Mathematics (JEE Advanced)
Sets, Relations and Functions
Representation of sets
Types of sets
Algebra of sets
Union, intersection, complement and difference of sets
De Morgan’s laws
Cartesian product of sets
Ordered pairs
Relations and their properties
Equivalence relations
Functions as mappings
Domain, codomain and range
One-one, onto and invertible functions
Even and odd functions
Special functions
Algebra of functions
Composition of functions
Algebra of Complex Numbers
Complex numbers and their representation
Algebra of complex numbers
Conjugate of a complex number
Modulus and argument
Polar representation
Triangle inequality
Cube roots of unity
Geometrical interpretation of complex numbers
Quadratic Equations and Theory of Equations
Quadratic equations with real coefficients
Nature of roots
Relations between roots and coefficients
Formation of quadratic equations
Symmetric functions of roots
Fundamental theorem of algebra (statement)
Sequences and Series
Arithmetic progression
Geometric progression
Arithmetic and geometric means
Sum of finite arithmetic and geometric series
Infinite geometric series
Sum of first n natural numbers
Sum of squares and cubes of natural numbers
Logarithms
Logarithms and their properties
Change of base
Applications of logarithms
Permutations and Combinations
Fundamental principle of counting
Permutations
Combinations
Properties of permutations and combinations
Applications of counting techniques
Binomial Theorem
Binomial theorem for positive integral index
General term of binomial expansion
Properties of binomial coefficients
Applications of binomial theorem
Matrices and Determinants
Matrices and their types
Algebra of matrices
Transpose of a matrix
Elementary row and column operations
Determinants up to order three
Properties of determinants
Adjoint and inverse of matrices
Solution of linear equations using matrices
Probability
Random experiment and sample space
Types of events
Addition rule of probability
Multiplication rule of probability
Conditional probability
Independence of events
Total probability theorem
Bayes’ theorem
Probability using permutations and combinations
Statistics
Measures of central tendency
Mean, median and mode
Measures of dispersion
Mean deviation
Standard deviation
Variance
Frequency distribution analysis
Random variables
Mean and variance of random variables
Trigonometry
Trigonometric functions and identities
Graphs and periodicity of trigonometric functions
Trigonometric equations
General solution of trigonometric equations
Inverse trigonometric functions
Properties of inverse trigonometric functions
Analytical Geometry – Two Dimensions
Cartesian coordinate system
Distance between two points
Section formula
Shift of origin
Equation of straight line in various forms
Angle between two lines
Distance of a point from a line
Concurrency of lines
Centroid, orthocentre, incentre and circumcentre of a triangle
Equation of circle in various forms
Tangents, normals and chords
Parametric equations of circle
Intersection of curves
Equation of conic sections
Parabola, ellipse and hyperbola
Tangents and normals to conics
Locus problems
Analytical Geometry – Three Dimensions
Coordinates of a point in space
Distance between two points
Direction ratios and direction cosines
Equation of a line in space
Skew lines
Shortest distance between two lines
Equation of a plane
Distance of a point from a plane
Angle between lines and planes
Coplanar lines
Differential Calculus
Limit of a function
Continuity of functions
Properties of limits and continuity
L’Hospital’s rule
Differentiation from first principles
Derivatives of standard functions
Chain rule
Implicit differentiation
Second order derivatives
Tangents and normals
Increasing and decreasing functions
Maxima and minima
Rolle’s theorem
Lagrange’s mean value theorem
Geometric interpretation of derivatives
Integral Calculus
Indefinite integrals
Standard integrals
Definite integrals
Properties of definite integrals
Fundamental theorem of calculus
Integration by substitution
Integration by parts
Integration by partial fractions
Area under curves
Area between curves
Formation of differential equations
Solution of first order differential equations
Homogeneous differential equations
Linear differential equations
Vector Algebra
Vectors and scalars
Addition and subtraction of vectors
Scalar multiplication
Dot product
Cross product
Scalar triple product
Vector triple product
Geometrical interpretation of vectors
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