The Council for the Indian School Certificate Examinations (CISCE) prescribes the Mathematics syllabus for ISC Class 12 students. The syllabus for the 2026-27 academic session is meant for students appearing in the ISC Year 2027 examination.
Mathematics (Subject Code 860) covers seven major units. These include relations and functions, matrices, calculus, vectors, three-dimensional geometry, linear programming and probability.
Also read: ISC Class 12 Syllabus 2026-27: Download Subject-Wise PDFs for CISCE Board Exam
ISC Class 12 Mathematics Exam Pattern 2026-27
The subject carries a total of 100 marks, divided between the written examination and project work.
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| Examination | Duration | Marks |
|---|---|---|
| Paper I: Theory | 3 hours | 80 |
| Paper II: Project Work | — | 20 |
| Total | 100 |
Unit-wise marks distribution
| No. | Units | Marks |
|---|---|---|
| 1 | Relations and Functions | 10 |
| 2 | Algebra | 10 |
| 3 | Calculus | 35 |
| 4 | Vector Algebra | 5 |
| 5 | Three-Dimensional Geometry | 6 |
| 6 | Linear Programming | 5 |
| 7 | Probability | 9 |
| Total | 80 |
The 2027 syllabus has seven compulsory units. The earlier arrangement in which students had to choose between Section B and Section C should not be confused with the 2027 syllabus. In the new structure, all seven units are included.
Complete ISC Class 12 Mathematics Syllabus 2026-27
The following table explains the topics covered under each unit. It follows the ISC Year 2027 syllabus structure.
1. Relations and Functions – 10 Marks
This unit introduces students to different types of relations and functions. Students learn how two sets are connected and how one value depends on another.
| Topics | What students will learn |
|---|---|
| Relations | Understanding the connection between elements of two sets. |
| Types of relations | Reflexive, symmetric, transitive and equivalence relations. |
| Identity relation | A relation in which every element is related to itself. |
| Empty relation | A relation in which no elements are related. |
| Universal relation | A relation in which every possible pair of elements is included. |
| Functions | Understanding how one value is connected to another through a rule. |
| Types of functions | One-one, many-one, into and onto functions. |
| Domain and range | Understanding the allowed input values and the output values of a function. |
| Invertible functions | Learning when a function can be reversed to find its original input. |
| Composite functions | Combining two or more functions to form a new function. |
| Graphs of functions | Drawing and understanding the graphs of functions and their inverses. |
| Inverse trigonometric functions | Studying inverse functions of sine, cosine, tangent and other trigonometric functions. |
| Properties of inverse trigonometric functions | Learning principal values, domain, range, graphs and important formulas. |
This chapter helps students understand how mathematical values are related and how functions work. It also teaches them how to reverse a function and understand its graph.
2. Algebra – 10 Marks
Algebra mainly covers matrices and determinants. Students learn how to arrange numbers in rows and columns and use them to solve mathematical problems.
| Topics | What students will learn |
|---|---|
| Introduction to matrices | Meaning, notation and order of a matrix. |
| Types of matrices | Zero, identity, diagonal, scalar, triangular, symmetric and skew-symmetric matrices. |
| Equality of matrices | Conditions under which two matrices are equal. |
| Transpose of a matrix | Changing rows into columns and columns into rows. |
| Addition and subtraction | Performing basic operations on matrices. |
| Scalar multiplication | Multiplying every element of a matrix by a number. |
| Matrix multiplication | Multiplying two matrices and understanding the conditions required. |
| Inverse of a matrix | Finding a matrix that reverses the effect of another matrix. |
| Determinants | Finding the value of determinants of square matrices up to order 3 × 3. |
| Minors and cofactors | Calculating smaller determinants and their corresponding signed values. |
| Properties of determinants | Understanding different rules that make determinant calculations easier. |
| Adjoint of a matrix | Finding the adjoint to calculate the inverse of a matrix. |
| Area of a triangle | Using determinants to calculate the area of a triangle. |
| Linear equations | Solving two or three linear equations using inverse matrices. |
| Consistency of equations | Checking whether a system of equations has a solution. |
Students learn how to arrange numbers in matrix form and use mathematical operations to solve multiple equations. Determinants also help in finding the area of a triangle and checking whether equations have solutions.
3. Calculus – 35 Marks
Calculus is the most important unit in the ISC Class 12 Mathematics syllabus in terms of marks. It covers differentiation, integration, their applications and differential equations.
| Chapters | Complete topics covered in the syllabus |
|---|---|
| Continuity | Continuity of a function at a particular point and within an interval; algebra of continuous functions; removable discontinuity and its types. |
| Differentiability | Differentiability of functions such as absolute value functions and greatest integer functions; relationship between continuity and differentiability. |
| Differentiation | Derivatives of trigonometric, exponential, logarithmic and inverse trigonometric functions. |
| Chain Rule | Finding derivatives of composite functions using the chain rule. |
| Implicit Differentiation | Finding derivatives when a function is not directly written in the form of y = f(x). |
| Parametric Differentiation | Finding derivatives when x and y are expressed using another variable. |
| Logarithmic Differentiation | Using logarithms to simplify and differentiate complicated expressions. |
| Second-order Derivatives | Finding the derivative of a derivative. |
| Applications of Derivatives | Rate of change, increasing and decreasing functions, tangents, normals and angles between curves. |
| Maxima and Minima | Finding the highest and lowest values of a function using first and second derivative tests. |
| Integrals | Integration as the reverse process of differentiation. |
| Methods of Integration | Integration by substitution, integration by parts and partial fractions. |
| Definite Integrals | Fundamental Theorem of Calculus and properties of definite integrals. |
| Applications of Integrals | Finding areas under curves, areas between two curves and areas bounded by coordinate axes. |
| Differential Equations | Order, degree, general and particular solutions, and formation of differential equations. |
| Methods of Solving Differential Equations | Variable separable method, homogeneous equations and first-order linear differential equations. |
Important details of Calculus:
Students should pay special attention to the following points:
- Differentiation of different types of functions is included
- Successive differentiation is covered up to the second order
- Integration includes substitution, partial fractions and integration by parts
- The Fundamental Theorem of Calculus is included without proof
- Differential equations are limited to first-order and first-degree equations. Second-order differential equations are excluded
- Application of integrals includes areas bounded by lines, circles, parabolas, ellipses, polynomial, modulus, exponential and logarithmic functions
Calculus teaches students how to calculate changes in quantities, find the highest and lowest values of a function, calculate areas and solve equations involving changing quantities.
4. Vector Algebra – 5 Marks
This unit deals with vectors, which are mathematical quantities that have both magnitude and direction. Students learn how to perform mathematical operations on vectors and use them to solve problems.
| Topics | What students will learn |
|---|---|
| Scalars and vectors | Difference between quantities having only magnitude and those having both magnitude and direction. |
| Types of vectors | Equal, unit, zero, parallel and collinear vectors. |
| Position vector | Representing the position of a point using a vector. |
| Components of vectors | Expressing vectors through their different components. |
| Direction cosines and ratios | Understanding the direction of a vector in space. |
| Unit vectors | Using i, j and k along the x, y and z axes. |
| Vector operations | Addition, subtraction and multiplication of vectors by scalars. |
| Section formula | Finding the position of a point dividing a line segment in a given ratio. |
| Scalar or dot product | Multiplying two vectors and understanding the geometrical meaning of the result. |
| Vector or cross product | Finding a vector perpendicular to two given vectors. |
| Projection of vectors | Finding the scalar and vector projection of one vector on another. |
| Applications | Finding the area of a triangle and parallelogram and checking collinearity. |
This chapter helps students understand direction and movement mathematically. It also explains how vectors can be used to calculate areas and solve geometrical problems.
5. Three-Dimensional Geometry – 6 Marks
Three-dimensional geometry deals with points, lines and planes in three-dimensional space. Unlike ordinary geometry, which generally works with length and breadth, this chapter also considers height.
| Topics | What students will learn |
|---|---|
| Three-dimensional coordinates | Understanding the x, y and z axes and coordinate planes. |
| Direction cosines and ratios | Finding the direction of a line in three-dimensional space. |
| Equation of a line | Writing Cartesian and vector equations of a line passing through one or two points. |
| Angles between lines | Finding angles between two lines. |
| Parallel and perpendicular lines | Understanding the conditions for lines to be parallel or perpendicular. |
| Coplanar and skew lines | Understanding lines lying in the same plane and lines that neither intersect nor lie in the same plane. |
| Intersection of lines | Finding whether two lines meet. |
| Distance from a point to a line | Calculating the shortest distance between a point and a line. |
| Shortest distance between two lines | Finding the minimum distance between two skew lines. |
| Equation of a plane | Writing Cartesian and vector equations of a plane. |
| Different forms of a plane | One-point, normal and intercept forms. |
| Angle between planes | Finding the angle between two planes. |
| Line and plane | Finding the angle between a line and a plane and their point of intersection. |
| Distance from a point to a plane | Calculating the shortest distance between a point and a plane. |
This chapter teaches students how to calculate distances, angles and positions of lines and planes in three-dimensional space.
Also read: ISC Class 12 Chemistry Syllabus 2026–27, Download PDF Here!
6. Linear Programming – 5 Marks
Linear Programming focuses on finding the best possible solution to a problem when certain conditions or limits are given. It is commonly used in business, production and resource management.
| Topics | What students will learn |
|---|---|
| Introduction to Linear Programming | Understanding the meaning and purpose of linear programming. |
| Constraints | Conditions or limits that must be followed while solving a problem. |
| Objective function | The mathematical expression that needs to be maximised or minimised. |
| Optimisation | Finding the best possible result, such as maximum profit or minimum cost. |
| Advantages and limitations | Understanding the benefits and restrictions of linear programming. |
| Applications | Using linear programming in business, production and other practical situations. |
| Mathematical formulation | Converting a word problem into mathematical equations and inequalities. |
| Graphical method | Solving problems involving two variables using graphs. |
| Feasible region | The area that satisfies all the given conditions. |
| Bounded and unbounded regions | Understanding whether the possible solution area has limits or extends indefinitely. |
| Feasible and infeasible solutions | Identifying whether a solution satisfies all the conditions. |
| Optimal feasible solution | Finding the best possible answer from the available solutions. |
Suppose a company wants to earn maximum profit while using limited money, workers and raw materials. Linear programming helps find the best possible combination to achieve that goal.
7. Probability – 9 Marks
Probability deals with the chances of an event happening. Students learn how to calculate the possibility of different outcomes and understand how events are connected.
| Topics | What students will learn |
|---|---|
| Random Experiments | Experiments in which the outcome is uncertain, such as tossing a coin or rolling a dice. |
| Events | Understanding different possible outcomes of an experiment. |
| Independent Events | Events in which the occurrence of one event does not affect the occurrence of another. |
| Dependent Events | Events in which the occurrence of one event affects the probability of another event. |
| Conditional Probability | Finding the probability of an event when another event has already occurred. |
| Addition Theorem of Probability | Calculating the probability of either one event or another event occurring. |
| Multiplication Theorem of Probability | Calculating the probability of two events occurring together. |
| Total Probability Theorem | Finding the overall probability of an event by considering different possible cases. |
| Bayes' Theorem | Calculating the probability of a particular event or cause when some related information is already known. |
| Random Variables | Understanding how numerical values are assigned to the outcomes of a random experiment. |
| Probability Distribution | Showing all possible values of a random variable along with their probabilities. |
| Mean of a Random Variable | Calculating the expected average value of a random variable. |
This chapter helps students calculate the chances of something happening. For example, students can find the probability of getting a particular number when rolling a dice or getting a head when tossing a coin.
Also check: ISC Class 12 History Syllabus for Board Exam 2026-27: Download PDF Here!
ISC Class 12 Mathematics Project Work 2026-27
Apart from the written examination, students have to complete project work carrying 20 marks.
As per the CISCE guidelines, students are required to complete two projects. Each project carries 10 marks. The projects are assessed by the subject teacher and a visiting examiner appointed locally and approved by CISCE.
Project Work Marking Scheme
| Assessment Criteria | Marks per Project |
|---|---|
| Overall Format | 1 |
| Content | 4 |
| Findings | 2 |
| Viva-voce based on the Project | 3 |
| Total | 10 |
Both projects together carry 20 marks.
Suggested Mathematics Project Topics
CISCE provides suggested assignments for students to select their project topics.
Some examples include:
- Using graphs to demonstrate one-one and onto functions
- Demonstrating an invertible function using graphs
- Drawing graphs of inverse trigonometric functions and finding their domain and range
- Understanding the principal values of inverse trigonometric functions using a unit circle
- Verifying the consistency of a system of linear equations
- Explaining increasing and decreasing functions using graphs
- Demonstrating the geometrical meaning of maxima and minima
- Finding areas under curves using integration
- Applying Bayes' theorem to real-life examples
- Solving practical problems using linear programming
Students should select topics from the suggested assignments given in the official syllabus and prepare their projects with proper explanations, calculations, graphs and findings.
Each project carries 10 marks, including 1 mark for format, 4 marks for content, 2 marks for findings and 3 marks for viva-voce. The viva-voce is conducted by the visiting examiner and is based on the project.
ISC Class 12 Maths Syllabus PDF Download
Students can download the complete ISC Class 12 Maths Syllabus 2026-27 PDF from the link given below. The official document contains the prescribed syllabus and examination scheme for the academic session 2026-27.
| Subject | Official Syllabus PDF |
|---|---|
| ISC Class 12 Maths Syllabus 2026-27 | Download PDF |