Class 12 Maths Part 1 PDF Download: A Complete Guide
Are you looking for a reliable source to download Class 12 Maths Part 1 PDF for free? Do you want to know what topics are covered in Class 12 Maths Part 1 and how to prepare for them effectively? If yes, then you have come to the right place. In this article, we will provide you with all the information you need to download and study Class 12 Maths Part 1 PDF. We will also give you some tips and tricks to ace the exam and score high marks. So, read on and get ready to master Class 12 Maths Part 1.
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Introduction
Mathematics is one of the most important subjects for Class 12 students, especially for those who aspire to pursue engineering, statistics, or other related fields. Mathematics helps to develop logical thinking, problem-solving, and analytical skills that are essential for higher studies and career. Therefore, it is crucial to have a strong foundation in Mathematics and clear all the concepts thoroughly.
Class 12 Maths is divided into two parts: Part 1 and Part 2. Part 1 consists of six chapters that deal with topics such as relations, functions, matrices, determinants, calculus, and its applications. These topics are not only important for the board exam but also for various competitive exams such as JEE Main, JEE Advanced, NEET, etc. Hence, it is advisable to study Class 12 Maths Part 1 with utmost dedication and sincerity.
What is Class 12 Maths Part 1?
Class 12 Maths Part 1 is a textbook published by the National Council of Educational Research and Training (NCERT) for the students of CBSE board. It is based on the latest syllabus prescribed by the CBSE board for the academic year 2022-23. It covers all the topics that are included in Unit I (Relations and Functions), Unit II (Algebra), and Unit III (Calculus) of the CBSE syllabus.
Class 12 Maths Part 1 is written in a simple and lucid language that makes it easy for the students to understand the concepts and apply them in solving problems. It also provides ample examples, solved exercises, unsolved exercises, previous year questions, and miscellaneous questions for practice and revision. It also contains summary points, formulas, tips, and tricks at the end of each chapter for quick reference.
Why is Class 12 Maths Part 1 Important?
Class 12 Maths Part 1 is important for several reasons. Some of them are:
It helps to build a strong foundation in Mathematics and prepare for higher studies and career.
It helps to develop logical thinking, problem-solving, and analytical skills that are essential for various fields.
It helps to score good marks in the board exam as well as in various competitive exams such as JEE Main, JEE Advanced, NEET, etc.
It helps to enhance interest and curiosity in Mathematics and appreciate its beauty and applications.
How to Download Class 12 Maths Part 1 PDF?
If you want to download Class 12 Maths Part 1 PDF for free, you can follow these simple steps:
Visit the official website of NCERT at .
Click on the tab "Textbooks" and select "PDF (I-XII)" from the drop-down menu.
Select "Class XII" from the list of classes and "Mathematics Part-I" from the list of subjects.
Click on the link "Download Complete Book" and save the PDF file on your device.
You can also download individual chapters by clicking on the respective links.
You can also download Class 12 Maths Part 1 PDF from other websites such as , etc. However, make sure that the PDF files are authentic and updated as per the latest syllabus.
Chapter-wise Overview of Class 12 Maths Part 1
Now that you have downloaded Class 12 Maths Part 1 PDF, let us take a look at the chapter-wise overview of the book. Here, we will briefly describe the main topics, subtopics, and formulas covered in each chapter. We will also provide a table that shows the weightage of each chapter in the board exam as per the latest CBSE marking scheme.
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Chapter 1: Relations and Functions
This chapter deals with the concepts of relations and functions, types of relations, types of functions, composition of functions, inverse of a function, binary operations, etc. It also introduces the concept of inverse trigonometric functions and their properties. Some of the important formulas in this chapter are:
If f and g are two functions, then (f g)(x) = f(g(x)) and (g f)(x) = g(f(x)).
If f is a one-one and onto function, then f(f(x)) = x and f(f(x)) = x.
If A and B are two sets, then a binary operation * on A B is a function that maps A B to A or B.
If y = sin(x), then x = sin y and -π/2 y π/2.
If y = cos(x), then x = cos y and 0 y π.
If y = tan(x), then x = tan y and -π/2 < y < π/2.
The weightage of this chapter in the board exam is 8 marks.
Chapter 2: Inverse Trigonometric Functions
This chapter deals with the concepts of inverse trigonometric functions, their domains and ranges, their graphs, their principal values, their properties, and their applications. It also covers some important results such as:
sin(x) + cos(x) = π/2 for all x [-1, 1].
tan(x) + cot(x) = π/2 for all x R.
sec(x) + cosec(x) = π/2 for all x (-, -1] [1, ).
sin(x) + sin(y) = sin(x(1 - y) + y(1 - x)) if x, y [-1, 1] and xy 0.
cos(x) + cos(y) = cos(xy - (1 - x)(1 - y)) if x, y [-1 , 1] and xy 0.
tan(x) + tan(y) = tan((x + y)/(1 - xy)) if x, y R and xy < 1.
The weightage of this chapter in the board exam is 8 marks.
Chapter 3: Matrices
This chapter deals with the concepts of matrices, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operations, inverse of a matrix, adjoint of a matrix, etc. It also covers some important results such as:
If A and B are two matrices of the same order, then (A + B) = A + B and (AB) = BA.
If A is a square matrix, then (A) = A and (A) = (A).
If A is a symmetric matrix, then A = A and if A is a skew-symmetric matrix, then A = -A.
If A is an invertible matrix, then A 0 and A = adj(A)/A.
If A and B are two invertible matrices of the same order, then (AB) = BA.
The weightage of this chapter in the board exam is 10 marks.
Chapter 4: Determinants
This chapter deals with the concepts of determinants, properties of determinants, minors and cofactors, expansion of determinants, applications of determinants in finding area of a triangle, equation of a line, equation of a plane, etc. It also covers some important results such as:
If A is a square matrix, then A = A.
If A and B are two square matrices of the same order, then AB = AB.
If A is a triangular matrix, then A is the product of the diagonal elements of A.
If A is an invertible matrix, then A = 1/A.
If A is a square matrix and k is a scalar, then kA = kA where n is the order of A.
The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by (x1, y1, 1), (x2, y2, 1), (x3, y3, 1)/2.
The equation of a line passing through two points (x1, y1) and (x2, y2 ) is given by (x, y, 1), (x1, y1, 1), (x2, y2, 1) = 0.
The equation of a plane passing through three points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3) is given by (x, y, z, 1), (x1, y1, z1, 1), (x2, y2, z2, 1), (x3, y3, z3, 1) = 0.
The weightage of this chapter in the board exam is 10 marks.
Chapter 5: Continuity and Differentiability
This chapter deals with the concepts of continuity and differentiability of a function, algebra of continuous and differentiable functions, chain rule, derivative of implicit functions, derivative of inverse trigonometric functions, logarithmic differentiation, etc. It also covers some important results such as:
If f and g are two continuous functions, then f + g, f - g, fg, and f/g (where g 0) are also continuous functions.
If f and g are two differentiable functions, then f + g, f - g, fg, and f/g (where g 0) are also differentiable functions and their derivatives are given by (f + g)' = f' + g', (f - g)' = f' - g', (fg)' = f'g + fg', and (f/g)' = (f'g - fg')/g.
If y = f(u) and u = g(x) are two differentiable functions, then y = f(g(x)) is also a differentiable function and its derivative is given by dy/dx = dy/du du/dx.
If y = f(x) is an implicit function of x, then dy/dx can be obtained by differentiating both sides with respect to x and solving for dy/dx.
If y = sin(x), then dy/dx = 1/(1 - x). Similarly, the derivatives of other inverse trigonometric functions can be obtained using the chain rule and the properties of inverse trigonometric functions.
If y = f(x), where n is any rational number, then dy/dx can be obtained by using logarithmic differentiation. That is, take logarithm on both sides, differentiate implicitly with respect to x, and solve for dy/dx.
The weightage of this chapter in the board exam is 20 marks.
Chapter 6: Application of Derivatives
This chapter deals with the applications of derivatives in finding rate of change of quantities, tangents and normals to curves, increasing and decreasing functions, maxima and minima of functions, Rolle's theorem, Lagrange's mean value theorem, etc. It also covers some important results such as:
If y = f(x) is a differentiable function, then dy/dx represents the rate of change of y with respect to x.
If y = f(x) is a differentiable function and P(x0, y0) is a point on the curve y = f(x), then the equation of the tangent to the curve at P is given by y - y0 = f'(x0) (x - x0) and the equation of the normal to the curve at P is given by y - y0 = -1/f'(x).
If y = f(x) is a differentiable function, then f'(x) > 0 implies that f(x) is increasing, f'(x) < 0 implies that f(x) is decreasing, and f'(x) = 0 implies that f(x) may have a local maximum or minimum at x.
If y = f(x) is a twice differentiable function, then f''(x) > 0 implies that f(x) is concave upward, f''(x) < 0 implies that f(x) is concave downward, and f''(x) = 0 implies that f(x) may have a point of inflection at x.
If y = f(x) is a continuous function on [a, b] and differentiable on (a, b), then Rolle's theorem states that there exists a point c (a, b) such that f'(c) = 0, provided that f(a) = f(b).
If y = f(x) is a continuous function on [a, b] and differentiable on (a, b), then Lagrange's mean value theorem states that there exists a point c (a, b) such that f'(c) = [f(b) - f(a)]/(b - a).
The weightage of this chapter in the board exam is 24 marks.
Tips and Tricks to Ace Class 12 Maths Part 1
Now that you have an overview of Class 12 Maths Part 1, you might be wondering how to study it effectively and score high marks in the exam. Well, don't worry, we have got you covered. Here are some tips and tricks to ace Class 12 Maths Part 1:
Revise the NCERT Book and Solutions
The NCERT book and solutions are the best resources to study Class 12 Maths Part 1. They cover all the topics in detail and provide ample examples and exercises for practice and revision. They also follow the latest CBSE syllabus and marking scheme. Therefore, you should revise the NCERT book and solutions thoroughly and solve all the questions given in them. You can also refer to the NCERT exemplar problems for more practice.
Practice Important Questions and Sample Papers
After revising the NCERT book and solutions, you should practice important questions and sample papers to test your understanding and preparation level. You can find important questions and sample papers from various sources such as previous year papers, mock tests, online platforms, etc. You should try to solve them within the stipulated time limit and check your answers with the solutions. You should also analyze your mistakes and work on them.
Learn Shortcuts and Formulas
Another tip to ace Class 12 Maths Part 1 is to learn shortcuts and formulas by heart. Shortcuts and formulas can help you save time and solve problems quickly and accurately. You should make a list of all the shortcuts and formulas given in each chapter and revise them regularly. You can also make flashcards or notes for easy reference. You should also apply the shortcuts and formulas in solving problems to memorize them better.
Conclusion
We hope that this article has helped you to download and study Class 12 Maths Part 1 PDF. We have provided you with the chapter-wise overview of the book, the important formulas, the weightage of each chapter in the board exam, and some tips and tricks to ace the exam. We hope that you will follow these tips and tricks and score high marks in Class 12 Maths Part 1. All the best!
FAQs
Here are some frequently asked questions about Class 12 Maths Part 1:
Q: How many chapters are there in Class 12 Maths Part 1?
A: There are six chapters in Class 12 Maths Part 1: Relations and Functions, Inverse Trigonometric Functions, Matrices, Determinants, Continuity and Differentiability, and Application of Derivatives.
Q: Which chapter has the highest weightage in Class 12 Maths Part 1?
A: The chapter Application of Derivatives has the highest weightage of 24 marks in Class 12 Maths Part 1.
Q: Where can I download Class 12 Maths Part 1 PDF for free?
A: You can download Class 12 Maths Part 1 PDF for free from the official website of NCERT or from other websites such as Vedantu, Byju's, Tiwari Academy, etc.
Q: How can I prepare for Class 12 Maths Part 1?
A: You can prepare for Class 12 Maths Part 1 by revising the NCERT book and solutions, practicing important questions and sample papers, learning shortcuts and formulas, and following some tips and tricks given in this article.
Q: What are the benefits of studying Class 12 Maths Part 1?
A: Studying Class 12 Maths Part 1 can help you to build a strong foundation in Mathematics, develop logical thinking, problem-solving, and analytical skills, score good marks in the board exam and various competitive exams, and enhance interest and curiosity in Mathematics.
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