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Set theory

  1. Introduction to set
  2. Subset and power set
  3. Intersectoin 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

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. Relation and Functions

Complex Numbers

  1. Introduction to imaginary number
  2. Structure of complex number and its operations
  3. Comparison of complex numbers
  4. Polar form of complex number
  5. Properties of polar form
  6. De-Moivres theorem
  7. Cube roots of unity
  8. Collinearity of origin and two non-zero complex numbers
  9. Inequalities
  10. Locus based on modulus_Theory
  11. Locus based on Modulus of Complex Number Questions
  12. Angle between two lines
  13. Geometry using Argument of complex numbers
  14. Rotation formula in complex numbers

Quadratic Equations

  1. General
  2. Remainder and factor theorem new
  3. Nature of roots
  4. Sum and product of roots
  5. Common roots
  6. Use of discriminant
  7. Sign of quadratic function
  8. Location of roots


  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. General term of AP
  2. Sum of AP
  3. GP and its general term
  4. Sum of n terms of GP
  5. Harmonic Progression
  6. Sigma operator and method of difference
  7. Finding nth term from the given sum of n terms
  8. Multiple sigma with dependent & independent variables
  9. AGP
  10. Sum of series by method of difference_I
  11. 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. Factorial notations
  2. Counting principal
  3. Permutations of distinct objects
  4. Permutation of objects in which some objects are identical
  5. Circular permutations
  6. Combination – formula
  7. Problems based on combinations
  8. Problems based on combinations – part 2
  9. All possible selections
  10. Division distribution of distinct objects
  11. Distribution of identical objects
  12. Principle of inclusion and exclusion
  13. Derangement


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Trigonometric ratios and identities                                                                                              

  1. Measurement of angle and trigonometry function for more than right angle
  2. Graphs of trigo. functions and their range
  3. Trigonometric ratios for allied angles
  4. Problems based on trig. identities
  5. Trig. Ratios for Compound angles
  6. C- D formula
  7. Multiple angle formulas_Part I
  8. Multiple angle formula_Part II
  9. Important results of multiple angle formula
  10. Multiple angle formula_Part III
  11. Value of sin 18 and cos 36
  12. Range of expression using trig. substitution
  13. Trigonometric inequalities in triangle

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

Coordinate Geometry

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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


  1. Circle equation
  2. Circle equation – part 2
  3. Tangent to circle
  4. Radical axis and different cases of two circels
  5. Angle between circles and orthogonal intersection
  6. Family of circles
  7. Locus problem


  1. Equation of parabola
  2. Focal Chord
  3. Tangent having given slope_Tangent at a given point on the curve_Theory
  4. Tangent having given slope_Tangent at a given point on the curve_Problems discussion
  5. Common Tangent
  6. Tangent from external point
  7. Properties of Tangent of parabola
  8. Normal to parabola at a point on it or having given slope
  9. Normal to parabola from a point not lying on it
  10. Normal – chord of contact to parabola


  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


  1. Hyperbola – equation
  2. Hyperbola – tangent – normal – coc etc
  3. Reflection property of ellipse and hyperbola

Algebra/Vectors & 3D Geometry

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  1. Introduction and Expansion of Determinant
  2. Sarrus rule of expansion
  3. Properties of determinant_Theory
  4. Problems based on property of determinant_NCERT Based
  5. Problems based on properties of determinant_Part II
  6. Problems based on properties of determinant_Part III
  7. Differentiation of Determinant
  8. Product of determinants
  9. System of equations in two variables
  10. System of equations in three variables


  1. Elementary matrices
  2. Product of matrices, transpose of matrices
  3. Adjoint and inverse of matrices
  4. Special matrices and system of equations
  5. Problems based on determinant of matrix


  1. Probability – elementary
  2. Independent events
  3. Dependent events and total probability theorem
  4. Bayes theorem

Introduction to Vectors

  1. Vectors(introduction)
  2. Dependent and independent vectors
  3. Dot and cross product
  4. Vector triple product
  5. Finding Vector
  6. Finding Vector by Solving Vector Equations
  7. Vector_Tetrahedron

3-D Geometry

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


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Inverse Trigonometric Functions(ITF)

  1. Domain, range, graphs of trigonometric inverse functions
  2. Principal Values of Inverse of sine_more detailed
  3. Principal values of cos inverse function_More detailed
  4. Relating Different ITF
  5. Simplifying ITF using substitution
  6. Complementary angles
  7. Sum of two arctanRX
  8. Addition-subtration of two or more inverse trigonometric functions
  9. Addition and subtration of angles in terms of cos inverse function

Functions and Relations

  1. Inequalities and its use in functions
  2. Modulus function
  3. Sign scheme method for solivng inequalities
  4. Domain and Range of Functions involving trigonomteric functions
  5. Domain and range of functions involving itf_video
  6. Exponential & Logarithmic functions
  7. Greatest integer, fractional part, signum and other miscellaneous functions
  8. Odd and even functions
  9. One-one, many-one, onto and into functions
  10. Periodic functions
  11. Functional Equations_part_1
  12. Functional Equations_Part_2
  13. Functional Equations_Part_3
  14. Functional Equations_Part 4
  15. Identical functions
  16. Graphical transformations
  17. Inverse functions
  18. Injectivity & Surjectivity of composite functions


  1. Limits – elementary
  2. Limits – algebraic
  3. Limits – trigonometric
  4. Limits – exp and logarithm
  5. Limits – One power infinity form_Part I
  6. One power infinity_Shortcut formula
  7. Limits – L’Hopital rule
  8. Limits – use of expansion
  9. Limits – finding unknowns

Continuity of Function 

  1. Continuity – definition
  2. Continuity of functions involving GIF_Part 1
  3. Continuity of functions involving GIF_Part II
  4. Cont. of fun. differently defined for rational and irrational numbers
  5. Algebraic operations of cont.-disc. functions
  6. Application of cont. functions and intermediate value theorem
  7. Differentiability of product function_Important concept

Differentiability of Functions

  1. Differentiability – part 1
  2. Differentiability – part 2

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 functions in parametric form
  7. Differentiation of determinant and misc.
  8. Successive differentiation
  9. Finding function or derivative from functional equation
  10. Differentiation of inverse function

Application of Derivatives

  1. Tangent and normals
  2. Angle between curves
  3. Application of Tangent – normal
  4. Approximations
  5. Rolle’s Theorem
  6. Rolle’s theorem_Selecting function
  7. LMVT

Monotonocity and Extremum of Functions

  1. Monotonocity
  2. Finding number of roots using monotonicity
  3. Inequalities using monotonicity
  4. Maxima-minima of functions
  5. Maxima_Minima when critical points cannot be evaluated
  6. Applications of maxima-minima
  7. Graph plotting_1
  8. Graph plotting_2

Indefinite Integration

  1. Indefinite integration(elementary)
  2. Integration by elemnetary substitution
  3. Reciprocal of quadratic
  4. Integration by partial fractions
  5. Integration by parts
  6. Integration by typical substitution
  7. 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 – even and periodic functions
  6. Substitution and by parts
  7. Reciprocal Substitution Definite Integration
  8. Substitution techniques in definite integration
  9. Leibnitz forumla and inequalities
  10. Miscellaneous


  1. Area bounded by curve and axis
  2. Area bounded by two curves
  3. Area bounded by curves involving Trigonometric Function
  4. Area bounded by curves involving logarithmic function
  5. Area bounded by implicit functions
  6. Finding Area without integration

Differential Equation

  1. Differential equations (elementary)
  2. Forming Differential Equations
  3. Solving Differential equations by variable sepration
  4. Solving Homogeneous differential equations
  5. Solving Linear Differential Equations
  6. Solving Equations reducible to L.D.E.
  7. Solving Differential equation by general form of variable seperation
  8. Application of Differential equation – Geometrical
  9. Application of Differential equation – Physics problems