Mathematics Class 12th for CBSE


This course is being taught by very experienced teacher Mr. Ved Prakash Sharma.

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There will be 5 online classes per week of about 1 hour each and the entire syllabus will be covered by December so that students will get sufficient time for the revision before the exams. This course is being taught by our expert faculty, Mr. Ved Prakash Sharma. He will also take live classes and clarify student’s doubts. Students will be given regular assignments, quizzes and tests to ensure their preparedness for Board Exams. Students will also receive a free booklet (worth Rs. 800) containing important formulas, notes and practice questions.

The entire syllabus has been divided into logical sections for better understanding of the students. All these sections will be covered sequentially as listed below.


Chapter 1: Relations & Functions
   – Types of Function
   –  composite functions
   – Inverse of a function
Chapter 2: Inverse Trigonometric Functions
 Introductions Inverse Trigonometric Functions
 Graphs of inverse trigonometric function
 Elementary properties of inverse trigonometric functions
Chapter 3: Matrices
 Algebra of Matrices
 Existence of non-zero matrices whose product is the zero matrix
 Proof of the uniqueness of inverse , if exist
 Concept of Elementary row and column operations
Chapter 4: Determinants
 Properties of Determinants
 Adjoint and Inverse of a Matrix
 Solution of Simultaneous Linear Equations
Chapter 5: Continuity
 Higher Order Derivatives
 Mean Value Theorems
Chapter 6: Applications of Derivatives
 Derivative as a Rate Measurer
 Differentials, Errors and Approximations
 Tangents and Normals
 Increasing and Decreasing Functions
 Maxima and Minima
Chapter 7: Integrals
 Indefinite Integrals
 Definite Integrals
 Integration as limit as sum
Chapter 8: Application of Integrals
 Area using vertical strips and horizontal strips
 Area between two curves
Chapter 9: Differential Equations
 Degree of differential equations
 Formation of differential equations solution of differential equations
 Methods of solving first order first degree differential equation
 Variable separable differential equation
 Homogeneous differential equation
 Linear differential equation
 Applications of differential equations
Chapter 10: Algebra of Vectors
 Algebra of Vectors
 Scalar Or Dot Product
 Vector or Cross Product
Chapter 11: Three Dimensional Geometry
 Scalar Triple Product
 Direction Cosines and Direction Ratios
 Straight line in space
 The plane
Chapter 12: Linear programming
 Solution of given LPP
 Mathematical formulation LPP & Unbounded
Chapter 13: Probability
 Conditional theorem
 Multiplication theorem
 Total theorem of probability
 Bayes Theorem probability
 Mean and variance of a random variable
 Binomial Distribution


Syllabus 2021-22


The course will cover the full syllabus as under :


Unit-I: Relations and Functions

  1. Relations and Functions

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function.

  1. Inverse Trigonometric Functions

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions Elementary properties of inverse trigonometric functions.


Unit-II: Algebra

  1. Matrices

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. On[1]commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

  1. Determinants

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.


Unit-III: Calculus

  1. Continuity and Differentiability

Continuity and differentiability, derivative of composite functions, chain rule, derivative of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretation.

  1. Applications of Derivatives

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

  1. Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by  partial fractions and by parts, Evaluation of simple integrals of the following types and problems  based on them.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof).Basic properties of definite integrals and evaluation of definite integrals.

  1. Applications of the Integrals

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

  1. Differential Equations

Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree.

Solutions of linear differential equation of the type:

dy/dx + py = q, where p and q are functions of x or constants.

d????/d???? + px = q, where p and q are functions of y or constants.


Unit-IV: Vectors and Three-Dimensional Geometry

  1. Vectors

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

  1. Three – dimensional Geometry

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.


Unit-V: Linear Programming

  1. Linear Programming

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).


Unit-VI: Probability

  1. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Binomial probability distribution.

Teacher Info

Ved Sir has 11 year of experience in teaching Mathematics. He has helped many students to get very impressive grades and to get selected into renowned institutes. Ved Sir has M.Sc. in Mathematics and B.Ed. Degrees. Some of his key achievements are –

  • Teaching at Ables Education,Talwandi, Kota, Rajasthan.
  • 100% results in Board exams for 11th and 12th grade students taught by him.
  • Served as Vice Principal at KP School for 3 years.
  • Has been examination head for many year and has very good understanding of CBSE exam pattern.

To know more details about him, click here.


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