Contents

• Foreword v
• Preface vii

1. Relations and Functions 1

• 1.1 Introduction 1
• 1.2 Types of Relations 2
• 1.3 Types of Functions 7
• 1.4 Composition of Functions and Invertible Function 12
• 1.5 Binary Operations 19

2. Inverse Trigonometric Functions 33

• 2.1 Introduction 33
• 2.2 Basic Concepts 33
• 2.3 Properties of Inverse Trigonometric Functions 42

3. Matrices 56

• 3.1 Introduction 56
• 3.2 Matrix 56
• 3.3 Types of Matrices 61
• 3.4 Operations on Matrices 65
• 3.5 Transpose of a Matrix 83
• 3.6 Symmetric and Skew Symmetric Matrices 85
• 3.7 Elementary Operation (Transformation) of a Matrix 90
• 3.8 Invertible Matrices 91

4. Determinants 103

• 4.1 Introduction 103
• 4.2 Determinant 103
• 4.3 Properties of Determinants 109
• 4.4 Area of a Triangle 121
• 4.5 Minors and Cofactors 123
• 4.6 Adjoint and Inverse of a Matrix 126
• 4.7 Applications of Determinants and Matrices 133

5. Continuity and Differentiability 147

• 5.1 Introduction 147
• 5.2 Continuity 147
• 5.3 Differentiability 161
• 5.4 Exponential and Logarithmic Functions 170
• 5.5 Logarithmic Differentiation 174
• 5.6 Derivatives of Functions in Parametric Forms 179
• 5.7 Second Order Derivative 181
• 5.8 Mean Value Theorem 184

6. Application of Derivatives 194

• 6.1 Introduction 194
• 6.2 Rate of Change of Quantities 194
• 6.3 Increasing and Decreasing Functions 199
• 6.4 Tangents and Normals 206
• 6.5 Approximations 213
• 6.6 Maxima and Minima 216

Appendix 1: Proofs in Mathematics 247

• A.1.1 Introduction 247
• A.1.2 What is a Proof? 247

Appendix 2: Mathematical Modelling 256

• A.2.1 Introduction 256
• A.2.2 Why Mathematical Modelling? 256
• A.2.3 Principles of Mathematical Modelling 257

Answers 268

Supplementary Material 286

Courtesy: ncert.nic.in

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