cbse class 10 maths assignment chapter wise

Assignments for Class 10 th

Download Sample Questions and Assignments for Class 10 with important Topic- Wise Questions. These Sample Questions and Assignments have been prepared as per the syllabus issued by CBSE, KVS and topics given in NCERT Books. Solving this Sample questions and Assignments will help in scoring in more marks in your class tests and school examinations.

Click on links below for Assignments with important questions for Class 10 Mathematics and Science chapter wise.

Assignment for Class 10th Mathematics Topic- Wise- PDF Download

1.real number.

Assignment for Class 10 Mathematics Real Number Assignment 1

2. Polynomials

Assignment for Class 10 Mathematics Polynomials Assignment

3. Linear Equation in Two Variables

Assignment for Class 10 Mathematics Linear Equation in Two Variables Assignment 1

Assignment for class 10 Mathematics Linear Equation in Two Variables Assignment 2

4. Coordinate Geometry

Assignment for Class 10 Mathematics Coordinate Geometry Assignment

5. Quadratic Equation

Assignment for Class 10 Mathematics Quadratic Equation Assignment

6. Arithmetic Progression

Assignment for Class 10 Mathematics Arithmetic Progression Assignment

7. Triangles

Assignment for Class 10 Mathematics Triangles Assignment

8. Coordinate Geometry

9. introduction to trigonometry.

Assignment for Class 10 Mathematics Introduction to Trigonometry Assignment

10. Some Application of Trigonometry

Assignment for Class 10 Mathematics Some Application to Trigonometry Assignment

11. Circles

Assignment for Class 10 Mathematics Circles Assignment

12. Constructions

Assignment for Class 10 Mathematics Constructions Assignment

13. Area Related to Circles

Assignment for Class 10 Mathematics Area Related to Circles Assignment

14. Surface Area and Volume

Assignment for Class 10 Mathematics Surface Area and Volumes Assignment

15. Statistics

Assignment for Class 10 Mathematics Statistics Assignment

16. Probability

Assignment for Class 10 Mathematics Probability Assignment

Assignment for Class 10th Biology Topic- Wise- PDF Download

1.life process.

Assignment for Class 10 Biology Life Process: Nutrition Assignment 1

Assignment for Class 10 Biology Life Process: Nutrition Assignment 2

Assignment for Class 10 Biology Life Process: Nutrition Assignment 3

Assignment for Class 10 Biology Life Process: Transportation Assignment 4

Assignment for Class 10 Biology Life Process: Transportation Assignment 5

Assignment for Class 10 Biology Life Process: Excretion Assignment 6

Assignment for Class 10 Biology Life Process: Respiration Assignment 7

Assignment for Class 10 Biology Life Process: Respiration Assignment 8

Assignment for Class 10th Chemistry Topic- Wise- PDF Download

1.chemical reactions and equation.

Assignment for Class 10 Chemistry Chemical Reactions and Equation Assignment 1

Assignment for Class 10 Chemistry Chemical Reactions and Equation Assignment 2

Assignment for Class 10 Chemistry Chemical Reactions and Equation Assignment 3

2. Acid, Bases and Salt

Assignment for Class 10 Chemistry Acid, Bases and Salt Assignment 1

Assignment for Class 10 Chemistry Acid, Bases and Salt Assignment 2

Assignment for Class 10 Chemistry Acid, Bases and Salt Assignment 3

3. Metals and Non- Metals

Assignment for Class 10 Chemistry Metals and Non-Metals Assignment 1

Assignment for Class 10 Chemistry Metals and Non-Metals Assignment 2

Assignment for Class 10 Chemistry Metals and Non-Metals Assignment 3

Assignment for Class 10 Chemistry Metals and Non-Metals Assignment 4

Assignment for Class 10 Chemistry Metals and Non-Metals Assignment 5

Assignment for Class 10th Physics Topic- Wise- PDF Download

1.electricity.

Assignment for Class 10 Physics Electricity Assignment 1

Assignment for Class 10 Physics Electricity Assignment 2

Assignment for Class 10 Physics Electricity Assignment 3

Assignment for Class 10 Physics Electricity Assignment 4

Assignment for Class 10 Physics Light Assignment 1

Assignment for Class 10 Physics Light Assignment 2

Assignment for Class 10 Physics Light Assignment 3

Assignment for Class 10 Physics Light Assignment 4

Assignment for Class 10 Physics Light: Human Eye Assignment 5

3. Magnetism and EMI

Assignment for Class 10 Physics Magnetism and EMI Assignment 1

Assignment for Class 10 Physics Magnetism and EMI Assignment 2

Assignment for Class 10 Physics Magnetism and EMI Assignment 3

4. Sources and Energy

Assignment for Class 10 Physics Sources of Energy Assignment 1

Assignment for Class 10 Physics Sources of Energy Assignment 2

Advantages of Sample Question Assignments of Class 10

i. By solving Sample Question of Class 10, students can improve their problem solving skills.

ii.Help to develop the subject knowledge.

iii.Solving Sample Question Assignment helps students to promotes hands on learning.

iv. Useful for classroom revision.

v. Practicing Assignments will be useful to test conceptual understanding.

Assignment Class 8 Science

Assignment Class 9 Science

Assignment Class 10 Science

Assignment Class 11 Physics

Assignment Class 11 Chemistry

Assignment Class 11 Biology

Assignment Class 12 Physics

Assignment Class 12 Chemistry

Assignment Class 12 Biology

Mathematics Assignments

Assignment Class 8 Math

Assignment Class 9 Math

Assignment Class 10 Math

Assignment Class 11 Math

Assignment Class 12 Math

Sample Papers

Sample Paper Class 8 Science

Sample Paper Class 9 Science

Sample Paper Class 10 Science

Sample Paper Class 8 Math

Sample Paper Class 9 Math

Sample Paper Class 10 Math

Sample Paper Class 11 Physics

Sample Paper Class 11 Chemistry

Sample Paper Class 11 Biology

Sample Paper Class 11 Mathematics

Sample Paper Class 12 Physics

Sample Paper Class 12 Chemistry

Sample Paper Class 12 Biology

Sample Paper Class 12 Mathematics

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Class 10 Mathematics Worksheets

We have provided below free printable  Class 10 Mathematics Worksheets  for Download in PDF. The worksheets have been designed based on the latest  NCERT Book for Class 10 Mathematics . These  Worksheets for Grade 10 Mathematics cover all important topics which can come in your standard 10 tests and examinations.  Free printable worksheets for CBSE Class 10 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 10 faculty. You can free download CBSE NCERT printable worksheets for Mathematics Class 10 with solutions and answers. All worksheets and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 10. Students can click on the links below and download all Pdf  worksheets for Mathematics class 10  for free. All latest Kendriya Vidyalaya  Class 10 Mathematics Worksheets  with Answers and test papers are given below.

Mathematics Class 10 Worksheets Pdf Download

Here we have the biggest database of free  CBSE NCERT KVS  Worksheets for Class 10  Mathematics . You can download all free Mathematics worksheets in Pdf for standard 10th. Our teachers have covered  Class 10 important questions and answers  for Mathematics as per the latest curriculum for the current academic year. All test sheets question banks for Class 10 Mathematics and  CBSE Worksheets for Mathematics Class 10  will be really useful for Class 10 students to properly prepare for the upcoming tests and examinations. Class 10th students are advised to free download in Pdf all printable workbooks given below.

Topicwise Worksheets for Class 10 Mathematics Download in Pdf

More worksheet for class 10 maths.

Advantages of Solving Class 10 Mathematics Worksheets

• As we have the best collection of Mathematics worksheets for Grade 10, you will be able to find important questions which will come in your class tests and examinations.
• You will be able to revise all important and difficult topics given in your CBSE Mathematics  textbooks for Class 10 .
• All Mathematics worksheets for standard 10 have been provided with solutions. You will be able to solve them yourself and them compare with the answers provided by our teachers.
• Class 10 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise assgnments and worksheets for free in Pdf
• Class 10 Mathematics Workbook will help to enhance and improve subject knowledge which will help to get more marks in exams

Frequently Asked Questions by Class 10 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free worksheets for Mathematics Class 10 which you can download in Pdf

We provide here Standard 10 Mathematics chapter-wise worksheets which can be easily downloaded in Pdf format for free.

You can click on the links above and get worksheets for Mathematics in Grade 10, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here subject-wise Mathematics Grade 10 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best quality question bank for Class 10 for all subjects. You can download them all and use them offline without the internet.

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CBSE 10th MATHS : Chapter-Wise Previous Years Questions with Solutions

This article contains the latest 10th class chapter-wise previous year questions of Subject Mathematics. PYQs help students in a better understanding of the syllabus and topics covered in the exam. Solving these questions certainly helps in boosting confidence as the exam is just around the corner. Given below are the chapter name with their respective links containing questions and their solution:

• NCERT Solutions for Class 12 Maths
• NCERT Solutions for Class 10 Maths
• CBSE Syllabus 2023-24
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• CBSE Class 10 Science 2024-25: Chapter 10 Human Eye and Colourful World Refraction Competency-Based Questions with Answers; Download Free PDF 24 October, 2024, 4:53 pm
• CBSE Board Exams 2025 : Practical Exam Schedule 2025 Released – Check Dates & Subject-Wise Marks Here 24 October, 2024, 11:03 am
• CBSE Class 10 Science 2024-25: Chapter 9 Light-Reflection and Refraction Competency-Based Questions with Answers; Download Free PDF 23 October, 2024, 3:49 pm
• CBSE Class 10 Science 2024-25: Chapter 8 Heredity and Evolution Competency-Based Questions with Answers; Download Free PDF 22 October, 2024, 4:03 pm
• CBSE Class 10 Science 2024-25: Chapter 7 Reproduction Competency-Based Questions with Answers; Download Free PDF 21 October, 2024, 4:42 pm
• CBSE Class 10 Science 2024-25: Chapter 6 Control and Co-ordination Competency-Based Questions with Answers; Download Free PDF 19 October, 2024, 3:30 pm
• CBSE Class 10 Science 2024-25: Chapter 5 Life Processes Competency-Based Questions with Answers; Download Free PDF 18 October, 2024, 4:46 pm
• CBSE Class 10 Science 2024-25: Chapter 4 Carbon and its Compounds Competency-Based Questions with Answers; Download Free PDF 17 October, 2024, 5:46 pm
• CBSE Class 10 Science 2024-25: Chapter 3 Metal and Non-metal Competency-Based Questions with Answers; Download Free PDF 16 October, 2024, 4:29 pm

CBSE Class 10 Science 2024-25: Chapter 10 Human Eye and Colourful World Refraction Competency-Based Questions with Answers; Download Free PDF

With the CBSE Class 10 board exams approaching, understanding the new 2024-25 exam pattern is crucial. CBSE will include 50% more competency-based questions, both multiple-choice and written, emphasizing real-life application. This article focuses on Chapter 10: Human Eye and Colourful World Refraction, highlighting key competency-based questions and answers. Prepare effectively for CBSE Class 10 Science with essential questions from Chapter 10.

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• Worksheet For class 10

CBSE Board worksheet for class 10 Maths

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Physics Wallah Academic team prepared a chapter-wise CBSE worksheet for class 10 Maths With detailed solutions. These CBSE BOARD class 10 Maths worksheets consist of all types of questions required to understand the concepts of class 10 Maths.

For another subject worksheet you can visit the parent page. All Worksheet for Class 10 science are with detail solutions for reference. Solve NCERT exercise with the help of Physics Wallah NCERT Solutions for Class 10 Maths that will help in the board exams.

Find below chapter-wise CBSE BOARD worksheets in pdf for class 10 Maths

• CBSE Worksheet for chapter- 9 Trigonometry class 10
• CBSE Worksheet for chapter- 10 Circle class 10
• CBSE Worksheet for chapter- 11 Circle class 10
• CBSE Worksheet for chapter- 13 Measures or Central tendency class 10
• CBSE Worksheet for chapter- 14 Probability class 10
• CBSE Worksheet for chapter- 5 Arithmetic Progression class 10
• CBSE Worksheet for chapter- 6 Co-ordinate Geometry class 10
• CBSE Worksheet for chapter- 7 Heights and Distance class 10
• CBSE Worksheet for chapter-1 Real Numbers class 10
• CBSE Worksheet for chapter-12 Mensuration-II class 10
• CBSE Worksheet for chapter-15 Construction – 1 class 10
• CBSE Worksheet for chapter-2 Polynomial class 10
• CBSE Worksheet for chapter-3 Linear Equation in two Variables class 10
• CBSE Worksheet for chapter-4 Quadratic Equation class 10
• CBSE Worksheet for chapter-8 Triangles class 10 class 10

Chapter wise worksheet for CBSE Board Class 10 Maths

• CBSE-X Real Numbers
• CBSE-X Polynomial
• CBSE-X Linear eqtn. in two vari.
• CBSE-X Quadratic Equation
• CBSE-X Arithmetic Progression
• CBSE-X Co-ordinate Geometry
• CBSE-X Heights & Distance
• CBSE-X Triangles
• CBSE-X Trigonometry
• CBSE-X Circle
• CBSE-X Mensuration
• CBSE-X Measures & Cen.
• CBSE-X Probability
• CBSE-X Construction

Frequently Asked Question (FAQs)

Q1. Which type of questions comes in standard maths class 10?

Ans. The important questions include the questions from chapters such as Real numbers, polynomials, Linear equations, Quadratic equations, Arithmetic Progressions, Triangles, and all other chapters given in the class 10 maths syllabus.

Q2. Which chapter is most challenging in class 10 maths?

Ans. Trigonometry is the most challenging chapter.

Q3. Which is the best question bank for CBSE class 10 maths?

Ans. Physics Wallah CBSE Maths Class 10 Question Bank. If you want to buy a question bank that can help you understand the exam pattern, this maths question bank by Educart can be an excellent option to consider.

Q4. Is Class 10 Maths easy?

Ans. However, mathematics isn't half as tricky as it seems. You will be able to ace the CBSE class 10 Maths exam if you stick to these simple, easy-to-follow tips and suggestions. It is essential to thoroughly review your syllabus course structure and unit-wise weightage.

Q5. Which is the easiest subject in 10th?

Ans. Every stream is easy and hard. It depends upon your perspective; some people hate maths, some hate biology, some commerce, and some history. Still, Art and commerce are the easiest streams to choose after 10th in comparison to Math and Biology; they require more focus and dedication.

Q6. Which is the easiest chapter in maths?

Ans. There are many easy chapters in Class 12th Mathematics, but if you ask for the easiest, it is Vector Algebra. Other easy chapters are Three Dimensional Geometry, Linear Programming, and Probability.

Q7. How to Score good marks in Maths

Ans. To score goode marks follow the step given below:

• Clear your Doubt First:
• Read the description carefully:
• Manage your time.
• Always check answers:
• Help your friends to solve their problems.
• Keep your solution Neat and Clean.
• Make the best of technology.

Q8. How many hours should I study maths?

Ans. As a general rule, for every 1 hour you spend in class, you will spend 3 hours out of class studying / reviewing what you have learned. Therefore, to learn math from zero (1st grade) through 12th grade, you will need 8 hours to study math.

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• Previous year Board Papers
• Sample Papers Maths Class 10
• Sample Papers Science Class 10
• NCERT Maths Solutions Class-10

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[Latest]Important Questions for Class 10 Maths CBSE Chapter Wise PDF

Available CBSE NCERT Chapter Wise Extra and Important Questions for Class 10 Maths with answers and solutions PDF will surely encourage students to secure graceful marks in the board examinations. Access the below links & practice well for your maths examination.

Class 10 Maths Important Questions with Answers PDF

Important Question of Maths Class 10 plays a vital role in scoring more marks in board exams. We have provided Important Extra questions for class 10 Mathematics & Class 10 Maths Board Important Questions with Answers.

• Real Numbers Class 10 Important Questions
• Polynomials Class 10 Important Questions
• Pair of Linear Equations in Two Variables Class 10 Important Questions
• Quadratic Equations Class 10 Important Questions
• Arithmetic Progressions Class 10 Important Questions
• Triangles Class 10 Important Questions
• Coordinate Geometry Class 10 Important Questions
• Introduction to Trigonometry Class 10 Important Questions
• Applications of Trigonometry Class 10 Important Questions
• Circles Class 10 Important Questions
• Constructions Class 10 Important Questions
• Areas Related to Circles Class 10 Important Questions
• Surface Areas and Volumes Class 10 Important Questions
• Statistics Class 10 Important Questions
• Probability Class 10 Important Questions

Candidates who are studying under CBSE, UP, MP, Gujarat boards, and in search of NCERT Important Questions Class 10 Maths with Solutions.

We hope the given NCERT Important Questions for Class 10 Maths with Solutions Answers Chapter Wise Pdf free download of Mathematics will help you.

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Cbse test series | class 10 maths.

CBSE chapter-wise practice papers with solution for class 10 Mathematics all the chapters for free download in PDF format. 10th Mathematics have many topics. All these topics are included in CBSE solved test papers of class 10 Mathematics chapter. CBSE solved test papers and chapter wise question papers for practice with solution have plenty of questions for daily practice and smart study.

Chapter 1 - Real Numbers :

• Question Paper

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

CBSE Practice papers with solution

Practice makes perfect. The more you practice the better you perform. CBSE practice question papers are based on NCERT syllabus and latest CBSE curriculum for this academic session. The unit tests, chapter wise solved papers, important questions, and questions asked in previous year exams are included in CBSE test papers and CBSE practice papers with solution and answer keys. The solved question papers from all the chapters have complete set & type of questions may be asked in annual exams such as VSA very short answer type questions, SA short answer type questions, LA long answer type questions, VBA value based questions and HOTS higher order thinking skill based questions.

Class 10 Maths Chapter 1 Assignments

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.

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

Download App for Class 10 all Subjects

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.

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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

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..

• NCERT Solutions
• NCERT Solutions for Class 10

NCERT Solutions for Class 10 Maths

Ncert solutions for class 10 maths updated for 2023-24 session – free pdf download.

The answers to the questions present in the NCERT books are undoubtedly the best study material a student can get hold of. These CBSE NCERT Solutions for Class 10 Maths 2023-24 will also help students to build a deeper understanding of concepts covered in the textbook. Practising the textbook questions will help students analyse their level of preparation and knowledge of concepts. The solutions to these questions present in the NCERT books can help students to clear their doubts quickly.

NCERT Solutions Class 10 Maths Chapters NCERT Solutions Class 10 Maths Chapter Details CBSE Class 10 Maths Exam Pattern 2023-2024 CBSE Class 10 Chapter-wise Marks Weightage CBSE Question Paper Design

NCERT Solutions Class 10 Maths Chapters

• 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 Areas Related to Circles
• Chapter 12 Surface Areas and Volumes
• Chapter 13 Statistics
• Chapter 14 Probability

The following are the chapters that have been removed from the NCERT Class 10 Maths textbook 2023-24.

Constructions

NCERT Solutions for Class 10 Maths Free PDF Download

NCERT Solutions of Class 10 Maths list comprises all the chapter-wise answers to the questions present in the NCERT Book for Class 10 Maths, written in a very precise and lucid manner, maintaining the objective of textbooks. The students can refer to the  NCERT Solutions for Class 10 as their additional references and study materials. Practising NCERT textbook exercise solutions will surely help the students in their preparation for the examination.

NCERT Solutions Class 10 Maths Chapter Details and Exercises

Ncert solutions for class 10 maths chapter 1 real numbers.

In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter starts with the Euclid’s Division Lemma, which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0≤r<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined, which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and the decimal expansion of rational numbers are explained with the help of the theorem.

Topics Covered in Class 10 Maths Chapter 1 Real Numbers :

Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples, Proofs of irrationality of √2, √3, √5

Important Steps –

To obtain the HCF of two positive integers, say c and d, with c > d, follow the steps below:

Step 1: Apply Euclid’s division lemma to c and d. So, we find whole numbers, q and r, such that c = dq + r, 0 ≤ r < d.

Step 2: If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.

Step 3: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF. This algorithm works because HCF (c, d) = HCF (d, r), where the symbol HCF (c, d) denotes the HCF of c and d, etc.

Also, access the following resources for NCERT Class 10 Chapter 1 Real Numbers, at BYJU’S:

• NCERT Real Numbers Class 10 Notes
• Real Numbers Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Real Numbers
• RD Sharma Solutions Real Numbers Class 10

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NCERT Solutions for Class 10 Maths Chapter 2 Polynomials

In Polynomials , the chapter begins with the definition of the degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises, including an optional exercise. Exercise 2.1 includes questions on finding the number of zeroes through a graph. It requires an understanding of the Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial, where students have to find the zeros of a quadratic polynomial and in some of the questions, they have to find the quadratic polynomial. In Exercise 2.3, the concept of the division algorithm is defined, and students will find the questions related to it. The optional exercise, 2.4, consists of the questions from all the concepts of Chapter 2.

Topics Covered in Class 10 Maths Chapter 2 Polynomials :

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

We first arrange the terms of the dividend and the divisor in the decreasing order of their degrees. Recall that arranging the terms in this order is called writing the polynomials in standard form.

Step 1: To obtain the first term of the quotient, divide the highest degree term of the dividend by the highest degree term of the divisor. Then carry out the division process.

Step 2: Now, to obtain the second term of the quotient, divide the highest degree term of the new dividend by the highest degree term of the divisor. Again, carry out the division process.

Step 3: Now, the degree of the remainder is less than the degree of the divisor. So, we cannot continue the division any further.

Here again, we see that Dividend = Divisor × Quotient + Remainder. What we are applying here is an algorithm which is similar to Euclid’s division algorithm that you studied in Chapter 1.

This says that

If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that

p(x) = g(x) × q(x) + r(x),

where r(x) = 0 or degree of r(x) < degree of g(x).

This result is known as the Division Algorithm for polynomials.

Also, access the following resources for NCERT Class 10 Chapter 2 Polynomials, at BYJU’S:

• NCERT Polynomials Class 10 Notes
• Polynomials Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Polynomials
• RD Sharma Solutions Polynomials Class 10

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

This chapter explains the concept of Pair of Linear Equations in Two Variables . This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through the Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, and Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving linear equations.

Topics Covered in Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables:

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. Algebraic conditions for number of solutions. Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems.

Important Formulas –

The general form for a pair of linear equations in two variables, x and y, is

a 1 x + b 1 y + c 1 = 0

and a 2 x + b 2 y + c 2 = 0,

where a 1 , b 1 , c 1 , a 2 , b 2 , c 2 are all real numbers and a 1 2 + b 1 2 ≠ 0, a 2 2 + b 2 2 ≠ 0.

Also, access the following resources for NCERT Class 10 Chapter 3 Pair of Linear Equations in Two Variables, at BYJU’S:

• NCERT Pair of Linear Equations in Two Variables Class 10 Notes
• Pair of Linear Equations in Two Variables Class 10 Important Questions ,
• NCERT Exemplar Solutions Class 10 Pair of Linear Equations in Two Variables
• RD Sharma Solutions Pair of Linear Equations in Two Variables Class 10

NCERT Solutions of Class 10 Maths Chapter 4 Quadratic Equations

In this chapter, students will get to know the standard form of writing a Quadratic Equation . The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots, which states that a quadratic equation ax² + bx + c = 0 has

• Two distinct real roots, if b² – 4ac > 0
• Two equal roots, if b² – 4ac = 0
• No real roots, if b² – 4ac < 0

Topics Covered in Class 10 Maths Chapter 4 Quadratic Equations :

The standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization and by using the quadratic formula. Relationship between discriminant and nature of roots. Situational problems based on quadratic equations related to day-to-day activities are to be incorporated.

If b 2 – 4ac > 0, we get two distinct real roots

If b 2 – 4ac = 0, then

So, the roots of the equation ax 2 + bx + c = 0 are both -b/2a.

Therefore, we say that the quadratic equation ax 2 + bx + c = 0 has two equal real roots in this case.

If b 2 – 4ac < 0, then there is no real number whose square is b 2 – 4ac. Therefore, there are no real roots for the given quadratic equation in this case.

Since b 2 – 4ac determines whether the quadratic equation ax 2 + bx + c = 0 has real roots or not, b 2 – 4ac is called the discriminant of this quadratic equation.

So, a quadratic equation ax 2 + bx + c = 0 has

(i) two distinct real roots, if b 2 – 4ac > 0,

(ii) two equal real roots, if b 2 – 4ac = 0,

(iii) no real roots, if b 2 – 4ac < 0.

Also, access the following resources for NCERT Class 10 Chapter 4 Quadratic Equations, at BYJU’S:

• NCERT Quadratic Equations Class 10 Notes
• Quadratic Equations Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Quadratic Equations
• RD Sharma Solutions Quadratic Equations Class 10

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions

This chapter introduces students to a new topic, Arithmetic Progression , i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula:

a n  = a + (n-1) d

The next exercise, i.e. 5.3, contains the questions on finding the sum of the first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

Topics Covered in Class 10 Maths Chapter 5 Arithmetic Progressions :

Motivation for studying Arithmetic Progression Derivation of the n th term and sum of the first n terms of A.P. and their application in solving daily life problems.

If a 1 , a 2 , a 3 , a 4 , a 5 , a 6 , …  are the terms of AP and d is the common difference between each term, then we can write the sequence as; a ,  a+d, a+2d, a+3d, a+4d, a+5d,…., nth term… where a is the first term. Now, n th  term for arithmetic progression is given as;

n th  term = a + (n-1) d

Sum of the first n terms in Arithmetic Progression;

S n  = n/2 [2a + (n-1) d]

Also, access the following resources for NCERT Class 10 Chapter 5 Arithmetic Progressions, at BYJU’S:

• NCERT Arithmetic Progressions Class 10 Notes
• Arithmetic Progressions Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Arithmetic Progressions
• RD Sharma Solutions Arithmetic Progressions Class 10

NCERT Solutions for Class 10 Maths Chapter 6 Triangles

In Chapter 6 of Class 10 CBSE Maths, students will study those figures which have the same shape, but not necessarily the same size. The chapter Triangles starts with the concept of a similar and congruent figure. It further explains the condition for the similarity of two triangles and theorems related to the similarity of triangles. After that, the areas of similar triangles have been explained with a theorem. At the end of this chapter, the Pythagoras Theorem and the Converse of Pythagoras Theorem are described.

Topics Covered in Class 10 Maths Chapter 6 Triangles :

Definitions, examples, and counter examples of similar triangles. 1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. 2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side. 3. (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional, and the triangles are similar. 4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal, and the two triangles are similar. 5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

Important Theorems –

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 6.2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 6.3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar.

Theorem 6.4: If in two triangles, the sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal, and hence the two triangles are similar.

Theorem 6.5: If one angle of a triangle is equal to one angle of the other triangle and the sides, including these angles, are proportional, then the two triangles are similar.

Theorem 6.6: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Theorem 6.8: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Theorem 6.9: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Also, access the following resources for NCERT Class 10 Chapter 6 Triangles, at BYJU’S:

• NCERT Triangles Class 10 Notes
• Triangles Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Triangles
• RD Sharma Solutions Triangles Class 10

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry

In this chapter, students will learn how to find the distance between two points whose coordinates are given, and to find the area of the triangle formed by three given points. Along with this, students will also study how to find the coordinates of the point which divides a line segment joining two given points in a given ratio. For this purpose, students will get introduced to the Distance Formula, Section Formula and Area of a Triangle in this chapter on Coordinate Geometry .

Topics Covered in Class 10 Maths Chapter 7 Coordinate Geometry :

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

Distance Formula

Section Formula

Also, access the following resources for NCERT Class 10 Chapter 7 Coordinate Geometry, at BYJU’S:

• NCERT Coordinate Geometry Class 10 Notes
• Coordinate Geometry Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Coordinate Geometry
• RD Sharma Solutions Coordinate Geometry Class 10

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry

This chapter will introduce students to Trigonometry . They will study some ratios of a right triangle with respect to its acute angles, called trigonometric ratios of the angles. The chapter also defines the trigonometric ratios for angles of 0 0 and 90 0 . Further, students will also know how to calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.

Topics Covered in Class 10 Maths Chapter 8 Introduction to Trigonometry :

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0 o and 90 o . Values of the trigonometric ratios of 30 0 , 45 0 and 60 0 . Relationships between the ratios. TRIGONOMETRIC IDENTITIES Proof and applications of the identity sin 2 A + cos 2 A = 1. Only simple identities to be given

Trigonometry Maths formulas for Class 10 cover three major functions Sine, Cosine and Tangent for a right-angle triangle. Let a right-angled triangle ABC is right-angled at point B and have ∠θ.

Sin θ= \(\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Hypotenuse}\end{array} \) = \(\begin{array}{l}\frac{Perpendicular}{Hypotenuse}\end{array} \) = P/H

Cos θ = \(\begin{array}{l}\frac{Adjacent\, side\, to\, angle\, \theta}{Hypotenuse}\end{array} \) = \(\begin{array}{l}\frac{Base}{Hypotenuse}\end{array} \) = B/H

Tan θ = \(\begin{array}{l}\frac{Side\, opposite\, to\, angle\, \theta}{Adjacent\, side\, to\, angle\, \theta}\end{array} \) = P/B

Trigonometry Table

Trigonometric Ratios of Complementary Angles

sin (90° – A) = cos A,

cos (90° – A) = sin A,

tan (90° – A) = cot A,

cot (90° – A) = tan A,

sec (90° – A) = cosec A,

cosec (90° – A) = sec A

sin 2 A + cos 2 A = 1,

sec 2 A – tan 2 A = 1 for 0° ≤ A < 90°,

cosec 2 A = 1 + cot 2 A for 0° < A ≤ 90°

Also, access the following resources for NCERT Class 10 Chapter 8 Trigonometry, at BYJU’S: 

• NCERT Introduction to Trigonometry Class 10 Notes
• Introduction to Trigonometry Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Introduction to Trigonometry
• RD Sharma Solutions Introduction to Trigonometry Class 10

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

This chapter is the continuation of the previous chapter; here, the students will study the applications of trigonometry . It is used in geography, navigation, construction of maps, and determining the position of an island in relation to the longitudes and latitudes. In this chapter, students will see how trigonometry is used for finding the heights and distances of various objects without actually measuring them. They will get introduced to the term line of sight, angle of elevation, and angle of depression.

Topics Covered in Class 10 Maths Chapter 9 Some Applications of Trigonometry:

HEIGHTS AND DISTANCES – Angle of elevation, Angle of Depression. Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30°, 45°, and 60°.

Important Points –

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e. the case when we raise our head to look at the object.

The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e. the case when we lower our head to look at the point being viewed.

You would need to know the following:

(i) The distance DE at which the student is standing from the foot of the minar

(ii) The angle of elevation, ∠ BAC, of the top of the minar

(iii) The height AE of the student.

Assuming that the above three conditions are known, how can we determine the height of the minar?

In the figure, CD = CB + BD. Here, BD = AE, which is the height of the student.

To find BC, we will use trigonometric ratios of ∠ BAC or ∠ A.

In ∆ ABC, the side BC is the opposite side in relation to the known ∠ A. Our search narrows down to using either tan A or cot A, as these ratios involve AB and BC.

Therefore, tan A = BC/AB or cot A = AB/BC, which on solving, would give us BC.

By adding AE to BC, you will get the height of the minar.

Also, access the following resources for NCERT Class 10 Chapter 9, Some Applications of Trigonometry, at BYJU’S: 

• NCERT Some Applications of Trigonometry Class 10 Notes
• Some Applications of Trigonometry Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Some Applications of Trigonometry
• RD Sharma Solutions Some Applications of Trigonometry Class 10

NCERT Solutions for Class 10 Maths Chapter 10 Circles

In earlier classes, students have studied about a circle and various terms related to a circle, such as a chord, segment, arc, etc. In this chapter, students will study the different situations that arise when a circle and a line are given in a plane. So, they will get thorough with the concept of Tangent to a Circle and Number of Tangents from a Point on a Circle.

Topics Covered in Class 10 Maths Chapter 10 Circles:

Tangent to a circle at point of contact 1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact. 2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

Theorem 10.1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 10.2: The lengths of tangents drawn from an external point to a circle are equal.

Number of Tangents from a Point on a Circle

Case 1: There is no tangent to a circle passing through a point lying inside the circle.

Case 2: There is one and only one tangent to a circle passing through a point lying on the circle.

Case 3: There are exactly two tangents to a circle through a point lying outside the circle.

Also, access the following resources for NCERT Class 10 Chapter 10 Circles at BYJU’S: 

• NCERT Circles Class 10 Notes
• Circles Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Circles
• RD Sharma Solutions Circles Class 10

NCERT Solutions for Class 10 Maths Chapter 11 Constructions

This chapter consists of a total of 2 exercises. Whatever students have learned about construction in earlier classes will also help them. In Exercise 11.1, students will study how to divide a line segment, whereas in Exercise 11.2, they will study the construction of tangents to a circle. Methods and steps for construction are explained, and also some examples are additionally given to make it clearer to the students.

Topics Covered in Class 10 Maths Chapter 11 Constructions :

1. Division of a line segment in a given ratio (internally). 2. Tangent to a circle from a point outside it. 3. Construction of a triangle similar to a given triangle.

Construction 11.1: To divide a line segment in a given ratio.

Construction 11.2: To construct a triangle similar to a given triangle as per the given scale factor.

Construction 11.3: To construct the tangents to a circle from a point outside it.

Also, access the following resources for NCERT Class 10 Chapter 11 Constructions, at BYJU’S:

• NCERT Constructions Class 10 Notes
• Constructions Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Constructions
• RD Sharma Solutions Constructions Class 10

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

This chapter begins with the concepts of the perimeter and area of a circle. Using this concept, the chapter further explains how to find the area of sector and segment of a circular region. Moreover, students will get clarity on finding  the areas of some combinations of plane figures involving circles or their parts.

Topics Covered in Class 10 Maths Chapter 12 Areas Related to Circles :

Area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of segment of a circle, problems should be restricted to the central angle of 60°, 90° and 120° only.

circumference = 2πr

area of the circle = πr 2

Area of the sector of angle θ = (θ/360) × π r 2

Length of an arc of a sector of angle θ = (θ/360) × 2 π r where r is the radius of the circle

Also access the following resources for NCERT Class 10 Chapter 12 Areas Related to Circles at BYJU’S: 

• NCERT Areas Related to Circles Class 10 Notes
• Areas Related to Circles Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Areas Related to Circles
• RD Sharma Solutions Areas Related to Circles Class 10

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

In Chapter 13, there are a total of 5 exercises. The first exercise consists of questions based on finding the surface area of an object formed by combining any two of the basic solids, i.e. cuboid, cone, cylinder , sphere and hemisphere. In exercise 13.2, questions are based on finding the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere. Exercise 13.3 deals with the questions in which a solid is converted from one shape to another. Exercise 13.4 is based on finding the volume, curved surface area and total surface area of a frustum of a cone. The last exercise is optional and has high-level questions based on all the topics of this chapter.

Topics Covered in Class 10 Maths Chapter 13 Surface Areas and Volumes:

Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemisphere

Diameter of sphere = 2r

Surface area of sphere = 4 π r 2

Volume of Sphere = 4/3 π r 3

Curved surface area of Cylinder = 2 πrh

Area of two circular bases = 2 πr 2

Total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr 2

Volume of Cylinder = π r 2  h

Slant height of cone = l = √(r 2  + h 2 )

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = ⅓ π r 2  h

Perimeter of cuboid = 4(l + b +h)

Length of the longest diagonal of a cuboid = √(l 2  + b 2  + h 2 )

Total surface area of cuboid = 2(l×b + b×h + l×h)

Volume of Cuboid = l × b × h

Also, access the following resources for NCERT Class 10 Chapter 13 Surface Areas and Volumes, at BYJU’S: 

• NCERT Surface Areas and Volumes Class 10 Notes
• Surface Areas and Volumes Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Surface Areas and Volumes
• RD Sharma Solutions Surface Areas and Volumes Class 10

NCERT Solutions for Class 10 Maths Chapter 14 Statistics

Here, students will learn the numerical representation of ungrouped data to grouped data and find the Mean, Mode and Median. Also, the concept of cumulative frequency, cumulative frequency distribution and how to draw cumulative frequency curves will be explained.

Topics Covered in Class 10 Maths Chapter 14 Statistics :

Mean, median and mode of grouped data (bimodal situation to be avoided).

The mean of the grouped data  can be found by 3 methods.

• Direct Method: x̅ = \(\begin{array}{l}\frac{\sum_{i=1}^{n}f_i x_i}{\sum_{i=1}^{n}f_i}\end{array} \) , where ∑f i x i is the sum of observations from value i = 1 to n And ∑f i is the number of observations from value i = 1 to n
• Assumed mean method : x̅ = \(\begin{array}{l}a+\frac{\sum_{i=1}^{n}f_i d_i}{\sum_{i=1}^{n}f_i}\end{array} \)
• Step deviation method : x̅ = \(\begin{array}{l}a+\frac{\sum_{i=1}^{n}f_i u_i}{\sum_{i=1}^{n}f_i}\times h\end{array} \)

The mode of grouped data:

The median for a grouped data:

Also, access the following resources for NCERT Class 10 Chapter 14 Statistics, at BYJU’S: 

• NCERT Statistics Class 10 Notes
• Statistics Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Statistics
• RD Sharma Solutions Statistics Class 10

NCERT Solutions for Class 10 Maths Chapter 15 Probability

The last chapter deals with Probability. The chapter starts with the theoretical approach of probability. Subsequently, the chapter explains the difference between  experimental probability and theoretical probability. There are various examples given to  explain it in a n effective way . So, before going through the exercise problems, students must solve the examples of CBSE Maths first.

Topics Covered in Class 10 Maths Chapter 15 Probability:

Classical definition of probability. Simple problems on finding the probability of an event.

• The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as

where we assume that the outcomes of the experiment are equally likely.

• The probability of a sure event (or certain event) is 1.
• The probability of an impossible event is 0.
• The probability of an event E is a number P(E) such that 0 ≤ P (E) ≤ 1
• An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.

Also, access the following resources for NCERT Class 10 Chapter 15 Probability, at BYJU’S: 

• NCERT Probability Class 10 Notes
• Probability Class 10 Important Questions
• NCERT Exemplar Solutions Class 10 Probability
• RD Sharma Solutions Probability Class 10

NCERT Solutions for Class 10 Maths PDF in English Medium, as well as Hindi Medium (हिंदी मीडियम) for the academic year 2023-24, are followed by not only CBSE but also UP Board, Uttarakhand board and all other boards following NCERT Textbooks.

CBSE Class 10 Maths Chapter-wise Marks Weightage for 2023-24

 internal assessment class 10, benefits of ncert solutions class 10 maths:.

The Class 10 NCERT Solutions of Maths given here in PDFs have several benefits, which include:

• The solutions given here are very easy-to-understand.
• Solutions are provided in steps for better understanding.
• Diagrams are given to help the students to visualise the solutions.
• All the questions from each chapter are covered.

Students are advised to prepare all the chapters covered in the solution modules, which will eventually help them to gain a deeper knowledge of concepts. For effective preparations, it is essential for students to understand all the steps provided in the solutions.

How are CBSE Class 10 Maths Solutions of NCERT Helpful for the Board Exams?

CBSE Class 10 Maths is an important subject for students. Here, we have provided complete assistance to students for their preparation. Class 10 is the first benchmark for any student that will reflect in future records of achievement. CBSE always prescribes the NCERT books for exam preparation.

Exam preparation is a rigorous process that requires an overall understanding of individual chapters. This process demands hard work towards studies and an effective approach to getting through the solutions. This significant role is played by NCERT 10 Class Maths Solutions to equip students in preparation for competitive entrance exams. NCERT books are best known for putting forth the concepts in a simple way for better understanding. NCERT Class 10 Books for Mathematics are written in the most lucid and clear manner that helps to break the complex problems in the most efficient way.

Keep visiting to get complete chapter-wise NCERT Solutions for Class 10 Maths PDF free download for all the classes. Students can also find the NCERT Solutions for Class 10 Science , at BYJU’S. Students can download BYJU’S App to get a personalised learning experience and prepare for the exams more effectively.

Frequently Asked Questions on NCERT Solutions for Class 10 Maths

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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.
• Polynomials : Dive into the world of algebraic expressions, factors, and polynomials.
• Pair of Linear Equations in Two Variables : Understand the principles of linear equations and their graphical representations.
• Quadratic Equations : Explore the solutions of quadratic equations and their applications.
• Arithmetic Progressions : Navigate the intricacies of arithmetic progressions and their properties.
• Triangles : Unravel the properties and theorems related to triangles.
• Coordinate Geometry : Explore the Cartesian plane and coordinate geometry concepts.
• Introduction to Geometry : Grasp the basics of Geometry.
• Some Applications of Trigonometry : Apply trigonometric concepts to solve real-world problems.
• Circles : Understand the properties and theorems related to circles.
• Constructions : Explore geometric constructions using a compass and straightedge.
• Area Related to Circles : Grasp the concepts of areas related to circles and their applications.
• Surface Area and Volumes : Navigate through problems related to surface areas and volumes of different shapes.
• Statistics : Understand the basics of statistics, including mean, median, and mode.
• Probability : Explore the fundamentals of probability and its applications.

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.

NCERT Solutions for Class 10 Maths

Ncert solutions for class 10 maths – free pdf.

Have you ever had this thought running in your mind that why suddenly the pressure of getting good grades increases once you start your 10 th grade? Well that’s because of the first time you are going to face a national level exam i.e. 10 th board examination. The marksheet of 10 th boards seem very important as it will always be in your resume unlike the other school exam’s result you have given till date. CBSE believes in to test only not the theoretical knowledge of the subject but also if the student can actually apply it in real life scenario. Therefore, it is very important for the students to have a very clear understanding and applications taught in the class. The very first step to ace this would be to know the Ncert book in and out.

Luckily, you have Mathongo… Mathongo provides Ncert Maths Solutions for class 10. All the questions of CBSE textbook are covered in NCERT Class 10 Maths Solutions. Free PDF download is also available at this page. All the mathematics solutions of the exercise of the Ncert textbook have been made with the help of the best teachers, academicians and subject experts so that the students score good marks in their first board exams. You can also share the Mathongo link of Class 10 NCERT solutions to your batchmates.

It is not just that NCERT only helps in cracking your class 10 th boards. But also, it is the foundation of your class 11 th and 12 th Mathematics too. On the other hand, many government based exams like JEE, AIIMS, UPSC and NDA prescribe the applicants to have a clear knowledge of the CBSE Ncert textbook as the questions are directly or indirectly based from it.

NCERT Class 10 Maths Chapterwise Solutions

• 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

Why Go for Mathongo’s NCERT Maths Solutions for Class 10

Mathongo provides NCERT class 10 maths solution at free of cost online and it’s easily accessible in the form of PDF. Each PDF constitutes of the chapter in which exercise wise solutions are given. It is very easy for the students to locate any answer from the exercise. All the solutions are made with the help of the best teachers and academicians. The solutions are plain easy and can be understood by anyone. The approaches and the methods used to solve the questions are also given in step by step method so that students score good in paper. For additional conceptual clarity, diagrams and formulas are also used.

Mathongo has provided the best solutions for class 10 maths Ncert textbooks. Students can refer these solutions which will help them in solving the previous year question papers. These NCERT maths class 10 solution will help the students to study more effectively and also present the answers in the most effective way to get the highest scores.

The back-end exercise questions given in NCERT books are very important for the class 10 board exams. These exercises often test the conceptual clarity and the subject knowledge of the student. NCERT Solutions will help you to understand these concepts better. On the other hand, the students who have problem in solving maths and require assistance and guidance can also refer class 10 Ncert Maths Solutions to clarify the complex questions concepts. Maths is all about practice. The more you practice, the better you will be in Maths. Maths is really an important subject. You must really focus on it. Ncert maths class 10 pdf download can help students to solve all their problems and also save their time as everything is at one place, one click away.

Which book is best for class 10 maths?

According to me, these are the list of books you can refer to. However, if you are planning to finish one whole book along with NCERT Maths, RD Sharma is more than enough to ace class 10 th boards.

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

Is Ncert enough for Class 10 boards?

It is advisable to study from NCERT for class 10 Board exams as the NCERT math problems helps in the development of understanding of the fundamental concepts of the topics. However, students are welcomed to refer other books such as RS Aggarwal and RD Sharma for more practice. But they must focus on NCERT as the paper designed by CBSE takes account of NCERT questions. Many a times, the questions are directly selected from the Ncert Textbook itself.

Which guide is best for class 10 CBSE?

I would personally recommend to solve Oswaal Question Bank if you are done with practicing Maths and towards your board exams. Ncert is more than enough but still if you wish to practice more. You can choose any reference book such as RD Sharma or RS Aggarwal.

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NCERT Solutions For Class 10 Maths

• NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter-Wise PDF Free Download

NCERT Solutions for Maths serve as a valuable resource for students navigating the complexities of mathematics at the 10th-grade level. These solutions are specifically designed to complement the NCERT class 10 Maths book PDF , offering clear explanations and step-by-step solutions to problems. The aim is to make mathematical concepts more accessible and understandable for students. Students can rely on these solutions to reinforce their understanding of fundamental mathematical principles and enhance problem-solving skills. One notable advantage of NCERT Solutions Class 10 Maths is their alignment with the curriculum prescribed by the Central Board of Secondary Education (CBSE) . This ensures that students are well-prepared for their board exams, as the solutions closely follow the CBSE class 10th maths guidelines and exam patterns.

Chapter-Specific NCERT Solutions for Class 10 Maths

Given below are the chapter-wise NCERT Solutions for Class 10 Maths . You can use it as your 10th maths guide . Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Note: The chapters on constructions have been excluded from the Class 10 Maths textbook for the 2024-25 academic year.

Glance on NCERT Solutions for Class 10 Maths | Vedantu

NCERT Solutions for Class 10 Maths for all the chapters and exercises from Chapters 1 to 14 are provided.

Practicing the textbook questions using these solutions can help students analyze their level of preparation and understanding of concepts.

The link also provides details about the exam pattern, marks weightage, and question paper design for CBSE Class 10 Maths.

The chapters include topics like Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Triangles, Coordinate Geometry, Introduction to Trigonometry, and more.

It also provides resources such as class notes, important questions and formulas, exemplar solutions, and other recommended books for further reference.

Get an idea about “ How will the Paper of NCERT Class 10 Maths be Conducted? ”

NCERT Solutions for Class 10 Maths Chapter Details, Formulas and Exercises PDF

Chapter 1 - real numbers.

In Class 10, Chapter 1 introduces real and irrational numbers. It begins with Euclid’s Division Lemma, stating that if you have two positive numbers, a and b, you can divide a by b and get a unique quotient q and remainder r. Euclid’s Division algorithm uses this idea to find the Highest Common Factor (HCF) of two positive numbers. Then, the chapter talks about the Fundamental Theorem of Arithmetic, which helps find both the Lowest Common Multiple (LCM) and HCF of two positive numbers. Lastly, it covers irrational and rational numbers, along with their decimal forms, using this theorem.

Topics Covered in Class 10 Maths Chapter 1 Real Numbers :

Real Numbers

Euclid’s Division Lemma

Fundamental Theorem of Arithmetic

Irrational Numbers

Rational Numbers

Important Steps:

The Fundamental Theorem of Arithmetic talks about how every number can be expressed as a unique product of prime numbers. To understand this, we look at examples and reasons. We also prove that $sqrt{2}, \sqrt{3},$ and $\sqrt{5}$ are irrational.

To find the highest common factor (HCF) of two positive numbers, follow these steps:

Use Euclid’s division method to divide the larger number by the smaller one. This gives a quotient and a remainder.

If the remainder is zero, the smaller number is the HCF. If not, repeat the division with the smaller number and the remainder.

Keep repeating this process until the remainder becomes zero. The divisor at this stage will be the HCF. This works because the HCF of two numbers is the same as the HCF of the smaller number and the remainder.

Students can access extra study materials for Real Numbers on Vedantu. These resources are available for download, offering additional support for your studies.

Real Numbers Important Questions

Real Numbers Important Formulas

Real Numbers Revision Notes

Real Numbers NCERT Exemplar Solutions

Real Numbers RD Sharma Solutions

Chapter 2 - Polynomials

The Polynomials chapter covers different types of polynomials like linear, quadratic, and cubic. It starts by explaining what the degree of a polynomial means. There are four exercises in total, one of which is optional.

Exercise 2.1 focuses on figuring out the number of zeroes using graphs. You'll need to understand what zeroes of a polynomial mean in terms of geometry.

Exercise 2.2 is about the connection between zeroes and coefficients of a polynomial. You'll be finding zeroes of quadratic polynomials and sometimes even figuring out the polynomial itself.

Exercise 2.3 introduces the division algorithm concept, with related questions.

The optional exercise, 2.4, combines questions from all the concepts in Chapter 2.

Focus on the steps to derive the Division Algorithm for polynomials as it is an important concept in the chapter.

Topics Covered in Class 10 Polynomials

Zeros of a polynomial. 

Relationship between zeroes 

Coefficients of quadratic polynomials only.

Arrange in Standard Form: First, we line up the terms of the numbers we're dividing so that the highest powers come first. This is called the standard form.

Step 1 - To get the first term of the quotient, divide the dividend's highest degree term by the divisor's highest degree term. Then, complete the dividing procedure.

Step 2 - To calculate the second term of the quotient, divide the highest degree term of the new dividend by the divisor's highest degree term. Continue the dividing process.

Step 3 - Now, the remainder's degree is smaller than the divisor's. So we can't prolong the separation any further.

Dividend = Divisor × Quotient + Remainder. What we are doing here is using an approach similar to Euclid's division algorithm, which you discussed in Chapter 1.

This states that.

If p(x) and g(x) are two polynomials with g(x) ≠ 0, we may find polynomials q(x) and r(x) such that

P(x) = g(x) × q(x) + r(x).

Where r(x) = 0 or  degree of r(x) <  degree of g(x).

This conclusion is referred to as the Division Algorithm for Polynomials.

Students can access extra study materials for Polynomials on Vedantu. These resources are available for download, offering additional support for your studies.

Polynomials Important Questions

Polynomials Important Formulas

Polynomials Revision Notes

Polynomials NCERT Exemplar Solutions

Polynomials RD Sharma Solutions

Chapter 3 - Pair of Linear Equations in Two Variables

Chapter 3 is about the linear equations in two variables. There are 7 exercises in this section. It explains what two-variable linear equations are and how to solve them.

Exercise 3.1, representing a problem or situation algebraically and graphically is taught. 

Exercise 3.2, depicts the methods of solving linear equations by graphical method.

Exercises 3.3, 3.4, 3.5 and 3.6 explain different methods for solving pairs of linear equations: algebraic, cross-multiplication, elimination, and substitution. 

Exercise 3.7  is an optional exercise as it has questions from all the previous exercises.

Topics Covered in Class 10 Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. 

Algebraic conditions for number of solutions. 

Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination. 

Simple situational problems. 

Simple problems on equations reducible to linear equations.

A pair of two-variable linear equations and a graphical technique for solving them, as well as consistency and inconsistency. Number of solutions is subject to algebraic conditions. Solve a pair of linear equations in two variables algebraically - using substitution and elimination. Simple situational problems.

The equations typically look like this:

The general form for a pair of linear equations in two variables, x and y, is

$a_1 x + b_1 y + c_1 = 0$

and $a_2 x + b_2 y + c_2 = 0$

where $a_1, b_1, c_1, a_2, b_2, c_2$ are real numbers

To solve them algebraically, you can use substitution or elimination methods.

Here are some key formulas to remember:

$a_1^2 + b_1^2 \neq 0$

$a_2^2 + b_2^2 \neq 0$

Students can access extra study materials for Pair of Linear Equations in Two Variables on Vedantu. These resources are available for download, offering additional support for your studies.

Pair of Linear Equations in Two Variables Important Questions

Pair of Linear Equations in Two Variables Important Formulas

Pair of Linear Equations in Two Variables Revision Notes

Pair of Linear Equations in Two Variables NCERT Exemplar Solutions

Pair of Linear Equations in Two Variables RD Sharma Solutions

Chapter 4 - Quadratic Equations

Chapter 4 focuses on quadratic equations. This chapter defines a quadratic equation and discusses several strategies for solving them. It also goes over the factorization approach for solving quadratic equations and the square method. The chapter describes the links between discriminants and the nature of roots. This chapter also provides instances of real-world challenges that have been solved. The chapter concludes with a discussion of determining the roots of a quadratic equation $ax^2 + bx + c = 0$.

If $b^2 - 4ac > 0$, the equation has two unique real roots.

Find two equal roots of $b^2 - 4ac = 0$.

No genuine roots if $b^2 - 4ac < 0$.

Topics Covered in Class 10 Quadratic Equations

Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). 

Solutions of quadratic equations (only real roots) by factorization, and by using the quadratic formulas. 

Relationship between discriminant and nature of roots. 

Situational problems based on quadratic equations.

The conventional form of a quadratic equation is $ax^2 + bx + c = 0$ where a ≠ 0. Quadratic equations (only real roots) can be solved by factoring and applying the quadratic formula. Relationship between the discriminant and the nature of roots.

Situational questions based on quadratic equations relating to daily activities have to be included.

If $b^2 - 4ac > 0$, we obtain two unique real roots.   

$-\dfrac{b}{2a}+\dfrac{\sqrt{b^2-4ac}}{2a}$ and $-\dfrac{b}{2a}-\dfrac{\sqrt{b^2-4ac}}{2a}$

If $b^2 - 4ac = 0$, then 

$x=-\dfrac{b}{2a}\pm 0$

So, the roots of the equation $ax^2 + bx + c = 0$ are both $-\dfrac{b}{2a}$.

As a result, we may conclude that the quadratic equation $ax^2 + bx + c = 0$ has two equal real roots in this situation.

If $b^2 - 4ac < 0$, there is no real number whose square equals $b^2 - 4ac$. As a result, the above quadratic equation does not have any real roots.

The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is defined as $b^2 - 4ac$.

So, a quadratic equation $ax^2 + bx + c = 0$ has

(i) two distinct real roots, if $b^2 - 4ac > 0$,

(ii) two equal real roots, if $b^2 - 4ac = 0$,

(iii) no real roots, if $b^2 - 4ac < 0$.

Students can access extra study materials for Quadratic Equations on Vedantu. These resources are available for download, offering additional support for your studies.

Quadratic Equations Important Questions

Quadratic Equations Important Formulas

Quadratic Equations Revision Notes

Quadratic Equations NCERT Exemplar Solutions

Quadratic Equations RD Sharma Solutions

Chapter 5 - Arithmetic Progressions

This chapter introduces a new topic to the students - Arithmetic Progression, commonly called AP. The chapter constitutes a total of 4 exercises. Learn what AP is, the derivation of the nth term, finding the sum of first n terms of the AP and solving the real-life problems using AP in this chapter.

Exercise 5.1 of the chapter teaches how to represent a problem or situation in the form of AP, how to find the first term and difference of the AP and to find whether the given series is AP or not. 

Exercise 5.2 explains how to find the nth term of the AP using the formula. 

$a_n = a + (n-1) d$

Exercise 5.3 describes how to find the sum of the first n terms of AP and contains questions related to the topic. 

Exercises 5.4 have questions related to the topics taught in the chapter.

Topics Covered in Class 10 Arithmetic Progressions

Motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of A.P. and their application in solving daily life problems.

Important Formulas

The sequence $a_1, a_2, a_3, a_4, a_5, a_6,…$ of AP terms is written as a, a+d, a+2d, a+3d, a+4d, a+5d, …., nth term , where $a_n$ is the initial term, d is the common difference between each term.

The nth term for arithmetic progression is given as,

$a + (n-1) d$

Sum of the first n terms in Arithmetic Progression.

$S_n = \dfrac{n}{2}[2a + (n-1) d]$.

Students can access extra study materials for Arithmetic Progressions on Vedantu. These resources are available for download, offering additional support for your studies.

Arithmetic Progressions Important Questions

Arithmetic Progressions Revision Notes

Arithmetic Progressions NCERT Exemplar Solutions

Arithmetic Progressions RD Sharma Solutions

Chapter 6 - Triangles

Chapter 6 of class 10 gives details about the triangles. The chapter gives details about the figures with the same shape but different sizes. It explains the similarity of the triangles, theorems associated with the similarity of triangles and the concept of congruent triangles. Further, theorems related to areas of triangles, the Pythagoras theorem and the converse of Pythagoras theorem is explained.

Topics Covered in Class 10 Triangles

Concept of a similar and congruent figure

Theorems related to the similarity of triangles

Areas of similar triangles

Pythagoras Theorem and converse of Pythagoras Theorem

Definitions, Examples, and Counterexamples for Similar Triangles.

If a line is drawn parallel to one side of a triangle and intersects the other two sides at separate spots, the remaining two sides are split in the same ratio - Prove

A line that splits two sides of a triangle in the same ratio is parallel to the third side - Motivate

If the angles of two triangles are equal, the sides are proportionate, and the triangles are identical - Motivate

If the sides of two triangles are proportionate, their angles are equal, and the triangles are identical - Motivate

If one angle of a triangle equals one angle of another triangle, and the sides that include these angles are proportionate, the two triangles are comparable - Motivate

Important Theorems:

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Theorem 6.2: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Theorem 6.3: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar.

Theorem 6.4: If in two triangles, the sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal, and hence the two triangles are similar.

Theorem 6.5: If one angle of a triangle is equal to one angle of the other triangle and the sides, including these angles, are proportional, then the two triangles are similar.

Theorem 6.6: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Theorem 6.7: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

Theorem 6.8: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Theorem 6.9: In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Students can access extra study materials for Triangles on Vedantu. These resources are available for download, offering additional support for your studies.

Triangles Important Questions

Triangles Revision Notes

Triangles NCERT Exemplar Solutions

Triangles RD Sharma Solutions

Chapter 7 - Coordinate Geometry

Chapter 7 introduces coordinate geometry, which is the mathematical process of identifying a given location using an ordered pair of integers. Coordinate or cartesian geometry is used to calculate the distance between two places given their coordinates. The notion of calculating the area of a triangle formed by three specified points. In addition, the chapter explains how to get the coordinates of the point that splits a line segment connecting two specified points in a certain ratio. This chapter of NCERT Solutions teaches students about the distance formula, the section formula, and the area of triangles.

Topics Covered in Class 10 Coordinate Geometry

Concepts of coordinate geometry

Graphs of linear equations

Distance formula 

Section formula (Internal division)

Important Formulas:

Distance Formula: $PQ = \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

Section Formula: $m_1: m_2=\left(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}\right)$

Area of Triangle: = $\frac{1}{2}\left[x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right]$

Students can access extra study materials for Coordinate Geometry on Vedantu. These resources are available for download, offering additional support for your studies.

Coordinate Geometry Important Questions

Coordinate Geometry Revision Notes

Coordinate Geometry NCERT Exemplar Solutions

Coordinate Geometry RD Sharma Solutions

Chapter 8 - Introduction to Trigonometry

Chapter 8 of NCERT Solutions introduces trigonometry to the students. Trigonometry is the study of the ratio of right triangles with respect to the acute angles, which are known as trigonometric ratios of the angles. Know the trigonometric ratios for angles $0^{\circ}$ and $90^{\circ}$ and the values of $30^{\circ}, 45^{\circ}$ and $60^{\circ}$. Students will also learn to calculate trigonometric ratios for the given angles and also a few trigonometric identities. The introductory formulas of trigonometry help to have a strong grip over the basics. In addition to the formulas, the relationship between the ratios and angles is also explained in the chapter.

Topics Covered in Class 10 Introduction to Trigonometry

Trigonometric ratios of an acute angle of a right-angled triangle. 

Proof of their existence. 

Values of the trigonometric ratios. 

Relationships between the ratios.

Trigonometry Maths formulae for Class 10 include the three major functions Sine, Cosine, and Tangent for a right-angle triangle. Let ABC be a right-angled triangle with ∠θ at point B.

$\sin \theta = \dfrac{\text{Side opposite to angle }\theta}{\text{Hypotenuse}} = \frac{\text { Perpendicular }}{\text { Hypotenuse }}$

$\cos \theta = \dfrac{\text{Adjacent side to angle }\theta}{\text{Hypotenuse}} = \dfrac{\text{Base}}{\text { Hypotenuse }}$

$\tan \theta = \dfrac{\text { Side opposite to angle } \theta }{\text { Adjacent side to angle } \theta}$

$\sec \theta = \frac{1}{\cos \theta}$

$\cot \theta = \frac{1}{\tan \theta}$

$\text{cosec} \theta = \frac{1}{\sin \theta}$

$\tan \theta = \frac{\sin \theta}{\cos \theta}$

Trigonometry Table

Trigonometric Ratios of Complementary Angles

$\sin (90^\circ - A) = \cos A$

$\cos (90^\circ - A) = \sin A$

$\tan (90^\circ - A) = \cot A$

$\cot (90^\circ - A) = \tan A$

$\sec (90^\circ - A) = \text{cosec} A$

$\text{cosec} (90^\circ - A) = \sec A$

$\sin^2 A + \cos^2 A = 1$

$\sec^2 A - \tan^2 A = 1$ for $0^\circ \leq  A < 90^\circ$

$\text{cosec}^2 A = 1 + \cot^2 A$ for $0^\circ < A \leq  90^\circ$

Students can access extra study materials for Introduction to Trigonometry on Vedantu. These resources are available for download, offering additional support for your studies.

Introduction to Trigonometry Important Questions

Introduction to Trigonometry Revision Notes

Introduction to Trigonometry & Its Equations NCERT Exemplar Solutions

Chapter 9 - Some Applications of Trigonometry

Chapter 9 is the continuation of Chapter 8 where the students will learn about the application of trigonometry. This chapter helps to understand how trigonometry is applied to our everyday life to find out the height and distance of various objects without measuring them, how it is used in navigation, map production, and calculating an island's location relative to longitudes and latitudes. They will learn about the terms line of sight, angle of elevation, and angle of depression.

Topics Covered in Class 10 Maths Chapter 9 - Some Applications of Trigonometry:

In Chapter 9, we delve into "Some Applications of Trigonometry" with a focus on "Heights and Distances." This involves exploring angles of elevation and depression, specifically at 30°, 45°, and 60°.

Let's understand a few key points:

Line of Sight: This is the line drawn from your eye to the point you're looking at.

Angle of Elevation: When the point you're viewing is above your eye level, like when you tilt your head up.

Angle of Depression: When the point you're viewing is below your eye level, like when you lower your head.

To apply these concepts practically to solve problems related to heights and distances, consider three key factors:

The distance from the observer (DE) to the base of the object (minar).

The angle of elevation (∠BAC) from the observer to the top of the object.

The height of the observer (AE).

Assuming you know these three conditions, you can determine the height of the object (minar). In the figure, we observe that CD equals CB plus BD. Here, BD is equivalent to AE, which represents the height of the observer.

To find BC, we utilize trigonometric ratios involving ∠BAC or ∠A in triangle ABC. Since BC is the opposite side concerning the known ∠A, our options are narrowed down to using either tan A or cot A, as these ratios involve AB and BC.

Therefore, we can use tan A = BC/AB or cot A = AB/BC to find BC. Adding AE to BC yields the height of the minar.

Students can access extra study materials for Some Applications of Trigonometry on Vedantu. These resources are available for download, offering additional support for your studies.

Some Applications of Trigonometry Important Questions

Some Applications of Trigonometry Revision Notes

Some Applications of Trigonometry RD Sharma Solutions

Chapter 10 - Circles

You have learned about circles and related terms like chords, segments, and arcs previously. Now, we are going to learn situations where a circle and a line are on the same plane. This chapter focuses on understanding Tangents to a Circle and the Number of Tangents from a Point on a Circle.

Prove the Tangent to a Circle at Point of Contact

1. The tangent at any point of a circle is perpendicular to the radius through the point of contact.

2. The lengths of tangents drawn from an external point to a circle are equal.

Tangent to a circle at the point of contact

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The lengths of tangents drawn from an external point to a circle are equal.

Theorem 10.1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem 10.2 : The lengths of tangents drawn from an external point to a circle are equal.

Case-based Theorem

Number of Tangents from a Point on a Circle

Case 1: There is no tangent to a circle passing through a point lying inside the circle.

Case 2: There is one and only one tangent to a circle passing through a point lying on the circle.

Case 3: There are exactly two tangents to a circle through a point lying outside the circle.

Topics Covered in Class 10 Circles

Various terms related to a circle such as a chord, segment.

Important Theorems

Tangent to a Circle.

Number of Tangents from a Point on a Circle.

Students can access extra study materials for Circles on Vedantu. These resources are available for download, offering additional support for your studies.

Circles Important Questions

Circles Revision Notes

Circles NCERT Exemplar Solutions

Circles NCERT RD Sharma Solutions

Chapter 11 - Areas Related to Circles

As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle are clarified here. This chapter further explains how to find the area of the figures that contains a circle or part of a circle.

Topics Covered in Class 10 Areas Related to Circles

Calculate the area of a circle

Area of sectors and segments of a circle. 

Problems based on areas and perimeter.

Circumference of the above plane figures.

(When computing the area of a circle segment, only the central angles of 60°, 90°, and 120° should be considered.)

Important formulas from within the chapter for the students to practice–

Circumference = $2 \pi r$

Area of the circle = $\pi r^2$

Area of the sector of angle $\theta = \dfrac{\pi}{360} \times \pi r^2$

Length of an arc of a sector of angle $\theta = \dfrac{\pi}{360} \times 2 \pi r$ where r is the radius of the circle

Students can access extra study materials for Area Related to Circles on Vedantu. These resources are available for download, offering additional support for your studies.

Areas Related to Circles Important Questions

Areas Related to Circles Revision Notes

Areas Related to Circles NCERT Exemplar Solutions

Areas Related to Circles RD Sharma Solutions

Chapter 12 - Surface Areas and Volumes

Chapter 12 is about the surface areas and volumes of different objects and shapes. In the five Exercises of this chapter

Exercise 12.1 consists of questions on calculating the surface area of an object made by combining any two of the fundamental solids, namely cuboid, cone, cylinder, sphere, and hemisphere. 

Exercise 12.2, questions are focused on determining the volume of objects generated by merging any two cuboids, cones, cylinders, spheres, or hemispheres. 

Exercise 12.3 addresses the questions in which a solid is transformed from one shape to another.

Exercise 12.4 requires you to calculate the volume, curved surface area, and total surface area of a cone's frustum. The final exercise is optional and consists of high-level questions covering all of the chapter's subjects.

Topics Covered in Class 10 Surface Areas and Volumes

Surface areas and volumes of combinations of any two figures like cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

Problems that involve converting one type of metallic solid into another and other mixed problems.

Important Formulas Used for Calculating Surface Areas and Volumes of Different Objects

TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemispheres

Diameter of sphere = 2r

The surface area of sphere = 4 π r2

The volume of Sphere = 4/3 π r3

The curved surface area of Cylinder = 2 πrh

Area of two circular bases = 2 πr2

The total surface area of Cylinder = Circumference of Cylinder + Curved surface area of Cylinder = 2 πrh + 2 πr2

Volume of Cylinder = π r2 h

Slant height of cone = l = √(r2 + h2)

Curved surface area of cone = πrl

Total surface area of cone = πr (l + r)

Volume of cone = ⅓ π r2 h

Perimeter of cuboid = 4(l + b +h)

Length of the longest diagonal of a cuboid = √(l2 + b2 + h2)

Total surface area of cuboid = 2(l×b + b×h + l×h)

Volume of Cuboid = l × b × h

Students can access extra study materials for Surface Areas and Volume on Vedantu. These resources are available for download, offering additional support for your studies.

Surface Areas and Volumes Important Questions

Surface Areas and Volumes Revision Notes

Surface Areas and Volumes NCERT Exemplar Solutions

Surface Areas and Volumes RD Sharma Solutions

Chapter 13 - Statistics

This is another excellent chapter in which students learn about the numerical representation of data, whether grouped or ungrouped. Learn how to find the mean, median, and mode of a given dataset. In the following assignment, you will learn about the cumulative frequency distribution and construct cumulative frequency curves.

Topics Covered in Class 10 Statistics

Mean, median and mode of grouped data. 

Mean by Direct Method and Assumed Mean Method only.

There are three ways to determine the mean of the grouped data.

The direct method is: $\bar{x} = \frac{\sum_{i=1}^n f_i x_i}{\sum_{i=1}^n f_i}$ 

Where ∑fi xi is the total of observations from value i = 1 to n. ∑fi represents the number of observations from i = 1 to n.

Assumed Mean Method: $\bar{x} = a+\frac{\sum_{i=1}^n f_i d_i}{\sum_{i=1}^n f_i}$  

The step deviation approach is: $\bar{x} = a+\frac{\sum_{i=1}^n f_i u_i}{\sum_{i=1}^n f_i} \times h$  

Mode of grouped data:

Mode = $l+\frac{f_1-f_0}{2 f_1-f_0-f_2} \times h$ 

The median for grouped data is:

Median = $l+\frac{\frac{n}{2}-c f}{f} \times h$

Students can access extra study materials for Statistics on Vedantu. These resources are available for download, offering additional support for your studies.

Statistics Important Questions

Statistics Revision Notes

Statistics RD Sharma Solutions

Chapter 14 - Probability

Chapter 14 begins with the theoretical approach to probability.  discusses and illustrates the distinction between experimental and theoretical probability.  The chapter is full of examples that help learners understand the idea of probability. Probability is also a very essential chapter for students to focus on, as it will be studied further grades. To stay up with the formulae and new subjects introduced in higher classes, students must first master the fundamentals of the chapter in class 10.

Topics Covered in Class 10 Probability

Classical definition of probability. 

Simple problems on finding the probability of an event.

The theoretical probability (also known as classical probability) of an event E, denoted as P(E), is

$P(E)=\frac{\text { Number of outcomes favourable to } E}{\text { Number of all possible outcomes of the experiment }}$

We assume that the experiment's outcomes are equally likely.

The probability of a definite event (or certain event) is one.

The chance of an impossible event is zero.

The probability of an occurrence E is a number P(E), where 0 < P(E) ≤ 1.

An elementary occurrence is one that has only one possible conclusion. The total of the probability of all elementary occurrences in an experiment equals one.

Students can access extra study materials for Probability on Vedantu. These resources are available for download, offering additional support for your studies.

Probability Important Questions

Probability Revision Notes

Probability RD Sharma Solutions

CBSE Class 10 Maths Chapter-Wise Marks Weightage

Internal assessment for cbse class 10 maths, cbse class 10 maths exam pattern for 2024-25.

The CBSE Class 10 Maths Exam Pattern for 2024-25 consists of two parts:

Internal Assessment: This is conducted by the school throughout the year and carries 20 marks. It typically includes periodic tests, project work, and other activities.

Board Exam: This is a 3-hour pen-and-paper exam conducted by the CBSE and carries 80 marks. The exam pattern is as follows:

CBSE Class 10th New Plan 2024-25

The following are some major changes that are planned to be introduced in the new CBSE Exam Pattern:

Question papers will be designed to assess students' problem-solving and analytical skills.

The paper design will be revised to include more short answer-type questions, like those ranging from 1 to 5 points.

Some vocational course exams might be held in February, and final board exams will be completed in March within 15 days.

Following the early completion of boards, the results are likely to be announced earlier than the existing structure's schedule.

Benefits of Refering to Vedantu’s NCERT Solutions for Class 10 Maths

The Vedantu’s Class 10 NCERT Solutions of Maths provided here in PDFs offer various benefits, including:

The answers provided here are simple and straightforward.

To facilitate comprehension, solutions are presented in phases.

Students are provided diagrams to assist them visualise the solutions.

All of the questions from each chapter are answered.

Students are urged to prepare all of the chapters covered in the solution modules, as this will help them obtain a deeper understanding of subjects. 

For effective preparations, comprehend all of the processes outlined in the answers.

Important Tips for Scoring Well in the Board Exams

Class 10 is an important class in most students’ school lives and is the first class where the students have to appear for a board exam. The class may seem daunting but if the students have been thorough with their studies or the whole academic year then it will not be difficult for them to score good marks at all. To achieve a good score it is necessary that the students keep the following tips and suggestions in mind for the whole year and especially while preparing for the exams.

1. Regular Revision is Key:

Consistency in revising and practicing daily lessons is crucial.

Regular practice ensures a better understanding and prevents topics from becoming overwhelming during exams.

2. Practice Extensively:

Practice all examples and exercises in the NCERT book .

Utilize solutions PDF for self-assessment and focus on areas with incorrect answers.

Refer to Vedantu's solutions for additional practice and clarity.

3. Concept Clarity Matters:

Seek teacher assistance for any doubts promptly.

Utilize Vedantu's Solutions PDF for easy-to-understand explanations.

Ensure a clear understanding of all concepts well in advance of exams.

4. Understand Syllabus and Paper Pattern:

Familiarize yourself with the syllabus, topic weights, and exam pattern.

This knowledge aids in efficient exam preparation.

5. Effective Time Management:

Create a timetable considering topic weights and personal strengths/weaknesses.

Set daily and weekly goals for focused and motivated study sessions.

Include breaks for effective learning and retention.

6. Identify Strengths and Weaknesses:

Allocate equal time to all topics; practice weaker areas more.

Ensure confidence in every topic by thorough practice.

7. Note-taking for Consolidation:

Write down theorems and formulas for consolidation and quick revision.

Notes act as a reference point and aid in better memorization.

8. Class 10 Maths Resources:

Master with our detailed class 10th Maths Guide.

Practice sample papers and previous years' question papers.

Understand the question patterns to prepare effectively.

Vedantu's website offers sample papers for practice.

9. Prioritize Rest and Preparation:

Ensure a good night's sleep and a healthy meal before the exam.

Gather necessary materials the night before to avoid last-minute stress.

10. Exam Simulation for Time Management:

Practice answering sample papers under timed conditions.

Assess and improve time management skills to attempt all questions.

11. Presenting Answers Effectively:

Answer questions in the order presented in the paper.

Highlight final answers and relevant formulas for clarity.

Avoid leaving any questions unattempted; partial answers can secure marks.

Following the above-mentioned tips and being sincere in your preparation will help you score good marks in the exams. Having a strong base in Maths in Class 10 is definitely beneficial for classes ahead and in the future. This will help you have an edge over others even in competitive exams. Most competitive exams have maths sections and the questions generally asked pertain to what you may have learnt in school. Having a good grip over the formulas and the topics will definitely help you perform well in these exams as well.

CBSE Class 10 Maths Study Materials

Faqs on ncert solutions for class 10 maths.

1. What are the topics covered in Class 10 chapters of Mathematics?

The topics covered in Class 10 chapters of Mathematics are:

1. Real Numbers 

2. Polynomials 

Zeros of a polynomial. 

Relationship between zeroes 

3. Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and graphical method of their solution, consistency/inconsistency. 

Algebraic conditions for number of solutions. 

Solution of a pair of linear equations in two variables algebraically – by substitution and by elimination. 

Simple situational problems. 

4. Quadratic Equations

Standard form of a quadratic equation ax 2 + bx + c = 0, (a ≠ 0). 

Solutions of quadratic equations (only real roots) by factorization, and by using the quadratic formulas. 

Relationship between discriminant and nature of roots. 

5. Arithmetic Progression

6. Triangles 

7. Coordinate Geometry

Concepts of coordinate geometry.

Graphs of linear equations. 

Distance formula. 

Section formula.

8. Introduction to Trigonometry

Trigonometric ratios of an acute angle of a right-angled triangle. 

Proof of their existence. 

Values of the trigonometric ratios. 

9. Some Applications of Trigonometry

Angle of elevation. 

Angle of Depression.

Simple problems on heights and distances.

10. Circles

11. Constructions

Dividing a line segment.

Construction of tangents to a circle.

12. Areas Related to Circles

Area of sectors and segments of a circle. 

13. Surface Areas and Volumes

Problems that involve converting one type of metallic solid into another and other mixed problems. 

14. Statistics

Mean, median and mode of grouped data. 

15. Probability

Classical definition of probability. 

2. How can I cover the whole Maths syllabus of Class 10 on time?

To cover the whole Maths syllabus of class 10 on time, you can refer to NCERT Solutions for class 10 provided by Vedantu. Compiled by a group of experts, these solutions will prove a true guide to you. Whether it's about covering the syllabus or scoring high marks, Vedantu’s NCERT Solutions always comes handy. So, download the solutions today and enjoy studying!

3. Can I get NCERT Solutions for Class 10 Maths for free?

Yes, you can download NCERT Solutions for class 10 Maths PDF completely free of cost from Vedantu’s official website. The solutions are prepared by the experts of Vedantu after a lot of research and these are as per the latest guidelines of CBSE. You can download it hassle free from the official website of Vedantu at free of cost.

4. If I am stuck on any Maths concept or numerical problem of Class 10, will NCERT Solutions help me?

Yes, definitely. NCERT Solutions are designed in such a way that it will help you in concept clearance and then practice. In Mathematics, concept clearance is very much required as the questions will be based on concepts only and you have to solve it logically. 

5. Is NCERT Solutions for Class 10 Maths enough for scoring high in exams?

Scoring high in exams depends on how well you are aware of the concepts and how well you can imply that on numerical and logical problems. NCERT Solutions will help you in clearing your concepts well and building a strong foundation. So, if your concepts are clear, and you practice well, NCERT Solutions are enough to score high marks in the exam.

6. Where will I get Class 10 NCERT Solutions for Maths PDF?

Solutions for Class 10 Mathematics is one of the best ways for you to prepare for your board exam. The solutions are present on Vedantu’s website (vedantu.com) free of cost. Vedantu’s NCERT solutions are available in PDF format so that you can download them and use them to study online. Students can download these from Vedantu mobile app as well. All the solutions are explained in an easy format along with the concepts. With these solutions in your hand, you won’t have to worry about finishing your NCERT syllabus.

7. How to master in Class 10 Maths CBSE?

In order to master your Class 10 CBSE, you need to focus on finishing your NCERT syllabus. This involves solving all the questions and the examples. To help you with this, Vedantu offers NCERT Solutions for Class 10 in PDF format . You can use these as a guide for finishing the NCERT exercises.

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

CBSE Class 10 NCERT Mathematics PDF solutions are nothing short of a blessing for the students. Vedantu offers PDFs of thoroughly written solutions where all the questions from NCERT exercises are explained in detail. Follow these steps to download them:

Visit the page of ‘ NCERT Solutions for Class 10 Maths ’ on the official website of Vedantu (vedantu.com).

Find the exercise for which you want a solution and click on the ‘Download PDF’ link.

The solutions will be downloaded into your system. You’ll also receive a message/ mail with a direct download button of your preferred solution.

9. What do the concepts explained in the NCERT Class 10 Maths Textbook?

The Vedantu’s solutions of Class 10 NCERT Maths textbook can help all the students of Class 10th with helpful tips and tricks for solving math problems. These tricks are provided at the end of all chapters. There are 15 chapters in total that students have to study for the Class 10 exam. All the chapters are explained in a detailed manner by the subject matter experts. 

10. How can I save these Class 10 NCERT Maths Solutions for reference?

Vedantu’s Class 10 NCERT Maths Solutions is the easiest way for you to prepare for your Class 10 exams. These solutions PDF cover the concepts as well as solutions to exercises. If you want to save them for reference, you will have to download their PDF files. There is a separate PDF file for each exercise that you can save on your mobile phone or computer for future reference. If you want, you can print these files for easy access.

11. How to grasp the important concepts covered in the NCERT Solutions for Class 10 Maths?

Students who want to do well in their Class 10 examinations should get NCERT Solutions from Vedantu. The solutions are carefully chosen by a team of academics with extensive knowledge in the field. Every minute element is discussed in an engaging manner to help pupils learn more effectively. The step-by-step answers are developed with the marks weightage provided according to CBSE norms.

12. Will the NCERT Solutions for Class 10 Maths help me to solve problems easily?

The Class 10 test is one of the most significant turning moments in students' lives. Mathematics is mostly a numerical subject, and grasping ideas helps students perform higher. To improve performance, students should first comprehend the academic year's syllabus and then master the ideas based on it. Solving textbook problems by referring to the answers PDF will help pupils enhance their logical thinking and analytical abilities.

13. Are the NCERT Solutions for Class 10 Maths useful for the students under the CBSE board?

The NCERT Maths Solutions for Class 10 provide several benefits,

Building a firm foundation of essential topics and boosting test confidence.

The strategy for addressing complicated problems is simple to learn.

It is an ideal study tool for students who want to complete their projects on time and earn higher grades in tests.

14. How to get an idea about the important concepts in the NCERT Solutions for Class 10 Maths?

Before the start of the academic year, students should download and read the CBSE curriculum to get a good understanding of the subjects that will be included in the tests. Students must tackle NCERT Textbook problems by selecting the appropriate study materials that meet their needs. Students' problem-solving abilities improve when they practise the problems on a regular basis using the NCERT Solutions for Class 10 Mathematics.

15. Is Vedantu’s NCERT Solutions for Class 10 Maths important?

The NCERT Solutions for Class 10 Maths PDFs at Vedantu are designed so that students may quickly comprehend the topics and solve any difficulties. The answers include detailed explanations to make the subject more engaging for pupils. Students can get the PDF of solutions and utilise it to strengthen their conceptual understanding.

16. Is the NCERT Solutions for Class 10 Maths the best reference guide for CBSE students?

Students should choose the best study material for their needs from among the many options available on the market today. The NCERT Solutions for Class 10 Maths from Vedantu is regarded as the greatest reference resource for CBSE students. The solutions are provided in both chapter- and exercise-specific versions, and can be downloaded and utilised by students. Students can view the PDF's links at any time.

NCERT SOLUTIONS FOR CLASS 10

Cbse class 10 study materials.

Scholarships

Test Series

Study Materials

CBSE Class 10

CBSE Class 10 Exam is a milestone in a student's academic journey. It is a turning point that lays the foundation for future success. As the CBSE board exams serve as a benchmark for progress, it is essential for students to have access to comprehensive and top-notch learning resources.

At ALLEN, we recognize the importance of excelling in this pivotal stage of education. That's why we offer free online learning resources designed explicitly for CBSE Class 10 subjects, including Math, Science, English, Hindi, and Social Science.

Students will greatly benefit from a systematic and organized approach to optimising their studies in class 10. Our blog guides and engages Class 10 CBSE students, providing valuable insights, tips, and strategies to make the most of their learning experience.

• 1.0 Overview of CBSE Class 10

Class 10 exams are crucial in a student's academic journey, marking a significant transition point. These exams, especially the CBSE board exams , are not just assessments but are essential in setting the groundwork for future academic and career prospects. The results from these exams play a pivotal role in determining the educational streams and opportunities available to students as they progress to higher secondary education.

These exams test a student's grasp of fundamental concepts, critical thinking, and problem-solving abilities. ALLEN offers a comprehensive selection of free online learning resources for CBSE Class 10 subjects, including Math, Science, English, Hindi, and Social Science, to support students in this vital stage. These resources include CBSE Solutions, past Question Papers, detailed Revision Notes, Syllabus outlines, and Sample Papers, all crafted by qualified educators. 

Highlights of CBSE Class 10 2025 Exam

Discover key Class 10 Board Exam highlights to help you organize your study schedule and understand essential exam terms.

• 2.0 CBSE Class 10 Exam Dates 2025

The official CBSE website, cbse.gov.in, has not released the Class 10 exam dates for the session 2025. The 2024 board exams were held from February 15th to March 13th, 2024, with most subjects being administered from 10:30 AM to 1:30 PM. So, it can be said that the exam for the upcoming session will be conducted in the same duration.

The official date sheet includes both regular and private student exams. Students can download the detailed CBSE Class 10 date sheet in PDF format for future reference. Here is a brief table of the latest exam dates for CBSE Class 10 Exam Dates 2025:

Details in the CBSE Class 10 Date Sheet

The CBSE Class 10 exam date sheet provides students with essential information. It is a comprehensive guide for students to effectively prepare and plan their study schedules.

• Names of the Subjects: List which subjects will be tested for clarity.
• Subject Codes: Unique codes for each subject to ensure accurate identification.
• Important Examination Dates: Key dates for each subject's 2025 CBSE Class 10th Board exam examination.
• Other Exam Schedule Details: Additional information regarding the exam timetable and schedule.
• 3.0 CBSE Class 10 Subjects

The subjects will be covered under the CBSE Class 10 Board curriculum. You must study all these subjects thoroughly to achieve good marks in your board exams.

• Social Science
• 4.0 CBSE Class 10 Syllabus 2025

The CBSE board has issued the CBSE Class 10 syllabus for the academic year 2025. The syllabus is an important study resource for preparing for board exams. The syllabus for class 10th is divided into the following categories:

• Languages - (Group-L)
• Main Subjects - (Group-A1)
• Other Academic Electives -(Group-A2)
• Subject of Internal Assessment

It comprises the course structure, how the unit grades are distributed, and how many periods are allotted for each unit. Students can better organise their studies if they fully comprehend the CBSE Class 10 syllabus 2025. The CBSE board syllabus for Class 10 clarifies the subjects and concepts that must be learned in each subject. The question paper for the board exam is also created using the CBSE 10th syllabus.

You can check the detailed Class 10 syllabus for the academic year 2024-25 here.

• 5.0 CBSE Class 10th Exam Pattern 2025

The Central Board of Secondary Education (CBSE) administers the Class 10 board exams for all CBSE-recognized schools. Students appearing for these exams should be well-versed in the format and updated annually to reflect the latest syllabus and student needs. Here are the critical details of the CBSE Class 10 exam pattern for 2025:

• Exam Structure: A single annual exam will be conducted.
• Marks Distribution: The exam carries a total of 100 marks, divided as follows:
• Board Examination: 80 marks
• Internal Assessment: 20 marks
• Passing Criteria: Students must score at least 33% in the board exam and the internal assessment.
• Question Types: The exam includes both objective and subjective questions.

The table below summarizes the detailed CBSE Class 10 exam pattern:

For detailed information and to download the CBSE class 10th exam pattern 2025, visit the official website: cbse.gov.in .

• 6.0 CBSE Class 10 Study Material

Key Features of CBSE Board Exam Class 10 Study Material:

Study materials provide students with a complete and comprehensive understanding of the subjects. They cover all the topics and concepts required for the curriculum, ensuring students have access to reliable and accurate information.

Experienced teachers make ALLEN's study materials. They are focused on helping students develop high-level skills. The materials are meant to help students prepare for important exams like JEE (Main+Advanced), JEE (Main), NEET(UG), and National/International Olympiads.

List of ALLEN’s Study Materials for CBSE Class 10 Board 

• CBSE Class 10 NCERT PDF Solutions for All Subject
• CBSE Class 10 Sample Papers 
• CBSE Class 10 Previous Year Question Papers

Also Check:

• 7.0 Recommended CBSE Class 10 Books

CBSE Class 10 books are recommended textbooks that align with the CBSE curriculum. They provide comprehensive syllabus coverage and are designed to help students prepare for the board exams. 

• 8.0 CBSE Class 10th Previous Year Question Papers

CBSE Class 10th Previous Year Question Papers benefit students preparing for their board exams. Regular practice with these papers can significantly lower exam anxiety and build self-confidence.

They also give a clear idea of the types of questions that might appear and the topics likely to be included in the actual board exams. By working through more of these past papers, students can enhance their speed, accuracy, confidence, exam approach, and time management skills.

In the table, we have provided CBSE Class 10 Previous Year Question Papers PDF and solutions for your reference. 

• 9.0 CBSE Sample Papers for Class 10

For the 2024-25 exams, CBSE has released sample papers for all Class 10 subjects. These sample papers give students an idea of the exam format as they are based on the updated syllabus and pattern. You can find downloadable PDFs of CBSE Class 10 Sample Papers and the solution here. 

Practicing with these papers helps students gain confidence and become familiar with the types and levels of questions on board exams. Additionally, you can explore more mock tests and sample papers prepared by academic experts at ALLEN.

• 10.0 CBSE Class 10 Admit Card 2025

The CBSE Class 10 admit card is a crucial document for all students taking the board exam. Here's what you need to know about the hall tickets:

Importance:

• Mandatory for Entry: You must bring your admit card to the exam center to be allowed into the examination room.

Distribution:

• Regular Students: Receive admit cards from their schools.
• Private Students: You must download admit cards from the CBSE website.

What to Check:

Once you receive your admit card, review the following details carefully:

• Exam Roll Number
• Exam Centre Location
• Candidate's Name
• Candidate's Photo
• Candidate's Signature
• Subject Names

Ensure all the information is accurate to avoid issues on the exam day.

• 11.0 CBSE Class 10th Result 2025

The Central Board of Secondary Education (CBSE) usually announces the Class 10 results in the first week of May. Students can check their results on the official CBSE websites, cbse.gov.in and cbseresults.nic.in . After the results are released, students should collect their original mark sheets from their schools.

Schools will distribute the original mark sheets once the CBSE Class 10 Result is announced. Students can choose their academic stream from Science, Commerce, or Arts for the next two years. Students who are unsatisfied with their results can request verification and re-evaluation. CBSE is expected to launch the online application process for re-evaluation and verification of results in June 2024.

• 12.0 Class 10 Exams Preparation Tips 2025

The Class 10 board exam is a crucial phase in a student’s life, laying the groundwork for their future career and success. To achieve your goals, it is essential to have a well-structured preparation strategy for the CBSE Class 10 exams. Here are some critical tips for students preparing for the 2025 board exams:

• Focus in Class: Pay close attention during lessons and ensure you go through the entire syllabus sequentially.
• Understand Marking Schemes: Learn the chapter-wise marking schemes for each subject to prepare effectively.
• Organize Study Materials: Collect all necessary handouts and revision tools and keep them organized for easy access during last-minute reviews.
• Use Flashcards: Break down subjects into bullet points, graphs, lists, and formulae. Flashcards can be helpful for memorisation.
• Teach to Learn: Explain answers to someone else. This technique helps reinforce your understanding and highlights areas needing more focus.
• Practice with Past Papers: Solve previous years' CBSE Class 10 exam papers to improve problem-solving speed and time management skills.
• Take Breaks: Short breaks between study sessions are essential to avoid burnout and maintain focus.
• Health and Wellness: Maintain good health, eat nutritious food, and get sufficient sleep to keep your mind and body in optimal condition for studying.

Table Of Contents:

• 1.1 Highlights of CBSE Class 10 2025 Exam
• 2.1 Details in the CBSE Class 10 Date Sheet

Frequently Asked Questions:

Can failing the pre-board exam prevent a student from taking the board exam?

Failing the pre-board exam does not disqualify a student from taking the board exam. Pre-boards are designed to assess a student’s readiness for the board exams. Even if a student fails in the pre-boards, as long as they meet other qualifications, they can still sit for the board exams.

What should I look for in CBSE Board Exam Class 10 study material?

When selecting study material, look for content aligned with the CBSE curriculum, clear explanations, ample practice questions, solved examples, chapter-wise summaries, and supplementary resources like sample papers and previous year question papers.

Do pre-board exam scores count towards the final board exam results?

No, pre-board exam scores are not included in the calculation of final board exam scores.

Can I rely solely on CBSE Class 10 textbooks for exam preparation?

CBSE Class 10 textbooks are the primary resource for exam preparation, covering the prescribed syllabus. However, it is recommended that you supplement your studies with additional practice materials, sample papers, and previous year question papers to enhance understanding and improve exam performance. You can easily access the latest CBSE Class 10 exam from previous years and sample papers at ALLEN.

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Related Articles:-

Cbse class 10 sample papers with solutions.

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CBSE Maths Class 10 Marks Distribution

Abhishek Joshi ,

Oct 22, 2024 | CBSE 10th

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In CBSE Class 12 Maths exam, the total marks are divided into two parts: Theory (70 marks) and Practical (30 marks). Check here CBSE Maths Class 10 Marks Distribution in detail!

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CBSE Maths Class 10 Marks Distribution For Theory Exams

Cbse maths class 10 marks distribution for practical exams, cbse class 10 mathematics marks weightage - chapter wise, how to use cbse maths class 10 marks distribution for study planning.

As per  CBSE Maths Class 10 Marks Distribution, the exam is assessed through two components: Theory (80 marks) and Internal Assessment (20 marks). The theory portion covers key units like Algebra, Geometry, Trigonometry, and Statistics, with a mix of very short, short, and long answer questions, ensuring a comprehensive evaluation of mathematical skills. For internal assessment, students are graded on periodic tests, lab activities, portfolios, and subject enrichment activities, each contributing 5 marks.

Understanding CBSE Maths Class 10 Marks Distribution is important for a student because it helps them plan and prioritize their study efforts effectively. Understanding how much weight each unit or section carries allows students to allocate time based on the importance of the topic. Check this page to know more about CBSE Maths Class 10 Marks Distribution!

Also Read: CBSE Class 10 Question Papers

CBSE Maths Class 10 theory exam is of a total of 80 marks. The detailed marks distribution for theory exams can be checked below:

• Very Short Answer Questions (1 mark each)
• Short Answer Questions (2-3 marks each)
• Long Answer Questions (4-5 marks each)

CBSE Maths Class 10 practical exam is of a total of 20 marks. The detailed marks distribution for theory exams can be checked below:

• Periodic Tests – 5 marks
• Mathematics Lab Work – 5 marks
• Portfolio – 5 marks (student's record of work)
• Subject Enrichment Activities – 5 marks (e.g., projects, practical activities)

Also Read: CBSE Science Class 10 Syllabus Details

The CBSE Class 10 Mathematics syllabus is presented in terms of 7 broad sections. The chapters vary in each unit, and they all are allocated to weight according to their significance and the level of difficulty. Here's how the marks are distributed across various units:

Also Read: CBSE Class 10 Sample Papers

To effectively prepare for the CBSE Class 10 Maths exam, follow these steps based on the marks distribution:

• Prioritize High-Weight Units: Start your revision with Algebra and Geometry, both of which are heavy marks.
• Don’t Neglect Low-Weight Units: Number Systems and Coordinate Geometry for example may not have as many marks, but they are also easier and quicker to revise.
• Consistent Practice: Regular practice is necessary in mathematics. Devote more time to the units like Trigonometry and Mensuration in which you need to apply formulas and concepts.
• Solve Sample Papers: Practising CBSE sample papers will acquaint you with the exam pattern, and the style of questions that are asked.

FAQs on CBSE Maths Class 10 Marks Distribution

Q: What is the distribution of marks for maths class 10?

A: The marks distribution for CBSE Class 10 Mathematics is divided into two parts: Theory (80 marks) and Internal Assessment (20 marks).

Q: What is the marking scheme for maths in CBSE Class 10?

A: The CBSE Class 10 Mathematics marking scheme includes 80 marks for the theory exam (covering units like Algebra, Geometry, and Trigonometry) and 20 marks for internal assessment, which consists of periodic tests, lab work, portfolios, and enrichment activities.

Q: What is the marks distribution of CBSE exams Class 10?

A: The marks distribution for CBSE Class 10 exams typically consists of 80 marks for the theory exam and 20 marks for internal assessment across subjects, including periodic tests, projects, and practical work, ensuring a comprehensive evaluation of students' performance.

Q: What is the weightage of maths marks in CBSE exam?

A: In the CBSE Class 10 exam, Mathematics carries a total weightage of 100 marks, comprising 80 marks for the theory exam and 20 marks for internal assessment, which includes periodic tests and practical work.

Q: How is 10th class mark percentage calculated?

A: To calculate the percentage for Class 10 marks, divide the total obtained marks by the maximum possible marks, then multiply by 100. For example, if a student scores 450 out of 500, the percentage is calculated as (450/500)×100=90%(450 / 500) \times 100 = 90\%(450/500)×100=90%

Q: Which chapter has the highest weightage in maths class 10?

A: In Class 10 Mathematics, the chapter with the highest weightage is Algebra, which typically carries around 20 marks in the theory exam, making it a crucial area for students to focus on.

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