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Curriculum

Ch 1: Relations and Functions

1.1 Types of Relations 1.2 Types of Functions 1.3 Composition of Functions 1.4 Invertible Functions 1.5 Binary Operations

Ch 2: Inverse Trigonometric Functions

2.1 Introduction and Conditions for Invertibility 2.2 Definitions and Graphs of Inverse Functions 2.3 Properties of Inverse Trigonometric Functions 2.4 Sum and Difference Formulas 2.5 Simplification by Substitution

Ch 3: Matrices

3.1 Introduction and Matrix Construction 3.2 Types of Matrices 3.3 Operations on Matrices 3.4 Transpose and Symmetric Matrices 3.5 Elementary Operations and Inverse

Ch 4: Determinants

4.1 Introduction and Definition 4.2 Properties of Determinants 4.3 Area of a Triangle using Determinants 4.4 Minors and Cofactors 4.5 Adjoint and Inverse of a Matrix 4.6 Applications: Solving Systems of Linear Equations

Ch 5: Continuity and Differentiability

5.1 Continuity 5.2 Differentiability 5.3 Exponential and Logarithmic Functions 5.4 Methods of Differentiation 5.5 Higher Order Derivatives 5.6 Mean Value Theorems

Ch 6: Application of Derivatives

6.1 Rate of Change of Quantities 6.2 Increasing and Decreasing Functions 6.3 Tangents and Normals 6.4 Approximations and Differentials 6.5 Maxima and Minima

Ch 7: Integrals

7.1 Indefinite Integrals 7.2 Methods of Integration 7.3 Definite Integrals 7.4 Properties of Definite Integrals

Ch 8: Application of Integrals

8.1 Area Under Simple Curves 8.2 Area of the Region Bounded by a Curve and a Line 8.3 Area Between Two Curves

Ch 9: Differential Equations

9.1 Introduction and Classification 9.2 Solutions of Differential Equations 9.3 Method 1: Variable Separable 9.4 Method 2: Homogeneous Differential Equations 9.5 Method 3: Linear Differential Equations

Ch 10: Vector Algebra

10.1 Basic Concepts and Types of Vectors 10.2 Algebra of Vectors 10.3 Scalar (Dot) Product 10.4 Vector (Cross) Product

Ch 11: Three Dimensional Geometry

11.1 Direction Cosines and Direction Ratios 11.2 Equation of a Line in Space 11.3 Angle and Distance between Lines 11.4 Equation of a Plane 11.5 Properties of Planes

Ch 12: Linear Programming

12.1 Introduction and Terminology 12.2 Graphical Method of Solution 12.3 Handling Unbounded Regions 12.4 Types of Linear Programming Problems

Ch 13: Probability

13.1 Conditional Probability 13.2 Multiplication Theorem and Independence 13.3 Bayes' Theorem 13.4 Random Variables and Probability Distributions 13.5 Bernoulli Trials and Binomial Distribution

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Calculus Algebra Geometry Trigonometry AI Assistant

6.2 Increasing and Decreasing Functions

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