ClassphereJEE Advanced Mathematics syllabus: chapters and topics
JEE Advanced Mathematics is mapped into 26 chapters and 195 topics. Open a chapter to see its topics; this is the map Classphere uses to tag questions and to show a student which chapters cost them marks.
All JEE Advanced Mathematics chapters
01
Fundamentals of Mathematics & Inequalities
8 topics- Number Systems and Types
- Modulus Function and its Properties
- Linear and Quadratic Inequalities
- Logarithms and their Properties
- Wavy Curve Method
- Rational Inequalities
- Greatest Integer Function
- Fractional Part Function
02
Sets, Relations and Functions
9 topics- Types of Sets and Set Operations
- Venn Diagrams
- Cartesian Product of Sets
- Types of Relations (Reflexive, Symmetric, Transitive, Equivalence)
- Domain, Co-domain and Range of a Function
- One-One and Onto Functions
- Composite Functions
- Inverse of a Function
- Even and Odd Functions
03
Trigonometric Ratios, Identities & Equations
7 topics- Trigonometric Ratios and Identities
- Compound Angle Formulae
- Multiple and Sub-Multiple Angle Formulae
- Transformation Formulae (Sum to Product and Vice Versa)
- Maximum and Minimum Values of Trigonometric Expressions
- General Solutions of Trigonometric Equations
- Conditional Trigonometric Identities
04
Inverse Trigonometric Functions (ITF)
6 topics- Domain and Range of Inverse Trigonometric Functions
- Principal Value Branch
- Graphs of Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
- Sum and Difference Formulae for Inverse Functions
- Conversion Between Inverse Trigonometric Functions
05
Quadratic Equations & Expressions
8 topics- Roots of a Quadratic Equation
- Nature of Roots (Discriminant)
- Relation Between Roots and Coefficients
- Formation of a Quadratic Equation from Given Roots
- Sign of a Quadratic Expression
- Location of Roots (Range of Parameter)
- Common Roots of Two Quadratic Equations
- Quadratic Expressions in Two Variables
06
Complex Numbers
10 topics- Algebraic and Polar Representation
- Argand Diagram
- Modulus and Argument
- Conjugate of a Complex Number
- Algebraic Operations on Complex Numbers
- Triangle Inequality
- De Moivre's Theorem
- Cube Roots and nth Roots of Unity
- Geometrical Applications of Complex Numbers
- Rotation Theorem
07
Permutations and Combinations (P&C)
9 topics- Fundamental Principle of Counting
- Factorial Notation
- Permutations of Distinct Objects
- Permutations with Repetition
- Circular Permutations
- Combinations and their Properties
- Division and Distribution of Objects into Groups
- Derangements
- Multinomial Theorem (Basic Applications)
08
Binomial Theorem
7 topics- Binomial Expansion for a Positive Integral Index
- General Term in an Expansion
- Middle Term(s) in an Expansion
- Greatest Term and Greatest Coefficient
- Properties of Binomial Coefficients
- Sum of Binomial Coefficients
- Binomial Theorem for Negative/Fractional Index
09
Sequences and Series (Progression)
7 topics- Arithmetic Progression (nth Term, Sum)
- Geometric Progression (nth Term, Sum, Infinite GP)
- Arithmetico-Geometric Progression
- Harmonic Progression and Harmonic Mean
- Relation Between AM, GM and HM
- Sum of Squares and Cubes of Natural Numbers
- Telescoping Series (Method of Difference)
10
Matrices and Determinants
12 topics- Types of Matrices
- Algebra of Matrices (Addition, Multiplication)
- Transpose of a Matrix
- Symmetric and Skew-Symmetric Matrices
- Adjoint of a Matrix
- Inverse of a Matrix
- Properties of Determinants
- Evaluation of Determinants (Order 2 and 3)
- Area of a Triangle Using Determinants
- Cramer's Rule
- Matrix Inversion Method
- Consistency of a System of Linear Equations
11
Straight Lines & Pair of Straight Lines
9 topics- Slope of a Line
- Different Forms of the Equation of a Line
- Distance Formula and Section Formula
- Angle Between Two Lines
- Distance of a Point from a Line
- Distance Between Two Parallel Lines
- Family of Lines
- Concurrency of Three Lines
- Foot of Perpendicular and Image of a Point
12
Circles
10 topics- Standard and General Equation of a Circle
- Equation of a Circle from Given Conditions
- Parametric Form of a Circle
- Position of a Point Relative to a Circle
- Tangent to a Circle
- Normal to a Circle
- Chord of Contact and Chord Bisected at a Point
- Family of Circles
- Radical Axis and Radical Centre
- Common Tangents to Two Circles
13
Parabola
7 topics- Standard Equation of a Parabola
- Focus, Directrix and Latus Rectum
- Parametric Coordinates on a Parabola
- Focal Chord Properties
- Tangent to a Parabola (Point, Slope, Parametric Form)
- Normal to a Parabola
- Pair of Tangents from an External Point
14
Ellipse
7 topics- Standard Equation of an Ellipse
- Eccentricity, Foci and Directrices
- Auxiliary Circle and Eccentric Angle
- Parametric Form of an Ellipse
- Tangent to an Ellipse
- Normal to an Ellipse
- Director Circle of an Ellipse
15
Hyperbola
6 topics- Standard Equation of a Hyperbola
- Eccentricity, Foci and Directrices
- Rectangular Hyperbola
- Asymptotes of a Hyperbola
- Conjugate Hyperbola
- Tangent and Normal to a Hyperbola
16
Limits, Continuity & Differentiability (LCD)
6 topics- Evaluation of Limits (Algebraic Methods)
- Standard Limits and L'Hopital's Rule
- Continuity of a Function at a Point
- Types of Discontinuity
- Differentiability of a Function at a Point
- Relation Between Continuity and Differentiability
17
Methods of Differentiation (MOD)
7 topics- Derivatives of Standard Functions
- Chain Rule
- Implicit Differentiation
- Parametric Differentiation
- Logarithmic Differentiation
- Differentiation of Determinants
- Higher Order Derivatives
18
Application of Derivatives (AOD)
8 topics- Rate of Change of Quantities
- Tangents and Normals to a Curve
- Increasing and Decreasing Functions
- Rolle's Theorem
- Lagrange's Mean Value Theorem
- Maxima and Minima (First Derivative Test)
- Maxima and Minima (Second Derivative Test)
- Applied Maxima-Minima Problems
19
Indefinite Integration
6 topics- Integration as the Inverse of Differentiation
- Standard Integral Formulae
- Integration by Substitution
- Integration by Parts
- Integration Using Partial Fractions
- Integration of Irrational Functions
20
Definite Integration
6 topics- Definite Integral as the Limit of a Sum
- Fundamental Theorem of Calculus
- Properties of Definite Integrals
- King's Rule and Queen's Rule
- Definite Integrals of Periodic Functions
- Leibniz Rule
21
Area Under Curves (AUC)
4 topics- Area Bounded by a Curve and the Coordinate Axes
- Area Between Two Curves
- Area Using Horizontal Strips
- Symmetrical Areas
22
Differential Equations
5 topics- Order and Degree of a Differential Equation
- Formation of a Differential Equation
- Variable Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
23
Vector Algebra
8 topics- Scalar and Vector Quantities
- Addition and Subtraction of Vectors
- Components of a Vector
- Dot (Scalar) Product and Projections
- Cross (Vector) Product
- Scalar Triple Product
- Vector Triple Product
- Vector Equation of a Line and a Plane
24
Three-Dimensional Geometry (3D)
7 topics- Direction Cosines and Direction Ratios
- Equation of a Line in Space (Vector and Cartesian)
- Angle Between Two Lines
- Shortest Distance Between Two Skew Lines
- Equation of a Plane
- Angle Between a Line and a Plane
- Distance of a Point from a Plane
25
Probability
10 topics- Sample Space and Events
- Axiomatic Approach to Probability
- Addition Theorem of Probability
- Conditional Probability
- Multiplication Theorem of Probability
- Independent Events
- Total Probability Theorem
- Bayes' Theorem
- Probability Using Permutations and Combinations
- Probability Distribution of a Random Variable
26
Statistics
6 topics- Measures of Central Tendency (Mean, Median, Mode)
- Measures of Dispersion (Range, Mean Deviation)
- Variance and Standard Deviation
- Standard Deviation of Grouped and Ungrouped Data
- Coefficient of Variation
- Analysis of Frequency Distributions
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