# ISC Class 12 Maths Syllabus

Class 12 is an important milestone in a student’s life. The Class 12 Syllabus contains several important topics that form a crucial part of higher education. Mathematics is a subject that has a crucial role in our everyday life. Having a good hold on the Maths subject will be a bonus point to students. So, to help them in preparing well for the Mathematics exam, we are providing theÂ  Maths Syllabus of ISC Class 12. They can also download the ISC Syllabus for Class 12 Maths PDF from the link below and refer to it while studying.

Having a good knowledge of the syllabus would help the students to study in a proper sequence. Along with the syllabus, they must be thorough with the marking scheme as well. So below, we have provided the ISC Class 12 Maths marks weightage of each chapter.

### ISC Class 12 Maths Syllabus Marks Distribution

By referring to the table below, students can have a good idea of the Maths exam pattern.

 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. 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 Total 80 Marks

## ISC Syllabus for Class 12 Maths

SECTION A

### 1. Relations and Functions

(i) Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto 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.

### 2. Algebra

#### Matrices and Determinants

(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 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).

(ii) Determinants

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.

### 3. Calculus

(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).

(iii) 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.

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. Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. 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.

### 4. Probability

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayesâ€™ theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

SECTION B

### 5. 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.

### 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 by simple curves and coordinate axes. Area enclosed between two curves.

SECTION C

### 8. Application of Calculus

Application of Calculus in Commerce and Economics in the following:
– Cost function,
– average cost,
– marginal cost and its interpretation
– demand function,
– revenue function,
– marginal revenue function and its interpretation,
– Profit function and breakeven point.
– Rough sketching of the following curves:
AR, MR, R, C, AC, MC and their mathematical interpretation using the
concept of maxima & minima and increasing-decreasing functions.

### 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.
– bxy x byx = r2, 0 â‰¤ bxy â‰¤ byxÂ â‰¤ 1
– 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 Classes 11 and 12 by visiting the ISC Syllabus page. Keep learning, and stay tuned for further updates on CBSE and other competitive exams. Download BYJUâ€™S – The Learning App and subscribe to the YouTube channel to access interactive study videos.