JEE Main Mathematics (JEE Main) Syllabus: Check the Latest Syllabus

• Roster or Tabular method or List method
• Set-Builder or Rule Method

• De Morgan's Law
• Some Properties of Complement Sets

• Sum, Difference,Product and Quotient of Function
• Addition of two real functions
• Subtraction of a real function from another
• Multiplication by a scalar
• Multiplication of two real functions
• Quotient of two real functions

• Imaginary number
• Complex Number

• Expressing complex number in a + ib form and their representation in a plane

• Equality of two Complex Numbers 
• Conjugate of a Complex Number 
• Properties of `barz`
• Addition of complex numbers - Properties of addition, Scalar Multiplication
• Subtraction of complex numbers - Properties of Subtraction
• Multiplication of complex numbers - Properties of Multiplication
• Powers of i in the complex number
• Division of complex number - Properties of Division
• The square roots of a negative real number
• Identities

• Properties of 1, w, w²

• Nature of roots(law)

• Matrices
• Determinants
• Cramer’s Rule
• Application in Economics

• Commutative Law
• Associative Law
• Existence of additive identity
• The existence of additive inverse

• Row Matrix
• Column Matrix
• Zero or Null matrix
• Square Matrix
• Diagonal Matrix
• Scalar Matrix
• Unit or Identity Matrix
• Upper Triangular Matrix
• Lower Triangular Matrix
• Triangular Matrix
• Symmetric Matrix
• Skew-Symmetric Matrix
• Determinant of a Matrix
• Singular Matrix
• Transpose of a Matrix

• Introduction
• Meaning
• Definition

• Property 1 - The value of the determinant remains unchanged if its rows are turned into columns and columns are turned into rows.
• Property 2 -  If any two rows  (or columns)  of a determinant are interchanged then the value of the determinant changes only in sign.
• Property 3 - If any two rows ( or columns) of a  determinant are identical then the value of the determinant is zero.
• Property  4  -  If each element of a row (or column)  of a determinant is multiplied by a  constant k then the value of the new determinant is k times the value of the original determinant.
• Property  5  -  If each element of a row (or column) is expressed as the sum of two numbers then the determinant can be expressed as the sum of two determinants
• Property  6  -  If a constant multiple of all elements of any row  (or column)  is added to the corresponding elements of any other row  (or column  )  then the value of the new determinant so obtained is the same as that of the original determinant. 
• Property 7 -  (Triangle property) - If all the elements of a  determinant above or below the diagonal are zero then the value of the determinant is equal to the product of its diagonal elements.

• Consistent System
• Inconsistent System
• Solution of a system of linear equations using the inverse of a matrix

• Define symmetric and skew symmetric matrix

• Concept
• Elementary Transformations and Equivalent matrices
• Echelon form and finding the rank of the matrix (upto the order of 3×4)

1. A system of equations with exactly one solution
2. A system of equations with infinitely many solutions
3. A system of equations that has no solution

•  Testing the consistency of non homogeneous linear equations (two and three variables) by rank method

• Tree Diagram 
• Addition Principle 
• Multiplication principle

• Motivating the Application of the Method by Looking at Natural Numbers as the Least Inductive Subset of Real Numbers

• Problems Based on Sum of Series
• Problems Based on Inequality and Divisibility

• History of Binomial Theorem

• Statement and Proof of the Binomial Theorem for Positive Integral Indices
• Proof of Binomial Therom by Induction
• Special Case in Binomial Therom
• Pascal's Triangle
• Binomial theorem for any positive integer n
• Some special cases-(In the expansion of (a + b)ⁿ)

• N^th Term of Geometric Progression (G.P.)
• General Term of a Geometric Progression (G.P.)
• Sum of First N Terms of a Geometric Progression (G.P.)
• Sum of infinite terms of a G.P.
• Geometric Mean (G.M.)

• Sum to infinite terms of a G.P.

• Continuity of a function at a point
• Definition of Continuity
• Continuity from the right and from the left
• Examples of Continuous Functions
• Properties of continuous functions
• Types of Discontinuities
• Jump Discontinuity
• Removable Discontinuity
• Infinite Discontinuity
• Continuity over an interval
• The intermediate value theorem for continuous functions

• Rolle’s Theorem
• Lagrange’s Mean Value Theorem
• Applications

Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)

• Evaluation of Limits when X → ∞
• Evaluation of Limits of the form 1^∞

1) `int (dx)/(x^2 - a^2) = 1/(2a) log |(x - a)/(x + a)| + C`

2) `int (dx)/(a^2 - x^2) = 1/(2a) log |(a + x)/(a - x)| + C`

3) `int (dx)/(x^2 - a^2) = 1/a  tan^(-1) (x/a) + C`

4) `int (dx)/sqrt (x^2 - a^2) = log |x + sqrt (x^2-a^2)| + C`

5) `int (dx)/sqrt (a^2 - x^2) = sin ^(-1) (x/a) +C`

6)  `int (dx)/sqrt (x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C`

7) To find the integral `int (dx)/(ax^2 + bx + c)`

8) To find the integral of the type `int (dx)/sqrt(ax^2 + bx + c)`

9) To find the integral of the type `int (px + q)/(ax^2 + bx + c) dx`

10) For the evaluation of the integral of the type `int (px + q)/sqrt(ax^2 + bx + c) dx`

• Simple curves: lines, parabolas, polynomial functions

• Definition of ordinary differential equation
• Order and degree of a differential equation
• Formation of ordinary differential equation

• Solution of a Differential Equation

• Formation of Differential equations from Physical Situations
• Formation of Differential Equations from Geometrical Problems

• Solutions of linear differential equation of the type:

1. `dy/dx` + py = q, where p and q are functions of x or constants.
2. `dx/dy` + px = q, where p and q are functions of y or constants.

• Differential equations, order and degree.
• Solution of differential equations.
• Variable separable.
• Homogeneous equations
• Linear form `dy/dx` + Py = Q where P and Q are functions of x only. Similarly, for `dx/dy`.

• Formula
• Division of Line Segment
• Proof
• Examples

• Equation of a locus

• Slope of a Line Or Gradient of a Line.
• Parallelism of Line
• Perpendicularity of Line in Term of Slope
• Collinearity of Points
• Slope of a line when coordinates of any two points on the line are given
• Conditions for parallelism and perpendicularity of lines in terms of their slopes
• Angle between two lines
• Collinearity of three points

• Points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle.

• Standard equation of the ellipse
• Special cases of an ellipse
• Tangent to an ellipse
• Equation of tangent to the ellipse
• Condition for tangency
• Tangents from a point to the ellipse
• Locus of point of intersection of perpendicular tangents
• Auxilary circle and director circle of the ellipse

• Coplanar
• Skew lines
• Distance between two skew lines
• Distance between parallel lines

• Introduction of Distance of a Point from a Line
• Distance between two parallel lines

3.3.1 Combined equation of the pair of straight lines

3.3.2 Pair of straight lines passing through the origin

3.3.3 Angle between pair of straight lines passing through the origin

3.3.4 The condition for general second degree equation to represent the pair of straight

lines

•  Equation of the bisectors of the angle between the lines
•  General form of Pair of Straight Lines

• Formula
• Division of Line Segment
• Proof
• Examples

• Direction cosines of a line passing through two points.

• Coplanar
• Skew lines
• Distance between two skew lines
• Distance between parallel lines

• Slope of a Line Or Gradient of a Line.
• Parallelism of Line
• Perpendicularity of Line in Term of Slope
• Collinearity of Points
• Slope of a line when coordinates of any two points on the line are given
• Conditions for parallelism and perpendicularity of lines in terms of their slopes
• Angle between two lines
• Collinearity of three points

• Introduction of Distance of a Point from a Line
• Distance between two parallel lines

• Distance between skew lines
• Distance between parallel lines

• Equation of a plane when a normal to the plane and the distance of the plane from the origin are given
• Equation of a plane perpendicular to a vector and passing through a given point
• Intercept form of the equation of a plane
• Equation of a plane passing through three given non-collinear points
• Equation of a plane passing through a given point and parallel to two given non-parallel vectors
• Equation of a plane passing through two given distinct points and is parallel to a non-zero vector
• Condition for a line to lie in a plane
• Condition for coplanarity of two lines
• Equation of plane containing two non-parallel coplanar lines
• Angle between two planes
• Angle between a line and a plane
• Distance of a point from a plane
• Distance between two parallel planes
• Equation of line of intersection of two planes
• Equation of a plane passing through the line of intersection of two given planes

• Passing through a point and perpendicular to a vector
• Passing through a point and parallel to two vectors
• Passing through three non-collinear points
• In normal form
• Passing through the intersection of two planes

• Introduction
• Scalars and Vectors
• Scalar vs Vector
• Key Points to Remember

• Formula
• Division of Line Segment
• Proof
• Examples

• Introduction

• Definition: Median
• Formula: Odd Number of Observations
• Formula: Even Number of Observations
• Example 1
• Example 2
• Example 3
• Key Points Summary

1. Variance and Standard Deviation for raw data
2. Variance and Standard Deviation for ungrouped frequency distribution
3. Variance and Standard Deviation for grouped frequency distribution

• Mean deviation for grouped data
• Mean deviation for ungrouped data

• Partition of a sample space
• Theorem of total probability

• Independent Events

• Properties of Δ
• Sine formula: `a/sinA=b/sinB=c/sinC`
• Cosine formula:`cosA=(b^2+c^2-a^2)/(2bc)`, etc
• Area of triangle:Δ = `1/2`bc A etc
• Simple applications of the above

• Definition:  Line of Sight
• Definition: Angles of Elevation
• Definition: Angle of Depression

• Domain and Range of Trignometric Functions and Their Graphs

• Validating the Statements Involving the Connecting Words
• statement with “and”
• Statements with “or”
• “Implies”
• “Implied by”
• Statements with “If then” 
• Statements with “if and only if”

• Universal quantifier (∀)
• Existential quantifier (∃)

• Definition:  Linear lnequations 
• Signs of Inequality
• Definition: Replacement Set / Domain of Variable
• Definition: Solution Set
• Properties

• Rules to solve inequation

• The Law of Sines or Sine Formula

• Law of Sines
• Law of Cosines
• Projection Formula
• Projection Formula
• Half-Angle formula

• Area of a triangle (Heron’s Formula )

• If all the sides and all the angles of a polygon are equal, it is called a regular polygon.
• Sum of interior angles of an 'n' sided polygon ( whether it is regular or not) = ( 2n - 4 )rt. angles and sum of its exterior angles = 4 right angles = 360°
• At each vertex of every polygon, Exterior angle + Interior angle = 180°.
• Each interior angle of a regular polygon = `[( 2n - 4 ) "rt. angles"]/[n] = [( 2n - 4 ) xx 90°]/n`
• Each exterior

• Definition:  Line of Sight
• Definition: Angles of Elevation
• Definition: Angle of Depression