CBSE Class 12 » CBSE Class 12 notifications » CBSE Class 12 Syllabus » Mathematics

Mathematics

Click on the link given above to access the mathematics syllabus for standard 12th.

Mathematics Syllabus for Standard 12th

Scoring well in mathematics requires a clear understanding of the concepts. Here is the module prepared for students to acquire knowledge about the CBSE mathematics syllabus for standard 12th of the academic year 2022-2023.

Unit-I: Relations and Functions

  1. Relations and Functions
  • One to one and onto functions
  • Types of relations: Reflexive, Symmetric, Transitive and Equivalence Relations
  1. Inverse Trigonometric Functions
  • Graphs of Inverse Trigonometric functions
  • Definition
  • Range
  • Domain
  • Principal Value Branch

Unit-II: Algebra

  1. Matrices
  • On commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
  • Operation on Matrices: 
    • Addition and multiplication and multiplication with a scalar
  • Simple properties of addition, multiplication and scalar multiplication 
  • Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew-symmetric matrices
  • Invertible matrices and proof of the uniqueness of inverse, if it exists
    • (here all matrices will have real entries)
  1. Determinants
  • Adjoint and inverse of a square matrix
  • Determinant of a square matrix (up to 3 X 3 matrices)
  • Minors
  • Cofactors and Applications of determinants in finding the area of a triangle
  • 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 
  • Second-Order Derivatives
  • Concept of Exponential and Logarithmic Functions 
  • Derivatives of Logarithmic and Exponential Functions 
  • Continuity and Differentiability
  • Chain Rule
  • Derivative of Inverse Trigonometric Functions, 𝑙𝑖𝑘𝑒 Sin−1 𝑥 , Cos−1 𝑥 And Tan−1 x
  • Derivative of Implicit Functions
  • Logarithmic Differentiation
  • Derivative of functions expressed in Parametric Forms

 

  1. Applications of Derivatives

  • Simple problems (That illustrate basic principles and understanding of the subject as well as real-life situations)
  • Applications of Derivatives: 
    • Rate of change of bodies
    • Increasing/Decreasing Functions
    • Maxima and Minima (First derivative test motivated geometrically and second derivative test given as a provable tool)

  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

dxx2a2, dxx2a2, dxa2-x2, dxax2+bx+c, dxax2+bx+c, px+qax2+bx+cdx, a2x2dx, x2-a2dx, ax2+bx+cdx

  • Basic properties of definite integrals and evaluation of definite integrals
  • Fundamental theorem of calculus (Without Proof)

  1. Applications of the Integrals 

  • Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

  1. Differential Equations

  • Solution of differential equations by method of Separation of Variables
  • Solutions of homogeneous differential equations of first order and first degree
  • Definition
  • Order and Degree
  • General and particular solutions of a Differential Equation
  • Solutions of linear differential equation of the type: 

 dydx + py = q, where p and q are functions of x or constants

 dydx + px = q, where p and q are functions of y or constants 

Unit-IV: Vectors and Three-Dimensional Geometry

  1. Vectors
  • Definition
  • Geometrical Interpretation
  • Properties and Application of Scalar (Dot) product of vectors
  • Vector (cross) product of vectors
  • 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
  • Vectors and scalars
  • Magnitude and Direction of a vector
  1. Three-Dimensional Geometry
  • Cartesian Equation and vector equation of a line
  • Skew Lines
  • Shortest Distance between two lines
  • Direction cosines and direction ratios of a line joining two points
  • Angle between two lines

Unit-V: Linear Programming

  1. Linear Programming
  • Introduction
  • Optimization
  • Feasible and Infeasible Solutions
  • Related Terminology such as constraints
  • Graphical Method of solution for problems in two variables
  • Feasible and infeasible regions (Bounded or Unbounded)
  • Objective Function
  • Optimal Feasible Solutions (Up To Three Non-Trivial Constraints)

Unit-VI: Probability

  1. Probability
  • Conditional Probability
  • Random Variable and its Probability Distribution
  • Bayes’ Theorem
  • Independent Events
  • Total Probability
  • Multiplication Theorem on Probability
  • Mean of Random Variable