Class 12th is an important milestone for the career life of the students. Class 12 syllabus contains several important topics that forms the crucial part in higher education. Mathematics is an important subject that shapes the career of the students after schooling. Having a good hold on the Maths subject will be a bonus point to students. So to help students in preparing well for the Mathematics exam, we are providing the ISC Class 12 Maths Syllabus. They can also download the ISC Syllabus for Class 12 Maths pdf from the link below and refer it while studying.
Having a good knowledge of the syllabus would help the students to study in a proper sequence. Along with the syllabus, it’s crucial that students should be thorough with the marking scheme as well. So, below we have provided the ISC Class 12 Maths marks weightage of each chapter. I
ISC Class 12 Maths Syllabus Marks Distribution
By looking at the table below, students can have a good idea of the Maths exam pattern.
|Section A: 65 Marks|
|1.||Relations and Functions||10 Marks|
|Section B: 15 Marks|
|6.||Three-Dimensional Geometry||6 Marks|
|7.||Application of Integral||4 Marks|
|Section C: 15 Marks|
|8.||Application of Calculus||5 Marks|
|9.||Linear Regression||6 Marks|
|10.||Linear Programming||4 Marks|
ISC Syllabus for Class 12 Maths
1. Relations and Functions
(i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.
(ii) Inverse Trigonometric Functions
Definition, domain, range, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Matrices and Determinants
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 upto 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).
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 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.
(i) Continuity, Differentiability and Differentiation. 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.
(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 given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
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.
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 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.
Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
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.
6. 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 (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.
7. Application of Integrals
Application in finding the area bounded b y simple curves and coordinate axes. Area enclosed between two curves. – Application of definite integrals – area bounded by curves, lines and coordinate axes is required to be covered. – Simple curves: lines, circles/ parabolas/ ellipses, polynomial functions, modulus function, trigonometric function, exponential functions, logarithmic functions.
8. Application of Calculus
Application of Calculus in Commerce and Economics.
9. Linear Regression
– Lines of regression of x on y and y on x.
– Scatter diagrams – The method of least squares.
– Lines of best fit.
– Regression coefficient of x on y and y on x.
– Identification of regression equations
– Angle between regression line and properties of regression lines.
– Estimation of the value of one variable using the value of other variable from appropriate line of regression.
10. 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).
Students can get the ISC syllabus for class 11 and 12 by visiting ISC Syllabus page. Keep learning and stay tuned for further updates on CBSE and other competitive exams. Download BYJU’S App and subscribe to YouTube channel to access interactive Maths and Science videos.