Class 11 Mathematics

Below is an overview of the key units and topics typically included in the Class 11 Mathematics syllabus:

1. Sets

• Introduction to Sets: Definition, types of sets (finite, infinite, null, equal, subset, universal).
• Operations on Sets: Union, intersection, difference, and complement of sets.
• Venn Diagrams: Representation of sets and operations using Venn diagrams.

2. Relations and Functions

• Relations: Definition of relations, types (one-to-one, onto, and many-to-one).
• Functions: Definition and representation of functions, types of functions (linear, quadratic, polynomial, and rational).
• Graphs of Functions: Sketching graphs of various types of functions.

3. Trigonometric Functions

• Trigonometric Ratios: Definitions of sine, cosine, tangent, cosecant, secant, and cotangent.
• Trigonometric Identities: Fundamental identities and their applications.
• Graphs of Trigonometric Functions: Understanding and sketching the graphs of trigonometric functions.

4. Complex Numbers

• Definition: Introduction to complex numbers in the form $a+bi$ where $i$ is the imaginary unit.
• Arithmetic Operations: Addition, subtraction, multiplication, and division of complex numbers.
• Modulus and Argument: Modulus of a complex number, polar representation, and De Moivre’s theorem.

5. Linear Inequalities

• Introduction to Inequalities: Understanding linear inequalities in one variable and two variables.
• Graphical Representation: Graphing linear inequalities and finding the solution set.
• Applications: Solving problems related to inequalities.

6. Permutations and Combinations

• Fundamental Principle of Counting: Basic counting techniques and applications.
• Permutations: Definition, formula, and applications in arrangements.
• Combinations: Definition, formula, and applications in selections.

7. Binomial Theorem

• Binomial Expansion: Understanding the binomial theorem and its applications.
• General Term: Finding the general term in a binomial expansion.
• Applications: Using the binomial theorem in problems involving combinations.

8. Sequence and Series

• Arithmetic Progression (AP): Definition, nth term, and sum of the first n terms of an AP.
• Geometric Progression (GP): Definition, nth term, and sum of the first n terms of a GP.
• Special Series: Sum of natural numbers, squares, and cubes.

9. Straight Lines

• Equations of Lines: Understanding different forms of equations of straight lines (slope-intercept, point-slope, and general form).
• Slope of a Line: Concept of slope, parallel and perpendicular lines.
• Applications: Intersection of lines and distance between two points.

10. Conic Sections

• Circles: Equation of a circle and its properties.
• Parabolas: Definition, equation, and properties of parabolas.
• Ellipses and Hyperbolas: Definitions, equations, and properties of ellipses and hyperbolas.

11. Introduction to Three-Dimensional Geometry

• Coordinates in Space: Understanding the concepts of 3D geometry and coordinates.
• Distance Formula: Distance between two points in three-dimensional space.
• Section Formula: Division of a line segment in a given ratio.

12. Limits and Derivatives

• Introduction to Limits: Concept of limits, properties, and evaluation of limits.
• Derivatives: Basic rules of differentiation and applications in finding slopes and tangents.

13. Mathematical Reasoning

• Statements and Logic: Understanding statements, logical connectives, and truth tables.
• Quantifiers: Use of universal and existential quantifiers.
• Mathematical Induction: Principle of mathematical induction and its applications.

14. Statistics

• Data Collection: Types of data, methods of collection, and representation of data.
• Measures of Central Tendency: Mean, median, and mode.
• Graphical Representation: Histogram, frequency polygon, and cumulative frequency graph.

15. Probability

• Basic Concepts: Definition and concepts of probability, sample space, and events.
• Calculation of Probability: Simple problems involving the probability of events.
• Conditional Probability: Understanding conditional probability and independence of events.