graphs of linear equations.

Awareness of geometrical representation of quadratic polynomials. Distance between two

points and section formula (internal). Area of a triangle.

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas

and perimeter / circumference of the above said plane figures. (In calculating area of segment

of a circle, problems should be restricted to central angle of 60°, 90°and 120° only. Plane figures

involving triangle, simple quadrilaterals and circle should be taken.)

(i) Problems on finding surface areas and volumes of combinations of any two of the

following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Frustum of a cone.

(ii) Problems involving converting one type of metallic solid into another and other mixed

problems. (Problems with combination of not more than two different solids be taken.)

Mathematics - Textbook for class IX - NCERT Publication

Mathematics - Textbook for class X - NCERT Publication

Guidelines for Mathematics Laboratory in Schools, class IX - CBSE Publication

Guidelines for Mathematics Laboratory in Schools, class X - CBSE Publication

A Handbook for Designing Mathematics Laboratory in Schools - NCERT Publication

Laboratory Manual - Mathematics, secondary stage - NCERT Publication

1.

2.

3.

4.

5.

6.

T

Area of cyclic Quadrilateral (with proof) - Brahma Gupta's Formula.

vii

... contd. Syllabus Q

ue

sti

on

Pa

pe

r D

esig

n F

orm

Ma

the

ma

tic

s

C

LA

SS I

X

Max. M

ark

s : 9

0T

IME

: 3

Ho

urs

(qu

esti

on

s o

f 10

Mar

ks)

.

viii

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

WRITING - NOTES

S U M M A T I V E SSA S S E S S M E N T

CHAPTER

1Real Numbers

SYLLABUS Review of representation of natural numbers, integers, rational numbers on the number line. Representation

of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.

Examples of non-recurring/non-termination decimals such as 2 , 3 , 5 etc. Existence of non-rational numbers (irrational numbers) such as 2 , 3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, every point on the number line represents a unique real number.

Rational numbers as recurring/terminating decimals. Existence of x for a given positive real number x (visual proof to be emphasized).

Definition of nth root of a real number. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by

particular cases, allowing learner to arrive at the general laws). Rationalisation (with precise meaning) of real numbers of the type (and their combinations).

1 + a b x

and 1

x + y, where x and y are natural numbers and a, b are integers.

INTRODUCTIONÅ Natural Numbers : Counting numbers are known as natural numbers, denoted by ‘N’.

N = {1, 2, 3, 4....... } Whole Numbers : All natural numbers together with ‘0’ (zero) form whole numbers, denoted by ‘W’.

W = {0, 1, 2, 3, 4, .......... } Integers : The collection of all whole numbers and negative of natural numbers are called integers, denoted by ‘Z’

or ‘I’.

Z Ior = {......... – 3, – 2, – 1}, 0, 1, 2, 3......,}

Negative Integers Zero Positive Integers

Real Numbers : All rational numbers and all irrational numbers taken together are known as real numbers, denoted by R. So, R = Q + Irrational numbers Irrational numbers = R – Q. In general, we can say that every real number can be represented by a unique point on the number line and vice

versa. Every point on the number line represents a unique real number.

UNIT-INumber System

2 ] OSWAAL CBSE CCE Question Bank (Term-1), Mathematics-IX

Number Line : On the right-hand side of 0, the points at distances of 1 unit, 2 units, 3 units etc. from 0 denote respectively the integers 1, 2, 3 etc.

Similarly, on the left side of 0, the points at distances of 1 unit, 2 units, 3 units etc. from 0 denote, respectively the integers –1, –2, –3 etc.

FLOWCHART

Real Number

Integer ( )Z

Whole Number ( )W

Natural Number ( )N

Non-TerminatingDecimal Number

Repeating DecimalNumber

Representation ofNumber on Real Line

RationalNumber ( )Q

IrrationalNumber

nth Root ofReal Number

Exponent ofReal Number Rationalisation

Topic-1Rational Number

QUICK REVIEWÅ Rational Number : A number ’r’ is called a rational number, if it can be written in the from p/q, where p and q are

co-prime integers and q ≠ 0, denoted by ‘Q’

For example :

12

, 34

, 45

, – 23

etc. are all rational numbers.

Symbolically, Q= , 0 and

pq p, q I

q

≠ ∈

Decimal Expansion of Real Numbers : The decimal expanation of real number used to represent a number on the number line.

If the decimal expansion of real number is either terminating or non-terminating recurring, than the real number called a Rational number.

Cases in Rational Number :

Case 1 : When Remainder becomes Zero— Every rational number

,pq

(q ≠ 0) can be expressed as a decimal. On

dividing p by q, when remainder becomes zero, then decimal is called terminating decimal.

e.g. : (i) 1

2 = 0.5

On dividing 1 by 2, we get value 0.5 i.e remainder equal to zero, so

12

is the terminating decimal.

(ii) 52

100= 0.52

On dividing 52 by 100, we get value 0.52 i.e remainder equal to zero, so

52100

is the terminating decimal.

Oswaal CBSE CCE Question Bank withcomplete solutions Mathematics For

Class 9 Term I April-Sep 2015

Publisher : Oswaal Books ISBN : 9789351274414 Author : Panel Of Experts

Type the URL : http://www.kopykitab.com/product/4252

Get this eBook

51%OFF