CBSE 12th Class Maths Syllabus

Course Syllabus

Chapter 1: Relations and Functions

Chapter 2: Inverse Trigonometric Functions

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

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

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

Chapter 1: Linear Programming

Chapter 1: Probability

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