ISC Class 12 Mathematics Syllabus

The ISC Class 12 Mathematics Syllabus for 2024-25 is designed to build a solid foundation for students preparing for higher studies in mathematics and related fields. It covers several key areas like Algebra, Calculus, Vectors, and more, focusing on both theoretical understanding and practical application.

Algebra is one of the main parts of the syllabus, where students learn about determinants, matrices, and their applications in solving linear equations. The syllabus also includes complex numbers and quadratic equations, helping students understand their properties, and operations, and how to solve different kinds of equations using these concepts.

Calculus is another significant portion of the syllabus and is divided into differential and integral calculus. In differential calculus, students explore the concepts of derivatives and their applications in finding rates of change and solving problems related to tangents and normals. In integral calculus, they learn about definite and indefinite integrals, techniques of integration, and their applications in calculating areas under curves and volumes of solids of revolution. Calculus is essential for developing problem-solving skills and understanding the behavior of functions.

The syllabus also includes Coordinate Geometry, which covers the study of lines, circles, parabolas, ellipses, and hyperbolas. Students learn how to calculate the distance between points, equations of various curves, and their properties. This helps in visualizing and solving geometric problems effectively.

In Vectors and 3D Geometry, students explore vector operations, dot and cross products, and their applications in solving problems related to geometry in three-dimensional space. The study of planes, lines, and their intersections forms an important part of this segment.

Probability and Statistics are also included in the syllabus to help students understand the concepts of probability, random variables, and distribution. These topics are crucial for solving real-world problems involving data analysis and predictions.

Additionally, the syllabus emphasizes mathematical reasoning, where students solve problems using logic and reasoning, enhancing their analytical skills. This comprehensive approach ensures that students gain the necessary skills for competitive exams and further studies in mathematics, engineering, and other technical fields.

ISC Class 12 Mathematics Semester-Wise Syllabus 2024-25

SECTION A

1. Relations and Functions

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

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 system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the 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 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.

(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 is the inverse process of differentiation. Integration of a variety of functions by substitution, partial fractions, and 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, Bayes’ theorem, Random variable, and its probability distribution, mean and variance of a 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, 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.

7. Application of Integrals

Application in finding the area bounded by simple curves and coordinate axes. The area is 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 ≤ bxy ≤ byx ≤ 1
– Identification of regression equations
– Angle between regression line and properties of regression lines.
– Estimating the value of one variable using the value of other variables from the appropriate regression line.

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 BYJU’S – The Learning App and subscribe to the YouTube channel for interactive study videos.

ISC class 12 Maths Exam Pattern

Math will also have 2 papers- theory and project work: 80 marks for theory and 20 marks for project work. Math Syllabus will comprise 3 sections wherein section A is compulsory for all the students, students can choose any one between section B and section C and attempt the questions.