**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. Quadratic Equations**

4.1 Introduction

4.2 Quadratic Equations

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

A1.7 Proof by Contradiction

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