Mathematics: Textbook for Class X

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

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