Set theory

1. Introduction to set
2. Subset and power set
3. Intersection of sets
4. Union of sets
5. Difference of sets
6. Complement of sets
7. Properties of Operations on Sets
8. Intervals
9. Cardinal number of set
10. lecture

Intervals Inequalities

1. Linear inequalities in one variable
2. Linear inequalities in two variables
3. Values of square
4. Values of reciprocal
5. Sign Scheme Method

Modulus of real number

1. Modulus_Introduction
2. General definition of modulus and equations
3. Inequalities involving Modulus
4. Modulus Advanced

Relation and functions

1. Cartesian product of sets
2. relation and functions
3. Range of elementary functions_Part I
4. Range of elementary functions_Part II
5. Graph of quadratic functions

Complex Numbers

1. Imaginary number
2. Complex number_Introduction
3. Algebraic operations of complex numbers
4. Properties of conjuage of complex number
5. Equality of complex numbers
6. Cube roots of unity_Part I
7. Cube roots of unity_Part I
8. Polar form of complex number_Theory
9. Polar form of complex number_Problems discussion
10. Problems based on modulus and argument_Part I
11. Problems based on modulus and argument_Part II
12. Multiplication and division of complex numbers in polar form_Part I
13. Multiplication and division of complex numbers in polar form_Part II
14. De’Moivres theorem
15. Product of complex number and its conjugate equals the square of modulus of complex number
16. Collinearity of two non-zero complex numbers and origin
17. Inequalities involving complex numbers
18. Locus based on modulus_Theory
19. Locus based on Modulus of Complex Number_Problems discussion
20. Locus based on argument of complex number_equation of ray
21. Angle between two lines in argand plane
22. Rotation formula_Part II
23. Rotation formula_Part II
24. Equation of line in complex number
25. nth roots of unity_Theory
26. nth roots of unity_Problems discussion

Quadratic Equations

1. General
2. Remainder and factor theorem new
3. Nature of roots
4. Sum and product of roots
5. One Common Root_Part I
6. One commont root_Part II
7. two common roots
8. Use of discriminant
9. Sign of quadratic function
10. Location of roots

Logarithm

1. Exponential Function
2. Logarithm and logarithmic function
3. Properties of logarithm_Part I
4. Properties of logarithm_Part II
5. Logarithmic equations
6. Logarithmic inequalities

Progression and Series

1. Sequence and series
2. Arithmetic progression_Introduction
3. Arithmetic mean of two numbers
4. Selection of terms in AP
5. Properties of AP
6. Arithmetic means
7. Sum of A.P._Part I
8. Sum of A.P._Part II
9. Geometric Progression_Introduction
10. Geometric mean of two numbers
11. Selection of terms of G.P.
12. Properties of G.P.
13. Geometric means
14. Sum of terms of G.P._Part I
15. Sum of terms of G.P._Part II
16. Applications of sum of GP
17. Infinite G.P. and its sum
18. Harmonic Progression_Part I
19. Harmonic Progression_Part II
20. Harmonic Means
21. Relations between AM, GM and HM
22. Sum of series using sigma_Part I
23. Sum of series using sigma_Part IIR
24. Finding nth term from the given sum of n
25. AGP
26. Multiple sigma with dependent & independent variables
27. Sum of series by method of difference_I
28. Sum of series by method of difference_II

Binomial Theorem

1. Binomial expansion – general
2. Finding coefficients
3. Sum of coefficients
4. Greatest term
5. Series – part 1
6. Series – part 2
7. Miscellaneous

Permutation and Combination

1. Counting principle_Part I
2. Counting principle_Part II
3. Factorial notation
4. Exponent of prime in factorial
5. Permutation_Formula
6. Permutations with restrictions_Part I
7. Permutations with restrictions_Part II
8. Permutations with identical objects
9. Combinations_Formula
10. Properties of Combinations formula
11. Problems based on combinations_Part I
12. Problems based on combinations_Part II
13. Combination and arrangement
14. Problems based on Chessboard
15. Selection from objects which are not all distinct
16. Circular permutations
17. All possible selection from distinct objects
18. All possible selection from identical objects
19. Divisors of natural number
20. Division and distribution of distinct objects_Unequal fixed group
21. Division and distribution of distinct objects_Mix of equal and unequal fixed groups
22. Distribution of distinct objects in any way
23. Distribution of identical objects_Theory
24. Distribution of identical objects_Problems discussion
25. Distribution of identical objects_applications
26. Principle of inclusion and exclusion
27. Derangement
28. Multinomial Theorem

Introduction to Limits

1. Limits

Probability 

1. Experiment and Sample space
2. Event
3. Axiomatic approach to probability
4. Probability based on permutation and combination_Part I
5. Probability based on permutation and combination_Part II
6. Probability based on permutation and combination_Part III
7. Addition theorem of probability

Mathematical Induction

1. PMI_Introduction_Problems based on series
2. Problems based on divisibility
3. Problems based on inequalities

Properties and Solutions of Triangle

1. Sine rule
2. Cosine ruleRX
3. Projection rule, half angle formula, area of triangle
4. Circumcircle of triangle and lengths associated with it
5. Incircle of triangle and lengths associated with it
6. Orthocentre and lengths associated with it
7. Excenters and lengths associated with it

Trigonometric ratios and identities       

1. Problems based on trig. identities
2. Measurement of angle and trigonometry function for more than right angle
3. Graphs of trigo. functions and their range
4. Trigonometric ratios for allied angles
5. Compound angle formulas for sine and cosine_Part I
6. Compound angle formulas for sine and cosine_Part II
7. Expression acos x + bsin x
8. Compound angle formulas for tangent
9. Transformation formula_Product to addition and difference
10. Transformation formulas_Addition and subtrction to product
11. Multiple angle formulas_Part I
12. Multiple angle formula_Part II
13. Multiple angle formula_Part III
14. Multiple angle formula_Part IV
15. Conditional identities in triangle
16. Value of sin18 and cos 36
17. Important results of multiple angle formula
18. Range of expression using trig. substitution
19. Trigonometric inequalities in triangle
20. Sum of sines and cosines when angles are in A.P.

Trigonometric equations

1. Trigonometric Equations – Part 1
2. Trigonometric Equations – Part 2
3. Important points for solving trigonometric  equations
4. Trigonometric Equations based on extreme values

Properties and Solution of triangles

1. Sine rule
2. Cosine rule
3. Projection rule, half angle formula, area of triangle
4. Circumcentre, incentre and lengths associated with it
5. Orthocentre and lengths associated with it
6. Ex-centers and lengths associated with it

Cartesian coordinate system and Straight Lines    

1. Section formula
2. Area of triangle
3. Slope of line
4. Centroid of triangle
5. Incenter of triangle
6. Orthocentre of triangle
7. Equation of line – Point slope form
8. Equation of line – slope intercept form
9. Equation of line – intercept form
10. Parametric form of straight lines_1
11. Parametric form of straight lines_2
12. Family of st. lines
13. Distance of point from the line
14. Equation of angle bisectors
15. Concurrency of lines
16. Position of point w.r.t. line
17. Locus
18. Pair of straight lines_introduction
19. Angle between pair of straight lines
20. Homogenization

Circles

1. Equation of circle_Center-radius form
2. Equation of circle in general form
3. Equation of circle_endpoints of chord and included angle
4. Equation of circle in parametric form
5. Elementary locus problems
6. Equation of midpoint chord of circle
7. Position of point w.r.t. circle
8. Length of tangent to circle
9. Position of line w.r.t. circle
10. Equation of tangent at a given point on the circle
11. Equation of tangnet having given slope
12. Tangent to circle from external point
13. Chord of contact of circle
14. Director circle
15. Radical axis of circles
16. Two non-intersecting circles_disjoint circles
17. Two circles touching each other
18. Two intersecting circles
19. Radical axis and orthogonal intersection of circles
20. Angle between circles and orthogonal intersection
21. Family of circles

Parabola

1. Parabola_Definition
2. Standard equation of parabola
3. Parametric equations of standard equation of parabola
4. Parabola having axis parallel to y-axis
5. Parabola having axis parallel to x-axis
6. Division of plane by parabola
7. Equation of midpoint chord of parabola
8. Focal chord of parabola and its properties
9. Tangent to parabola having eq. y^2=4ax_Part I
10. Tangent to parabola having eq. y^2=4ax_Part II
11. Tangent to parabola having eq. other than y^2=4ax
12. Point of intersection of tangents to parabola y^2=4ax
13. Locus problems of pt. of intersection of tangents to parabola y^2=4ax
14. Tangents to parabola from external point
15. Chord of contact of parabola
16. Normal to parabola at a point on it or having given slope
17. Normal to parabola from a point not lying on parabola
18. Properties of normal to parabola
19. Conormal points of parabola and its properties

Ellipse

1. Equation of ellipse
2. Tangent to ellipse_Theory
3. Tangent to ellipse at at point on it_Problems discussion
4. Tangent having given slope and tanent from outside point
5. Director Circle of Ellipse
6. Tangent and normal to ellipse

Hyperbola

1. Hyperbola_Definition_1
2. Hyperbola_Definition_2
3. Standard equation of hyperbola
4. Problems based on standard equation of hyperbola
5. Equation of hyperbola having axes parallel to coordinate axes
6. Equation of hyperbola having given lines as its axes
7. Rectangular hyperbola xy = c^2
8. Equation of hyperbola in parametric form
9. Chords of hyperbola
10. Equation of tangent to hyperbola at a point on it
11. Asymptotes of hyperbola
12. Tangent to hyperbola having given slope_Part I
13. Tangent to hyperbola having given slope_Part II
14. Tangent to hyperbola from a point not lying on it
15. Normal to hyperbola_Part I
16. Normal to hyperbola_Part II
17. Properties of tangent
18. Orthogonal intersection of ellipse and hyperbola
19. Problems based on rectangular hyperbola xy=c^2

Determinant

1. Introduction and Expansion of Determinant_Part I
2. Introduction and Expansion of Determinant_Part II
3. Sarrus rule of expansion
4. Properties of determinant_Theory_Part I
5. Properties of determinant_Theory_Part II
6. NCERT problems on prop. of det._Part I
7. NCERT problems on prop. of det._Part II
8. Problems_Prop. of det._Part I
9. Problems_Prop. of det._Part II
10. Problems_Prop. of det._Part III
11. Differentiation of Determinant
12. Product of determinants_Part I
13. Product of determinants_Part II
14. System of equations in two variables
15. System of equations in two variables_Part I
16. System of equations in two variables_Part II

Matrices

1. Matrices_Introduction
2. Classification of matrices
3. Important points about matrix
4. Addition of matrices
5. Multiplication of matrix by scalar
6. Product of matrices
7. Product of matrices_Problems discussion
8. Elementary properties of of product of matrices
9. Associative property of product of matrices
10. Commutative property of product of matrices
11. Transpose of product of matrices
12. Determinant of product of matrices
13. Some special matrices
14. Adjoint of matix
15. Properties of adjoint of matrix
16. Inverse of matrix
17. Properties of inverse of matrix_Part I
18. Properties of inverse of matrix_Part II
19. Inverse of matrix using elementary transformations
20. Solving system of equations using matrix

Probability

1. Conditional probability
2. Multiplication theorem on probability
3. Independent events
4. Total probability theorem
5. Bayes theorem
6. Random variable and probability distribution
7. Bernoulli’s trials and binomial distribution

Introduction to Vectors

1. Vectors(introduction)
2. Dependent and independent vectors

Different product of vectors

1. Dot product
2. Problem based on dot product
3. Dot product_Square of sum of vectors
4. Solving Vector equations using dot product
5. Vector cross product_theory
6. Problems based on cross product_Part I
7. Problems based on cross product_Part II
8. Cross product as area of parallelogram
9. Cross product_JEE problems
10. Scalar triple product_definition
11. Problems based on STP
12. Properties of STP
13. STP as volume of parallelepiped
14. Vector triple product_Part I
15. Vector triple product_Part II
16. 16_Solving vector equations using VTP
17. Vector product of four vectors
18. Reciprocal system of vectors

3-D Geometry

1. Straight lines
2. Plane – part 1
3. Plane – part 2
4. Line and plane in space

Inverse Trigonometric Functions(ITF)

1. ITF_Defintion
2. ITF_Graphs
4. Problems based on definition of ITFs
5. Problems based on definition of ITF_Part II
6. sin inverse of sin x and cosec inverse of cosec x
7. cos inverse of cos x and sec inverse of sec x
8. Tan inverse of tan x and cot inverse of cot x
9. Writing one ITF in terms of other ITF
10. Relating ITFs of arguments of opposite sign and equal in magnitude
11. Relating ITFs of arguments which are reciprocal to each other
12. Simplifying ITFs using substitution
13. Complementary angles in terms of ITFs
14. Addition of tan inverse functions_Part I
15. Addition of tan inverse functions_Part II
16. Addition of tan inverse functions_Part III
17. Sum of series using diff. of angles in tan inverse functions
18. Sum and difference of cos inverse functions

Functions and Relations

1. Cartesian product and relation
2. Different types of relations
3. Function_definition
4. Sign scheme (wavy curve) method for solving inequalities_Part I
5. Sign scheme (wavy curve) method for solving inequalities_Part II
6. Applications of sign scheme method
7. Concept of squaring in inequalities
8. Concept of reciprocal in in equaliities
9. Functions involving quadratic expressions_Part I
10. Functions involving quadratic expressions_Part II
11. Domain and range of functions involving trig, functions_Part I
12. Domain and range of functions involving trig, functions_Part II
13. Domain and range of functions involving itf
14. Exponential function
15. Logarithmic function_Part I
16. Logarithmic functions_Part II
17. Applications of logarithmic inequalities
18. Greatest integer function
19. Properties of GIF
20. Graph of GIF and its applications
21. Fractional part function
22. Graph of fractional part function and its applications
23. Signum function
24. Function max. of and min. of
25. Idential functions
26. Methods to check injective and surjective nature of the fun._Part I
27. Methods to check injective and surjective nature of the fun._Part II
28. Odd even functions
29. Properties of odd and even functions
30. Functional equations of odd and even functions
31. Periodic functions
32. Period of transformed and composite functions
33. Period of fun. obtained algebraic operations
34. Functional equations of periodic functions
35. Inverse function_Part I
36. Inverse function_Part II
37. Properties of inverse functions
38. Composite function
39. Definition of composite function
40. Injectivity and surjectivity of composite functions
41. Finding function from funcational equations
42. Transformation of graphs
43. Transformation of graphs involving modulus
44. Function based on max.-min value in variable interval

Limits

1. Limits – elementary
2. Limits – algebraic
3. Limits – trigonometric
4. Limit of function involving exponential functions
5. Limit of function involving logarithmic functions
6. One power infinity form_Part 1
7. One power infinity form_Part 2
8. L’Hospital rule
9. L’Hospital rule to evaluate limits of other indeterminate forms
10. Limits – use of expansion
11. Limits – finding unknowns

Method of Differentiation

1. Differentiation – elementary
2. Differentiation using chain rule
3. Differentiation involving inverse trigo. functions
4. Differentiation of implicit functions
5. Differentiation using Logarithm
6. Differentiation of parametric from of equation
7. Differentiation of determinant and misc
8. Successive differentiation
9. Successive differentiation of parametric form of function
10. Differentiation of inverse function
11. Finding function or derivative from functional equation_Part 1
12. Finding function or derivative from functional equation_Part 2

Continuity of Function 

1. Continuity of Function_Definition
2. Different types of discontinuity of function
3. Defining a func at missing point discont
4. Finding unknowns if function is continuous
5. Continuity of function involving signum function
6. Continuity of function involving limit at infinity
7. Cont. of fun. differently defined for rational and irrational numbers
8. Continuity of functions involving GIF_Part 1
9. Continuity of functions involving GIF_Part II
10. Algebraic operations of cont.-disc. functions
11. Application of cont. functions and intermediate value theorem

Differentiability of Functions

1. Differentiability – part 1
2. Differentiability – part 2
3. Differentiability of product function_Important concept

Application of Derivatives

1. Slope of tangent and normal
2. Equation of tangent and normal at a given point on the curve
3. Equation of tangent and normal having given slope
4. Equation of tangent and normal from a point not lying on the curve
5. Angle between curves
6. Application of Tangent – normal
7. Approximations
8. Derivative as rate of change
9. Rolles theorem
10. Rolles theorem_Selecting function
11. Mean value theorem_Introdution
12. Selecting function for mean value theorem
13. Inequalities using mean value theorem
14. Cauchy’s mean value theorem

Monotonocity and 

1. Increasing_Decreasing function
2. Monotonicity_Important points
3. Seperating the intervals of Monotonicity
4. Finding unknowns using monotonicity
5. Finding numbre of roots using monotonicity_Part I
6. Inequalities using monotonicity

Extremum of Functions

1. Maxima-minima of functions
2. Maxima_Minima when critical points cannot be evaluated
3. Applications of maxima-minima
4. Graph plotting_1
5. Graph plotting_2

Indefinite Integration

1. Indefinite integration(elementary)
2. Integration by elementary substitution
3. Reciprocal of quadratic
4. Integration by partial fractions
5. Integration by parts
6. Integration by Cancellation
7. Integration by typical substitution
8. Integration of irrational function_substitution technique

Definite Integration

1. Definition and definite integration as limit of sum
2. Properties of definite integration_Part I
3. Properties of definite integration_Part II
4. Properties of definite integration_Part III
5. Definite integration of odd and even function
6. Definite integration of periodic functions
7. Definite integration using substitution_Part I
8. Definite integration using substitution_Part II
9. Definite integration using substitution_Part III
10. Leibniz rule_Introduction
11. Leibniz rule_Higher level problems
12. Leibniz rule when integrand is function to two independent variables
13. Finding limit of function using leibniz rule and l’ho
14. Applications of leibniz rule in monotonicity of function
15. Miscellaneous

Area

1. Area bounded by curve and axis_Part I
2. Area bounded by curve and axis_Part II
3. Area bounded by two curves_Part I
4. Area bounded by two curves_Part II
5. Area bounded by curves involving Trigo Function
6. Area bounded by curves involving logarithmic function
7. Area bounded by implicit functions
8. Finding Area without integration

Differential Equation

1. Differential eq._definition and formation
2. Solving Diff. Eq._Variable separable type
3. Solving Diff. Eq._Homogeneous diff. equations
4. Solving Diff. Eq._General form of variable separation
5. Solving Diff. Eq._Linear Diff. Equations
6. Solving Diff. Eq._Reducible to LDE
7. Applications of Diff. Equations
8. Miscellaneous problems_Linear Diff. Eq.