NCERT Class 12 Maths Book PDF
CBSE Class 12 NCERT Books for Maths PDF – Free Download
Class 12 students follow a syllabus designed by the National Council of Education Research and Training (NCERT). They release books for students taking examinations given by the CBSE that are based on this syllabus. Therefore, if you are having difficulty navigating through the course, you should consider using these books as a resource. This PDF for Class 12 maths from NCERT offers the knowledge that is required to address the numerous subjects that are covered in the subject. In addition, you won’t have to put in nearly as much effort to grasp the concepts presented in each chapter thanks to the breakdowns provided in this PDF. If mathematics was one of the subjects that you found particularly challenging, then these PDFs will be of assistance to you in overcoming those challenges. It is now easy to get a free download of the NCERT Mathematics Class 12 PDF.
Maths Class 12 NCERT PDF on Extramarks
The NCERT book for class 12 mathematics provides a comprehensive analysis of each topic covered by the syllabus. It addresses each primary topic as well as all of the subtopics, and it includes a solution organised by exercise. Students benefit from solutions such as these by gaining a more in-depth explanation of every topic and improving their ability to find solutions to problems. To get a better grasp of the material, download NCERT Books for Class 12 Maths.
There are a total of thirteen chapters in the NCERT Maths 12 book. These chapters cover a variety of important topics such as applications of derivatives, matrices, relations, functions and vector algebra. In addition, if you are studying for other competitive exams such as JEE, NEET, etc., then the information in these books can help you achieve your goals.
Unit-Wise Weightage for Class 12:
Below, in a table format, we have made available information on the distribution of marks for the mathematics unit for students in Class 12. It will be of assistance to students in finding solutions to many types of problems. Because of the frequency with which the Mathematics syllabus undergoes revisions, it is imperative that students remain up to date on all modifications. There is not a fair distribution of the marks across each chapter. We have placed a strong emphasis on the Class 12 Mathematics marks distribution by unit to ensure that students are able to comprehend every facet of the syllabus and achieve success in their planning and preparation for the CBSE Board Exam 2023.
Unit No. | Unit Name | Marks |
1 | Relation and Function | 08 |
2 | Algebra | 10 |
3 | Calculus | 35 |
4 | Vectors and Three–Dimensional Geometry | 14 |
5 | Linear Programming | 05 |
6 | Probability | 08 |
Total Marks | 80 | |
Internal assessment | 20 |
Question Paper Designing for Class 12:
S.No | Typology of questions | Marks | Weightage(in %) |
1 | Remembering: Demonstrate that you have retained the information that you have learned by bringing back facts, terminology, fundamental concepts, and responses. Understanding: To demonstrate that you understand the material, you will need to organise, compare, translate, interpret, give descriptions of it and state the important ideas. |
44 | 55 |
2 | Applying: Utilise the knowledge, facts, processes and rules that you have acquired in creative ways to find solutions to problems that arise in various contexts. | 20 | 25 |
3 | Analysing: Analysing something involves looking at it carefully, dissecting it into component parts and figuring out the reasons or motivations behind it. First you need to make some assumptions, and then you need to gather evidence to back up your claims.
Evaluating: For the purpose of presenting and defending one’s ideas, one must evaluate information, the soundness of ideas, and the calibre of work based on a predetermined set of criteria. Creating: Compile data in a novel way by combining pieces in a new pattern or suggesting alternate options. |
16 | 20 |
Total | 80 | 100 |
The information was gathered straight from a board article published by the CBSE. NCERT released a new examination syllabus this year that is thirty percent shorter than the one that was used previously. As a result of the extensive changes made to the CBSE Class 12 mathematics marking scheme in 2023, it is essential to keep a close eye on the official pdf. There is no differentiation in terms of chapter weight. It is imperative that each of the chapters is covered.
It is possible to make internal changes in order to generate a variety of different templates while at the same time keeping the overall weightage of the various types of questions and the question typology unchanged. There will not be a choice of overall topics offered in the question paper. Internal alternatives, on the other hand, will account for 33% of all parts.
Internal Assessment for CBSE Class 12:
Out of 100 marks for the exam, students receive marks from a total of 20 marks for the internal assessment. There will be a total of three periodic examinations, the best two of which will each be worth 10 marks. In addition to that, another 10 marks will come from the mathematical activities that will be run by the school or other institutions.
NCERT Maths Class 12 Chapterwise Details
Chapter 1: Relations and Functions
The theories that pertain to relations and functions are the topics of discussion in the first chapter of this PDF. They are broken down for you in a way that is simple and straightforward so that you can comprehend them. In addition, this chapter contains an introduction as well as sections on the different kinds of relations and functions, the composition of functions, invertible functions, domains, co-domains and binary operations.
This chapter offers in-depth information on the subject, and a thorough understanding is required for every examination. In addition, this PDF provides an in-depth explanation of each sub-topic for your improved understanding of the concepts that are connected to it. In addition, there are four exercises located at the end of this chapter, and the solutions to those exercises are also included for the student’s convenience. Through the links that have been provided, you will be able to quickly complete the NCERT class 12 maths part 1 PDF download.
Chapter 2: Inverse Trigonometric Functions
The topic of inverse trigonometric functions as well as its concepts and properties are covered in depth in the subsequent chapter of this NCERT mathematics textbook for Class 12. In addition, the final section of this book includes two exercises, each of which has a solution. As a result, comprehending the ideas should not be too difficult for you. In these two exercises, the ranges of a variety of trigonometric functions are discussed, and attention is drawn to the behaviour of these functions via graphical representation.
In addition, these books are written by highly qualified mathematicians, and the straightforward organisation of such books makes it much simpler for you to understand the material. Simply by clicking on the links provided, you will be able to quickly and easily download the NCERT PDF for Class 12.
Chapter 3: Matrices
Matrix-related topics are covered in depth in the third chapter of the NCERT mathematics textbook for class 12. This consists of –
- Introduction
- Definition
- Types of matrices
- Equality of matrices
- Operations, which include addition and multiplication by scalar
- Properties of matrices during addition and multiplication
- Transpose and its properties
- Symmetric and elementary operations or transformation of matrices
- Skew symmetric matrices
- The inverse of matrices and its elementary operations
- Miscellaneous examples
There are four exercises in addition to an easily understandable description of these subtopics. Additionally, the solutions are given to assist you in better understanding this topic.
Chapter 4: Determinants
Every topic and subtopic of determinants of the Matrix are covered in the following chapter of this NCERT 12 maths textbook. This PDF will help you rapidly understand what determinants are and what they mean. It also has an introduction to the chapter, a description of the determinant, its properties, how to figure out the area of a triangle, minors and cofactors, how to join and flip a matrix, examples, etc.
The sixth exercise is also part of this chapter’s content. You can better understand the ideas related to the matrix and its determinants with the help of these exercises. There are also a few different examples, and then a summary comes next.
Chapter 5: Continuity and Differentiability
For simple concept understanding, this chapter of the NCERT 12 maths book PDF has eight exercises with solutions. It begins with an introduction and then discusses continuity using a variety of examples and exercises. A similar justification for differentiability follows that. This differentiability explanation covers several sub-topics and examples.
Exponential and logarithmic functions, derivatives of functions in parametric forms, the mean value theorem and other examples are the remaining subjects covered in this chapter after that. A succinct overview of the entire chapter is given in the summary section. Download the class 12 maths NCERT PDF.
Chapter 6: Application of Derivatives
The various applications of derivatives are thoroughly explained in this chapter of the math textbook for classes 12 and 13. It begins with a customary introduction that provides background information on the chapter’s elements. Following that, it continues to explain the following subjects:
- Rate of change of quantities
- Increasing and decreasing functions
- Tangents and normal
- Approximations
- Maxima and Minima
This chapter’s topics are broken down into multiple examples, explanations of the related theorems and exercises. Furthermore, chapters with such a clear format will make it easier for you to understand the idea quickly.
Chapter 7: Integrals
One of the most important chapters in mathematics for class 12 is integrals. It deals with the challenge of determining and quantifying the size of a particular region that is constrained by function graphs.
This chapter includes integration, its techniques, the purposes of particular integrals, definite integrals and their evaluation by substitutions, among others. This chapter includes several examples and exercises to help readers learn integrals, much like the earlier chapters did. The NCERT Maths Book Class 12 Part 2 PDF is easily downloadable.
Chapter 8: Applications of Integrals
This chapter clarified its uses as well as the mathematical side of it. Additionally, this chapter will cover the following subjects:
- Finding the area enclosed by a line and a curve which is a subtopic of Area Under Curve.
- The space separating two curves
There are numerous examples and computations to further aid your understanding of the chapter. Each topic is followed by a specific activity that you can complete to get a better understanding of the material.
There are also various examples, and a summary and historical note comes next. If you have any questions about the uses of integrals, you can download this NCERT 12 maths PDF and get them answered.
Chapter 9: Differential Equations
Differential equations have uses outside of just mathematics. They can also be used in biology, chemistry, economics, etc. As a result, it is a crucial chapter for Class 12 students. This chapter starts with the basic idea of a differential equation and then talks about both general and specific ways to solve this equation.
The formation of these equations is then explained, along with the general solutions. You also learn how to solve differential equations of the first degree and order. Following these subjects are a variety of examples that can assist you in clarifying your questions. Moreover, the exercises and pictures in this NCERT 12 maths PDF might help you understand the idea better.
Chapter 10: Vector Algebra
You will learn about vectors and the problems they might cause in this chapter of the class 12 maths NCERT PDF. Typically, vectors are used to represent things like force, momentum, weight and displacement. You will learn about the definition, fundamental ideas, operations, and other things related to vectors here.
In addition, the following is a list of the subjects covered in this chapter:
- Basic concepts of vectors
- Types of vectors
- Addition of vectors
- Multiplication of vectors by a scalar
- Product of two vectors
For you to better understand this subject, there are also illustrations, examples and activities with solutions. Additionally, each practice set includes comprehensive solutions with diagrams for a clearer understanding.
Chapter 11: Three-Dimensional Geometry
You will now learn how to apply vector algebra to three-dimensional geometry, which comes after the chapter on vector algebra. The fundamentals of 3D geometry are covered in this chapter, including the following:
Direction cosines and Direction Ratios of a line
- Equation of a line in space
- The angle between two lines
- The shortest distance between two lines
- Plane surface
- Coplanarity of two lines
- The angle between two planes
- The distance of a point from a plane
- The angle between a line and a plane
Additionally, other examples and summary sections are included after these subjects to wrap up the chapter. With the aid of the NCERT class 12 maths book PDF, you may easily grasp the concept of three-dimensional geometry, which is an important subject.
Chapter 12: Linear Programming
One major area of mathematics is optimisation problems, and one of their well-known subtypes is linear programming. The idea of linear programming and its practical implementations have already been covered. Additionally, you also learned about the same things in class 11 with the help of pictures.
You will also learn linear programming through graphical representations in this chapter. This chapter only covers one subject, namely linear programming problems and their mathematical formulation. There are numerous examples and activities for you to complete under this section. A random part follows this chapter’s conclusion in the maths NCERT class 12 textbook.
Chapter 13: Probability
You have already learned how to measure the uncertainty of experiment results using probability in prior courses. We have talked about the axiomatic method, which was developed by the Russian mathematician A.N. Kolmogorov. Furthermore, we considered probability as a result of experimentation. In the case of similar results, you have also examined the equivalence of the axiomatic theory and the classical theory equivalence.
You will also discover the ideas of conditional probability, the Bayes theorem, the multiplication rule and other independent events in this chapter. In addition, the concept of a random variable and the probability distribution is covered in this. You will learn about binomial distribution in this chapter’s penultimate section. This chapter of the class 12 maths NCERT PDF contains a tonne of examples and exercises, much like the chapters before it.
NCERT Books Ideal for Class 12 Maths
It is not an uncommon query to wonder why NCERT books are favoured over those published by other organisations. The following is a list of the most important reasons why NCERT books are given preferential attention.
- The authenticity of the content is the primary selling point of these publications. All of the data and information that is presented here has been checked for accuracy and gathered from reputable sources. If you follow the instructions in the NCERT books, you will lessen the likelihood that you will learn and present inaccurate information on the test.
- Content is Accumulated Over Time: The NCERT series of books is well-known for the comprehensive manner in which they approach each subject. In addition to this, they provide an in-depth analysis of any subject, which incorporates all the necessary and relevant facts as well. So, reading a book from the NCERT is a good way for students to learn more about any topic and get a better understanding of it.
- The fact that the NCERT class 12 maths textbook uses language that is simple and straightforward is another important benefit of using this book. The choice of words and the manner of writing are appropriate for all of the students. As a consequence, they have no trouble understanding the material.
- These books have a lot of information in them along with a comprehensive presentation. They go into great detail on every aspect of a subject and provide numerous examples and exercises. The students will have an easier time comprehending the subject because of the activities and examples that have been provided to them. In addition to this, the inclusion of diagrams is yet another perk of reading such books. They take the subject and make it easier to understand for the students.
- A key advantage of it is that you might find similar questions on the CBSE exam which you’ve already solved in this book. This is one of the many reasons why purchasing this book is so beneficial.
Exam Pattern for Class 12:
The explanation for this question paper can be broken down into two parts: A and B. Each and every component is necessary. While Part A is worth a total of 24 marks, Part B is worth a total of 56 marks. In Part A, there are questions of an objective nature, and in Part B, there are questions of a descriptive nature. There are choices to be made in both Part A and Part B of the exam.
Part – A:
It is divided into two sections: I and II.
The first section of the exam consists of 16 multiple-choice questions with answers that are mostly brief.
In Section II, there are two case studies presented. Each multiple-choice question (MCQ) based on a case study contains a total of five questions. The examinee is allowed to attempt any four of the available five multiple-choice questions.
Part B:
It is broken up into three distinct parts: the III, IV, and V sections.
There are ten questions worth two marks each in Section III.
The questions in Section IV are each worth a total of three points.
In the fifth and final section, there are three questions, and each one is worth five points.
There are three multiple choice questions in Section III, two multiple choice questions in Section IV, and three multiple choice questions in Section V. You are only allowed to choose one of the options when faced with questions like these.
Why Should Students Opt for Extramarks?
Extramarks is one of the most successful online education platforms in India. Through our website, you will have access to a variety of study materials, including online books, CBSE revision notes, and more. In addition, you are able to participate in the daily live classes by downloading our official app. These courses are taught by professionals in their fields who hail from all over the country. You could join our live classes if you have questions or concerns about the NCERT mathematics textbook for Class 12.
NCERT Solutions for 12 Maths - Chapterwise PDF
NCERT Books for Class 12
NCERT Solutions for Class 12
FAQs (Frequently Asked Questions)
1. What exactly are the chapters of the NCERT mathematics book for Class 12?
Mathematical topics that must be covered by students in Class 12 include Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of Integrals, Differential Equations, Vector Algebra, Three-Dimensional Geometry, Linear Programming and Probability. Class 12 students must also be familiar with Linear Programming and Probability. There are thirteen essential chapters drawn from the NCERT book that make up the CBSE syllabus for Class 12. The article contains both NCERT books and NCERT solutions pertaining to mathematics.
2. What are the areas in which CBSE and NCERT textbooks differ from one another?
There is not really any difference between the books that are published by CBSE and the books that are published by NCERT. The reason for this is that the National Council of Educational Research and Training, also known as NCERT, is the organisation that is responsible for developing the curriculum of schools that are accredited by the CBSE. On the other hand, the Central Board of Secondary Education (CBSE) is an educational board or governing body that oversees multiple schools all over the country. In addition, CBSE is not responsible for the publication of any books. Both NCERT and CBSE are connected. Books from NCERT are clear and easy to understand, while books from CBSE are more difficult to understand.
3. In order to prepare for the JEE mathematics exam, what are some good books to read?
For preparation for the JEE exam, the use of NCERT maths textbooks for Class12 is always recommended. Approximately sixty to seventy percent of the JEE questions are taken directly from these books. In addition, the sample questions and exercise sections that are included in these books help to simplify a chapter, making it much simpler to understand for the reader. Textbooks are invariably the most useful resources, both for academic and professional examinations. The JEE, on the other hand, is a very difficult exam. Therefore, you should make it a goal to read as many books as you possibly can. You can get additional details and resources about the JEE exam by going to the official website for Extramarks.
4. How do I get Class 12 NCERT solutions?
The official NCERT website typically has NCERT books and NCERT solutions. To assist students, Extramarks has included all of the textbooks and explanations in this article. They are completely free to download. There is a link to download the books in this article. All of the solutions are included in NCERT solutions, which have been meticulously written so that students may understand the approach taken. On the Extramarks website, all answers are freely accessible.