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Class 10 Maths Chapter 1 Assignments

maths assignment for class 10 pdf

Class 10 Maths Chapter 1 Real Numbers Assignments and Worksheets with solutions and answers updated for academic session 2024-25. All the chapter is divided into 4 assignments taking easy, average, and difficult questions. These set of questions provide a complete revision for the preparation of CBSE and State board exams 2024-25.

Class: 10Mathematics
Chapter: 1Assignments and Worksheets

CBSE NCERT Class 10 Maths Chapter 1 Real Numbers Assignments

  • Class 10 Maths Chapter 1 Real Numbers Assignments 1
  • Class 10 Maths Chapter 1 Real Numbers Assignments 1 Solutions
  • Class 10 Maths Chapter 1 Real Numbers Assignments 2
  • Class 10 Maths Chapter 1 Real Numbers Assignments 2 Solutions
  • Class 10 Maths Chapter 1 Real Numbers Assignments 3
  • Class 10 Maths Chapter 1 Real Numbers Assignments 3 Solutions
  • Class 10 Maths Chapter 1 Real Numbers Assignments 4
  • Class 10 Maths Chapter 1 Real Numbers Assignments 4 Solutions
  • Class 10 Maths Chapter 1 Real Numbers Solution Page

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There are 4 assignments and worksheets. Assignments contains MCQ, Fill in the Blanks, and True false questions. We have covered every topic in the chapter 1 of class 10 Maths. Answers and solutions of each assignment is also given free to use. Students can download these assignments and solve themselves. After solving they can check the answers given on website.

There are some easy questions based on understanding only. Some questions contains tricky methods and 17 percent questions are little bit difficult one. Students need to put effort to explore these questions. These assignments are guarantee to get good marks in exams. The questions based on Case Study will also be included in later chapters.

Download links are given for each assignments. Download and print it and solve it. Match the answers and solutions given on website to know the accuracy. Assignments are deign level wise, so do the first assignment first and the fourth assignment in the last.

Please suggest us, if any, about these assignments, so that we can improve the quality of the contents. We are preparing assignments for all the chapters. Gradually it will be uploaded before the final exams. Students are advised to solve these assignments to prepare the chapter and get confidence in topics.

Are assignments helpful in final exams?

Assignments are helpful in the revision of chapter as well as preparation for exams.

How many assignment should do to prepare the chapter?

At least 3 or 4 assignments which cover the entire chapter will be sufficient to know the chapter well.

How do solve the assignment?

Do yourself each assignment. If a part of assignment is not cleared or creating confusion, discuss with your classmate or teachers and solve it again.

Assignments for Class 10 Maths Chapter 1

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    Term) of an Arithmetic Progression (AP)
      
      
      
      
    Term) from the End of an Arithmetic Progression (AP)
   
    Terms of an Arithmetic Progression (AP)
       Terms is Given (AP)
      
      
      
   
   
   
   
      
      
   
   
      
      
      
      
      
   
   
   
   
   
      
      
      
      
      
      
      
      
   
   
   
      
      
   
   
   
   
   
   
   
   
   
   
   
      
      
      
      
      
      
      
      
   
      
         
         
         
      
      
   
      
      
   
      
      
      
   
   
   
   
   

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 10 Maths – Class 10 Maths NCERT Solutions

NCERT Solutions for Class 10 Maths are solved by experts of LearnCBSE.in in order to help students to obtain excellent marks in their board examination. All the questions and answers that are present in the CBSE NCERT Books has been included in this page. We have provided all the Class 10 Maths NCERT Solutions with a detailed explanation i.e., we have solved all the question with step by step solutions in understandable language. So students having great knowledge over NCERT Solutions Class 10 Maths can easily make a grade in their board exams. Read on to find out more about  NCERT Solutions for Class 10 Mathematics. You can also practice  Extra Questions for Class 10 Maths  on LearnCBSE.in

CBSE NCERT Solutions for Class 10 Maths in PDF in Hindi Medium (हिंदी मीडियम) as well as English Medium session 2023-24 for CBSE, UP Board, Gujrat Board, MP Board, Bihar, AP SSC, TS SSC, Uttarakhand board and all other boards following new CBSE Curriculum.

NCERT Class 10 Maths Solutions – NCERT Solutions Class 10 Maths

In this page, each and every question originate with a step-wise solution. Working on NCERT Solutions for Class 10 will help students to get an idea about how to solve the problems. With the help of these NCERT Solutions for Class 10 Maths you can easily grasp basic concepts better and faster. Moreover, it is a perfect guide to help you to score good marks in CBSE board examination. Just click on the chapter wise links given below to practice the NCERT Solutions for the respective chapter.

  • Chapter 1 Real Numbers
  • Chapter 2 Polynomials
  • Chapter 3 Pair of Linear Equations in Two Variables
  • Chapter 4 Quadratic Equations
  • Chapter 5 Arithmetic Progressions
  • Chapter 6 Triangles
  • Chapter 7 Coordinate Geometry
  • Chapter 8 Introduction to Trigonometry
  • Chapter 9 Applications of Trigonometry
  • Chapter 10 Circle
  • Chapter 11 Constructions
  • Chapter 12 Areas related to Circles
  • Chapter 13 Surface Areas and Volumes
  • Chapter 14 Statistics
  • Chapter 15 Probability

With the aim of imbibing skills and hard work among the students, the 10th class maths NCERT solutions have been designed. It contains previous years’ questions along with answers except those which are not included in the CBSE 10 maths syllabus.

CBSE NCERT solutions for class 10 maths will help the students in acquiring adequate practice to do their CBSE Class 10th exam with confidence.

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

Real Numbers Class 10 has total of four exercises consists of 18 Problems. Prove Irrational, Problems based on Euclid’s division lemma, HCF and LCM and Divisibility are mostly asked topics in previous board exams. Other topics included are Fundamental Theorem of Arithmetic, important properties of positive integers, fraction to decimals and decimals to a fraction.

  • Class 10 Maths Real Numbers Ex 1.1
  • प्रश्नावली 1.1 का हल हिंदी में वास्तविक संख्याएँ
  • Class 10 Maths Real Numbers Ex 1.2
  • प्रश्नावली 1.2 का हल हिंदी में वास्तविक संख्याएँ
  • Class 10 Maths Real Numbers Ex 1.3
  • प्रश्नावली 1.3 का हल हिंदी में वास्तविक संख्याएँ
  • Class 10 Maths Real Numbers Ex 1.4
  • प्रश्नावली 1.4  का हल हिंदी में वास्तविक संख्याएँ
  • Real Numbers Class 10 Extra Questions
  • Real Numbers Class 10 Important Questions
  • Real Numbers Class 10 Notes

Class 10 Maths Real Numbers Properties

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

Polynomials Class 10 has total of four exercises consists of 13 Questions. Problems related to finding polynomials, Properties zeros and coefficient, long division of polynomials, finding a quadratic polynomial, finding zeros of polynomials are scoring topics.

  • Class 10 Maths Polynomials Ex 2.1
  • प्रश्नावली 2.1 का हल हिंदी में
  • Class 10 Maths Polynomials Ex 2.2
  • प्रश्नावली 2.2 का हल हिंदी में
  • Class 10 Maths Polynomials Ex 2.3
  • प्रश्नावली 2.3 का हल हिंदी में
  • Class 10 Maths Polynomials Ex 2.4
  • प्रश्नावली 2.4 का हल हिंदी में
  • Polynomials Class 10 Extra Questions
  • Polynomials Class 10 Important Questions
  • Polynomials Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

Pair of Linear Equations Class 10 has total of seven exercises consists of 55 Problems. The problems will be based on concepts like linear equations in two variables, algebraic methods for solving linear equations, elimination method, cross-multiplication method Time and Work, Age, Boat Stream and equations reducible to a pair of linear equations these answers will give you ease in solving problems related to linear equations.

  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.1
  • प्रश्नावली 3.1 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.2
  • प्रश्नावली 3.2 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.3
  • प्रश्नावली 3.3 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.4
  • प्रश्नावली 3.4 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.5
  • प्रश्नावली 3.5 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.6
  • प्रश्नावली 3.6 का हल हिंदी में
  • Pair Of Linear Equations In Two Variables Class 10 Ex 3.7
  • प्रश्नावली 3.7 का हल हिंदी में
  • Extra Questions for Class 10 Maths Linear Equations in Two Variables
  • Pair of Linear Equations in Two Variables Class 10 Important Questions
  • Pair of Linear equations in Two Variables Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations

Quadratic Equations Class 10  has total of four exercises consists of 24 Problems. The Questions are related to find roots of quadratic equations and convert world problem into quadratic equations are easily scoring topics in board exams.

  • Class 10 Maths Quadratic Equations Ex 4.1
  • प्रश्नावली 4.1 का हल हिंदी में
  • Class 10 Maths Quadratic Equations Ex 4.2
  • प्रश्नावली 4.2 का हल हिंदी में
  • Class 10 Maths Quadratic Equations Ex 4.3
  • प्रश्नावली 4.3 का हल हिंदी में
  • Class 10 Maths Quadratic Equations Ex 4.4
  • प्रश्नावली 4.4 का हल हिंदी में
  • Quadratic Equations Class 10 Extra Questions
  • Quadratic Equations Class 10 Important Questions
  • Quadratic Equations Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

Arithmetic Progressions Class 10 has total of four exercises consists of 49 Problems. find the nth terms and the sum of n consecutive terms are important topics in this chapter 5.

  • Class 10 Maths Arithmetic Progressions Ex 5.1
  • प्रश्नावली 5.1 का हल हिंदी में
  • Class 10 Maths Arithmetic Progressions Ex 5.2
  • प्रश्नावली 5.2 का हल हिंदी में
  • Class 10 Maths Arithmetic Progressions Ex 5.3
  • प्रश्नावली 5.3 का हल हिंदी में
  • Class 10 Maths Arithmetic Progressions Ex 5.4
  • प्रश्नावली 5.4 का हल हिंदी में
  • Arithmetic Progressions Class 10 Extra Questions
  • Arithmetic Progressions Class 10 Important Questions
  • Arithmetic Progressions Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

Triangles Class 10 has total of six exercises consists of 64 Problems. The Questions are based on properties of triangles and 9 important theorems which are important in scoring good marks in CBSE Class 10 Exams.

  • Triangles Class 10 Mind Map
  • Triangles Class 10 Ex 6.1
  • Triangles Class 10 Ex 6.1 in Hindi Medium
  • Triangles Class 10 Ex 6.2
  • Triangles Class 10 Ex 6.2 in Hindi Medium
  • Triangles Class 10 Ex 6.3
  • Triangles Class 10 Ex 6.3 in Hindi Medium
  • Triangles Class 10 Ex 6.4
  • Triangles Class 10 Ex 6.4 in Hindi Medium
  • Triangles Class 10 Ex 6.5
  • Triangles Class 10 Ex 6.5 in Hindi Medium
  • Triangles Class 10 Ex 6.6
  • Triangles Class 10 Ex 6.6 in Hindi Medium
  • Extra Questions for Class 10 Maths Triangles
  • Triangles Class 10 Notes Maths Chapter 6
  • NCERT Exemplar Class 10 Maths Chapter 6 Triangles
  • Important Questions for Class 10 Maths Chapter 6 Triangles
  • Triangles Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

Coordinate Geometry Class 10  has total of four exercises consists of 33 Problems. The Questions related to finding the distance between two points using their coordinates, Area of Triangle, Line divided in Ratio (Section Formula) are important models in class 10 boards.

  • Class 10 Maths Coordinate Geometry Ex 7.1
  • प्रश्नावली 7.1 का हल हिंदी में
  • Class 10 Maths Coordinate Geometry Ex 7.2
  • प्रश्नावली 7.2 का हल हिंदी में
  • Class 10 Maths Coordinate Geometry Ex 7.3
  • प्रश्नावली 7.3 का हल हिंदी में
  • Class 10 Maths Coordinate Geometry Ex 7.4
  • प्रश्नावली 7.4 का हल हिंदी में
  • Coordinate Geometry Class 10 Extra Questions
  • Coordinate Geometry Class 10 Important Questions
  • Coordinate Geometry Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Introduction to Trigonometry Class 10  has total of four exercises consists of 27 Problems. The questions based on trigonometric ratios of specific angles, trigonometric identities and trigonometric ratios of complementary angles are the main topics you will learn in this chapter. Trigonometry Formulas plays important role in getting 100% marks in Board Exams.

  • Class 10 Maths Introduction to Trigonometry Ex 8.1
  • प्रश्नावली 8.1 का हल हिंदी में
  • Introduction to Trigonometry Class 10 Ex 8.2
  • प्रश्नावली 8.2 का हल हिंदी में
  • Introduction to Trigonometry Class 10 Ex 8.3
  • प्रश्नावली 8.3 का हल हिंदी में
  • Introduction to Trigonometry Class 10 Ex 8.4
  • प्रश्नावली 8.4 का हल हिंदी में
  • Introduction to Trigonometry Class 10 Extra Questions
  • Introduction to Trigonometry Class 10 Important Questions
  • Introduction to Trigonometry Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry

Some Applications of Trigonometry Class 10  has one exercise consists of 16 Problems. In this chapter, you will be studying about real life applications of trigonometry and questions are based on the practical applications of trigonometry.

  • Some Applications of Trigonometry Class 10 Ex 9.1
  • प्रश्नावली 9.1 का हल हिंदी में
  • Applications of Trigonometry Class 10 Extra Questions
  • Some Applications of Trigonometry Class 10 Important Questions
  • Some Applications of Trigonometry Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 10 Circles

Circle Class 10  has total of two exercises consists of 17 Problems. Understand concepts such as tangent, secant, number tangents from a point to a circle and more.

  • Circles Class 10 Ex 10.1
  • प्रश्नावली 10.1 का हल हिंदी में
  • Circles Class 10 Ex 10.2
  • प्रश्नावली 10.2 का हल हिंदी में
  • Circles Class 10 Extra Questions
  • Circles Class 10 Important Questions
  • Circles Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

Constructions Class 10 has total of four exercises consists of 14 Problems. The Questions are based on drawing tangents and draw similar triangles are important topics.

  • Constructions Class 10 Ex 11.1
  • प्रश्नावली 11.1 का हल हिंदी में
  • Constructions Class 10 Ex 11.2
  • प्रश्नावली 11.2 का हल हिंदी में
  • Extra Questions for Class 10 Maths Constructions
  • Constructions Class 10 Important Questions
  • Constructions Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles

Areas Related to Circles Class 10  has total of three exercises consists of  35 Problems. Solve problems related to ‘Perimeter and Area of a Circle’, ‘Areas of Combinations of Plane Figures’ and ‘Areas of Sector and Segment of a Circle’.

  • Areas Related to Circles Class 10 Ex 12.1
  • प्रश्नावली 12.1 का हल हिंदी में
  • Areas Related to Circles Class 10 Ex 12.2
  • प्रश्नावली 12.2 का हल हिंदी में
  • Areas Related to Circles Class 10 Ex 12.3
  • प्रश्नावली 12.3 का हल हिंदी में
  • Areas Related to Circles Class 10 Extra Questions
  • Areas Related to Circles Class 10 Important Questions
  • Areas related to Circles Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes

Surface Areas and Volumes Class 10  has total of five exercises consists of 36 Problems. In CBSE class 10 Maths, the ‘Surface Areas and Volumes’ chapter is a part of mensuration unit. The problems are based on finding areas and volumes of different solids such as cube, cuboid and cylinder, frustum, combination of solids.

  • Surface Areas and Volumes Class 10 Ex 13.1
  • प्रश्नावली 13.1 का हल हिंदी में
  • Surface Areas and Volumes Class 10 Ex 13.2
  • प्रश्नावली 13.2 का हल हिंदी में
  • Surface Areas and Volumes Class 10 Ex 13.3
  • प्रश्नावली 13.3 का हल हिंदी में
  • Surface Areas and Volumes Class 10 Ex 13.4
  • प्रश्नावली 13.4 का हल हिंदी में
  • Surface Areas and Volumes Class 10 Ex 13.5
  • प्रश्नावली 13.5 का हल हिंदी में
  • Surface Areas and Volumes Class 10 Extra Questions
  • Surface Areas and Volumes Class 10 Important Questions
  • Surface Areas and Volumes Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Statistics Class 10  has total of four exercises consists of 25 Problems. Problems related to find mean, mode or median of grouped data will be studied in this chapter. Solve questions by understanding the concept of cumulative frequency distribution.

  • Statistics Class 10 Ex 14.1
  • प्रश्नावली 14.1 का हल हिंदी में
  • Statistics Class 10 Ex 14.2
  • प्रश्नावली 14.2 का हल हिंदी में
  • Statistics Class 10 Ex 14.3
  • प्रश्नावली 14.3 का हल हिंदी में
  • Statistics Class 10 Ex 14.4
  • प्रश्नावली 14.4 का हल हिंदी में
  • Statistics Class 10 Extra Questions
  • Statistics Class 10 Important Questions
  • Statistics Class 10 Notes

NCERT Solutions for Class 10 Maths Chapter 15 Probability

Probability Class 10 has total of two exercises consists of 30 Problems. Questions based on the concept of theoretical probability will be studied in this chapter.

  • Probability Class 10 Ex 15.1
  • प्रश्नावली 15.1 का हल हिंदी में
  • Probability Class 10 Ex 15.2
  • प्रश्नावली 15.2 का हल हिंदी में
  • Probability Class 10 Extra Questions
  • Probability Class 10 Important Questions
  • Probability Class 10 Notes

Maths NCERT Solutions Maths Formulas for Class 10

Advantages of Solving NCERT Solutions for Class 10 Maths From LearnCBSE.in

NCERT Solutions For Class 10 Maths

  • All the Class 10 Maths NCERT Solutions provided in this page are clear and concise in nature.
  • NCERT Solutions for Class 10 Mathematics are solved in easily understandable language to help students to grasp everything on the go.
  • Accessible to everyone at any time anywhere without any difficulty.
  • All the questions are solved strictly based on the NCERT (CBSE) Syllabus and Books. So mastering these solutions will definitely help students to score good marks in the examination.
  • NCERT Solutions for Class 10 Maths PDF given in this page are of free of cost.

CBSE Class 10 Maths Unit-wise Weightage 2011-2024.

1 Number Systems 6
2 Algebra 20
3 Coordinate Geometry 6
4 Geometry 15
5 Trigonometry 12
6 Mensuration 10
7 Statistics and Probability 11
Total 80

FAQs for NCERT Solutions for Class 10 Maths

How to master in Class 10 Maths CBSE?

Students who are seeking for tips and tricks to master in class 10 maths, can go for the latest NCERT Class 10 Maths Solutions Books and prepare effectively. Just referring to the CBSE NCERT Solutions is enough to master in Class 10 Maths.

How do I solve Class 10 Mathematics problems easily?

If you prepare the latest CBSE Class 10 Maths Syllabus with the help of NCERT Solutions Pdf for Maths, then you can solve any type of problems in the final board examination.

Where can I download CBSE Class 10 NCERT Mathematics PDF Solutions?

You can quickly get Class 10 Mathematics NCERT Solutions Pdf from our page to access. So, make use of the available quick links over here and download CBSE Class 10 NCERT Solutions PDF for Maths, it helps you to prepare at your required time & easily understand the concepts of Class 10 Maths.

How these NCERT Solutions for class 10 Maths will be beneficial for CBSE Students?

Here are the few benefits of NCERT Solutions for Class 10 mathematics:

  • It helps you to build a strong base of maths and increase confidence to face all boards and competitive exams in the future.
  • With Class Maths NCERT Solutions, you can easily perceive and learn the steps to resolve some tough kind of problems.
  • Moreover, it is a perfect guide to complete your homework and aid you to score better marks in the CBSE board examinations.

What are the concepts explained in the solutions of NCERT Class 10 Maths Textbook?

NCERT Maths Solutions assists all CBSE Class 10 Students in offering some helpful tricks and tips to solve math problems at the end of each chapter. Class 10 maths is having 15 chapters to learn by the students in this academic year. All 15 chapters included in CBSE Class 10 Maths NCERT Solutions PDF are explained by subject experts. So, get the NCERT Class 10 Mathematics Solutions Pdf from our page and check out the list of 15 chapters contained in the syllabus.

How to use NCERT Solutions for scoring in class 10 maths CBSE Board Exams?

  • First of all, download the NCERT Solutions for Class 10 Maths Pdf which are designed by subject experts as per the latest CBSE Maths Syllabus curriculum 2020.
  • Then, Go to the chapter that you wish to learn.
  • Tap on the link provided for that particular chapter of class 10 maths.
  • Now, it will open the chapter page with solutions of NCERT class 10 maths.
  • Check the solved and unsolved questions and solutions presented in the NCERT class 10 maths & score the highest marks in the exam.

Why NCERT solutions for class 10 maths are important?

NCERT Solutions are designed in a way that every student can quickly understand the concept into their minds and clarifies all their doubts within a few seconds. The book is self-explanatory and helps students to innovate and explore in maths. Also, aspirants can assess their learning abilities with the solutions of NCERT Maths Books for their Class 10 board exam preparation.

Which book is best for Class 10 maths?

As per the survey conducted by educational analysts, around 78% of CBSE Class 10 students prefers NCERT Textbook solutions for their maths exams.

Which guide is best for Class 10 CBSE?

NCERT Solutions provided by LearnCBSE.in is the best guide for Class 10 CBSE. You will get all the NCERT Solutions for Class 10.

Is NCERT enough for Class 10 boards Maths 2024?

NCERT Class 10 Maths is Textbook and Solutions prepared by LearnCBSE Expert Teachers is enough for preparing your first class 10 board examination.

What are the best reference books for class 10 CBSE? Best Reference Books for Class 10 Maths, Science and SST are:

  • RD Sharma Class 10 Maths Textbook – Student Friendly, Healthy Explanation of Concepts, Variety of Problems Improves Student Analytical Skills. RD Sharma Helps you to solve Level 3 Questions asks in the board questions and for compelling HOTS. You can check RD Sharma Class 10 Solutions prepared by LearnCBSE.in Expert Teachers for Solving Problems easily. RD sharma Class 10 Maths Textbook covers entire CBSE Class 10 Maths Syllabus compare to RS Aggarwal Class 10 Maths.
  • RS Aggarwal Class 10 Maths Textbook – Students must Start with NCERT Class 10 Maths Textbook before getting solving any reference book. RS Aggarwal has questions that are a level below those of the RD Sharma. If you crack the RD Sharma Problems, you’ll easily do the RS Aggarwal Maths Solutions. If you’re looking for questions that are on moderate level then you should practice from the RS Aggarwal. If you want to challenge yourself with math, pick up the RD Sharma Solutions.
  • Lakhmir Singh and Manjith Kaur is Best Reference book for Solving NCERT Class 10 Science (Physics, Chemistry and Biology)

How do you get maximum marks in maths?

In Class 10 Maths NCERT Textbook 15 Chapters given as per CBSE Class 10 Maths Syllabus. Algebra (20 Marks), Trigonometry (12 Marks) , Statistics and Probability (11 Marks) are easy scoring topics from class 10 Board Maths Marking Scheme. Trigonometry formulas, Surface Area and Volume Formulas, Algebra Identities, Proving Rational Number, Long Division of Polynomials helps you to get maximum marks in maths.

NCERT Solutions

We hope the NCERT Solutions for Class 10 Maths provided in this page helps in your board exam preparation. If you have any questions, ping us through the comment section below and we will get back to you as soon as possible.

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CBSE Class 10 Maths- Standard – Study Notes Chapter Wise

CBSE Class 10  Science CBSE Class 10 Social Science CBSE Class 10 Maths

CBSE Class 10  Maths- Standard Study Materials All Chapters

  • Real Number
  • Polynomials
  • Linear Equation in Two Variables
  • Quadratic Equation
  • Arithmetic Progression
  • Coordinate Geometry
  • Construction
  • Trigonometry
  • Height and Distance
  • Area Related With Circles
  • Probability
  • Surface Area and Volume

CBSE Class 10  Mathematics Syllabus

+bx+c=0=0, (a ≠ 0)
 term

Best Reference Books CBSE Class 10  For Mathematics

  • Mathematics for Class 10 – R D Sharma
  • Secondary School Mathematics for Class 10 – RS Aggarwal
  • All in one mathematics – Arihant

CBSE Class 10 Mathematics, Notes ,Test Papers, Sample Papers, NCERT,NCERT Exemplar Solutions,RD Sharma and RS Aggarwal Solution and Help from Ex- IITian for Mathematics

NCERT Exemplar Solutions for Class 10 Mathematics

Get 100 percent accurate NCERT,NCERT Exemplar Solutions for Class 10 Mathematics explained by expert Mathematics teachers. We provide step by step solutions for the questions given in Class 10 Mathematics textbook as per CBSE Board guidelines from the latest NCERT book for Class 10 Mathematics.

CBSE Class 10 Mathematics Notes

Get Notes prepared by Ex-IITIan for CBSE Class 10 Mathematics

RD Sharma and RS Agarwal Mathematics Class 10 Solutions

RD Sharma and RS Agarwal Solutions for Class 10 Mathematics  are provided here with simple step-by-step explanations. These solutions for  are extremely popular among class 10 students for Mathematics.  Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RD Sharma and RS Agarwal Book of class 10 Mathematics are provided here for . I will help you online for any doubt / clarification.

CBSE Class 10 Mathematics Assignments

Chapter wise assignments are being given by teachers to students to make them understand the chapter concepts. Its extremely critical for all CBSE students to practice all assignments which will help them in gaining better marks in examinations. All assignments available for free download on the website are developed by the best teachers having many years of teaching experience in CBSE schools all over the country. Students, teachers and parents are advised to contact me online incase of any doubt / clarification

Past Many Years Question Mathematics Class 10 Solutions

Past Many Years Question Papers Solutions for Class 10 Mathematics  are provided here with simple step-by-step explanations. These solutions for are extremely popular among class 10 students for Mathematics . Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Past Many Years Question Papers Book of class 10 Mathematics are provided here for . I will help you online for any doubt / clarification.

In CBSE Class 10, Mathematics is a combination of theoretical and Numericals knowledge. In Mathematics , you can really score 100% if you study well and understand the concept.At iitianacademy, we provide excellent notes prepared by Ex-IITIan along with Sample Papers and past years question papers. You will be provided with Lakhmir Singh question and Answers. iitianacademy provide real time help for any doubt clarification and topic explanations. We suggest you to follow below mantra to score good marks in class 10 Mathematics

Following are the tips to prepare for Mathematics :-

  • First make a note of formulas & derivations separately. Get a reference from iitianacademy Notes
  • Learn it by heart, we will help for any doubt detail explanation
  • Learn all the principles and theories.
  • Practice diagrams and do it neatly on your answer sheet and label it properly.
  • Take help of different guides or references for practising different types of numericals.
  • Always answer your questions as per marks. If it contains less marks then try to answer in brief and if it contains more marks then try to make your answer lengthy, and also make diagrams if necessary. It doesn’t matter whether it is mentioned or not to make diagrams. Do it as per marks.
  • Solve previous years question papers so that you can understand the patterns of question paper.
  • Always practice all the definitions by writing it.

CBSE Class 10 Mathematics, Notes ,Test Papers, Sample Papers, NCERT,NCERT Exemplar Solutions,RD Sharma and RS Aggarwal Solution and many more..

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  • NCERT Maths Textbook Class 10 PDF
  • NCERT Books

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CBSE Maths Textbook Class 10 Free Download

NCERT (National Council of Education Research and Training) is the main publisher behind Maths Textbook Class 10 and their subject materials are used in competitive tests like the JEE, NEET, and college entrance exams too.

What are the similarities between Einstein, Newton, and Kepler? A strong foundation in Mathematics! If you've ever felt stumped about how concepts were taught to you in high school, then our NCERT Class 10 Maths Book PDF 2024-25 free download will help you. Our 10th Maths Book PDF guides break concepts down step-by-step in a chapter-wise format, with questions and answers related to every Mathematical topic included for yours truly. If you've wanted to test and identify any knowledge gaps in your foundations, then the Maths Textbook Class 10 PDF for free is a must. Students can download the Class 10 Maths NCERT Book PDF from the link below. Students can also find the subject and class-wise NCERT Solutions on Vedantu.   

NCERT Class 10 Maths Book PDF (English and Hindi )Free Download

The maths textbook class 10 provides clear explanations, solved examples, and practice exercises to enhance conceptual understanding and problem-solving skills. you can download the ncert maths textbook class 10 in both english and hindi languages. get the link to download 10th maths book pdf, of ncert from the table below..

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NCERT Solutions for Class 10 Maths | Chapterwise PDF

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Explore More Class 10 NCERT Books

Ncert maths books for class 10 pdf - free download online.

Maths is the building block for the other Sciences and life in general. You can't survive or thrive without having a basic foundation of Mathematical concepts in your mind and you will need to acquire a conceptual (but intuitive) understanding of core concepts to succeed as a student in high school and beyond. The CBSE NCERT Class 10 Maths Book Free PDF download will help you with that as it has been drafted by subject experts at Vedantu who have analyzed question papers of the previous CBSE Class 10 board exams.

The CBSE NCERT Maths Textbook Class 10 in Free PDF format provide questions and answers to every topic. Each topic is arranged in a chapter-wise format thus making sure that every inch of the Class 10 Maths and Science syllabus is covered before students appear for their board exams. We recommend that you sequentially work through these PDFs while also paying attention to your regular high school classes for best results, especially if you're self-studying with them.

How Vedantu Gives you the Competitive Edge For Class 10 Exams?

Vedantu excels at pushing students beyond their limit and taking them to the next level where learning is concerned. From teaching basic and advanced subject concepts from scratch, Vedantu delivers cutting-edge online learning by streaming lessons digitally and connecting mentors and mentees on a singular platform. Students get to choose from a list of mentors and study with whoever they want once they finish their designated pre-assessment test once they sign up at our platform. We deliver personalised online home tuitions in the core science subjects for students of CBSE, ICSE, IGCSE and other boards, thus making learning flexible and education a lot more hassle-free. Get access to Vedantu NCERT Solutions for Class 10 Maths also.

When you study with Vedantu, you can study whenever you want and wherever you want, thus making learning, not just a commitment but a lifestyle.

Importance of Maths Text Book Class 10:

A lot of people ask us why the NCERT 10th Maths Book PDF is so important? So in this post, we will answer this question: what makes the NCERT 10th Maths Textbook PDF so important and how can you use it to your advantage. 

We will start by discussing how the syllabus changes every year and why you need an NCERT Class 10 Maths Book PDF 2024-25. You can then find out how to make use of these books in school and colleges with thoughtful assignments.

All in all, this post will be a complete guide on why and how you can use the NCERT 10th Maths Book PDF.

NCERT BOOK: A Why  and How Guide

This article is relevant for class 10 students and parents looking for an answer to the question what is the point of ncert so let's get started..

There are many moments in your life when you have no idea what your teacher is trying to explain. I know, I had several such instances. However, I was lucky because my parents helped me understand what my teachers were going on about.

It's probably a feeling that every single kid has had at least once in his/her life. That one time when you could not understand a word out of your teacher's mouth and you're left to deal with the situation all by yourself.

The same thing happens when you enter Class 10 and study NCERT books as your curriculum for Maths. You might not be able to make sense of everything that's being taught.

This happens because the syllabus is very different from the ever-changing topic to topic, unit to unit format.

We used a small sample of topics for this post and you can access them by clicking on the links below:

As you can see, many topics can confuse you when you begin with NCERT Class 10 Maths Book.

What Are The Features Of NCERT  Maths Textbook Class 10?

The NCERT  Maths Textbook Class 10 is the most amazing Maths Book that has ever existed. This book is one of the few books which can help advance your Mathematical skills. Maths Class 10 Textbook PDF has all the necessary topics included so that this book would be beneficial for you throughout your lifetime. It has subjects like Algebra, Trigonometry, Geometry, Linear Algebra, and Calculus. It is said that Class 10 Maths Book PDF can help you learn everything you need to know about Mathematics. The problem-solving ability of the students is greatly enhanced by this book.

The unique feature which makes this Class 10 Maths NCERT Book PDF different from other books is that even the most difficult problems are asked in a very easy way so that students can solve them easily. The NCERT  Maths Textbook Class 10 gives you a complete understanding of all the relevant topics. Every exercise is important for your success in the Maths subject because it will help your achievement in this subject better.

The NCERT 10th Maths Book is beneficial for students as it has such a wide range of topics. The activities and exercises given in Class 10 Maths Book PDF 2024-25 have the standards which every student must follow to improve their marks in the Maths subject. The problems asked have been solved by thousands of other students. So that you can learn from their mistakes and become a better student. 10th Class Maths Textbook also helps students to maintain a good speed level while solving problems.

10th Maths Textbook PDF can come as a great help to the students who are preparing for competitive exams like SSC Maths.  Maths Textbook Class 10 has been written for those students who want to gain more knowledge about Mathematical concepts and obtain a good score in their future competitive exams. If you wish to obtain better knowledge about facts and figures then Class 10 Maths NCERT Book PDF is something that you should buy for yourself.

The problems asked in Class 10 Maths Book PDF are very easy, and it is always beneficial to the student who has the knack for solving problems.

Other Free CBSE Class 10 Maths Study Material

Prepare for your CBSE Class 10 Maths exam with these study materials along with Maths Class 10 Textbook PDF.

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CBSE Maths Material for Class 10

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The availability of the NCERT Class 10 Maths Book PDF 2024-25 offers students a convenient and accessible resource for their studies. With this free download, students can access the textbook anytime, anywhere, facilitating effective learning and revision. The comprehensive content of the 10th Class Maths Textbook, coupled with its accessibility, empowers students to excel in their mathematics studies and achieve academic success.

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FAQs on NCERT Maths Textbook Class 10 PDF

1. What is the Difference Between NCERT and CBSE Books?

CBSE or Central Board of Secondary Education is the board of education while the National Council of Educational Research and Training (NCERT) is the authority that is responsible for publishing the textbooks. Therefore, in a nutshell, NCERT publishes the textbooks which are used in the CBSE board schools for the students.

2. Are These Books Enough for Entrance Level Examinations?

The books by NCERT act as good references for exam preparation but are not sufficient. These books will help you in understanding the core concepts of various subjects but these will not help in advance problems. Hence students shall refer to reference books to understand the higher difficulty level’s problems. However, textbooks must not be avoided as these help to ace in the MCQ section as nearly 60-70 percent of MCQ type questions come directly from these textbooks. Apart from the books, sample papers and previous years' question papers are helpful for entrance level examinations like JEE Main, Olympiad, NEET, etc.

3. For what reason are the NCERT Maths Textbook Class 10 significant for the board test?

The NCERT Books for Class 10 Maths is ready to give students a reasonable comprehension of ideas that would show up in the test. By alluding to the arrangements, students will want to get ready for the board test and score well. students can get to the arrangements from the Vedantu site anyplace and whenever at no cost. The arrangements contain clarifications in an itemized and elaborate way to assist students with acquiring a superior scholastic score.

4. Why should Maths Textbook Class 10 be taken seriously?

NCERT books are extremely important and beneficial for the students at the same time because they are the source of many question papers for various exams. If you take a closer look at the previous years’ papers of the board exam or any entrance exams, you will understand the frequency of the usage of these CBSE textbooks there. Thus these books shall be taken seriously as they help to understand various topics with in-depth knowledge and solve the exercise questions or sample papers effortlessly. It also helps to prepare for many entrance exams such as NEET, JEE Main, etc.

5. How to Read 10th Class Maths Textbook PDF More Effectively?

Below are the ways one can follow to read these books more effectively.

To get a good understanding of each topic, students must read the textbooks thoroughly and jot down the important points for quick reference.

Students must solve all the questions from the textbook exercises so that it becomes easy to understand all the complex concepts and formulas from an individual subject.

Practising previous year's questions papers and sample papers benefit the students to increase their speed of solving problems with a high accuracy rate. Hence they will become more efficient before the exam.

Good practise of drawing diagrams or flowcharts for a better understanding of the topics help to achieve a good score in the exam as well.

6. What is the significance of the Maths 10th book in CBSE curriculum?

The Class 10 Maths textbook is crucial as it covers the entire syllabus prescribed by the CBSE board for Mathematics in the 10th grade. It provides a comprehensive understanding of various mathematical concepts and formulas required for board exams and beyond.

7. How can I access additional resources to supplement my studies along with the Maths 10th book?

You can access additional resources such as online study materials, practice worksheets, video tutorials, and solved examples from educational platforms like Vedantu, and NCERT's official website to supplement your studies alongside the Class 10th Maths textbook PDF. These resources offer a deeper insight into complex topics and provide extra practice to enhance your understanding and problem-solving skills.

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maths assignment for class 10 pdf

CBSE Class 10 Math Workbook

CBSE Class 10 Maths Workbook : Practising CBSE Class 10 Maths Worksheets is of utmost importance in order to build strong knowledge over the subject. As solving Worksheets of CBSE Class 10 Maths will help students to acquire knowledge in an interactive way. After revising the whole syllabus effectively, students are advised to solve worksheets to analyze their preparation level to secure good marks in the exam. Solving worksheets of CBSE Class 10 Maths will help students to build their confidence in logical, analytical, and problem-solving capabilities. All our CBSE Chapter wise Test Papers for Class 10 Maths  are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance.  

So in this article, we will provide you with CBSE 10 Maths Worksheet s . Students can download the CBSE worksheets pdf for free and make use of them during their revision. Also, Teachers and Parents who are in search of worksheets can also get from this page. By solving these worksheets, students will get to know their mistakes and weaknesses and further learn from them. Additionally, solving class 10 maths worksheets, extra questions, important questions and sample papers helps students to boost their confidence and help them score higher and higher.

CBSE Class 10 Maths Worksheets and Assignments PDF

As a conclusion, by solving class 10 maths assignments , students will get inspired to build a purposeful and joyful development through learning. Students can just click on the download link given below to download the CBSE Class 10 Maths Worksheets and use it in offline mode as well . 

CBSE Class 10 Maths Areas Related To Circles Worksheets

  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 1
  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 2
  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 3
  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 4
  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 5
  • CBSE Worksheets for Class 10 Maths Areas related to Circles Assignment 6

CBSE Class 10 Maths Arithmetic Progression Worksheets

  • CBSE Worksheets for Class 10 Maths Arithmetic Progression Assignment 1
  • CBSE Worksheets for Class 10 Maths Arithmetic Progression Assignment 2
  • CBSE Worksheets for Class 10 Maths Arithmetic Progression Assignment 3
  • CBSE Worksheets for Class 10 Maths Arithmetic Progression Assignment 4

CBSE Class 10 Maths Circles Worksheets

  • CBSE Worksheets for Class 10 Maths Circles Assignment 1
  • CBSE Worksheets for Class 10 Maths Circles Assignment 2
  • CBSE Worksheets for Class 10 Maths Circles Assignment 3
  • CBSE Worksheets for Class 10 Maths Circles Assignment 4
  • CBSE Worksheets for Class 10 Maths Circles Assignment 5
  • CBSE Worksheets for Class 10 Maths Circles Assignment 6
  • CBSE Worksheets for Class 10 Maths Circles Assignment 7

CBSE Class 10 Maths Coordinate Geometry Worksheets

  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 1
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 2
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 3
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 4
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 5
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 6
  • CBSE Worksheets for Class 10 Maths Coordinate Geometry Assignment 7

CBSE Class 10 Maths Linear Equations Worksheets

  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 1
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 2
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 3
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 4
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 5
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 6
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 7
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 8
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 9
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 10
  • CBSE Worksheets for Class 10 Maths Linear Equations Assignment 11

CBSE Class 10 Maths Number System Worksheets

  • CBSE Worksheets for Class 10 Maths Number System Assignment

CBSE Class 10 Maths Polynomials Worksheets

  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 1
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 2
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 3
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 4
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 5
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 6
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 7
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 8
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 9
  • CBSE Worksheets for Class 10 Maths Polynomials Assignment 10

CBSE Class 10 Maths Probability Worksheets

  • CBSE Worksheets for Class 10 Maths Probability Assignment 1
  • CBSE Worksheets for Class 10 Maths Probability Assignment 2
  • CBSE Worksheets for Class 10 Maths Probability Assignment 3
  • CBSE Worksheets for Class 10 Maths Probability Assignment 4
  • CBSE Worksheets for Class 10 Maths Probability Assignment 5
  • CBSE Worksheets for Class 10 Maths Probability Assignment 6
  • CBSE Worksheets for Class 10 Maths Probability Assignment 7

CBSE Class 10 Maths Quadratic Equation Worksheets

  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 1
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 2
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 3
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 4
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 5
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 6
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 7
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 8
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 9
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 10
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 11
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 12
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 13
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 14
  • CBSE Worksheets for Class 10 Maths Quadratic Equation Assignment 15

CBSE Class 10 Maths Real Numbers Worksheets

  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 1
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 2
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 3
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 4
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 5
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 6
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 7
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 8
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 9
  • CBSE Worksheets for Class 10 Maths Real Numbers Assignment 10

CBSE Class 10 Maths Statistics Important Questions Worksheets

  • CBSE Worksheets for Class 10 Maths Statistics Assignment 1
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 2
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 3
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 4
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 5
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 6
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 7
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 8
  • CBSE Worksheets for Class 10 Maths Statistics Assignment 9

CBSE Class 10 Maths Workbook | Surface Area And Volume Worksheets

  • CBSE Worksheets for Class 10 Maths Surface Area and Volume Assignment 1
  • CBSE Worksheets for Class 10 Maths Surface Area and Volume Assignment 2
  • CBSE Worksheets for Class 10 Maths Surface Area and Volume Assignment 3

CBSE Class 10 Maths Triangles Important Questions Worksheets

  • CBSE Worksheets for Class 10 Maths Triangles Assignment 1
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 2
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 3
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 4
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 5
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 6
  • CBSE Worksheets for Class 10 Maths Triangles Assignment 7

CBSE Class 10 Maths Workbook | Applications Of Trigonometry Worksheets

  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 1
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 2
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 3
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 4
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 5
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 6
  • CBSE Worksheets for Class 10 Maths Applications of Trigonometry Assignment 7

CBSE Class 10 Maths Workbook – SA 1 Worksheets

  • CBSE Worksheets for Class 10 Maths SA1 Assignment 1
  • CBSE Worksheets for Class 10 Maths SA1 Assignment 2
  • CBSE Worksheets for Class 10 Maths SA1 Assignment 3
  • CBSE Worksheets for Class 10 Maths SA1 Assignment 4
  • CBSE Worksheets for Class 10 Maths SA1 Assignment 5
  • CBSE Worksheets for Class 10 Maths SA1 Assignment 6
  • CBSE Worksheets for Class 10 Maths SA2 Assignment 1
  • CBSE Worksheets for Class 10 Maths SA2 Assignment 2
  • CBSE Worksheets for Class 10 Maths SA2 Assignment 3
  • CBSE Worksheets for Class 10 Maths Assignment 1
  • CBSE Worksheets for Class 10 Maths Assignment 2
  • CBSE Worksheets for Class 10 Maths Assignment 3
  • CBSE Worksheets for Class 10 Maths Assignment 4
  • CBSE Worksheets for Class 10 Maths Assignment 5
  • CBSE Worksheets for Class 10 Maths Assignment 6

Advantages of CBSE Class 10 Maths Worksheets

  • CBSE Worksheets are one of the quality resources which should be practised at the time of revision.
  • Solving worksheets will help students to identify their weak concepts which need to be revised further. 
  • Class 10 Maths Chapter wise worksheets will be extremely useful in students board exam preparation.
  • Helps to boost self-confidence and students do their best to score good marks.
  • As students solve a good number of CBSE Class 10 Maths Worksheets Guide will reduce their mistakes and helps to improve in speed and accuracy.

Now that you are provided all the necessary information regarding CBSE NCERT Class 10 Maths Worksheets. Once completing the syllabus, students are advised to solve enough number of worksheets to revise the concepts.  It is recommended to students to solve one worksheet within a stipulated time as this will help progress question-solving speed and accuracy to score good marks. Students can also download CBSE Class 10 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. We hope this detailed article on CBSE Class 10 Maths revision Worksheets are helpful.

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  • Class 10 TextBooks
  • NCERT Maths 10 Books

NCERT Books for Class 10 Maths

Ncert books class 10 maths – free pdf download for 2023-24.

NCERT Textbooks for Maths Class 10 are the prime pick for students looking for the best study materials under the CBSE Board. These NCERT Books for Class 10 Maths help the students to understand the concepts in a simple method. It is highly recommended that CBSE students refer to and learn the Maths Book of NCERT as it covers the entire syllabus.

NCERT Class 10 Maths books help students to prepare well for board exams as well as competitive exams. These textbooks are specially designed by subject experts to provide students with authentic information for all subjects. We, at BYJU’S, provide NCERT Maths Book Class 10 PDF for free download. It is strongly recommended that the students of CBSE Class 10 prepare from this book as it comprises a set of questions that will build a strong foundation for all the concepts and topics covered. These NCERT Class 10 Books for Maths are written in the most comprehensible manner to make it easy for the students to understand.

To ace Mathematics, students can refer to NCERT Books for Class 10 Maths. This book provides a wide range of illustrative problems and solutions as well. Hence, it is recommended that all students choose to study textbooks. It is advisable to practise NCERT solutions, sample papers and previous years’ question papers as it helps the students in solving the questions faster. When the students do not get a proper solution for the Maths problems, they search for NCERT Books for Class 10 Maths . Besides, it is good to brush up on the fundamentals from the NCERT Books of previous classes.

After finishing all the exercise problems of the NCERT Book of Maths , students must solve the CBSE Class 10 Sample Papers to get an idea of the types of questions asked in the exam.

Which is the best app for learning math?

Now that you have downloaded the NCERT book for class 10, you should be able to get an idea of the topics that will be covered in this grade. Now, to gain a clear and thorough understanding of the concepts in the book, you should get BYJU’S The Learning App. It contains all the information you need to score well in your exams.

For math, the grade 10 BYJU’S The Learning App offers:

  • 80+ math video lessons (1800+ minutes of content!)
  • Coverage of your school syllabus
  • 50+ gamified interactive learning activities
  • Important questions
  • Summary cards to revise formulae
  • Practice tests
  • 24 X 7 access to learning resources

BYJU’S The Learning App for Class 10 also covers Biology, Chemistry, Physics, Economics, Civics, History, and Geography.

Just click here to know more about why BYJU’S The Learning App is the best app for learning math.

NCERT Book for Class 10 Maths Chapter-wise in English

Chapters Solutions
Chapter 1 –
Chapter 2 –
Chapter 3 –
Chapter 4 –
Chapter 5 –
Chapter 6 –
Chapter 7 –
Chapter 8 –
Chapter 9 –
Chapter 10 –
Chapter 11 –
Chapter 12 –
Chapter 13 –
Chapter 14 –

NCERT Book for Class 10 Maths Chapter in Hindi

CBSE Maths Book of NCERT consist of total 15 chapters.

 
अध्याय 1.
अध्याय 2.
अध्याय 3.
अध्याय 4.
अध्याय 5.
अध्याय 6.
अध्याय 7.
अध्याय 8.
अध्याय 9.
अध्याय 10.
अध्याय 11.
अध्याय 12.
अध्याय 13.
अध्याय 14.

Access NCERT Solutions here.

Foundation Class 10

Why One Should Read NCERT Book for Class 10 Maths?

The chapter-wise NCERT Maths Books PDF are provided above, keeping in mind the objectives of the NCERT books in assisting students in the board exam preparation . If the students have any queries, they can get them clarified easily by referring to the NCERT Books for Class 10. Referring to these books is helpful for the students to score well in the upcoming board examination. They help to simplify the complex topics and formulas of Class 10 Maths and clear any doubts students may have.

  • Students can get complete knowledge about the topics covered in Class 10 Maths
  • These books help students during revision time
  • It helps students to self-evaluate their knowledge gap using these books and prepare accordingly
  • Students can increase their knowledge about the key topics and concepts
  • Homework and assignments are given based on these books

Students can also download NCERT Maths Class 10 Solutions free PDFs at BYJU’S.

Frequently Asked Questions on NCERT Books for Class 10 Maths

Where can i obtain the ncert books for class 10 maths for free, what are the major insights of using the ncert books for class 10 maths, why are the ncert books for class 10 maths important for the board exam.

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CBSE Class 10 Maths Notes (Chapter-wise PDF)

As Class 10 students delve into the world of advanced mathematics, a strategic and focused approach to revision becomes essential. While NCERT textbooks lay the groundwork, the expansive nature of the subject demands a more targeted study plan. NCERT revision notes for Class 10 Mathematics serve as a valuable resource, offering chapter-wise insights, simplifying complex concepts, and guiding students toward a more profound understanding of each mathematical realm.

The Crucial Role of NCERT Notes in Class 10 Mathematics:

  • Chapter-wise Precision: Delve into specific chapters for an in-depth exploration of advanced mathematical concepts.
  • Conceptual Distillation: Complex theorems and problems distilled into manageable portions, ensuring a solid conceptual grasp.
  • Exam Emphasis: Align your revision with examination requirements, focusing on key formulas and critical concepts.
  • Time Efficiency: Streamlined revision allows for effective time management and comprehensive coverage of mathematical disciplines.

Embark on a Mathematical Odyssey with Chapter-wise NCERT Revision Notes for Class 10:

  • Real Numbers: Grasp the fundamentals of real numbers, rational and irrational numbers. Click for Chapter 1 Notes.
  • Polynomials: Dive into the world of algebraic expressions, factors, and polynomials. Click for Chapter 2 Notes.
  • Pair of Linear Equations in Two Variables: Understand the principles of linear equations and their graphical representations. Click for Chapter 3 Notes.
  • Quadratic Equations: Explore the solutions of quadratic equations and their applications. Click for Chapter 4 Notes.
  • Arithmetic Progressions: Navigate the intricacies of arithmetic progressions and their properties. Click for Chapter 5 Notes.
  • Triangles: Unravel the properties and theorems related to triangles. Click for Chapter 6 Notes.
  • Coordinate Geometry: Explore the Cartesian plane and coordinate geometry concepts. Click for Chapter 7 Notes.
  • Introduction to Trigonometry: Grasp the basics of trigonometry, including sine, cosine, and tangent. Click for Chapter 8 Notes.
  • Some Applications of Trigonometry: Apply trigonometric concepts to solve real-world problems. Click for Chapter 9 Notes.
  • Circles: Understand the properties and theorems related to circles. Click for Chapter 10 Notes.
  • Constructions: Explore geometric constructions using a compass and straightedge. Click for Chapter 11 Notes.
  • Areas Related to Circles: Grasp the concepts of areas related to circles and their applications. Click for Chapter 12 Notes.
  • Surface Areas and Volumes: Navigate through problems related to surface areas and volumes of different shapes. Click for Chapter 13 Notes.
  • Statistics: Understand the basics of statistics, including mean, median, and mode. Click for Chapter 14 Notes.
  • Probability: Explore the fundamentals of probability and its applications. Click for Chapter 15 Notes.

Class 10 Mathematics is not just a subject; it’s a foundation for advanced mathematical concepts in the coming years. Enhance your learning experience with NCERT revision notes, designed to cater to each chapter’s nuances. Embark on this mathematical journey, chapter by chapter, to fortify your understanding and confidently face the challenges of mathematical exploration.

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NCERT Books Class 10 Maths PDF Download

NCERT Books Class 10 Maths in English and Hindi Medium with NCERT solutions free pdf download . Download Maths exam support material for the students studying in Class 10. PDF download NCERT Maths books Class 10.

NCERT Books Class 10 Maths Free PDF Download

PDF Download official prescribed Maths Class 10 NCERT textbook below. Book based on Latest Maths Class 10 Syllabus . Class X NCERT Maths Books are easy to understand with fundamental explanations.

NCERT Books Class 10 Maths

NCERT Maths Class 10 PDF

Maths textbook class 10 pdf chapter-wise download.

  • Chapter 1 Real Numbers
  • Chapter 2 Polynomials
  • Chapter 3 Pair of Linear Equations in Two Variables
  • Chapter 4 Quadratic Equations
  • Chapter 5 Arithmetic Progressions
  • Chapter 6 Triangles
  • Chapter 7 Coordinate Geometry
  • Chapter 8 Introduction to Trigonometry
  • Chapter 9 Some Applications of Trigonometry
  • Chapter 10 Circles
  • Chapter 11 Constructions
  • Chapter 12 Areas Related to Circles
  • Chapter 13 Surface Areas and Volumes
  • Chapter 14 Statistics
  • Chapter 15 Probability
  • PROOFS IN MATHEMATICS
  • MATHEMATICAL MODELLING

गणित – Class 10th Maths Book in Hindi Medium

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  • CBSE Class 10 NCERT Books

NCERT Books for Class 10: Download Latest Books of All Subjects for 2024-2025

Ncert books for class 10: get a complete set of ncert books for class 10 here. the latest class 10 ncert books of all subjects for the academic session 2024-25 are provided here in pdf format. .

Gurmeet Kaur

NCERT Books for Class 10 (2023-24): NCERT Books for Class 10 are prescribed by CBSE and most of the state boards functional in India as these books provide students with a strong foundation in the basic concepts of various subjects. The books are updated occasionally to reflect the latest trends and developments in education. In this article, we have provided the latest NCERT Books for all subjects of class 10. Read these books thoroughly to prepare well for the upcoming session 2024-25.

The National Council of Educational Research and Training (NCERT) revised the textbooks of all subjects for class 10 back in 2022-23, the session affected by the COVID-19 pandemic. These revisions were part of an effort to streamline the syllabus and reduce the academic burden on students, who faced significant disruptions to their education due to school closures and the shift to online learning. Some significant topics and chapters were deleted from the NCERT textbooks. You can also check the list of rationalised content or the deleted parts of NCERT books . The same changes are to be retained for the current academic session as well.

Below are the latest NCERT Books for Class 10, essential for students preparing for the 2025 board exams. These textbooks are available in chapter-wise PDF format for convenient access and study.

NCERT Books for Class 10 All Subjects PDF:

NCERT Class 10 Maths Book: Download Chapter-Wise PDF:

  • Chapter 1: Real Numbers
  • Chapter 2: Polynomials
  • Chapter 3: Pair of Linear Equations in Two Variables
  • Chapter 4: Quadratic Equations
  • Chapter 5: Arithmetic Progression
  • Chapter 6: Triangles
  • Chapter 7: Coordinate Geometry
  • Chapter 8: Introduction to Trigonometry
  • Chapter 9: Some Applications of Trigonometry
  • Chapter 10: Circles
  • Chapter 11: Constructions
  • Chapter 12: Area Related to Circles
  • Chapter 13: Surface Areas and Volumes
  • Chapter 14: Statistics
  • Chapter 15: Probability

NCERT Class 10 Science Book - Download Chapter-Wise PDF

  • Chapter 1: Chemical Reactions and Equations
  • Chapter 2: Acid, Base and Salt
  • Chapter 3: Metals and Non-Metals
  • Chapter 4: Carbon and Its Compounds
  • Chapter 5: Periodic Classification of Elements
  • Chapter 6: Life Processes
  • Chapter 7: Control and Coordination
  • Chapter 8: How Do Organisms Reproduce
  • Chapter 9: Heredity and Evolution
  • Chapter 10: Light - Reflection and Refraction
  • Chapter 11: The Human Eye and the Colourful World
  • Chapter 12: Electricity
  • Chapter 13: Magnetic Effects of Electric Current
  • Chapter 14: Sources of Energy
  • Chapter 15: Our Environment
  • Chapter 16: Management of Natural Resources

NCERT Class 10 Social Science Book - Download Chapter-Wise PDF

India and the contemporary world ii.

  • Chapter 1: The Rise of Nationalism in Europe
  • Chapter 2: Nationalism in India
  • Chapter 3: The Making of a Global World
  • Chapter 4: The Age of Industrialisation
  • Chapter 5: Print Culture and The Modern World

Contemporary India II

  • Chapter 1: Resources and Development
  • Chapter 2: Forest and Wildlife Resources
  • Chapter 3: Water Resources
  • Chapter 4: Agriculture
  • Chapter 5: Minerals and Energy Resources
  • Chapter 6: Manufacturing Industries
  • Chapter 7: Lifelines of National Economy

Democratic Politics II

  • Chapter 1: Power Sharing
  • Chapter 2: Federalism
  • Chapter 3: Democracy and Diversity
  • Chapter 4: Gender, Religion and Caste
  • Chapter 5: Popular Struggles and Movements
  • Chapter 6: Political Parties
  • Chapter 7: Outcomes of Democracy
  • Chapter 8: Challenges to Democracy

Understanding Economic Development

  • Chapter 1: Development
  • Chapter 2: Sectors of the Indian Economy
  • Chapter 3: Money and Credit
  • Chapter 4: Globalisation and the Indian Economy
  • Chapter 5: Consumer Rights

NCERT Class 10 Hindi Book - Download Chapter-Wise PDF:

Ncert class 10 hindi - kshitij part ii textbook.

  • Chapter 1: सूरदास
  • Chapter 2: तुलसीदास
  • Chapter 3: देव
  • Chapter 4: जयशंकर प्रसाद
  • Chapter 5: सूर्यकांत त्रिपाठी ‘ निराला'
  • Chapter 6: नागार्जुन
  • Chapter 7: गिरिजा कुमार माथुर
  • Chapter 8: ऋतुराज
  • Chapter 9: मंगलेश डबराल
  • Chapter 10: स्वयं प्रकाश
  • Chapter 11: रामवृक्ष बेनीपुरी
  • Chapter 12: यशपाल
  • Chapter 13: सर्वेश्वर दयाल सक्सेना
  • Chapter 14: मन्नू भंडारी
  • Chapter 15 - महावीर प्रसाद द्विवेदी
  • Chapter 16: यतीन्द्र मिश्रा
  • Chapter 17: भदंत आनंद कौसल्यायन

NCERT Class 10 Hindi - Kritika Textbook:

  • Chapter 1:  माता का अँचल
  • Chapter 2: जॉर्ज पंचम की नाक
  • Chapter 3: साना – साना हाथ जोड़ि…
  • Chapter 4: एही ठैयाँ झुलनी हेरानी हो रामा!
  • Chapter 5: मैं क्यों लिखता हूँ?

NCERT Class 10 Hindi - Sparsh Textbook:

  • Chapter 1: कबीर – साखी
  • Chapter 2: मीरा – पद
  • Chapter 3: बिहारी – दोहे
  • Chapter 4: मैथिलीशरण गुप्त – मानुषीता
  • Chapter 5: सुमित्रानंदन पंत – परवत प्रदेश के पावस
  • Chapter 6: महादेवी वर्मा – मधुर मधुर मेरे दीपक जल
  • Chapter 7: वीरेन डंगवाल – तोप
  • Chapter 8: कैफ़ी आज़मी – कर चले हम फ़िदा
  • Chapter 9: रवींद्रनाथ ठाकुर – आत्मत्राण
  • Chapter 10: प्रेमचंद – बडे भाई साहब
  • Chapter 11:  सीताराम  सेकसरिया –  डायरी  का  एक  पन्ना
  • Chapter 12:  तताँरा  वामीरो  कथा
  • Chapter 13:  प्रह्लाद  अग्रवाल –  तीसरी  कसम  के  शिल्पकार  शैलेंद्र
  • Chapter 14:  अंतोन  चेखव –  गिरगिट
  • Chapter 15:  निदा  फाजली –  अब  कहाँ  दूसरे  के  दुख  से  दुखी  होने  वाले
  • Chapter 16:  रवीन्द्र  केलेकर –  पतझर  में  टूटी  पत्तियाँ
  • Chapter 17:  हबीब  तनवीर —  कारतूस

NCERT Class 10 Hindi - Sanchayan Part II Textbook:

  • Chapter 1: हरिहर काका मिथिलेश्वर
  • Chapter 2: सपनों के से दिन गुरदयाल सिंह
  • Chapter 3: टोपी शुक्ला राही मासूम रज़ा

NCERT Class 10 English Book - Download Chapter-Wise PDF:

Ncert class 10 english - first flight textbook.

  • Chapter 1: A Letter to God
  • Chapter 2: Nelson Mandela: Long Walk to Freedom
  • Chapter 3: Two Stories about Flying
  • Chapter 4: From the Diary of Anne Frank
  • Chapter 5: The Hundred Dresses–I
  • Chapter 6: The Hundred Dresses–II
  • Chapter 7: Glimpses of India
  • Chapter 8: Mijbil the Otter
  • Chapter 9: Madam Rides the Bus
  • Chapter 10: The Sermon at Benares
  • Chapter 11: The Proposal

NCERT Class 10 English - Footprints without Feet Supplementary Reader

  • Chapter 1: A Triumph of Surgery
  • Chapter 2: The Thief’s Story
  • Chapter 3: The Midnight Visitor
  • Chapter 4: A Question of Trust
  • Chapter 5: Footprints without Feet
  • Chapter 6: The Making of a Scientist
  • Chapter 7: The Necklace
  • Chapter 8: The Hack Driver
  • Chapter 9: Bholi
  • Chapter 10: The Book That Saved the Earth

NCERT Class 10 English - Words and Expressions Workbook

  • Unit 1 - A Letter to God
  • Unit 2 - Nelson Mandela: Long Walk to Freedom
  • Unit 3 - Two Stories about Flying
  • Unit 4 - From the Diary of Anne Frank
  • Unit 5 - The Hundred Dresses–I
  • Unit 6 - The Hundred Dresses–II
  • Unit 7 - Glimpses of India
  • Unit 8 - Mijbil the Otter
  • Unit 9 - Madam Rides the Bus
  • Unit 10 - The Sermon at Benares
  • Unit 11 - The Proposal

Importance of NCERT Books for Class 10 students

Textbooks curated by NCERT are prescribed by CBSE board for class 10 students because they contain authentic, valid information which is relevant for students to have a strong base for further education. NCERT books for class 10 provide simple explanations and in-depth knowledge of all major and minor topics. This makes it easy for all students. Additionally, NCERT strictly follows the CBSE Curriculum which is designed to help students grow holistically.

Online Mock Tests and Video Lectures for CBSE Class 10

Get here latest School , CBSE and Govt Jobs notification in English and Hindi for Sarkari Naukari and Sarkari Result . Download the Jagran Josh Sarkari Naukri App .

  • How to download NCERT Books for class 10 in PDF form? + In this article by Jagran Josh, we have provided all NCERT books for class 10 in PDF form, free of cost.
  • Is class 10 ncert book available online? + Yes you can check the complete list of NCERT books for class 10 on Jagran Josh. The PDFs are also available for all subjects and all chapters.
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  • TECHNOLOGY FEATURE
  • 03 July 2024

Inside the maths that drives AI

  • Michael Brooks 0

Michael Brooks is a science writer in Lewes, UK.

You can also search for this author in PubMed   Google Scholar

Credit: Getty

People usually talk about the race to the bottom in artificial intelligence as a bad thing. But it’s different when you’re discussing loss functions.

Loss functions are a crucial but frequently overlooked component of useful artificial intelligence (AI), and they’re all about getting to the bottom — albeit of a literal curve on a graph — as quickly as possible. When training an algorithm to automate tedious data analysis, such as looking for specific features in millions of photographs, you need a way of measuring its performance. That’s the ‘loss function’: it measures an algorithm’s error relative to the ‘ground truth’ of the data — information that is known to be real or true. Then you adjust the algorithm’s parameters, rinse and repeat, and hope the error is smaller next time. “You’re trying to find a minimum: the point where the error is as small as possible — hopefully zero,” says Anna Bosman, a computational-intelligence researcher at the University of Pretoria.

Dozens of off-the-shelf loss functions have been written. But choose the wrong one, or just handle it badly, and the algorithm can lead you astray. It could blatantly contradict human observations, make random fluctuations (known as experimental noise) look like data, or even obscure the central results of an experiment. “There are lots of things that can go wrong,” Bosman says. And worst of all, the opacity of AI means you might not even know that you’ve been misled.

That’s why a growing number of scientists are abandoning ready-made loss functions and constructing their own. But how do they get it right? How do you make a home-made loss function your go-to tool and not a time-swallowing mistake?

Error assessment

Machine-learning algorithms are generally trained on annotated data, or by being told when they get the answer wrong. Loss functions provide a mathematical measure of wrongness, but there are multiple ways to quantify that.

‘Absolute error’ functions, for example, report the difference between the algorithm’s prediction and the target value. Then there’s mean squared error: square the differences between your predictions and the ground truth, and then average them out across the whole data set.

Mean squared error is a simple, straightforward and proven approach that works well when errors are relatively small and consistent. But it can be problematic if your data are full of outliers, because the algorithm amplifies their impact. A loss function called pseudo-Huber (a smooth approximation of an approach called the Huber loss function) considers whether each data point’s error is large or small, providing a compromise between the mean squared error and absolute error loss functions.

Absolute error, mean squared error and Huber are most useful for regression analysis, which uses past data on continuous variables such as height or weight in a population to predict what shape future data sets will take (see ‘Quantifying loss’). Classification tasks, by contrast, answer questions such as what type of object something is and how many of them are in the data set. In this case, the machine-learning algorithm determines the probability that an object belongs to a particular class — how likely it is that a particular collection of pixels represents a dog, for example. The most useful loss functions include cross entropy, a measure that compares probability distributions related to the model’s output and the real-world value (also known as maximum likelihood), and hinge loss. The latter finds the curve that is the farthest possible distance from every data point, providing the cleanest possible decision about which category a data point falls into.

QUANTIFYING LOSS: figure showing three of the most popular ways to measure accuracy in artificial intelligence.

These generalized loss functions are not always the best option, however. Take Arjun Raj’s experience, for example.

A geneticist at the University of Pennsylvania in Philadelphia, Raj uses fluorescence microscopy to quantify gene expression in single cells. In these experiments, each RNA transcript is a discrete spot in an image: the trick is to count the spots and assign them to the correct cell. Finding the spots — which are two or three pixels across — is trivial for a human. “One summer, I had a high-school student working with me who had never seen these images, and I was able to teach him how to perfectly annotate the images within two minutes,” says William Niu, a former undergraduate student in Raj’s laboratory.

Unfortunately, the lab generates data sets that might represent thousands of fluorescent spots in millions of cells, too many to analyse by hand. Even more unfortunately, the analysis is much harder for machines than it is for humans. When Raj and his colleagues tried to automate the process, they found that no known loss function could return a reliable result.

The problem mainly came down to ‘class imbalance’, Raj says: when spots are few and far between, the algorithm might think that it is performing well if it simply labels every pixel as ‘not-spot’. But that gives a catastrophically high false-negative rate. “You could make a really ‘good’ classifier that just said there’s no spots in this image because 99.9% of the time, there are no spots,” Raj says. “It’s very, very accurate in some sense, even though it’s basically doing nothing useful at all.”

maths assignment for class 10 pdf

AI and science: what 1,600 researchers think

Niu, Raj and others in their lab worked together to translate their understanding of the issues into a loss function called SmoothF1 1 . F1 is a metric that balances false negatives against false positives. However, the mathematical function behind F1 cannot be differentiated, which means it can’t be used to train a neural network, because it lacks a way to minimize the algorithm’s error. SmoothF1 approximates the F1 score in a way that compensates for class imbalance while allowing the algorithm to find its way to the bottom of the error slope. The team then used this function to drive a spot-detection algorithm called Piscis.

The work Niu did “made a huge difference to our lab”, Raj says. “It has allowed us to power through analyses with much higher throughput.” But Piscis should be useful for a range of applications, Niu says. “Theoretically, our method should be able to get better performance on any type of object in which the objects that you’re looking for occupy less than, say, 5% of the image,” he says.

Pedro Seber, a chemical-engineering student at the Massachusetts Institute of Technology in Cambridge, created his own loss function to teach a machine-learning algorithm to predict sites of glycosylation — sugar chain addition — in mammalian proteins. Such a task is potentially useful in understanding the pathways of diseases, including cancer 2 .

Seber didn’t set out to delve into the machine-learning side of his research — he was trying to train his model using a loss function based on cross entropy, but this impaired the model’s performance. “Sometimes, the model with the lowest cross entropy was not necessarily the model with the best metrics,” Seber says. Digging deeper, he found that this was because the cross entropy didn’t actually relate to the prediction task. “It was optimizing something that I didn’t really care about,” he explains.

maths assignment for class 10 pdf

How to spice up your bioinformatics skill set with AI

Seber decided to create a bespoke loss function that focused on something he did care about: a tweaked version of the Matthews correlation coefficient (MCC), a function similar to F1 that provides a metric for training an algorithm. It might not have the snappiest name, but Seber’s ‘weighted focal differentiable MCC loss function’ boosted MCC performance by about 10%. That’s not very high, he acknowledges, “but at that point, every improvement counts”. Seber says that even this improvement is enough to achieve state-of-the-art performance — a highly desirable outcome because glycosylation sites represent potential targets for drug and biotherapeutic development.

Not every venture into creating loss functions will be a huge success, warns Andrew Engel, a data scientist at the Pacific Northwest National Laboratory in Richland, Washington. Engel has had mixed results, for instance, with a loss function designed to help neural networks assess the redshift of galaxies in telescope images 3 — a measure used to derive the distance of objects from Earth.

Engel had wondered whether supplementing an existing loss function with astronomical knowledge might improve its performance. To his surprise, it didn’t, probably because the new information he was feeding the algorithm was effectively reiterating what it already knew. But at least he didn’t waste a lot of time: training the model wasn’t particularly time-consuming, meaning he could test different approaches — to “fail quickly”, as Engel puts it. “The nice thing about this field is we get constant feedback on whether our idea is working or not.”

What to measure?

That said, researchers can’t always articulate what their loss function should be measuring. You want the AI to do better, but in what way? “There’s always going to be some barrier in translating what your desires are to what it means mathematically,” Niu says.

That view is supported by a study 4 published in 2023 by engineering researchers Hansol Ryu and Manoj Srinivasan at the Ohio State University in Columbus. Ryu and Srinivasan asked scientists and engineers to manually perform the work of a loss function, fitting curves to a variety of data sets by eye. To the team’s surprise, each individual’s approach varied from data set to data set and person to person.

maths assignment for class 10 pdf

AI under the microscope: the algorithms powering the search for cells

“Humans are a lot more variable than computer algorithms,” Ryu says. For instance, many of those who said they were trying to visualize mean-squared error were subconsciously using a different method — one that involved finding the most frequently occurring value, called the mode of the data set, instead of the mean. What’s more, researchers were inconsistent in how they handled outliers, and they seemed to reject outliers more as the amount of data increased.

Complicating matters, training an AI is about more than minimizing error. Researchers must also avoid ‘overfitting’, in which the training has been too narrow to allow the model to work with real-world data — creating a loss function that is extremely efficient, but not in a good way. “If your model is overly complex, then you might have an extremely complex [function] that crosses every single point in your data set,” Bosman says. “On paper, it looks like your model is absolutely great, but if you try to apply it to some real points, the output will be absolutely horrendous and the predictions will be completely wrong.”

However, Bosman’s main advice is: know your noise. “In the real world, data is very, very messy,” she points out. A generic loss function makes assumptions — which might not necessarily apply to your data. Mean squared error, the most common loss function for regression problems, assumes a normal distribution of data points, for example. But your data might conform better to a different shape. Bosman is part of a team that has investigated loss functions that use the Cauchy distribution for such data. This distribution looks similar to a normal distribution but has heavier tails — that is, more of the data lie outside the most common values. Cauchy-based loss functions can give a better performance when there is noise in the data that doesn’t conform to a normal distribution, she says.

Choose your function

It’s hard to overstate the importance of such considerations, says Jonathan Wilton, a machine-learning graduate student at the University of Queensland in Brisbane, Australia. “If you’re in a situation where you believe that there are probably errors or problems with your data … then it’s probably a good idea to consider using a loss function that’s not so standard,” he says.

Working with Nan Ye, a statistics, data-science and machine-learning researcher at the University of Queensland, Wilton constructed a framework for creating loss functions that are robust against noise in classification tasks 5 . Here, the problem can be summed up as mislabelling: training data that has a dog incorrectly labelled as a cat, for example. That’s a common problem in machine learning, Ye says. “If your loss function is not robust to that kind of noise, then you might end up encouraging the model to fit the noise, not the regularities in the data.”

To create his function, Wilton started with a loss function for a machine-learning architecture called a decision tree — something that might analyse a slew of highly disparate medical information to make a disease diagnosis, for example. Now, Wilton is trying to develop an equivalent function for neural-net architectures. Decision trees, he explains, are “really versatile”. “But neural nets are particularly useful in situations where you collect very large data sets, in the order of hundreds of thousands or millions of examples, all of a similar type.” So far, he says, the results are promising.

Beyond knowing your noise, one crucial thing specialists advise is incorporating ‘domain knowledge’: seek to create a loss function that reflects what a real-world practitioner knows about the system. The reason Niu’s loss function was so successful, Raj says, is that Niu “really paid attention to what real users needed and how to make it work best for them”.

Engel agrees. “I see many new AI scientists being deployed to problems or data sets where they lack domain knowledge,” he says. “In those cases, they should sit down with a domain expert for a long time to really ingest and jargon-bust that field.” It might take a few iterations to apply that knowledge successfully, he says, but it’s worth the effort.

maths assignment for class 10 pdf

NatureTech hub

That said, as the pool of available loss functions grows larger, picking the right function will only grow more complex. Programming libraries such as PyTorch and scikit-learn allow researchers to swap loss functions fairly easily, and Bosman suggests playing around with several functions to see what works. “My recommendation is usually to try [a couple of options], train for 30 times with each, and then we have a statistical sample and we can figure out if one is statistically better on average than the other,” she says.

The problem could get easier soon, however. Wilton, who is curating a library of loss functions for decision trees, says one possibility is a unification of loss functions — an overarching method that will work broadly across many kinds of data and problem. Another option is a machine-learning algorithm that chooses and optimizes its own loss function, or what Bosman calls a ‘meta-model’ that could recommend the best loss function for your problem from a list of available options.

Niu imagines an even more radical idea: you just tell a generative AI about your research, and it will recommend the right tool. “A generative AI model might just give you this for free,” he suggests.

Some researchers are already doing this. Machine-learning researcher Juan Terven at the National Polytechnic Institute in Mexico City regularly converses with the chatbot ChatGPT about his loss function requirements. “You need to specify the nature of your problem and the nature of your data, but it will give you a list of things to try,” he says. Last year, Terven and his colleagues conducted an extensive review of loss functions and their applications 6 and is impressed by ChatGPT’s ability to select the right ones.

In the end, says Ye, finding the best loss function for your problem “is both a science and an art”. A science, because loss functions can be quantified and compared; and an art, because the blending of maths and domain knowledge often requires creative thinking. But whether art or science, loss functions deserve your attention. Ignore them, and AI will remain a black, and sometimes befuddling, box.

Nature 631 , 244-246 (2024)

doi: https://doi.org/10.1038/d41586-024-02185-z

Niu, Z. et al. Preprint at bioRxiv https://doi.org/10.1101/2024.01.31.578123 (2024).

Seber, P. Preprint at arXiv https://doi.org/10.48550/arXiv.2402.17131 (2024).

Engel, A. & Strube, J. Preprint at arXiv https://doi.org/10.48550/arXiv.2310.13624 (2023).

Ryu, H. X. & Srinivasan, M. Preprint at bioRxiv https://doi.org/10.1101/2023.09.19.558376 (2023).

Wilton, J. & Ye, N. Preprint at arXiv https://doi.org/10.48550/arXiv.2312.12937 (2024).

Terven, J., Cordova-Esparza, D. M., Ramirez-Pedraza, A. & Chavez-Urbiola, E. A. Preprint at arXiv https://doi.org/10.48550/arXiv.2307.02694 (2023).

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World Bank country classifications by income level for 2024-2025

Eric metreau, kathryn elizabeth young, shwetha grace eapen.

The World Bank Group assigns the world’s economies [1]  to four income groups: low, lower-middle, upper-middle, and high. The classifications are updated each year on July 1, based on the GNI per capita of the previous calendar year. GNI measures are expressed in United States dollars [2]  using conversion factors derived according to the  Atlas method , which in its current form was introduced in 1989 [3] . The World Bank’s income classification aims to reflect a country’s level of development, drawing on  Atlas GNI per capita  as a broadly available indicator of economic capacity. The classification of countries into income categories has evolved significantly over the period since the late 1980s. In 1987, 30% of reporting countries were classified as low-income and 25% as high-income countries. Jumping to 2023, these overall ratios have shifted down to 12% in the low-income category and up to 40% in the high-income category.  The scale and direction of these shifts, however, varies a great deal between world regions. Here are some regional highlights:

  • 100% of South Asian countries were classified as low-income countries in 1987, whereas this share has fallen to just 13% in 2023.
  • In the Middle East and North Africa there is a higher share of low-income countries in 2023 (10%) than in 1987, when no countries were classified to this category.
  • In Latin America and the Caribbean , the share of high-income countries has climbed from 9% in 1987 to 44% in 2023.
  • Europe and Central Asia has a slightly lower share of high-income countries in 2023 (69%) than it did in 1987 (71%).  

These changing compositions are depicted visually in the diagram below, which shows country classifications by region and over time since 1987.  

Classification changes

The updated country income classifications for FY25, based on the GNI per capita of 2023, are available  here .

From a statistical perspective, classifications can change for two reasons:

  • Changes to Atlas GNI per capita : In each country, factors such as economic growth, inflation, exchange rates, and population growth can all influence the level of Atlas GNI per capita. Revisions to improve methods and data can also have an impact. Updated data on Atlas GNI per capita for 2023 can be accessed  here .
  • Changes to classification thresholds : To keep income classification thresholds fixed in real terms, they are adjusted annually for inflation using the  Special Drawing Rights (SDR) deflator , a weighted average of the GDP deflators of China, Japan, the United Kingdom, the United States, and the Euro Area. The new thresholds for Atlas GNI per capita (in US$) are as follows:  

Image

The chart below shows the economies moving to new income categories this year:  

This year, three countries—Bulgaria, Palau, and Russia—moved from the upper-middle-income to the high-income category:

  • Bulgaria  has been steadily approaching the high-income threshold with modest growth throughout the post-pandemic recovery period, which continued in 2023 as real GDP grew 1.8%, supported by consumption demand.
  • Palau  also continued its post-pandemic recovery as GDP returned to previous levels, growing by 0.4% in real terms. With inflation (as measured by the GDP deflator) at 8.1%, nominal GNI increased 10.0%.
  • Economic activity in  Russia  was influenced by a large increase in military related activity in 2023, while growth was also boosted by a rebound in trade (+6.8%), the financial sector (+8.7%), and construction (+6.6%). These factors led to increases in both real (3.6%) and nominal (10.9%) GDP, and Russia’s Atlas GNI per capita grew by 11.2%.  

Algeria, Iran, Mongolia, and Ukraine all moved up from the lower-middle-income to the upper-middle-income category this year: 

  • While the  Algeria n economy grew 4.1% in 2023, the main reason for the upward reclassification was a comprehensive revision to national accounts statistics undertaken by the Algerian authorities (Office National des Statistiques) to align with current international standards. This realignment resulted in an upward revision to the level of GDP (on average 13.3% higher over the 2018-2022 period) due, for example, to the expansion of investment estimates to include research and development, improved methods for measuring production in public administration, and improved coverage of the non-observed economy.
  • Iran ’s economy grew 5.0% in 2023, driven mainly by oil exports and supported by gains in services and manufacturing. GNI jumped 39.5% in nominal terms which, combined with the depreciation of the Iranian rial, resulted in a 17.6% increase of the Atlas GNI per capita.
  • Mongolia  continued its recovery after the pandemic, with real GDP increasing 7.0% in 2023. Growth was driven by expansions in mining of 23.4%, along with higher export prices which boosted exports by 53.4%.
  • Ukraine ’s upward change in classification resulted from a resumption of economic growth in 2023 (real GDP grew 5.3%, following a drop of 28.8% in 2022) along with a continued decline in population, which has fallen more than 15% since the invasion from Russia began. These factors were further amplified by price increases of domestically produced goods and services to result in a large increase in nominal Atlas GNI per capita of 18.5%. While Ukraine’s economy was significantly impaired by Russia’s invasion, real growth in 2023 was driven by construction activity (24.6%), reflecting a sizable increase in investment spending (52.9%) supporting Ukraine’s reconstruction effort in the wake of ongoing destruction.

West Bank and Gaza was the only country whose classification moved downward this year. The conflict in the Middle East began in October 2023, and while the impact on West Bank and Gaza was limited to the fourth quarter, its scale was nonetheless sufficient to lead to a 9.2% drop in nominal GDP (-5.5% in real terms). Since West Bank and Gaza’s economy was close to the threshold (it entered the upper-middle-income category only last year), these declines brought Atlas GNI per capita back down to the lower-middle-income category.

More information

Detailed information on how the World Bank Group classifies countries is available  here . The  country and lending groups  page provides a complete list of economies classified by income, region, and World Bank lending status and includes links to prior years’ classifications. The classification tables include World Bank member countries, along with all other economies with populations greater than 30,000. These classifications reflect the best available GNI figures for 2023, which may be revised as countries publish improved final estimates. Data for  GNI ,  GNI per capita ,  GDP ,  GDP PPP , and  Population  for 2023 are now available on the World Bank's Open Data Catalog. Note that these are estimates and may be revised. For more information, please contact us at  [email protected] .  

[1]  The term country, used interchangeably with economy, does not imply political independence but refers to any territory for which authorities report separate social or economic statistics. [2]  In countries where dual or multiple exchange rates are in use, the exchange rate used to convert local currency units to US$ is an average of these exchange rates, provided necessary data are available. [3]  For data beginning in reference year 1987. The authors are pleased to acknowledge the essential contributions of our colleagues,  Charles Kouame , and  Tamirat Yacob to the preparation of this piece. Please note: The country classification described here aims to serve analytical purposes and changes have no direct impact on the eligibility for World Bank resources. In the classification used for World Bank operational purposes, a range of additional criteria are considered to determine country eligibility and the terms and conditions of Bank financing. For more information, please see the  IBRD Financial Products web page.

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