How Many Chapters in Maths Class 12

Introduction

The importance of board exams in a student's life cannot be overstated. Gaining success in these tests has a significant impact on their career. Aspirants should therefore work diligently and honestly to reach this milestone. The goal shouldn't be to just ace the test by memorising the material. To obtain knowledge, students should instead consult the NCERT Syllabus for Class 12 Maths 2022–23 before systematically and methodically preparing for the CBSE 12th Exams.

Maths is a subject that is often the focus of excitement, although it's not all that difficult. It focuses on assessing one's comprehension of the subject's fundamentals. Students should therefore get ready for it to broaden their knowledge and focus on the core principles. As a result, the NCERT Syllabus for Class 12 Maths 2022–23 is essential for thorough exam preparation. Learn more about the Maths NCERT Syllabus for Class 12 in the article, which also includes chapter-by-chapter solutions, course structure, and grading guidelines.

NCERT Syllabus for Class 12 Maths

• Given that it was created by specialists, the NCERT CBSE Syllabus for Class 12 Maths 2022–23 seeks to give students information that is both pertinent and helpful.

• These books can be studied to assist you to get ready for competitive exams and some scholarship tests like KVPY, etc.

• The only aim of NCERT is to set forward a curriculum that will be extremely helpful to pupils in their future endeavours.

• The class 12 NCERT Maths Syllabus for 2022–2023 does not go into great detail. In actuality, it provides information concisely and understandably. This facilitates better comprehension.

• NCERT Solutions for Class 12 Math help candidates by answering all of their questions and removing any doubts they may have.

• Exemplar problems from the NCERT Book for Class 12 Maths are particularly helpful for candidates as they frequently appear in the CBSE Class 12th board exams.

• NCERT Exemplar Class 12th Maths Solutions should also be read.

• Class 12 Math NCERT Syllabus 2022–23

• The class 12 maths CBSE syllabus for 2022 is provided below, along with chapter-by-chapter solutions, significant subjects, and a grading scheme.

Internal Assessment for CBSE Class 12

The internal evaluation is worth 20 out of the exam's 100 possible points. There will be three periodic tests, and the top two will each receive ten points. Additional mathematical tasks worth 10 points will be carried out by the school or organisation.

Chapter 1: Relations and Functions

You can understand them because they are explained in a very simple way. Introduction, categories of relations and functions, the composition of functions, invertible functions, domain, co-domain, and binary operations are also included in this chapter. This chapter offers in-depth knowledge on the subject and is crucial reading for all exams. Additionally, each sub-topic is thoroughly discussed in this PDF so you can better understand the concepts involved. Students can also discover the answers to the four activities that are included at the end of this chapter. With the help of the aforementioned links, you can easily download the NCERT class 12 maths part 1 PDF.

Chapter 2: Inverse Trigonometric Functions

An introduction to the subject as well as the ideas and characteristics of inverse trigonometric functions can be found in the following chapter of this NCERT class 12 math textbook. Additionally, two exercises with solutions are included at the end of this chapter. As a result, it is simpler for you to comprehend the principles. These two exercises explain the graphical representations of the behaviour of several trigonometric functions and their ranges. Furthermore, these publications are written by qualified mathematicians, and the straightforward layout makes it simpler for you to understand the subject. By clicking on the links, you can quickly get the class 12 maths NCERT PDF.

Chapter 3: Matrices

Every component of matrices is covered in the third chapter of the NCERT class 12 maths book in PDF format. It consists of

• Introduction

• Definition

• Various matrices

• A matrix's equality

• Operations such as addition and scalar multiplication

• Matrix properties for addition and multiplication

• The qualities of transposition

• Matrix transformations or operations that are simple and symmetric

• Symmetric skew matrices

• The fundamental operations of a matrix's inverse

• Numerous instances

There are four exercises in addition to an easily understood description of these subtopics.

Chapter 4: Determinants

It also includes the chapter introduction, a description of the determinant, properties, how to compute a triangle's area, minors and cofactors, how to adjoin and invert a matrix, applications, etc.

Chapter 5: Continuity and Differentiability

A similar justification for differentiability follows that. This explanation of differentiability includes a number of examples and subtopics. 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. Download the class 12 maths NCERT PDF as a result for better training.

Chapter 6: Application of Derivatives

• Rate of quantity change

• Functions that increase and decrease

• Normal and tangential

• Approximations

• Minima and maxima

Chapter 7: Integrals

It deals with the challenge of determining and quantifying the size of a particular region that is constrained by function graphs. These topics cover, among others, integration, its methods, the objectives of specific integrals, definite integrals, and their assessment by replacements. Similar to how the preceding chapters did, this chapter offers several examples and tasks to aid readers in learning integrals.

Chapter 8: Applications of Integrals

Both the mathematics side of it and its applications were made clear in this chapter. Additionally, the following topics will be covered in this chapter:

• Finding the region enclosed by a line and a curve is a subtopic of the topic of the area under simple curves.

• The space separates two curves.

• There are also various examples, and then a summary and historical note part comes next.

Chapter 9: Differential Equation

Differential equations have uses outside of just mathematics. Additionally, it can be used in biology, chemistry, economics, etc. Beginning with the fundamental idea of a differential equation, this chapter goes on to discuss both general and specific solutions to this equation. The general solutions and how these equations came to be are then described. Differential equations of the first degree and order are another thing you learn how to solve. These topics are followed by a range of examples that can help you explain your queries.

Chapter 10: Vector Algebra

In this chapter of the class 12 maths NCERT PDF, you will study vectors and the issues they may raise. Usually, vectors are used to describe things like force, momentum, weight, and displacement. Here, you will learn about the definition, core concepts, operations, and other vector-related topics.

• Basic vector principles

• Various vector types

• Adding more vectors

• Vectors multiplied by a scalar

• Combination of two vectors

For you to better understand this subject, there are also illustrations, examples, and activities with solutions. Each practice set also comes with comprehensive solutions and pictures for a better understanding.

Chapter 11: Three-Dimensional Geometry

After the chapter on vector algebra, you will now discover how to use vector algebra in three-dimensional geometry. This chapter covers the principles of 3D geometry, including the following:

• A line's direction cosines and direction ratios.

• The expression for a line in space.

• The inclination of two lines.

• The distance between two lines that are the shortest

• A flat surface coherence of two lines.

• The arc is formed by a line and a plane.

Chapter 12: Linear Programming

A major area of mathematics is optimization problems, and one of its well-known subtypes is linear programming. Additionally, you covered the identical material with the aid of graphical representations in class 11 earlier.

You will also discover linear programming through graphical representations in this chapter. This chapter only covers one subject, namely. Problems in Linear Programming and Their Mathematical Formulation. There are numerous examples and activities for you to complete under this section.

Chapter 13: Probability

As a result, we have talked about the axiomatic method, which was developed by the Russian mathematician A.N. Kolmogorov. In case of similar results, you have also examined the axiomatic theory and classical theory's equivalence.

You will also discover the ideas of conditional probability, the Bayes theorem, the multiplication rule, and independent events in this chapter. In addition, the concept of a random variable and the probability distribution is covered in this. We will learn about binomial distribution in this chapter's penultimate section.

NCERT Math 12

Why NCERT books are favoured over other texts is a common query. Here are a few notable explanations for why NCERT books are given preferential treatment.

Authenticity: These books' primary USP is their authenticity. Verified and gathered from dependable sources, the statistics and information shown here are accurate. As a result, if you study from NCERT books, your chances of learning and presenting false information in the exam are lower.

Knowledge in-Depth: NCERT books are renowned for their thorough treatment of every topic. Additionally, they offer a thorough analysis of any subject and incorporate all viable and pertinent information. Thus, reading an NCERT book aids students in learning a subject thoroughly.

Presentation in Depth: These books are quite thorough. They cover every facet of a subject and include numerous illustrations and exercises. The problems are made simpler for the pupils to understand through these activities and illustrations. Moreover, another advantage of these books is their usage of diagrams. For the pupils, they further simplify the idea.

Last but not least, a key advantage of it is that you can encounter questions identical to those you've already answered in this book on the CBSE exam.

Exam Pattern for Class 12

This test contains the following two sections: A and B. Each element is necessary. Part B is worth 56 points, compared to Part A's 24 points. Both Part A and Part B have options, with Part A containing questions of the Objective Type and Part B containing questions of the Descriptive Type.

Part - A:

I and II make up its two portions.

16 multiple-choice questions with brief answers make up Section I.

Section II contains two case studies, each of which has five case-based multiple-choice questions. The examinee may attempt any four of the five MCQs.

Part - B:

III, IV, and V make up its three sections.

Ten two-mark questions make up Section III.

Chapter IV contains seven questions with three points each.

Three questions make up Section V, and each one is worth five points.

Internal choice is included in three of the questions in Section III, two of the questions in Section IV, and three of the questions in Section V. We may only select one answer per question of this type.

Conclusion

There are 13 chapters in all in the NCERT Math 12 Solutions, which cover crucial subjects like Relations and Functions, Matrices, Vector Algebra, Applications of Derivatives, etc. Additionally, if you are preparing for additional competitive examinations like JEE, NEET, etc.