HELLO! Friends, this academic year and life will never be the same for most of us. We all have lost someone dear to us because of this deadly second wave of Covid-19. Normally here, we talk about what’s new in our books. But instead, we just want to say Thank you to our country’s Doctors and especially Nurses and Sanitary workers. Nothing matters more to us all than the good health of our family. And the above public servants have truly risen to the task. Not to mention, the hard-working Teachers, who aren’t really appreciated enough. Especially at this difficult time, when they are trying to balance both personal and teaching responsibilities that have actually doubled. This year is all about maintaining caution, strengthening determination and more self-learning. And we continue to be thankful and do our very small part in providing quality books at affordable prices. Stay safe!

CENTRAL BOARD OF SECONDARY EDUCATION (An Autonomous Organisation under the Ministry of Education , Govt. of India)

Dated: 22.04.2021 CBSE/ACAD./DIR./2021/

Circular No 31/2021

All Heads of CBSE affiliated schools Subject: Assessment and Evaluation Practices of the Board for the Session 2021-22 In order to move towards Competency Based Education (CBE), the Board vide Circular No. Acad- 05/2019 dated 18.01.2019 had asked schools to adopt NCERT Learning Outcomes; made corresponding changes in the Examination and Assessment practices for the year 2019-20 vide Circular No. Acad-11/2019 dated 06.03.2019 and the year 2020-21 vide Circular No. Acad-18/2020 dated 16.03.2020; and supported schools and teachers through online capacity building programmes under this specific theme for the year 2020. The National Education Policy 2020 has affirmed the need to move from rote to competency-based learning making it more focused on developing the creative and critical thinking capacities of students to meet the challenges of the 21st century proactively. It emphasizes that learners must be equipped with the ability to solve problems and assessment must shift from testing primarily rote memorization skills to one that is more formative, is more competency-based, promotes learning and development for our students, and tests higher-order skills, such as analysis, critical thinking, and conceptual clarity. Augmenting the thrust towards CBE, the Board is initiating further corresponding changes in the Examination and Assessment practices for the year 2021-22. While the overall marks and duration of examination shall remain same, change in the composition of assessment tasks would help us achieve the desired ends. Therefore, in the forthcoming sessions a greater number of Competency Based Questions or questions that assess application of concepts in real-life/ unfamiliar situations will be part of the question paper. The changes for classes IX-X (2021-22) internal year-end/Board Examination are as under:

Classes IX-X Year-end Examination/ Board Examination (Theory)

Composition

(2020-21) Existing

(2021-22) Modified

Objective type Questions including Multiple Choice Question-20%

Competency Based Questions would be minimum 30% These can be in the form of Multiple-Choice Questions, Case- Based Questions, Source Based Integrated Questions or any other types

Case-based/Source- based Integrated Questions-20%

Objective Questions will be 20%

Short Answer/ Long Answer Questions- Remaining 60%

Remaining 50% Short Answer/ Long Answer Questions- (as per existing pattern)

Curriculum document released by the Board vide Circular No. Acd-26/2021 dated 31stMarch 2021 for the Academic Session 2021-22 and the Sample Question Papers may also be referred to for details of changes in the QP design of individual subjects.



(Dr. Joseph Emmanuel) Director (Academics)

INDEX CBSE Future Announcements

6

Term-Based Breakdown

10

Syllabus

11

Internal Assessment

13

TERM-1 18

6. Introduction to Trigonometry

121-134

20



• Topic Notes

122



• Objective Questions

126

7. Areas Related to Circles

135-156



• Topic Notes

136



• Objective Questions

143

1. Real Numbers

17-30



• Topic Notes



• Objective Questions

2. Polynomials

31-48



• Topic Notes

32



• Objective Questions

36

3. Pair of Linear Equations in Two Variables 49-70

• Topic Notes

50

8. Probability

157-174



• Objective Questions

59



• Topic Notes

158



• Objective Questions

162

4. Triangles

71-98



• Topic Notes

72



• Objective Questions

81

5. Coordinate Geometry

99-120



• Topic Notes

100



• Objective Questions

106

SOLUTIONS Self Practice Solutions 175-200

TERM-BASED

BREAKDOWN (TERM - I Only)

Units

Unit Names

I

Number Systems

Marks Term 1 06

II

Algebra

10

III

Coordinate Geometry

06

IV

Geometry

06

Trigonometry: Introduction

05

V

10

09

Trigonometry: Applications

VI VII

Term 2

07

Mensuration

04

Statistics & Probability: Probability

03

06

Statistics & Probability: Statistics

08

INTERNAL ASSESSMENT (Periodic Tests (03) + Multiple Assessments (02) + Portfolio (02) + Student Enrichment Activities/ Practical Work (03))

10

TOTAL

10 100

Chapters Breakdown Term 1

Term 2

Real Numbers

Quadratic Equations

Polynomials

Arithmetic Progressions

Pair of Linear Equations in Two Variables

Circles

Coordinate Geometry

Constructions

Triangles

Applications of Trigonometry

Introduction to Trigonometry

Surface Areas and Volumes

Areas Related to Circles

Statistics

Probability (10)

Syllabus (TERM - I Only) Unit I: Number Systems Chapter 1: Real Numbers

l

Euclid’s division lemma



l

Fundamental Theorem of Arithmetic - statements after reviewing work done earlier and after illustrating and motivating through examples.



l

Proofs of irrationality of √2, √3, √5. Decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

Unit II: Algebra Chapter 2: Polynomials

l

Zeroes of a polynomial



l

Relationship between zeroes and coefficients of quadratic polynomials only.



l

Statement and simple problems on division algorithms for polynomials with real coefficients.

Chapter 3: Pair of Linear Equations in Two Variables

l

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency.



l

Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically - by substitution, and by elimination methodand and by cross multiplication method.



l

Simple situational problems. Simple problems on equations reducible to linear equations.

Unit III: Coordinate Geometry Chapter 7: Coordinate Geometry

l

Lines (in Two Dimentions)



l

Review: Concepts of coordinate geometry, graphs of linear equations.



l

Distance formula.



l

Section formula (internal division).



l

Area of a triangle.

Unit IV: Geometry Chapter 6: Triangles

Definitions, examples, counter examples of similar triangles.



l

(Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.



l

(Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. (11)



l

(Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.



l

(Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.



l

(Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.



l

(Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.



l

(Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. (This topic was removed for the previous session i.e. 2020-21 but now it is added back for the 2021-22 Term 1 session.)



l

(Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides, the angles opposite to the first side is a right angle.



l

(Prove) In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, the angle opposite to the f irst side is a right angle. (This topic was removed for the previous session i.e. 2020-21 but now it is added back for the 2021-22 Term 1 session.)

Unit V: Trigonometry Chapter 8: Introduction to Trigonometry

l

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined).



l

Motivate the ratios whichever are defined at 0° and 90°.



l Values



l

Trigonometric Identities



l

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.



l

Trigonometric ratios of complementary angles.

ratios.

of the trigonometric ratios of 30°, 45° and 60°. Relationships between the

Unit VI: Mensuration Chapter 12: Areas Related to Circles

l

Motivate the area of a circle; area of sectors and segments of a circle.



l

Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating the area of the segment of a circle, problems should be restricted to a central angle of 60°, 90° only. Plane figures involving triangles, simple quadrilaterals and circles should be taken.)



l

Problems should be restricted to a central angle of 120°.

Unit VII: Statistics and Probability Chapter 15: Probability

l

Classical definition of probability. Simple problems on finding the probability of an event.

* Text in red are topics removed for 2021-22 (reduced syllabus). (12)

Internal Assessment (TERM - I Only)

As per the Guidelines for Internal Assessment provided by CBSE on 22nd July 2021 and with the help of CBSE Circular No. Acad-51/2021, Class 10 Term-based Examinations will include 10 marks of Internal Assessment in each term. The breakdown given below is applicable to Term 2 as well! Internal Assessment

Description

Marks

Periodic Tests*

Pen Paper Test/ Online Test

03

Multiple Assessments

Assessment using multiple strategies; for example: Quiz, Group Discussion, Visual Expression, Interactive Bulletin Boards, Exit Cards, Concept Maps, Peer Assessment, Self-Assessment, etc.

02

Portfolio

Classwork and Assignments Any exemplary work done by the student Reflections, Narrations, Journals, etc. Achievements of the student in the subject throughout the year Participation of the student in different activities like Quizzes and GDs.

02

Student Enrichment Activities

Practical work

03

TOTAL

10

*Periodic Tests will be restricted to 3. The school may decide to distribute them between Term I and Term II; for instance, there may be 1 in Term I and 2 in Term II or vice versa.

(13)