Mathematics: Textbook for Class X

Description

Mathematics for Class X from NCERT. 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 Answers/Hints