Class 12 Maths Notes PDF for CBSE Exams, Topic-wise Revision PDF, Solved Exams, Practice Question And Answers

NCERT Class 12 Maths 2025

nitesh singh
Updated on Aug 6, 2025 15:13 IST

By nitesh singh, Senior Executive

Students find Class 12 Maths one of the most important and complex subjects for board and competitive exams. Shiksha offers comprehensive Class 12 Maths NCERT Notes designed to provide high-quality NCERT Notes for Class 12 Maths. These notes offer conceptual clarity, quick revision bullet points, and problem-solving methods with a formula list.

These topic-wise Class 12 Maths Notes are aligned with the latest CBSE 2025 - 26 syllabus. These concise, short notes for class 12 Maths also include solved examples based on the latest CBSE exam pattern. These notes are one of the best quick revision modules for Class 12 board exams, covering all chapters from relations and functions to probability.

Our Maths NCERT notes for Class 12 include NCERT Definitions, Derivations, Formulas, Solved Examples, and key theorem explanations. We offer Class 12 Maths short notes in easy and lucid language with step-by-step explanations. Students can download CBSE Class 12 Notes in free downloadable PDF  and use it for offline study.

These Class 12th Maths Notes are very useful for quick revision, not only for CBSE exams but also for competitive exams such as JEE Mains, CUET UG, JEE Advanced, and others. You can read the full article below for more information.

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Class 11 Maths NCERT Notes

Table of contents
  • NCERT Class 12 Maths Chapter-wise Notes
  • Class 12 Maths Chapter-wise NCERT Solutions
  • Topic covered in CBSE Class 12 Maths Notes: Chapter-wise
  • Complete Study Material for Class 12th
  • Importance of Class 12 Maths NCERT Notes for CBSE
  • How to use Class 12 NCERT Maths ?
  • CLass 12 Maths NCERT Notes-FAQs
View More
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NCERT Class 12 Maths Chapter-wise Notes

You can check the list of chapter-wise notes for Class 12 Mathematics below:

Chapter No. Chapter Notes
1 Relations and Functions
2 Inverse Trigonometric Functions
3 Matrices
4 Determinants
5 Continuity and Differentiability
6 Application of Derivatives
7 Integrals
8 Application of Integrals
9 Differential Equations
10 Vector Algebra
11 Three-Dimensional Geometry
12 Linear Programming
13 Probability

 

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Topic covered in CBSE Class 12 Maths Notes: Chapter-wise

NCERT Textbook covers major concepts that are important for ensuring the full marks in the CBSE exams. You can check below relevant topics for all the chapters below; 

Chapter 1: Relations and Functions Topics-wise Notes

This chapter offers fundamentals for the whole Class 12 algebra syllabus for Class 12 maths. Class 12 Relation and Function contains 8 marks weightage in the CBSE Examination and 1 question is frequently asked in JEE Mains. Check the topics provided.

Section Topics Covered
1.1 Introduction
1.2 Types of Relations
1.3 Types of Functions
1.4 Composition of Functions and Invertible Function
1.5 Binary Operations

Chapter 2: Inverse Trigonometric Functions Maths Topics-wise Notes

Inverse Trigonometric Functions are asked for 6 marks in the Class 12 Board Examinations, and often, 1-2 direct or indirect questions are asked from this chapter. The topics covered in this chapter below.

Section Topics Covered
2.1 Introduction: Inverse trigonometric functions
2.2 Basic Concept of Inverse Trigonometric Functions
2.3 Properties of inverse trigonometric functions

Chapter 3: Matrices Topics

This chapter is usually combined with Determinants and the combined weightage of these two chapters is very significant. Matrices and Determinants contribute around 10 marks in 80 80-mark theory paper. You can read the important topics below;

Section Topics Covered
3.1 Introduction
3.2 Matrix
3.3 Types of Matrix
3.4 Operations on Matrices
3.5 Transpose of a Matrix
3.6 Symmetric and Skew Symmetric Matrices
3.7 Elementary Operation (Transformation) of a Matrix
3.8 Invertible Matrices

Chapter 4: Determinants Topics-wise Notes

A determinant is a kind of sub-concept of Matrices. Determinant is defined for each and every square matrix, and it provides the scalar value of the matrix. Check the topics covered below;

Section Topics Covered
4.1 Introduction
4.2 Determinant
4.3 Properties of Determinants
4.4 Area of a Triangle
4.5 Minors and Cofactors
4.6 Adjoint and Inverse of a Matrix
4.7 Applications of Determinants and Matrices

Chapter 5: Continuity and Differentiability Topic-wise Notes

This chapter serves as the backbone of fundamental understanding for the entire Class 12 calculus unit. You learn the concepts of Continuity and Differentiability. You can explore the topics covered in this chapter:

Section Topics Covered
5.1 Introduction: Continuity and Differentiability
5.2 Continuity
5.3 Differentiability
5.4 Exponential and Logarithmic Functions
5.5 Logarithmic Differentiation
5.6 Derivatives of Functions in Parametric Forms
5.7 Second Order Derivative
5.8 Mean Value Theorem

Cjapter 6: Application of Derivatives Topic-wise Notes

Ch 6  AOD is one of the most useful chapters in class 12 mathematics, not only in maths but also in other subjects such as chemistry and physics. This chapter mainly deals with the rate of change in many aspects.Topics covered in this chapter below;

Section Topics Covered
6.1 Introduction
6.2 Rate of Change of Quantities
6.3 Increasing and Decreasing Functions
6.4 Tangents and Normals
6.5 Approximations
6.6 Maxima and Minima

Chapter 7: Class 12 Integrals Topic-wise Notes

Class 12th Chapter 7 on Integrals explains both indefinite and definite integrals along with their fundamental properties. In CBSE Class 12 board Exams, this chapter is allocated 10 marks!. Read the topics covered in integrals below;

Section Topics Covered
7.1 Introduction: Integral Calculus
7.2 Integration as an Inverse Process of Differentiation
7.3 Methods of Integration
7.4 Integrals of Some Particular Functions
7.5 Integration by Partial Fractions
7.6 Integration by Parts
7.7 Definite Integral
7.8 Fundamental Theorem of Calculus
7.9 Evaluation of Definite Integrals by Substitution
7.10 Some Properties of Definite Integrals

Chapter 8: Application of Integrals Topic-wise Notes

The application of Integrals deals with summation or finding the total area covered under curves and other real-life problems. You can expect a 2-3 questions in Boards. Below are the topics covered in the Application of Integrals chapter;

Section Topics Covered
8.1 Introduction
8.2 Area under Simple Curves
8.3 Area between Two Curves

Chapter 9: Differential Equations Topic-wise Notes

Differential equations are a kind of Polynomial equations of calculus, similar to algebra. These equations. You can check the important topics below;

Section Topics Covered
9.1 Introduction: Differential Equations
9.2 Basic Concepts
9.3 General and Particular Solutions of a Differential Equation
9.4 Formation of a Differential Equation whose General Solution is given
9.5 Methods of Solving First-Order, First-Degree Differential Equations
9.6 Linear Differential Equations

Chapter 10: Vector Algebra Topic-wise Notes

Vector Algebra consists of several key topics equally useful in physics and mathematics. Vector Algebra has around 6 marks weight in CBSE Exams, and 5-6% weight in JEE Mains. Check the topics in this chapter below;

Section Topics Covered
10.1 Introduction
10.2 Some Basic Concepts
10.3 Types of Vectors
10.4 Addition of Vectors
10.5 Multiplication of a Vector by a Scalar
10.6 Product of Two Vectors

Chapter 11: Three-Dimensional Geometry Topic-wise Notes

3D Geometry explores various real-life concepts and deals with the orthogonal plane consists of 3 axises. it provides around 6 marks in the class 12 boards. You can read topics below.

Section Topics Covered
11.1 Introduction
11.2 Direction Cosines and Direction Ratios of a Line
11.3 Equation of a Line in Space
11.4 Angle between Two Lines
11.5 Shortest Distance between Two Lines
11.6 Plane
11.7 Coplanarity of Two Lines
11.8 Angle between Two Planes
11.9 Distance of a Point from a Plane
11.10 Angle between a Line and a Plane

Chapter 12: Linear Programming Topic-wise Notes

This chapter deals with linear programming problems and their solutions by various methods, including the graphical method. This chapter is important for CBSE exams not that significant for competitive exams. Also, check the topics below;

Section Topics Covered
12.1 Introduction
12.2 Linear Programming Problem and its Mathematical Formulation
12.3 Different Types of Linear Programming Problems

Chapter 14: Probability Topic-wise Notes

Class 12 Probability is an important chapter with a high weightage of 8 marks for the Class 12 board exam. In the chapter Probability, students will learn the important concept of conditional probability. Read the topics below.

Section Topics Covered
13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes' Theorem
13.6 Random Variables and its Probability Distributions
13.7 Bernoulli Trials and Binomial Distribution

 

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Complete Study Material for Class 12th

Shiksha offers complete study material for class 12 students. The study material consists of NCERT notes, revision notes PDF, NCERT solutions and NCERT exemplar solutions. Access the study material for CBSE class 12th below.

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Importance of Class 12 Maths NCERT Notes for CBSE

You can check few reasons why our NCERT Notes for Class 12 Maths are important;

  • Revision-Friendly: These notes for Class 12 Mahs are designed to help students revise quickly during the exam days. We have included concise summaries, relevant formulas, and highlighted concepts for each topic of the chapter.
  • Well-Structured & Chapter-Wise: Students dont need to wander in several place instead, we offer organized CBSE notes in one place as per the latest CBSE syllabus for all the chapters.
  • Perfect for Last-Minute Revision: We have not only provided the thoroughly detailed version but also the concise summary that can be real time-saving for students. Students can use this to recall important topics efficiently.
  • In-Depth Conceptual Explanation: We have ensured each topic is provided with a step-by-step explanation that gives a clear understanding of core concepts and theorems.
  • Solved Practice Problems: Shiksha has curated notes and included important NCERT and previous year questions so that you can practice these concepts firsthand.
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How to use Class 12 NCERT Maths ?

There are a few methods that you can use to get the best out of these Notes, check below;

Start with the NCERT Book: You should ensure to begin each chapter through the NCERT first and then combine with the notes to understand the key concepts for problem-solving or NCERT exercises.

Highlight Imp and Weak Areas: Students should mark important formulas and theorems and also weak sections while solving, and add side notes for quick future reference.

Timely Revision: Make a schedule to regularly revise topics on a daily, weekly or monthly basis to retain the concepts and formulas well.

Solve Examples with Notes: We suggest aspirants to attempt the solved examples and other practice problems after finishing the notes and formulas. 

Formula Sheet: These notes are designed for all students from baords to competive, you should make your own key formulas list from each chapter's notes as per the targeted exam.

 

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CLass 12 Maths NCERT Notes-FAQs

Here are the frequently asked questions related to thes Class 12 Maths Notes;

Q&A Icon
Commonly asked questions
Q:  

How can I get full marks in the Class 12 Maths exam?

A: 

All students work hard to get a full score. Here are a few tips that can make your dream come true.

  • Master the concepts from the NCERT textbook before using any other notes and mark importnt points.
  •  Consistentantly practice problems, highlight important formulas and theorems, and creating a personalized formula sheet.
  • Regular- daily and weekly revision of the important concepts and formulas.
  • Solve all examples and practice questions given in NCERT Textbooks.
Q:  

How useful are the Shiksh's NCERT notes for exam preparation?

A: 

Shiksha's NCERT notes are extremely useful for efficient preparation. We offer structured chapter-wise notes for the latest CBSE  syllabus and provide concise summaries and key formulas. These notes are designed for quick and last-minute revision. These short revision notes offer step-by-step explanations for conceptual clarity and include important questions from previous years' papers and NCERT Textbooks. Our notes are equally beneficial for competitive exams like JEE Mains, NEET and other exams as well.

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NCERT Class 12 Maths Exam

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