CBSE EXAM CLASS 12TH LATEST UPDATE
Finally, wait is over and Central Board of Secondary Education (CBSE) has announced class 12 Board exams date. This year class 12th board exam will be started from 15 February 2025 and will last upto 04 April 2025, it will take around 49 days to complete the class 12th board exam. The first exam will be held on 15 February 2025 for Entrepreneurship (Including Vocational Students) subject and the last exam will be held on 04 April 2025 for Psychology subject. The practical exams/Internal Assesment/Projects & the board's annual theory examinations are scheduled to start w.e.f 01th January 2025 and 15th February 2025.
OFFICIAL SYLLABUS
UNIT | TOPICS |
Relations and Functions | Relations and Functions |
Inverse Trigonometric Functions |
Algebra | Matrices |
Determinants |
Calculus | Continuity and Differentiability |
Applications of Derivatives |
Integrals |
Applications of the Integrals |
Differential Equations |
Vectors and Three-Dimensional Geometry | Vectors |
Three - dimensional Geometry |
Linear Programming |
Probability |
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, the inverse of a function.
2. 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. Non- commutativity of multiplication of matrices and the existence of non-zero matrices whose product is the zero matrices (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).
2. Determinants
Determinants 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 a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the 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 is a derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
2. 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).
3. Integrals
Integration is the inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and by parts, Evaluation of simple integrals.
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), and Area between any of
...
CBSE EXAM CLASS 12TH LATEST UPDATE
Finally, wait is over and Central Board of Secondary Education (CBSE) has announced class 12 Board exams date. This year class 12th board exam will be started from 15 February 2025 and will last upto 04 April 2025, it will take around 49 days to complete the class 12th board exam. The first exam will be held on 15 February 2025 for Entrepreneurship (Including Vocational Students) subject and the last exam will be held on 04 April 2025 for Psychology subject. The practical exams/Internal Assesment/Projects & the board's annual theory examinations are scheduled to start w.e.f 01th January 2025 and 15th February 2025.
OFFICIAL SYLLABUS
UNIT | TOPICS |
Relations and Functions | Relations and Functions |
Inverse Trigonometric Functions |
Algebra | Matrices |
Determinants |
Calculus | Continuity and Differentiability |
Applications of Derivatives |
Integrals |
Applications of the Integrals |
Differential Equations |
Vectors and Three-Dimensional Geometry | Vectors |
Three - dimensional Geometry |
Linear Programming |
Probability |
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, the inverse of a function.
2. 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. Non- commutativity of multiplication of matrices and the existence of non-zero matrices whose product is the zero matrices (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).
2. Determinants
Determinants 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 a system of linear equations by examples, solving a system of linear equations in two or three variables (having unique solution) using the 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 is a derivative of functions expressed in parametric forms. Second-order derivatives. Rolle’s and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
2. 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).
3. Integrals
Integration is the inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and by parts, Evaluation of simple integrals.
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only), and Area between any of the two above said curves (the region should be clearly identifiable).
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 the method of separation of variables, solutions of homogeneous differential equations of the 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
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, the 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, a scalar triple product of vectors.
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, the Shortest distance between two lines. Cartesian and vector equation of a plane. The 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
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
Probability
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable, and its probability distribution, mean and variance of a random variable. Binomial probability distribution.
Prescribed Books:
1. Mathematics Textbook for Class XI, NCERT Publications
2. Mathematics Part I - Textbook for Class XII, NCERT Publication
3. Mathematics Part II - Textbook for Class XII, NCERT Publication
4. Mathematics Exemplar Problem for Class XI, Published by NCERT
5. Mathematics Exemplar Problem for Class XII, Published by NCERT
6. Mathematics Lab Manual class XI, published by NCERT
7. Mathematics Lab Manual class XII, published by NCERT.
TO KNOW MORE
For Official Website: click here
For Time Table: click here
For Practical & Projects Circulars: click here