ISC Class 12 Mathematics Syllabus 2026-27

The ISC Class 12 Mathematics syllabus for 2026-2027, prescribed by the Council for the Indian School Certificate Examinations (CISCE), is one of the most rigorous and comprehensive mathematics programmes at the senior secondary level.

The syllabus covers Pure Mathematics through a structured single paper covering topics from Calculus, Algebra, Probability, Coordinate Geometry, and more, ensuring that students develop both theoretical understanding and strong problem-solving proficiency.

This page provides a complete, section-by-section breakdown of the ISC Mathematics syllabus 2026-2027, the exam pattern, detailed topic coverage, marking scheme, recommended reference books, and actionable preparation strategies to help students maximise their scores in the ISC 2027 board examination.

Quick Facts

Exam Pattern

The ISC Mathematics paper is divided into three sections. Section A is compulsory for all candidates and covers core topics. Sections B and C offer internal choice, allowing students to attempt either the Section B topics or Section C topics depending on their preparation and preference.

Detailed Syllabus: Section A (Compulsory)

Unit 1: Relations and Functions

This unit extends students' understanding of relations and functions beyond Class 11, introducing inverse functions, the composition of functions, and the concept of binary operations. Students must also study the properties of algebraic structures.

•         Types of relations: reflexive, symmetric, transitive, equivalence relations

•         Types of functions: one-one, onto, bijective

•         Composite functions and inverse of a function

•         Binary operations and their properties

Unit 2: Algebra

The Algebra unit covers matrices and determinants in depth, providing the foundational tools used in solving systems of equations and understanding linear transformations. The ability to perform matrix operations and interpret determinants is essential.

•         Matrices: types, operations, transpose, symmetric and skew-symmetric matrices

•         Determinants: properties, cofactors, adjoint and inverse of a matrix

•         Solution of system of linear equations using matrix method (Cramer's Rule)

•         Consistency and inconsistency of a system of equations

Unit 3: Calculus

Calculus is the most substantial unit in the ISC Mathematics syllabus, covering both differential and integral calculus. Students must develop strong conceptual clarity as well as computational speed, as this unit carries the highest weightage in the examination.

Differential Calculus

•         Continuity and differentiability of functions

•         Derivatives of composite functions (chain rule), implicit functions, inverse trigonometric functions

•         Logarithmic and exponential differentiation

•         Second order derivatives

•         Applications: increasing and decreasing functions, tangents and normals, maxima and minima

•         Mean Value Theorems: Rolle's Theorem, Lagrange's Mean Value Theorem

Integral Calculus

•         Integration as the inverse of differentiation

•         Integration by substitution, by parts, and by partial fractions

•         Definite integrals and their properties

•         Fundamental Theorem of Integral Calculus

•         Applications of definite integrals: area under curves

Differential Equations

•         Order and degree of differential equations

•         Formation of differential equations

•         Solution of differential equations: variable separable, homogeneous, linear

Unit 4: Probability

This unit covers probability theory including conditional probability, Bayes' Theorem, and random variables. Students must understand both the theoretical foundation and practical applications of probability.

•         Conditional probability and multiplication theorem

•         Independent events

•         Bayes' Theorem and total probability

•         Random variables and probability distributions

•         Mean and variance of a random variable

•         Binomial distribution

Detailed Syllabus: Section B (Optional)

Unit 5: Vectors

•         Vectors and scalars, magnitude and direction of a vector

•         Types of vectors: zero, unit, coinitial, collinear

•         Addition of vectors, multiplication by a scalar

•         Position vector of a point dividing a line segment

•         Dot product (scalar product) and cross product (vector product)

•         Scalar triple product and its geometric interpretation

Unit 6: Three-Dimensional Geometry

•         Direction cosines and direction ratios of a line

•         Equation of a line in space (Cartesian and vector form)

•         Angle between two lines

•         Equation of a plane (Cartesian and vector form)

•         Angle between a line and a plane; coplanarity of two lines

•         Distance of a point from a plane

Detailed Syllabus: Section C (Optional)

Unit 7: Application of Calculus

•         Application of calculus in Commerce and Economics: cost function, revenue function, profit function

•         Marginal cost, marginal revenue, and their relationship

•         Average cost and average revenue

•         Break-even point and its graphical interpretation

Unit 8: Linear Regression

•         Regression of y on x and x on y

•         Lines of regression, regression coefficients

•         Correlation and coefficient of correlation

•         Rank correlation

Unit 9: Linear Programming

•         Linear programming problem formulation

•         Feasible region and optimal solution

•         Graphical method for solving LPP (maximisation and minimisation)

•         Corner point theorem

Chapter Overview Table

Marking Scheme

Preparation Tips

Building Concept Clarity

Mathematics at the Class 12 level requires a solid understanding of foundational concepts before attempting complex problems. Students should avoid the habit of memorising procedures without understanding the underlying principles. A concept misunderstood in Differentiation will compound into errors in Integration and Differential Equations.

•         Study each unit systematically, mastering one topic before progressing to the next

•         Create a formula sheet for each chapter and review it at the beginning of every study session

•         Solve NCERT examples and exercises first, then move to ISC-specific problems

•         Identify weak areas early in the year and allocate extra time to those units

Examination Strategy

•         Spend the first 15 minutes reading the paper and planning your answer order

•         Attempt all Section A questions, as they are compulsory and carry the most marks

•         Choose Section B or Section C based on your stronger preparation, not on impulse during the exam

•         Show all steps clearly; partial marks are awarded for correct method even if the final answer is wrong

•         Revise at least 10 years of ISC past papers to familiarise yourself with the question style and difficulty

Frequently Asked Questions

Q1. Is Calculus the most important topic in ISC Mathematics?

Yes. Calculus is the highest-weightage topic in Section A, contributing approximately 40 marks. Students must ensure thorough preparation in both Differential and Integral Calculus. Differential Equations is a frequently tested subsection and should not be neglected.

Q2. Should a student choose Section B or Section C?

The choice depends on the student's stream and interests. Students from a Science background may find Vectors and 3D Geometry (Section B) more intuitive, while students with a Commerce background may find Application of Calculus and Linear Programming (Section C) more accessible. Both sections carry equal marks, so the choice should be driven by preparation depth.

Q3. Is internal assessment compulsory in ISC Mathematics?

Yes. The 20-mark project-based internal assessment is compulsory and is evaluated by the school. It contributes to the final result and cannot be skipped. Students must complete and submit the project work as directed by their mathematics teacher.

Q4. How many questions are asked from each section?

Section A typically contains questions with internal choices covering all four units. Sections B and C each contain a set number of questions from which students must attempt a prescribed number. Students should check the latest sample paper released by CISCE for exact question distribution for 2026-2027.

Q5. What is the difficulty level of ISC Mathematics compared to CBSE?

ISC Mathematics is generally considered to be at a similar or slightly higher difficulty level than CBSE Mathematics, particularly in terms of the depth of Calculus and the optional sections. However, the single-paper format with internal choices provides flexibility. Regular practice with ISC-specific past papers is the most effective preparation strategy.