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Curriculum

Ch 1: Sets

1.1 Introduction and Definitions 1.2 Representation of Sets 1.3 Types of Sets 1.4 Subsets and Power Sets 1.5 Set Operations and Venn Diagrams 1.6 Algebra of Sets and De Morgan's Laws 1.7 Cardinality and Practical Problems 1.8 Cartesian Product and Advanced Concepts

Ch 2: Relations and Functions

2.1 Cartesian Product of Sets 2.2 Relations 2.3 Functions 2.4 Standard Functions and their Graphs 2.5 Algebra of Functions 2.6 Finding Domain and Range (Techniques)

Ch 3: Trigonometric Functions

3.1 Angles and Arc Length 3.2 Trigonometric Functions: The Unit Circle Approach 3.3 Graphs and Periodicity 3.4 Compound Angles (Sum and Difference Formulas)3.5 Multiple and Sub-multiple Angles 3.6 Transformation Formulas (Product <-> Sum)3.7 Trigonometric Equations 3.8 Applications: Sine and Cosine Rules 3.9 JEE Advanced Extension: Inequalities & Max/Min

Ch 4: Complex Numbers and Quadratic Equations

4.1 The Need for Complex Numbers 4.2 Algebra of Complex Numbers 4.3 Conjugate and Modulus 4.4 Argand Plane and Polar Representation 4.5 Quadratic Equations 4.6 Square Root of a Complex Number 4.7 JEE Advanced Extensions

Ch 5: Linear Inequalities

5.1 Introduction to Inequalities 5.2 Algebraic Solutions and Interval Notation 5.3 Graphical Solution (Two Variables)5.4 Applications and Word Problems 5.5 Advanced JEE Extensions

Ch 6: Permutations and Combinations

6.1 Fundamental Principles of Counting 6.2 Factorial Notation 6.3 Permutations (Order Matters)6.4 Combinations (Order Does Not Matter)6.5 Advanced JEE Extensions

Ch 7: Binomial Theorem

7.1 Introduction and Pascal's Triangle 7.2 Binomial Theorem for Positive Integral Index 7.3 General Term and Middle Terms 7.4 Properties of Binomial Coefficients (JEE Foundation)7.5 Applications: Divisibility and Approximations 7.6 Advanced Extension: Multinomial Theorem

Ch 8: Sequence and Series

8.1 Introduction to Sequences 8.2 Arithmetic Progression (A.P.)8.3 Geometric Progression (G.P.)8.4 Relationship Between A.M. and G.M.8.5 Sum of Special Series

Ch 9: Straight Lines

9.1 Introduction and Review of Coordinate Geometry 9.2 Slope of a Line 9.3 Angle Between Two Lines 9.4 Forms of Equation of a Line 9.5 General Equation of a Line 9.6 Distance of a Point from a Line

Ch 10: Conic Sections

10.1 Introduction to Conic Sections 10.2 The Circle 10.3 The Parabola 10.4 The Ellipse 10.5 The Hyperbola

Ch 11: Introduction to Three Dimensional Geometry

11.1 Coordinate Axes and Coordinate Planes 11.2 Coordinates of a Point in Space 11.3 Distance Formula 11.4 Section Formula

Ch 12: Limits and Derivatives

12.1 Introduction to Calculus 12.2 The Concept of Limit 12.3 Evaluation of Limits (Algebraic)12.4 Trigonometric Limits and Sandwich Theorem 12.5 Derivatives: Introduction and First Principles 12.6 Algebra of Derivatives and Standard Rules

Ch 13: Statistics

13.1 Introduction: Why Central Tendency is Not Enough 13.2 Mean Deviation (M.D.)13.3 Variance and Standard Deviation 13.4 Analysis of Frequency Distributions

Ch 14: Probability

14.1 Random Experiments and Sample Space 14.2 Events and Their Algebra 14.3 Axiomatic Approach to Probability 14.4 Addition Theorems and Inequalities

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Calculus Algebra Geometry Trigonometry AI Assistant

8.5 Sum of Special Series

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