Class 11 NCERT Chemistry Chapter Names
Chapter 1: Sets
Chapter 2: Relations and Functions
Chapter 3: Trigonometric Functions
Chapter 4: Complex Numbers and Quadratic Equations
Chapter 5: Linear Inequalities
Chapter 6: Permutations and Combinations
Chapter 7: Binomial Theorem
Chapter 8: Sequences and Series
Chapter 9: Straight Lines
Chapter 10: Conic Sections
Chapter 11: Introduction to Three Dimensional Geometry
Chapter 12: Limits and Derivatives
Chapter 13: Statistics
Chapter 14: Probability
Topics Covered – Class 11 Mathematics, Chapter 1: Sets
- Introduction to sets
- Representation of sets
- Types of sets (empty set, finite set, infinite set, equal sets, subsets, universal set, power set)
- Venn diagrams
- Operations on sets (union, intersection, difference, complement)
- Properties of set operations
- Practical problems on union and intersection of two or three sets
Class 12 Maths – Chapter 2: Relations and Functions
Topics Covered
- Revision from Class 11
- Cartesian Product of Sets
- Definition of Relation and Function
- Domain, Co-domain, and Range
- Types of Relations
- Reflexive Relation
- Symmetric Relation
- Transitive Relation
- Equivalence Relation
- Types of Functions
- One-one (Injective) Function
- Onto (Surjective) Function
- Bijective Function
- Composition of Functions
- Definition and notation (g∘f)(x)(g \circ f)(x)
- Finding composite functions
- Domain of composite functions
- Invertible Functions
- Definition of inverse of a function
- Algebraic method to find inverse
- Condition for invertibility (bijective functions only)
- Binary Operations
- Definition
- Examples of binary operations on sets
- Properties: commutativity, associativity, identity, inverse
Class 11 Mathematics – Chapter 3: Trigonometric Functions (NCERT)
Topics Covered – Chapter 3: Trigonometric Functions
- Measurement of Angles
- Radian measure and degree measure
- Relation between radian and degree
- Conversion from one measure to another
- Trigonometric Functions
- Definition of trigonometric functions using a unit circle
- Signs of trigonometric functions in different quadrants
- Domain and Range of Trigonometric Functions
- For sinx\sin x, cosx\cos x, tanx\tan x, cotx\cot x, secx\sec x, cscx\csc x
- Trigonometric Functions of Sum and Difference of Two Angles
- sin(A±B)\sin(A \pm B)
- cos(A±B)\cos(A \pm B)
- tan(A±B)\tan(A \pm B) and cot(A±B)\cot(A \pm B)
- Trigonometric Equations
- General solutions of equations like sinx=a\sin x = a, cosx=a\cos x = a, tanx=a\tan x = a
- Graphs of Trigonometric Functions
- Graphs of sine, cosine, tangent, cotangent, secant, and cosecant functions
- Simple Applications
- Problems based on heights and distances (only simple cases)
Topics Covered – Class 11 Mathematics Chapter 4: Complex Numbers and Quadratic Equations
- Need for complex numbers, especially −1\sqrt{-1}
- Algebraic properties of complex numbers
- Argand plane and representation of complex numbers
- Modulus and argument of a complex number
- Polar representation of complex numbers
- Algebra of complex numbers (addition, subtraction, multiplication, division)
- Square root of a complex number
- Quadratic equations in the complex number system
- Fundamental Theorem of Algebra
- Nature of roots of a quadratic equation
- Cube roots of unity
Topics Covered – Class 11 Mathematics Chapter 5: Linear Inequalities
- Introduction to linear inequalities
- Algebraic solutions of linear inequalities in one variable and their representation on the number line
- Graphical solution of linear inequalities in two variables
- Solution of a system of linear inequalities in two variables graphically
Topics Covered – Class 11 Mathematics Chapter 6: Permutations and Combinations
- Fundamental principle of counting
- Factorial notation
- Permutations as arrangements (with and without repetition)
- Permutations of objects when some are identical
- Circular permutations
- Combinations as selections (with and without repetition)
- Relation between permutations and combinations
Topics Covered – Class 11 Mathematics Chapter 7: Binomial Theorem
- Statement and proof of the binomial theorem for positive integer index
- General term of the binomial expansion
- Middle term(s) in the binomial expansion
- Properties of binomial coefficients
- Simple applications of the binomial theorem
Topics Covered – Class 11 Mathematics Chapter 8: Sequences and Series
- Sequence and series basics
- Arithmetic progression (A.P.) and general term of an A.P.
- Sum of first nn terms of an A.P.
- Arithmetic mean (A.M.)
- Geometric progression (G.P.), general term, and sum of first nn terms of a G.P.
- Geometric mean (G.M.)
- Relation between A.M. and G.M.
- Sum to infinity of a G.P. (for ∣r∣<1|r| < 1)
- Sum of nn terms of special series (e.g., 12+22+32+…1^2 + 2^2 + 3^2 + \dots, 13+23+33+…1^3 + 2^3 + 3^3 + \dots)
Topics Covered – Class 11 Mathematics Chapter 9: Straight Lines
- Slope of a line and various forms of the equation of a line
- Angle between two lines
- Condition for parallelism and perpendicularity of lines
- Distance of a point from a line
- Distance between two parallel lines
- Collinearity of three points
Topics Covered – Class 11 Mathematics Chapter 10: Conic Sections
- Sections of a cone and definition of conic sections
- Circle, ellipse, parabola, and hyperbola as special cases of conic sections
- Standard equations and simple properties of a parabola
- Standard equations and simple properties of an ellipse
- Standard equations and simple properties of a hyperbola
- Standard equation of a circle
Topics Covered – Class 11 Mathematics Chapter 11: Introduction to Three Dimensional Geometry
- Coordinate axes and coordinate planes in three-dimensional space
- Coordinates of a point in space
- Distance formula in three dimensions
- Section formula in three dimensions
Topics Covered – Class 11 Mathematics Chapter 12: Limits and Derivatives
- Intuitive idea of limits
- Limits of polynomials and rational functions
- Limits of trigonometric functions
- Derivatives introduced as the rate of change
- Derivative of a function using the first principle
- Derivatives of polynomial and trigonometric functions
Topics Covered – Class 11 Mathematics Chapter 13: Statistics
- Measures of dispersion
- Range, mean deviation, and standard deviation for ungrouped and grouped data
- Variance and its relation to standard deviation
- Analysis of frequency distributions
Topics Covered – Class 11 Mathematics Chapter 14: Probability
- Random experiments and sample space
- Events: simple, compound, sure, and impossible events
- Complement of an event
- Algebra of events
- Axiomatic (Kolmogorov) approach to probability
- Probability of an event
- Simple problems based on probability