The Class 12 NCERT Book Maths is among the best resource materials for board and competitive examinations. Math book class 12 NCERT is an all-inclusive book covering all essential concepts, theories, and applications of mathematics in higher secondary education. It explains various complex topics clearly and conceptually through numerous examples. The class 12 NCERT math book is available in PDF format. It mainly helps students gain a detailed understanding of the fundamentals of mathematics.
Class 12 Maths NCERT Book PDF Download
The curriculum of CBSE in a structured way has made The Class 12 NCERT Maths Book trusted across India. This book develops basic knowledge through theoretical knowledge, solved examples, and exercises. Download your free PDF of Maths Class 12 NCERT in English and Hindi. Get the download link for the NCERT 12th Maths book, Part 1 and Part 2, from the table below.
| Download PDF for NCERT Class 12 Maths Book | |
| NCERT Maths book Part 1 for Class 12 in English | Download PDF |
| NCERT Maths book Part 2 for Class 12 in English | Download PDF |
| NCERT Maths book Part 1 for Class 12 in Hindi | Download PDF |
| NCERT Maths book Part 2 for Class 12 in Hindi | Download PDF |
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Class 12 Maths Chapters PDF Free Download: Part 1
The Class 12 NCERT Mathematics Part 1 textbook is designed to strengthen your foundations in key mathematical concepts: calculus, algebra, and functions. It provides a detailed approach to problem-solving and is perfect for building math skills.
| Class 12 NCERT Math Book (Part I) | |
| Class 12 NCERT Math Chapter 1 | Download PDF |
| Class 12 NCERT Math Chapter 2 | Download PDF |
| Class 12 NCERT Math Chapter 3 | Download PDF |
| Class 12 NCERT Math Chapter 4 | Download PDF |
| Class 12 NCERT Math Chapter 5 | Download PDF |
| Class 12 NCERT Math Chapter 6 | Download PDF |
Class 12 Maths Chapters PDF Free Download: Part 2
Class 12 NCERT Mathematics Part 2 deals with advanced topics like vectors, 3D geometry, probability, and differential equations. It provides a comprehensive understanding with clear explanations and practice exercises. Great for mastering higher-level mathematical concepts!
| Class 12 NCERT Math Book (Part II) | |
| Class 12 NCERT Math Chapter 7 | Download PDF |
| Class 12 NCERT Math Chapter 8 | Download PDF |
| Class 12 NCERT Math Chapter 9 | Download PDF |
| Class 12 NCERT Math Chapter 10 | Download PDF |
| Class 12 NCERT Math Chapter 11 | Download PDF |
| Class 12 NCERT Math Chapter 12 | Download PDF |
| Class 12 NCERT Math Chapter 13 | Download PDF |
NCERT Class 12th Maths Book: Chapter- Wise Details
The NCERT Class 12th Maths textbook is designed to fully meet the CBSE syllabus’s needs and promote students’ mathematical proficiency. Every chapter is carefully planned to present concepts in a logical order, providing a strong foundation of knowledge and making higher learning easier. Here, we offer in-depth coverage of each chapter, including the main topics and the mathematical concepts they introduce. This makes it easier for students to work through and become proficient with the material.
| Chapter | Title |
|---|---|
| Chapter 1 | Relations and Functions |
| Chapter 2 | Inverse Trigonometric Functions |
| Chapter 3 | Matrices |
| Chapter 4 | Determinants |
| Chapter 5 | Continuity and Differentiability |
| Chapter 6 | Application of Derivatives |
| Chapter 7 | Integrals |
| Chapter 8 | Applications of Integrals |
| Chapter 9 | Differential Equations |
| Chapter 10 | Vector Algebra |
| Chapter 11 | Three-Dimensional Geometry |
| Chapter 12 | Linear Programming |
| Chapter 13 | Probability |
Chapter 1: Relations and Functions
This first chapter of the PDF discusses the basic concepts of relations and functions, which are explained simply for better understanding. It deals with various sub-topics, such as the introduction to relations and functions, their types, composition and invertibility of functions, and domains, co-domains, and binary operations.
The chapter provides an in-depth understanding of these subjects, which are significant for academic studies. Each sub-topic is well explained to further your understanding of the concepts. Four exercises with solutions at the end of the chapter can be used for revision and practice. To have easy access, you can download the NCERT Class 12th Maths Book Part 1 PDF using the above-given links.
Chapter 2: Inverse Trigonometric Functions
This chapter in the PDF of the NCERT Class 12th Maths textbook introduces the fundamental concepts and properties of inverse trigonometric functions. It ends with two detailed exercises and solutions to make it easier for you to grasp the material. These exercises examine the ranges of different trigonometric functions and study their behavior through graphs.
Written by professional mathematicians, the textbook is designed to allow easy understanding of intricate subjects. To download this material, you can easily download the Maths Class 12 NCERT PDF through the given links.
Chapter 3: Matrices
The third chapter of the NCERT Class 12th Maths PDF textbook is an in-depth analysis of matrices, a basic building block in higher mathematics. This chapter is organized to allow a thorough grasp of the subject by a thorough and systematic discussion of different sub-topics:
- Introduction: A brief discussion of the general idea of matrices.
- Definition: A clear definition of matrices and what constitutes them.”.
- Matrix Types: Categorize matrices according to their properties and structures, such as square, rectangular, diagonal, scalar, and identity matrices.
- Matrix Equality: Conditions under which two matrices are equal.
- Operations: A step-by-step procedure for adding matrices and multiplication using a scalar.
- Matrix Properties: Examination of properties demonstrated by matrices while being added and multiplied, such as associative and distributive properties.
- Transpose and its Properties: Concept of the transpose of a matrix and its important properties.
- Symmetric and Skew Symmetric Matrices: Properties and differences between symmetric and skew-symmetric matrices.
- Elementary Operations or Transformation of Matrices: Methods and procedures for carrying out elementary row and column operations.
- The Inverse of Matrices: In-depth discussion on determining the inverse of a matrix and using elementary operations in this determination.
- Miscellaneous Examples: Different examples to demonstrate and use the concepts covered.
This chapter contains four exercises that explore these topics to facilitate learning, enabling you to apply practically and reinforce the learned material. Solutions are also given for every exercise to enable you to grasp the concepts and enhance your problem-solving skills.
Chapter 4: Determinants
This chapter from the NCERT Class 12th Maths is a detailed analysis of determinants, which are important to identify the properties and applications of matrices. It offers a comprehensive learning framework for students to understand and apply concepts concerning determinants:
- Introduction: A preliminary introduction that serves as a foundation for the following discussion.
- Explanation of Determinants: A clear definition and analysis of determinants and why they matter in mathematics.
- Properties of Determinants: A study of the most important properties determinants have, properties that are critical in solving matrix-related issues.
- Finding the Area of a Triangle: An application of determinants in geometry for calculating the area of triangles.
- Minors and Cofactors: Exhaustive explanation of minors and cofactors plays a key role in determining the determinant and inverse of a matrix.
- Adjoint and the Inverse of a Matrix: The procedure is to obtain the adjoint and apply it to calculate the inverse of a matrix, detailing the process with simplicity.
- Applications: Different applications of determinants to solve real-world problems and mathematical equations.
To further consolidate understanding, the chapter contains six guided exercises that address these issues, allowing students to reinforce their understanding of the subject matter. Furthermore, miscellaneous examples are given throughout, culminating in a summary summarising the main points discussed, providing a comprehensive understanding of the determinants.
Chapter 5: Continuity and Differentiability
This NCERT Class 12 Maths book PDF chapter deeply covers continuity and differentiability, pivotal to comprehending higher-level calculus. The chapter introduces continuity, accompanied by multiple examples and exercises to help the reader understand the topic better. Detailed descriptions of differentiability, several sub-topics, and exemplary examples for easy understanding follow this.
Additional sections cover exponential and logarithmic functions, derivatives of functions in parametric forms, and the Mean Value Theorem, each with relevant examples. To recap the vast information covered, a summary section at the end of the chapter gives a brief overview, which helps reinforce your understanding of the subject matter.
Chapter 6: Application of Derivatives
This chapter in the Class 12th Maths book delves deeply into the various applications of derivatives, beginning with a traditional introduction that provides insights into the key components of the chapter. Following the introduction, the discussion covers significant topics such as the rate of change of quantities, the behaviour of increasing and decreasing functions, and the principles of tangents and normals. It also explores how derivatives assist in making approximations and in determining the maxima and minima of functions.
Each topic is supported by numerous examples and detailed explanations of relevant theorems, accompanied by exercises to practice and reinforce the concepts learned. The structured layout of the chapter ensures that you can easily understand and apply the concepts of derivatives with minimal difficulty.
Chapter 7: Integrals
Integrals are a crucial chapter in Class 12 mathematics that deals with the problem of determining and computing the area under curve lines drawn by function graphs. The chapter presents an extensive overview of integration with multiple methods and integrals. It encompasses an elaborate discussion on functions with definite integrals and determining definite integrals using substitution methods.
Chapter 8: Applications of Integrals
This chapter focuses on the practical applications of integrals, particularly in determining areas related to various geometric shapes. Here, you’ll explore how to calculate the area under simple curves, including the specific case of regions bounded by a line and a curve. Additionally, the chapter covers the calculation of areas between two curves.
The chapter includes numerous examples and detailed calculations to aid in understanding these concepts. Dedicated exercises are provided following each topic to reinforce the material and enhance your mastery of applying integrals in these contexts.
Chapter 9: Differential Equations
Differential equations find applications beyond mathematics and are used in physics, chemistry, biology, and economics, making this chapter a must for Class 12 students. The chapter begins with an introduction to the fundamental concepts of differential equations, progressing to general and particular solutions.
The text then explains how differential equations are formed when the general solution is known. Further, you will learn the procedures for solving first-order, first-degree differential equations. To facilitate understanding and implementation, the chapter has numerous miscellaneous examples intended to remove all confusion. The exercises and examples in this Class 12 Maths NCERT Book PDF enhance further understanding and help achieve a greater involvement with the subject.
Chapter 10: Vector Algebra
In this Class 12 Maths textbook PDF chapter, you will learn about vectors employed to describe quantities like displacement, force, velocity, weight, and momentum. You will begin by understanding vectors’ definitions and fundamental concepts and then proceed to how they can be operated and utilized.
You will study the following topics:
- Fundamental concepts of vectors
- Vectors
- Vectors Addition
- Scalar multiplication of vectors
- The dot product of two vectors
For a better understanding, the chapter features diagrams, examples, and exercises with solutions. Every practice set has detailed solutions and diagrams to offer clear explanations and facilitate your learning process.
Chapter 11: Three-Dimensional Geometry
As a foundation of what you studied in the vector algebra chapter, this section presents you with the exciting field of three-dimensional geometry. Here, you will learn the basics of 3D geometry in practical applications and theory.
You will study the following main topics:
- Direction cosines and direction ratios of a line
- Equations of lines in space
- Finding the angle between two lines
- Shortest distance between two lines
- Plane surfaces
- Whether two lines are coplanar or not
- Angle between two planes
- Distance of a point from a plane
- Angle between a line and a plane
All these concepts have elaborate explanations that will assist you in effectively understanding the intricate three-dimensional relationships and geometrical characteristics.
Chapter 12: Linear Programming
Linear programming, one of mathematics’s most important optimization problems, is discussed in this chapter. You may remember learning the fundamentals of linear programming and its real-world applications through graphical techniques in Class 11.
This chapter explores linear programming using graphical methods to enhance your knowledge further. This chapter contains several examples and exercises to improve your ability to formulate and solve such problems. The chapter ends with a miscellaneous chapter to clarify the concepts and offer more practice. This organized format in the Class 12 Maths NCERT book is meant to strengthen your understanding of linear programming.
Chapter 13: Probability
Investigating probability to measure the uncertainty of results in different experiments using the axiomatic method pioneered by Russian Mathematician A.N. Kolmogorov. The method approaches probability as an outcome of experiments, closely relating it to classical and axiomatic theories when results are comparable.
This chapter builds your probability knowledge by introducing the concept of conditional probability, Bayes’ theorem, the rule of multiplication, and independent events. The concept of a random variable and probability distribution are also discussed. By the latter half of the chapter, you will be working on the Binomial distribution, giving you further skills in analysing and calculating probability for more advanced scenarios.
Benefits of NCERT CBSE Class 12 Maths Book
CBSE Class 12 Maths textbooks help students clear doubts via teacher guidance or self-study through NCERT books. Reading these books is particularly helpful in doing well in board exams. NCERT Books for Class 12 Maths simplify difficult topics and formulas more comprehensively. NCERT Books are the best for students who must reinforce their understanding of important mathematical concepts. Some of the benefits of NCERT Books for Class 12 Maths are given below:
- They enhance students’ understanding of concepts of Class 12 Maths.
- They offer thorough insights into everything, including the curriculum.
- They are very good for revision.
- They assist students in identifying and filling knowledge gaps.
- They deepen their understanding of important subjects.
- They are commonly used for homework and assignments to ensure learning aligns with the curriculum.
Class 12 NCERT Math Book FAQs
Is the Class 12 NCERT Maths book available in Hindi?
Yes, students can download the class 12 maths NCERT book pdf download in Hindi from the NCERT website. It ensures that Hindi-medium students can also access quality study material in their preferred language.
Can the Class 12 NCERT Maths book help in preparing for the JEE exams?
Absolutely, the class 12 NCERT book maths provides a strong foundation for competitive exams. Topics like calculus, algebra, and probability covered in the book are key for JEE preparation.
How can I download the NCERT Class 12 Maths Book PDF for free?
The NCERT Class 12 Maths Book PDF can be downloaded from the official NCERT website for free in both Hindi and English mediums. You can also get the download link provided above in this article.
What are the main topics covered in the Class 12 NCERT Maths Book?
The book covers various topics, including calculus, algebra, probability, and vector geometry, which are essential for a comprehensive understanding of Class 12 Mathematics.
