JEE Mathematics for 12th Class Timeline

Real Functions (April) 

1. Set Theory, Cartesian Product of Sets, Definition of Relation.

2. Types of Relations, Domain, Co-domain & Range of a Relation.

3. Definition of Function, Domain, Co-domain and Range of a Function.

4. Domain, Range, Properties & Graphs Of Standard Functions

5. Different Method of Finding Range

6. Even and Odd Functions and their properties

7. Classification of Function : 

   • One One & Many One Functions

   • Onto & Into Functions

8. Transformation of Graphs

9. Composition of Functions

10. Homogeneous Functions & Bounded Functions.

11. Implicit & Explicit Functions

12. Periodic Functions

13. Inverse of a Function 

14. Functional Equation

15. Miscellaneous Problem

Inverse Trigonometric Functions (May)

1. Definition Of Standard I.T.F.

2. Domain , Codomain & Range of I.T.F.

3. Properties of I.T.F.

4. Interconversion of one I.T.F. into other

5. ITF Equation

6. ITF Inequality

7. Simplification of Composite ITF into Standard ITF

8. Series involving I.T.F.

9. Miscellaneous Illustrations

Limits (May)

1. Definition of Limits of a Function

2. Existence of limit of function about a Point.

3. Indeterminate Forms

4. Algebra of Limits

5. Methods of Evaluating Limits 

6. Standard Limits

7. Evaluation of Algebraic Limits Tending to Infinity

8. Ľ Hospital's Rule

9. Sandwich Theorem

10. Finding Unknowns When Limit is given

11. Limits using Expansion

12. Miscellaneous

Continuity (June)

1. Definition of Continuity about a Point

2. Types of Discontinuity

3. Continuity in an Interval

4. Theorems on Continuity

5. Intermediate Value Theorem

6. Single Point Continuity

7. Properties of Functions Continuous in a Closed Interval

8. Miscellaneous Illustrations

Differentiability (June)

1. Differentiability about a point

2. Relation Between Differentiability & Continuity

3. Properties / Standard Results on Differentiability

4. Differentiability in an Interval

5. Functional Equations

6. Miscellaneous

Method of Differentiation (July)

Geometrical Meaning of Derivative

Standard Derivatives.

Diff- of I.T.F

Theorems on Derivatives

Diff. Of composite Functions. (Chain Rule)

Diff. of Implicit fn.

Diff. of Functions in Parametric Form

Diff using Logarithms

Diff. of a Fn. W.R.T. Other Fn

Higher order Derivatives.

Miscellaneous

Tangent & Normal (July)

Equation of Tangent to a Curve at a Given Point

Equation of Normal to a Curve at a Given Point

Angle between the Curves

Orthogonality of Curves

Length of Tangent & Sub-Tangent

Length of Normal & Sub-Normal

Shortest Distance Between Two Curves.

Rate Measurement (July)

Interpretation of dy/dx are a Rate Measurer.

Approximations.

Monotonicity (July)

Monotonicity of a fn. at a Point.

Monotonicity of a Function in an Interval.

Strictly Increasing / Decreasing Functions.

Point of Inflection, Concavity

Inequalities using Monotonicity

Maxima & Minima (July)

Local Maxima, Local Minima

Second Order Derivative Test in Ascertaining the Maxima or Minima

nth Derivative Test, Global Max./Min.

Applications of extremum (optimization, Plane Geometry,)

Mean Value Theorem (July)

Rolle's Theorem

Applications of Rolle's Theorem

L.M.V.T (Statement)

Applications L.M.V.T

Miscellaneous

Determinants (August)

Introduction, Minors & Co-Factors.

Evaluations of determinants using Co-Factors.

Properties of Determinants

Multiplication of Determinants.

Differentiation of Determinant

Cramer's Rule.

Miscellaneous

Matrix (August)

Introduction

Order of a Matrix.

Types of Matrix

Algebra of matrices

Properties of Addition (Commutative, Associative, Existence of identity, Inverse )

Multiplication of Matrices by Scalar.

Multiplication of two Matrices

Properties of matrix Multiplication

Nilpotent Matrix.

Idempotent matrix

Involutory Matrix.

Transpose of a matrix

Properties of Transpose.

Symmetric & Skew Symmetric matrices

Properties of Symmetric & Skew Symmetric

Adjoint of a Matrix.

Properties of adjoint of Matrix

Inverse of a Matrix

Properties of Inverse of a Matrix

Characteristic Equation

Miscellaneous

Indefinite Integration (September)

Introduction: Integration as reverse process of Differentiation.

Fundamental Integration Formula

Properties Indefinite Integration

Some more Standard Formula∫tanxdx,∫cotxdx,∫sec x dx,∫cosec x dx)

Integration by Substitution

Integrations of the Form∫dx/quadratic

Integrations of the form∫(px+q)dx/ax²+bx+c

Integrations by Parts

Integration of the form(ex(f(x)+f'(x)dx

Integration of the form∫sinbx dx

Integration by partial Fractious

Integration of the form∫√Quad.dx

Integration of the form (Linear.∫√Quad dx)

Integral of the form∫(sinmx.cosnx)dx

Integral of the form(∫dx/a+bsinx+bcosx)

Integral of the form(∫dx/a+bsin²x+cos²x)

Integral of the form∫(pcosx+qsinx+r/acosx+bsinx+c)dx

Integration of the form∫dx/L√L, ∫dx/L√Q, ∫dx/Q√L, ∫dxQ√Q

Miscellaneous

Definite Integration (September)

Fundamental Theorem of Integral Calculus

Geometrical Interpretation of Definite Integration

Property a,b

Property c,d

Property e,f

Property g,h,I

Newton Leibnitz Theorem

Wallis method

Definite integral by first principle (as sum of Infinite Series)

Estimations

Reduction Formula

Miscellaneous

Area under the curve (October)

Area under the Curves (Introduction)

Curve Tracing

Area Bounded between two Curves.

Miscellaneous

Differential Equation (October)

Definition of D.E

Order of D.E

Degree of D.E

D.E. first order & first Degree

Formation of D.E.

Solution of D.E.

Method of variable Separable

Homogenous D.E.

Linear D.E.

Equations reducible to Homogeneous Form.

Equations reducible to linear Form.

Trajectory. (Orthogonal)

Other Geometrical applications of D.E.

Word problems of D.E.

Miscellaneous

Vector (November)

Introduction

Null or Zero Vector, Unit Vector.

Equal Vectors, Parallel Vectors

Like Vectors, Unlike Vectors

Negative Vectors.

Co-initial Vectors, Co-terminus Vectors

Fixed Vectors, Free Vectors

Collinearity, Co-planar Vectors

Vector addition (Triangle law, Parallelogram Laws)

Position vector, Distance Formula, Section Formula

Vector equation of a straight line passing through a given point & parallel to a given Vectors.

Cartesian Equation of Line.

Vector & Cartesian form & straight live through two given Points

Angle between two Lines

Intersection of Lines

Skew lines. (Definition)

Dot product (Scalar product )

Cross product (vector product) of two Vectors

Shortest distance between Two Lines

Scalar Triple Product

Vector Triple Product

Linearly Dependent & Independent Vectors.

Reciprocal System of Vectors

Miscellaneous

Three Dimensional Geometry (December)

Introduction, D.C, D'R of Line.

Introduction of Plane

Equation of plane in Normal Form

Equation of plane through a given point and perpendicular to a given Direction

Equation of plane through three non-collinear Points.

Equation of plane through two given points & parallel to a given Vector

Plane passing through a given point & parallel to two given Vectors.

Intercept form of a Plane.

Angle b/w two Planes

Condition of perpendicularity of two Planes

Condition of parallelism of two Planes

Angle b/w line & a Plane.

Image of a point in a Plane

Distance of a point from a Plane

Equation of a plane through the intersection of two Planes

Equation of planes bisecting the angles between two given Planes

Miscellaneous

Probability (December)

Introduction

Definitions: Random Experiments, Sample Space, Events

Types of Events: (Simple / Elementary Event) & Mixed Event or Compound Event

Equally likely Events

Exhaustive Events.

Mutually Exclusive Events

Mutually Independent Events.

Dependent Events

Complementary Events

Probability of Occurrence of an Event.

Odds in favour & Odds Against an Event

Algebra of Events, Venn Diagrams.

Conditional Probability, Multiplication Theorem of Probability

Law of Total Probability

Bayes theorem

Binomial Theorem on Probability.

Probability distribution of the random variable.

Binomial Distribution

Coincidence Testimony.

Geometrical Probability

Statistical Probability

Miscellaneous Illustrations