CBSE 12th Class Maths Syllabus

Course Structure

Units Topics Marks
I Relations and Functions 10
II Algebra 13
III Calculus 44
IV Vectors and 3-D Geometry 17
V Linear Programming 6
VI Probability 10
Total 100

Course Syllabus

Unit I: Relations and Functions

Chapter 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
    • Binary operations

Chapter 2: Inverse Trigonometric Functions

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

Unit II: Algebra

Chapter 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

  • Noncommutativity 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).

Chapter 2: Determinants

  • Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle

  • Ad joint 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

Chapter 1: Continuity and Differentiability

  • Continuity and differentiability, derivative of composite functions, chain rule, derivatives 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

Chapter 2: Applications of Derivatives

  • Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normal, 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)

Chapter 3: 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

    $\int \frac{dx}{x^2\pm {a^2}'}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}'}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$

    $\int \frac{px+q}{ax^2+bx+c}dx$, $\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx$, $\int \sqrt{a^2\pm x^2}dx$, $\int \sqrt{x^2-a^2}dx$

    $\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$

  • Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof)

  • Basic properties of definite integrals and evaluation of definite integrals

Chapter 4: 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)

Chapter 5: 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

    • dx/dy + px = q, where p and q are functions of y or constants

Unit IV: Vectors and Three-Dimensional Geometry

Chapter 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

Chapter 2: 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 −

    • Two lines

    • Two planes

    • A line and a plane

  • Distance of a point from a plane

Unit V: Linear Programming

Chapter 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 and unbounded)
    • Feasible and infeasible solutions
    • Optimal feasible solutions (up to three non-trivial constraints)

Unit VI: Probability

Chapter 1: Probability

  • Conditional probability
  • Multiplication theorem on probability
  • Independent events, total probability
  • Baye's theorem
  • Random variable and its probability distribution
  • Mean and variance of random variable
  • Repeated independent (Bernoulli) trials and Binomial distribution

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