Updated On : September 15, 2023
Class 12th is a significant step for the student's academic life because their future career depends on the marks obtained by them in the board examination. The CBSE Class 12 syllabus contains a few significant topics that form a major part of the higher education. Mathematics subject is a significant subject that shapes the career of the students after schooling. Mathematics subject is a very important subject in every competitive and school level examination. Having a decent hold on the Maths subject will be a reward for the students. So, students should know the 12th Maths syllabus in detail.
We are providing here the previous year’s paper for the students so that they will get to know the pattern and syllabus of the exam. Also, they will get some preparation tips after seeing the previous year's papers.
In this article, you will get to know about the detailed class 12th maths syllabus, deleted portion of class 12th maths syllabus, and weightage of each topic of the 12th maths syllabus.
The table below shows the weightage of each topic of class 12th Maths subject (CBSE): -
Units | Topics | Periods | Marks |
I | Relations and Functions | 30 | 08 |
II | Algebra | 50 | 10 |
III | Calculus | 80 | 35 |
IV | Vectors – Three Dimensional Geometry | 30 | 14 |
V | Linear Programming | 20 | 05 |
VI | Probability | 30 | 08 |
Total | 240 | 80 | |
Project Work (Internal Assessment) | 20 |
Let us have a look at the detailed revised class 12th Maths syllabus from below.
To help candidates, we have provided chapter-wise important topics for all the units. Go through the syllabus and plan your preparation accordingly.
Candidates can check the detailed class 12 Maths Syllabus of Algebra from below.
Here is the detailed chapter-wise syllabus of Calculus.
$\int \frac{dx}{x^2\pm {a^2}'}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}'}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$
$\int \frac{px+q}{ax^2+bx+c}dx$, $\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx$, $\int \sqrt{a^2\pm x^2}dx$, $\int \sqrt{x^2-a^2}dx$
$\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$
Unit IV: Vectors and Three-Dimensional Geometry
Go through the detailed syllabus of Vectors and three-dimensional geometry which is given below.
Here is the detailed syllabus of Class 12th maths Syllabus for linear programming.
CBSE 12th Maths Syllabus Deleted Portion for session 2020-21 Chapter-wise, is mentioned below:
The table below shows the weightage of each topic of class 12th Maths subject (ICSE).
S.No | UNIT | TOTAL WEIGHTAGE |
SECTION A: 65 MARKS | ||
1 | Relations and Functions | 10 Marks |
2 | Algebra | 10 Marks |
3 | Calculus | 32 Marks |
4 | Probability | 13 Marks |
SECTION B: 15 MARKS | ||
5 | Vectors | 5 Marks |
6 | Three - Dimensional Geometry | 6 Marks |
7 | Applications of Integrals | 4 Marks |
OR SECTION C: 15 MARKS | ||
8 | Application of Calculus | 5 Marks |
9 | Linear Regression | 6 Marks |
10 | Linear Programming | 4 Marks |
Total | 80 Marks |
Let us have a look at the detailed revised syllabus of Class 12th from below.
(i) Types of relations
Reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions, composite functions, the inverse of a function.
(ii) Inverse Trigonometric Functions
Definition, domain, range, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
(i) 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 existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order up to 3). 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).
(ii) Determinants
The 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 the number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.
(i) Continuity and Differentiability
Continuity, Differentiability, and Differentiation. Continuity and differentiability, a 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.
(ii) 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 is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
(iii) Integrals
Integration as the 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.
(iv) Differential Equations
Definition, order, and degree, general, and particular solutions of a differential equation. Formation of differential equations whose general solution is given. The 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 the linear differential equation.
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem.
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.
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. The distance of a point from a plane.
Application in finding the area bounded by simple curves and coordinate axes. The area enclosed between two curves.
Application of Calculus in Commerce and Economics.
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).
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September 15, 2023
Class 12th is a significant step for the student's academic life because their future career depends on the marks obtained by them in the board examination. The CBSE Class 12 syllabus contains a few significant topics that form a major part of the higher education. Mathematics subject is a significant subject that shapes the career of the students after schooling. Mathematics subject is a very important subject in every competitive and school level examination. Having a decent hold on the Maths subject will be a reward for the students. So, students should know the 12th Maths syllabus in detail.
We are providing here the previous year’s paper for the students so that they will get to know the pattern and syllabus of the exam. Also, they will get some preparation tips after seeing the previous year's papers.
In this article, you will get to know about the detailed class 12th maths syllabus, deleted portion of class 12th maths syllabus, and weightage of each topic of the 12th maths syllabus.
The table below shows the weightage of each topic of class 12th Maths subject (CBSE): -
Units | Topics | Periods | Marks |
I | Relations and Functions | 30 | 08 |
II | Algebra | 50 | 10 |
III | Calculus | 80 | 35 |
IV | Vectors – Three Dimensional Geometry | 30 | 14 |
V | Linear Programming | 20 | 05 |
VI | Probability | 30 | 08 |
Total | 240 | 80 | |
Project Work (Internal Assessment) | 20 |
Let us have a look at the detailed revised class 12th Maths syllabus from below.
To help candidates, we have provided chapter-wise important topics for all the units. Go through the syllabus and plan your preparation accordingly.
Candidates can check the detailed class 12 Maths Syllabus of Algebra from below.
Here is the detailed chapter-wise syllabus of Calculus.
$\int \frac{dx}{x^2\pm {a^2}'}$, $\int \frac{dx}{\sqrt{x^2\pm {a^2}'}}$, $\int \frac{dx}{\sqrt{a^2-x^2}}$, $\int \frac{dx}{ax^2+bx+c} \int \frac{dx}{\sqrt{ax^2+bx+c}}$
$\int \frac{px+q}{ax^2+bx+c}dx$, $\int \frac{px+q}{\sqrt{ax^2+bx+c}}dx$, $\int \sqrt{a^2\pm x^2}dx$, $\int \sqrt{x^2-a^2}dx$
$\int \sqrt{ax^2+bx+c}dx$, $\int \left ( px+q \right )\sqrt{ax^2+bx+c}dx$
Unit IV: Vectors and Three-Dimensional Geometry
Go through the detailed syllabus of Vectors and three-dimensional geometry which is given below.
Here is the detailed syllabus of Class 12th maths Syllabus for linear programming.
CBSE 12th Maths Syllabus Deleted Portion for session 2020-21 Chapter-wise, is mentioned below:
The table below shows the weightage of each topic of class 12th Maths subject (ICSE).
S.No | UNIT | TOTAL WEIGHTAGE |
SECTION A: 65 MARKS | ||
1 | Relations and Functions | 10 Marks |
2 | Algebra | 10 Marks |
3 | Calculus | 32 Marks |
4 | Probability | 13 Marks |
SECTION B: 15 MARKS | ||
5 | Vectors | 5 Marks |
6 | Three - Dimensional Geometry | 6 Marks |
7 | Applications of Integrals | 4 Marks |
OR SECTION C: 15 MARKS | ||
8 | Application of Calculus | 5 Marks |
9 | Linear Regression | 6 Marks |
10 | Linear Programming | 4 Marks |
Total | 80 Marks |
Let us have a look at the detailed revised syllabus of Class 12th from below.
(i) Types of relations
Reflexive, symmetric, transitive, and equivalence relations. One to one and onto functions, composite functions, the inverse of a function.
(ii) Inverse Trigonometric Functions
Definition, domain, range, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
(i) 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 existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order up to 3). 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).
(ii) Determinants
The 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 the number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.
(i) Continuity and Differentiability
Continuity, Differentiability, and Differentiation. Continuity and differentiability, a 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.
(ii) 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 is given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
(iii) Integrals
Integration as the 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.
(iv) Differential Equations
Definition, order, and degree, general, and particular solutions of a differential equation. Formation of differential equations whose general solution is given. The 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 the linear differential equation.
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem.
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.
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. The distance of a point from a plane.
Application in finding the area bounded by simple curves and coordinate axes. The area enclosed between two curves.
Application of Calculus in Commerce and Economics.
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).
Download Your Free CBSE Prep Material
Fill your details