MATHEMATICS

2nd EDITION

I SBN SYLLABUS COVERED

YEAR 2021-22 “978-93-5423-973-1”

CENTRAL BOARD OF SECONDARY EDUCATION DELHI

PUBLISHED BY

COPYRIG HT

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TABLE OF CONTENTS l Latest CBSE Circular & Syllabus released on 22, July 2021 for Academic Year 2021-22 (CBSE Cir. No. Acad 53/2021)

8 - 13

l New Chapters, Topics and Typologies introduced by CBSE Board for

17 - 71

2021-22 Exam l Sample Question Paper

72 - 79

In each chapter, for better understanding, questions have been classified the typology issued by CBSE as : R

- Remembering,

A - Applying

U

- Understanding,

AE - Analyzing & Evaluating

C - Creating

Unit I : Number Systems

6. Triangles Term-I

1. Real Numbers



(Number System) Term-I

1 - 24



Topic 1. Rational and Irrational Numbers



*Topic 2. Real Numbers : nth Root and its



Rationalisation

2. Polynomials Term-II

Topic 1. Polynomials



Topic 2. Factorisation of Polynomials

25 - 57



of Triangles



Topic 2. Some More Properties of Triangles



Topic 3. Inequalities of a Triangle



Topic 3. Mid-Point Theorem and its Properties

190 - 232

Topic 1. Circle and its Related Terms Topic 2. Properties of Circle

3. Linear Equations in Two 58 - 82

Topic 3. Cyclic Quadrilateral



Topic 1. Introduction of Linear Equation

9. Constructions Term-II



Topic 2. Graphical Representation





4. Coordinate Geometry Term-I



83 - 97

Segments and Angles

Topic 2. Construction of Triangles with Some



Topic 1. Cartesian System





Topic 2. Plotting a Point in a Plane

Unit V : Mensuration

Unit IV : Geometry

233 - 252

Topic 1. Construction of Bisectors of Line

Unit III : Coordinate Geometry

5. Lines and Angles Term-I

158 - 189

Topic 1. Quadrilaterals and its Properties

8. Circles Term-II

Topic 4. Algebraic Identities

Variables Term-I

Topic 1. Criteria for Congruence

7. Quadrilaterals Term-II

Unit II : Algebra

125 - 157

Given Properties

10. Areas 98 - 124



Topic 1. Lines and Different Types of Angles



Topic 2. Parallel Lines and a Transversal Lines



Topic 3. Angle Sum Property of a Triangle

(Heron's Formula) Term-I

253 - 277



Topic 1. Area of a Triangle by Heron’s Formula



*Topic 2. Application of Heron’s Formula in



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Finding Areas of Quadrilaterals

TABLE OF CONTENTS Unit VI : Statistics & Probability

11. Surface Areas and Volumes Term-II

278 - 319

12. Statistics Term-I

320 - 353



Topic 1. Surface Area of Different 3-D Objects



Topic 1. Data and its terms



Topic 2. Volume of Different 3-D Objects



Topic 2. Graphical Re-presentation of data



Topic 3. Application



*Topic 3. Measures of Central Tendency

13. Probability Term-II

354 - 368

qq Kindly note that the following chapters/topics will not be covered in Term I & II Exams. They are just for your reference: (*) These are not in syllabus REAL NUMBERS(Number system) l Representation of terminating / non-terminating recurring decimals on the number line through successive magnification. l Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number. l Definition of nth root of a real number. POLYNOMIALS l Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. l Identities: x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) LINEAR EQUATIONS IN TWO VARIABLES l Problems on Ratio and Proportion CIRCLES l (Motivate) There is one and only one circle passing through three given non-collinear points l (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle. CONSTRUCTIONS l Construction of a triangle of given perimeter and base angles AREAS (Heron's formula) l its application in finding the area of a quadrilateral. STATISTICS l frequency polygons. Mean, median and mode of ungrouped data.

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LET'S BEGIN THE QUEST Why Oswaal One for All for you? Oswaal One for All, as the name suggests is a Complete Package for Excellence. It recognizes the need of students to not only get exam-oriented study material for success but also to save time and energy by having all the content in one place, in one book!! Alluring words like “Holistic” “Experiential” “Multi-Disciplinary” “Discovery Oriented” “Inquiry Driven” are peppered everywhere. Oswaal One for All is developed keeping in mind this noise. Innovative cognitive learning tools like Revision Notes, Mind Maps, Grammar Charts & Previous Years’ Board Questions, NCERT Questions, NCERT Exemplar Questions (in Math & Science), Questions from Deeksha & Questions for Olympiad & NTSE preparation, all put together make Oswaal One for All a Trusted Examination Companion for every student. Our book Oswaal One for All is going to break down the actual studying strategies. The purpose of this book is an elevated one: Building problem solvers, creative thinkers, dynamic innovators & shaping the youth in a way that they are future ready.

Learning How to learn “When using a deep approach, you intend to understand. Information may be memorized, but this is viewed as an almost unintentional by-product” Isn’t this moving? Isn’t this something our teachers have been advocating for a long time now? We don’t intend to undermine the importance of memory but we only mean that understanding will naturally lead to memories being formed.



Our Heartfelt Gratitude to all the Readers & Contributors We have taken due care in developing this book. There have been a lot of people who have helped us in our journey. We would like to offer heartfelt gratitude to all of them- our authors, editors, reviewers and especially students who regularly send us suggestions which help us in continuous improvement! Here are the names of the students who have helped us make this book better: 1.

Deepak from Faridabad

2.

Rizvi from Meerut

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Rani from Patna

4. Anuj from Varanasi

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Riya from Ghaziabad

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Oswaal Books wishes you all Happy Learning and a Successful 2021-22!

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WISH TO KNOW WHAT WE HAVE FOR YOU UNDER FREE RESOURCES? HERE YOU GO: Date Sheet

Latest Sample Question Paper

Board Syllabus 2022 Exams

Project Report

Solved Board Paper 2018, 2019, 2020

Lab Activities (Science & Math only)

Toppers’ Answer 2015 to 2019

Flowcharts & Mind Maps

How to decode icons given throughout the book?

Where to report any plausible content or technical error?

Write to us on: [email protected]

Topic-wise & Chapter-wise

and remember to mention the following.

Mnemonics Previous Years’ Board Papers Mind Maps

Full name of the book with its ISBN

Topper’s Answer

Mention the page number and specify the error

Concept Videos

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Highly Expected Questions

detail of the error.

for the upcoming exam

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CBSE CIRCULAR 2021-22 dsUæh; ek/;fed f'k{kk cksMZ

CENTRAL BOARD OF SECONDARY EDUCATION

NO.: F.1001/CBSE-Acad/Curriculum/2021

Date: July 22, 2021 Circular No: Acad- 53/2021

All the Heads of Schools affiliated to CBSE Subject:

Term wise syllabus for Board Examinations to be held in the academic session 2021-22 for Secondary and Senior Secondary classes and guidelines for the conduct of the Internal Assessment/Practicum/Project.

This is in continuation to Board’s circular number Acad 51/2021 dated July 05, 2021 regarding Special Scheme of Assessment for Board Examination for Classes X and XII for the Session 2021- 22. The syllabus for the two terms mentioned in the scheme in all subjects for classes IX to XII are hereby notified vides this circular. In addition to syllabus for term end board examinations, guidelines for the conduct of Internal Assessment/Practicum/Project are also enclosed. Schools are requested to share the term wise syllabus and guidelines for the conduct of board examinations and Internal Assessment / Practicum / Project available on CBSE Academic Website http://www.cbseacademic.nic.in at the link http://cbseacademic.nic.in/Term-wise-curriculum_2022.html with all their teachers and students.

(Dr. Joseph Emmanuel) Director (Academics)

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SYLLABUS Latest Syllabus issued by CBSE for Academic Year 2021-22

MATHEMATICS Class - IX (Code No. 041) COURSE STRUCTURE FIRST TERM One Paper 90 Minutes NO.

UNIT NAME

MARKS

I

NUMBER SYSTEMS

8

II

ALGEBRA

5

III

COORDINATE GEOMETRY

4

IV

GEOMETRY

13

V

MENSURATION

4

VI

STATISTICS & PROBABILITY

6 TOTAL

40

INTERNAL ASSESSMENT

10

TOTAL

50

UNIT- NUMBER SYSTEMS 1. NUMBER SYSTEM

Review of representation of natural numbers, integers, rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.



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



2 , 3 and their representation on the number line.

2. Rationalization (with precise meaning) of real numbers of the type

1 a+b x

and

1 x+ y

(and their

combinations) where x and y are natural number and a and b are integers.

3. 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.)

UNIT-ALGEBRA 2. LINEAR EQUATIONS IN TWO VARIABLES

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax+by+c=0. Explain that a linear equation in two variables has infinitely many (9)

SYLLABUS solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line. Graph of linear equations in two variables. Examples, problems from real life with algebraic and graphical solutions being done simultaneously UNIT-COORDINATE GEOMETRY 3. COORDINATE GEOMETRY

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane.

UNIT-GEOMETRY 4. LINES AND ANGLES

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180˚ and the converse.



2. (Prove) If two lines intersect, vertically opposite angles are equal.



3. (Motivate) Results on corresponding angles, alternate angles, interior angles when a transversal intersects two parallel lines.



4. (Motivate) Lines which are parallel to a given line are parallel.



5. (Prove) The sum of the angles of a triangle is 180˚.



6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

5. TRIANGLES

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).



2. (Motivate) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)



5. (Prove) The angles opposite to equal sides of a triangle are equal.



6. (Motivate) The sides opposite to equal angles of a triangle are equal.



7. (Motivate) Triangle in equalities and relation between 'angle and facing side' inequalities in triangles.

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SYLLABUS UNIT-MENSURATION 6. HERON’S FORMULA

Area of a triangle using Heron's formula (without proof)

UNIT-STATISTICS & PROBABILITY 7. STATISTICS

Introduction to Statistics: Collection of data, presentation of data — tabular form, ungrouped / grouped, bar graphs, histograms INTERNAL ASSESSMENT

MARKS

Periodic Tests

3

Multiple Assessments

2

Portfolio

2

Student Enrichment Activities-practical work

3

TOTAL MARKS

10

SECOND TERM No.

UNIT NAME

MARKS

I

ALGEBRA(Cont.)

12

II

GEOMETRY(Cont.)

15

III

MENSURATION(Cont.)

9

IV

STATISTICS & PROBABILITY(Cont)

4 Total

INTERNAL ASSESSMENT

40 10

TOTAL

50

UNIT-ALGEBRA 1. POLYNOMIALS

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem.



Recall of algebraic expressions and identities. Verification of identities

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SYLLABUS (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx (x ± y)3 = x3 + y3 + 3xy (x ± y)

x3 ± y3 = (x ± y) (x2 ± xy + y2)



and their use in factorization of polynomials.

UNIT-GEOMETRY 2. QUADRILATERALS

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.



2. (Motivate) In a parallelogram opposite sides are equal, and conversely.



3. (Motivate) In a parallelogram opposite angles are equal, and conversely.



4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.



5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.



6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

3. CIRCLES

Through examples, arrive at definition of circle and related concepts-radius, circumference, diameter, chord, arc, secant, sector, segment, subtended angle.



1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse.



2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.



3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre (or their respective centres) and conversely.



4. (Motivate) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.



5. (Motivate) Angles in the same segment of a circle are equal.



6. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

4. CONSTRUCTIONS

1. Construction of bisectors of line segments and angles of measure 60˚, 90˚, 45˚ etc., equilateral triangles.



2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle.

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SYLLABUS UNIT-MENSURATION 5. SURFACE AREAS AND VOLUMES

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

UNIT-STATISTICS & PROBABILITY 6. PROBABILITY

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real - life situations, and from examples used in the chapter on statistics). INTERNAL ASSESSMENT

MARKS

Periodic Tests

3

Multiple Assessments

2

Portfolio

2

Student Enrichment Activities-practical work

3

TOTAL MARKS

10 marks for the term



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HEAR IT FROM OUR HAPPY READERS!

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