# NCERT Maths Class 10

Categories SYLLABUS

1. Real Numbers

1.1 Introduction

1.2 Euclid’s Division Lemma

1.3 The Fundamental Theorem of Arithmetic

1.4 Revisiting Irrational Numbers

1.5 Revisiting Rational Numbers and Their Decimal Expansions

1.6 Summary

2. Polynomials

2.1 Introduction

2.2 Geometrical Meaning of the Zeroes of a Polynomial

2.3 Relationship between Zeroes and Coefficients of a Polynomial

2.4 Division Algorithm for Polynomials

2.5 Summary

3. Pair of Linear Equations in Two Variables

3.1 Introduction

3.2 Pair of Linear Equations in Two Variables

3.3 Graphical Method of Solution of a Pair of Linear Equations

3.4 Algebraic Methods of Solving a Pair of Linear Equations

3.4.1 Substitution Method

3.4.2 Elimination Method

3.4.3 Cross-Multiplication Method

3.5 Equations Reducible to a Pair of Linear Equations in Two Variables

3.6 Summary

4.1 Introduction

4.3 Solution of a Quadratic Equation by Factorisation

4.4 Solution of a Quadratic Equation by Completing the Square

4.5 Nature of Roots

4.6 Summary

5. Arithmetic Progressions

5.1 Introduction

5.2 Arithmetic Progressions

5.3 nth Term of an AP

5.4 Sum of First n Terms of an AP

5.5 Summary

6. Triangles

6.1 Introduction

6.2 Similar Figures

6.3 Similarity of Triangles

6.4 Criteria for Similarity of Triangles

6.5 Areas of Similar Triangles

6.6 Pythagoras Theorem

6.7 Summary

7. Coordinate Geometry

7.1 Introduction

7.2 Distance Formula

7.3 Section Formula

7.4 Area of a Triangle

7.5 Summary

8. Introduction to Trigonometry

8.1 Introduction

8.2 Trigonometric Ratios

8.3 Trigonometric Ratios of Some Specific Angles

8.4 Trigonometric Ratios of Complementary Angles

8.5 Trigonometric Identities

8.6 Summary

9. Some Applications of Trigonometry

9.1 Introduction

9.2 Heights and Distances

9.3 Summary

10. Circles

10.1 Introduction

10.2 Tangent to a Circle

10.3 Number of Tangents from a Point on a Circle

10.4 Summary

11. Constructions

11.1 Introduction

11.2 Division of a Line Segment

11.3 Construction of Tangents to a Circle

11.4 Summary

12. Areas Related to Circles

12.1 Introduction

12.2 Perimeter and Area of a Circle — A Review

12.3 Areas of Sector and Segment of a Circle

12.4 Areas of Combinations of Plane Figures

12.5 Summary

13. Surface Areas and Volumes

13.1 Introduction

13.2 Surface Area of a Combination of Solids

13.3 Volume of a Combination of Solids

13.4 Conversion of Solid from One Shape to Another

13.5 Frustum of a Cone

13.6 Summary

14. Statistics

14.1 Introduction

14.2 Mean of Grouped Data

14.3 Mode of Grouped Data

14.4 Median of Grouped Data

14.5 Graphical Representation of Cumulative Frequency Distribution

14.6 Summary

15. Probability

15.1 Introduction

15.2 Probability — A Theoretical Approach

15.3 Summary

Appendix A1 : Proofs in Mathematics

A1.1 Introduction

A1.2 Mathematical Statements Revisited

A1.3 Deductive Reasoning

A1.4 Conjectures, Theorems, Proofs and Mathematical Reasoning

A1.5 Negation of a Statement

A1.6 Converse of a Statement

A1.8 Summary

Appendix A2 : Mathematical Modelling

A2.1 Introduction

A2.2 Stages in Mathematical Modelling

A2.3 Some Illustrations

A2.4 Why is Mathematical Modelling Important?

A2.5 Summary