# Download Class 10 Mathematics NCERT Solutions Pdf Free

NCERT solutions for Class 10 mathematics is immensely beneficial for students preparing for their board exams. These solutions, which provide comprehensive answers to the Class 10 Mathematics NCERT Solutions, serve as a valuable resource for understanding complex concepts and problem-solving techniques.

By referring these Class 10 mathematics NCERT solutions, students can clear their doubts and ensure a strong grasp of the syllabus. These solutions are meticulously designed to align with the CBSE curriculum, ensuring that students are well-prepared for their exams.

With step-by-step explanations and detailed answers, the 10th class NCERT solutions make it easier for students to practice and excel in their mathematics exams. The CBSE Class 10 mathematics solutions are particularly helpful in providing a clear and concise understanding of various topics, thus enabling students to achieve better results and build a solid foundation for higher studies.

NCERT Solutions For Class 10 Maths CBSE 2024-25 Edition – Free PDF Download given below Practicing these solutions is essential for students who want to achieve high marks in their Maths board exams. If you’re having trouble with problems from the Class 10 NCERT textbook, you can use our free solutions provided below.

We recommend students practice these solutions, available in PDF format, to easily grasp the basic concepts. For those who find it difficult to find detailed and thorough NCERT Solutions for Class 7, we have created step-by-step solutions with clear explanations. Our expert tutors have prepared these exercises to help you prepare for exams and score well in Maths. Here are the NCERT Solutions for Class 10 Maths

## Class 10 Mathematics NCERT Solutions

The Class 10 Mathematics NCERT Solutions are a comprehensive resource designed to help students excel in their mathematics studies. Covering all 15 chapters included in the Class 10 mathematics syllabus, these solutions provide detailed and accurate answers to every problem presented in the NCERT textbook. With a focus on clarity and thoroughness, the 10th class NCERT solutions offer step-by-step explanations that simplify complex concepts and problem-solving techniques.

These solutions are aligned with the CBSE curriculum, ensuring that students are well-prepared for their exams. Additionally, the NCERT Class X Maths Solutions include answers for miscellaneous exercises, making them a complete reference tool for mastering Class 10 mathematics. Accessible and easy to understand, these solutions are an invaluable aid for students aiming to achieve high scores in their board exams.

Chapter Number | View/Download |
---|---|

1. Real Numbers | View/Download |

2. Polynomials | View/Download |

3. Pair of Linear Equations in Two Variables | View/Download |

4. Quadratic Equations | View/Download |

5. Arithmetic Progressions | View/Download |

6. Triangles | View/Download |

7. Coordinate Geometry | View/Download |

8. Introduction to Trigonometry | View/Download |

9. Some Applications of Trigonometry | View/Download |

10. Circles | View/Download |

11. Constructions | View/Download |

12. Areas Related to Circles | View/Download |

13. Surface Areas and Volumes | View/Download |

## CBSE Class 10 Maths Chapter-Wise Marking Scheme 2024

Unit | Weightage |
---|---|

I. Number systemsChapter 1: Real Numbers | 06 |

II. AlgebraChapter 2: Polynomials Chapter 3: Pair of Linear Equations in Two Variables Chapter 4: Quadratic Equations Chapter 5: Arithmetic Progressions | 20 |

III. Coordinate GeometryChapter 7: Coordinate Geometry | 06 |

IV. GeometryChapter 6: Triangles Chapter 10: Circles | 15 |

V. TrigonometryChapter 8: Introduction to Trigonometry Chapter 9: Some Applications of Trigonometry | 12 |

VI. MensurationChapter 11: Area Related to Circles Chapter 12: Surface Areas and Volumes | 10 |

VII. Statistics & ProbabilityChapter 13: Statistics Chapter 14: Probability | 11 |

Total | 80 |

## Key Features of CBSE Class 10 Maths NCERT Solutions

- These solutions offer comprehensive and detailed answers to all the problems in the NCERT textbook for Class 10 Mathematics, ensuring that every concept is thoroughly explained.
- The step-by-step approach adopted in the 10th class NCERT solutions helps students understand the methodology behind solving each problem, which is crucial for mastering mathematical concepts
- These solutions aligned with the CBSE curriculum, ensuring that students are well-prepared for their board exams.
- The 10 class math NCERT solution cover all chapters and topics systematically, providing a structured learning path.
- Class 10 Mathematics NCERT solutions make complex topics accessible, helping students build a strong foundation in mathematics.
- The 10 class CBSE maths solutions enable students to tackle similar questions with confidence.
- These solutions often incorporate tips and tricks to simplify problem-solving, which can be particularly beneficial during exams.
- NCERT Class X maths solutions are a valuable resource for Class 10 students, offering detailed explanations, structured content, and practical problem-solving strategies that enhance their learning experience and exam readiness of Students.

## Why Choose Ybstudy NCERT Maths Solutions for Class 10

- We offers free NCERT Class 10 Maths solutions online, conveniently accessible as PDFs.
- Each PDF contains chapter-wise solutions for each exercise, making it easy for students to find any answer they need. These Class 10 Mathematics NCERT Solutions are created by top teachers and academicians to ensure clarity and ease of understanding.
- The step-by-step methods provided help students perform well on exams. To enhance conceptual understanding, diagrams and formulas are also included.
- Students can use these solutions to tackle previous years’ question papers effectively.
- These solutions help students study more efficiently and present their answers in the best way to achieve high scores.
- These Class 10 Mathematics NCERT Solutions help students grasp these concepts better.
- Those struggling with Maths can refer to these solutions for guidance on complex questions.
- Success in Maths comes from practice—the more you practice, the better you get.
- The downloadable PDFs of NCERT Maths solutions for class 10 save students time by providing all necessary resources in one place, just a click away.

## How to Study Class 10 Mathematics NCERT Solutions

Studying Class 10 mathematics solutions effectively requires a strategic approach. Begin by thoroughly reviewing the NCERT solutions for Class 10 math, as these provide accurate and detailed answers to the textbook problems. Use the 10th class NCERT solutions as a primary resource to understand each concept step-by-step. Focus on solving problems from the NCERT maths Class 10 book, and cross-reference your answers with the provided solutions to identify any mistakes and understand the correct methodology.

Additionally, regularly practicing problems using the Class 10 mathematics NCERT solutions will help reinforce your understanding and improve problem-solving speed. It’s crucial to break down complex problems into smaller, manageable parts, and then solve each part while referring to the CBSE Class 10 mathematics solutions for guidance.

Utilize the answer of NCERT maths Class 10 to clear any doubts you encounter during your practice. This ensures you grasp the fundamental concepts effectively. Supplement your studies with online resources and video tutorials that explain the Class 10 mathematics NCERT solutions in an easy-to-understand manner.

Lastly, keep a consistent study schedule, revising regularly and solving various types of problems from the NCERT Class X maths solutions to build confidence and proficiency in mathematics. By following this structured approach, you can make the most of the available CBSE Class 10 mathematics solutions and excel in your studies.

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

Studying Class 10 maths solutions, there are several important points to keep in mind to maximize your understanding and performance. First, focus on understanding the fundamental concepts presented in the NCERT Class 10 maths solutions. Each chapter builds on previous knowledge, so having a strong grasp of the basics is crucial.

Pay special attention to the step-by-step methods used in the 10th class NCERT solutions. These detailed explanations help in understanding how to approach and solve different types of problems. Practice regularly with the problems given in the NCERT textbook and cross-check your answers with the Class 10 mathematics NCERT solutions to ensure accuracy. Review the solutions for miscellaneous exercises provided in the NCERT maths Class 10 book. These exercises often contain a mix of problems that can help in testing your overall understanding of the concepts.

Focus on key topics that frequently appear in exams, such as quadratic equations, triangles, and coordinate geometry, which are thoroughly covered in the CBSE Class 10 mathematics solutions. Make sure to understand and practice the examples provided in the solutions, as they often highlight common problem-solving techniques and tips. NCERT Class X maths solutions to clarify any doubts immediately. This will help in building a strong conceptual foundation and avoid confusion later.

## Class 10 Mathematics NCERT Solutions Important Points to Study

Chapter Number | Important Points to Study |
---|---|

1. Real Numbers | – Understand the concept of rational and irrational numbers. |

– Learn to find the HCF and LCM of given numbers. | |

– Understand the Euclid’s division lemma and its applications. | |

2. Polynomials | – Understand the types of polynomials: linear, quadratic, cubic, etc. |

– Learn how to perform operations on polynomials: addition, subtraction, multiplication, and division. | |

– Study factorization methods like factor theorem and remainder theorem. | |

3. Pair of Linear Equations in Two Variables | – Understand what linear equations are and how they are represented graphically. |

– Learn methods to solve pairs of linear equations: substitution method, elimination method, and cross-multiplication method. | |

– Solve word problems involving pair of linear equations. | |

4. Quadratic Equations | – Understand the standard form of a quadratic equation and how to solve it using factorization, completing the square, and formula. |

– Learn how to find the nature of roots of a quadratic equation. | |

– Solve word problems based on quadratic equations. | |

5. Arithmetic Progressions | – Understand the concept of arithmetic progression (AP) and its common difference. |

– Learn to find the nth term and sum of first n terms of an AP. | |

– Solve word problems related to arithmetic progressions. | |

6. Triangles | – Learn about different types of triangles and their properties. |

– Understand the congruence criteria of triangles. | |

– Learn about the Pythagoras theorem and its applications. | |

– Study similarity of triangles and its properties. | |

7. Coordinate Geometry | – Understand the concept of coordinate geometry and the Cartesian plane. |

– Learn about the distance formula and section formula. | |

– Understand how to find the area of a triangle formed by three given points. | |

8. Introduction to Trigonometry | – Understand trigonometric ratios: sine, cosine, and tangent. |

– Learn to find the values of trigonometric ratios for given angles. | |

– Study the trigonometric identities and their applications. | |

9. Some Applications of Trigonometry | – Learn how to solve problems related to heights and distances using trigonometry. |

– Understand how to find the angle of elevation and depression. | |

– Solve real-life problems involving trigonometry. | |

10. Circles | – Understand the properties of circles, chords, tangents, and secants. |

– Learn about the angle subtended by an arc at the center and at a point on the circle. | |

– Study the theorems related to circles and their applications. | |

11. Constructions | – Learn basic constructions using ruler and compass. |

– Understand how to construct bisectors of line segments and angles. | |

– Study constructions of triangles, quadrilaterals, and circles. | |

12. Areas Related to Circles | – Understand the concept of areas related to circles: sector, segment, and the area of a combination of figures. |

– Learn how to find the area of a sector and segment of a circle. | |

– Solve problems based on areas related to circles. | |

13. Surface Areas and Volumes | – Understand the concept of surface areas and volumes of different solid shapes: cube, cuboid, cylinder, cone, and sphere. |

– Learn how to find the surface area and volume of these solids. | |

– Solve problems involving surface areas and volumes of solids. |

## CBSE Class 10 Mathematics Syllabus

Chapter Number | Description and Importance |
---|---|

1. Real Numbers | Students learn about the properties of real numbers, including rational and irrational numbers. They explore Euclid’s division lemma, fundamental theorem of arithmetic, and methods to find HCF and LCM. Understanding real numbers and their properties forms the foundation for higher mathematics. Knowledge of HCF and LCM is crucial for solving various mathematical problems. |

2. Polynomials | This chapter covers different types of polynomials (linear, quadratic, cubic) and operations on them. Students learn about the factor theorem, remainder theorem, and methods to factorize polynomials. Polynomials are a fundamental concept in algebra. Mastering polynomials helps in understanding higher algebraic concepts and solving algebraic equations. |

3. Pair of Linear Equations in Two Variables | Students explore methods to solve pairs of linear equations, such as the graphical method, substitution method, elimination method, and cross-multiplication method. Solving linear equations is a critical skill for mathematical modeling and problem-solving in various real-life situations and advanced mathematics. |

4. Quadratic Equations | This chapter focuses on quadratic equations, including their standard form, methods to solve them (factorization, completing the square, quadratic formula), and the nature of roots. Quadratic equations are widely used in science and engineering. Understanding how to solve them is essential for tackling more complex mathematical problems. |

5. Arithmetic Progressions | Students learn about arithmetic progressions (AP), their common difference, nth term, and the sum of the first n terms. Arithmetic progressions are used in various fields, including economics and computer science. Knowledge of AP helps in understanding sequences and series, which are crucial for higher studies in mathematics. |

6. Triangles | This chapter covers the properties and types of triangles, congruence criteria, Pythagoras theorem, and the concept of similarity in triangles. Triangles are a fundamental shape in geometry. Understanding their properties and theorems is vital for advanced geometric concepts and applications in various fields, such as engineering and architecture. |

7. Coordinate Geometry | Students explore the Cartesian plane, distance formula, section formula, and the area of a triangle formed by three given points. Coordinate geometry is essential for visualizing and solving geometric problems algebraically. It forms the basis for analytical geometry, which is widely used in physics, engineering, and computer graphics. |

8. Introduction to Trigonometry | This chapter introduces trigonometric ratios (sine, cosine, tangent), their values for specific angles, and trigonometric identities. Trigonometry is crucial for studying periodic phenomena and is widely used in fields such as astronomy, physics, engineering, and architecture. Understanding trigonometric ratios and identities is fundamental for higher-level mathematics. |

9. Some Applications of Trigonometry | Students learn to solve problems involving heights and distances using trigonometric ratios, including finding angles of elevation and depression. Practical applications of trigonometry in real-life scenarios, such as navigation, surveying, and construction, make this chapter highly relevant and useful. |

10. Circles | This chapter covers the properties of circles, including chords, tangents, and secants. Students learn about angles subtended by arcs and theorems related to circles. Understanding the properties and theorems of circles is essential for advanced geometry. Circles and their properties are widely used in design, architecture, and engineering. |

11. Constructions | Students learn basic constructions using a ruler and compass, including bisectors of line segments and angles, and constructions of triangles and quadrilaterals. Geometric constructions are fundamental skills in geometry. They are essential for practical applications in drafting, design, and engineering. |

12. Areas Related to Circles | This chapter focuses on areas related to circles, such as sectors and segments, and solving problems involving the area of combinations of figures. Understanding areas related to circles is crucial for solving problems in geometry and real-life applications like designing circular objects and calculating land areas. |

13. Surface Areas and Volumes | Students learn about surface areas and volumes of different solid shapes, including cubes, cuboids, cylinders, cones, and spheres. Knowledge of surface areas and volumes is essential for solving practical problems in various fields, such as architecture, engineering, and manufacturing, where measurement and calculation of space are crucial. |

## CBSE Class 10 Maths Exam Highlights

Aspect | Details |
---|---|

Board Name | CBSE (Central Board of Secondary Education) |

Class Level | Class 10 |

Subject | Mathematics |

Syllabus | Key topics include: Number Systems, Algebra (Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions) Coordinate Geometry, Geometry (Triangles, Circles, Constructions), Trigonometry, Mensuration (Areas related to Circles, Surface Areas and Volumes), Statistics and Probability |

Exam Pattern | The exam is divided into: Section A: Objective Type Questions Section B: Short Answer Questions Section C: Long Answer Questions Section D: Case Study Based Questions |

Total Marks | 80 marks for the written exam, 20 marks for internal assessment (Periodic Tests, Notebook Submission, and Subject Enrichment Activities) |

Duration | 3 hours |

Marking Scheme | No overall negative marking, but internal marking criteria apply. Each section carries a specific weightage. |

Medium | English, Hindi |

Difficulty Level | Moderate to high, covering basic to advanced concepts |

Textbook | NCERT Mathematics textbook for Class 10 |

Internal Assessment | 20 marks divided into: Periodic Tests (10 marks),Notebook Submission (5 marks) and Subject Enrichment Activities (5 marks) |

Preparation Tips | Regular practice and solving previous years’ papers, Focus on understanding concepts rather than rote learning, Timed practice sessions to improve speed and accuracy |

Official Website | https://www.cbse.gov.in |

## CBSE Class 10 Maths Question Paper Pattern 2024

Section | Number of Questions | Type of Questions | Marks Per Question | Weightage |
---|---|---|---|---|

A | 20 | MCQs | 1 | 20 |

B | 5 | Very Short Answer Questions | 2 | 10 |

C | 6 | Short Answer Questions | 3 | 18 |

D | 4 | Long Answer Questions | 5 | 20 |

E | 3 | Case Based Questions | 4 | 12 |

Total | 38 | 80 Marks |

## FAQs on NCERT Solutions for Class 10 Maths

**Q1. How many chapters are there in NCERT Solutions for Class 10 Maths?Answer: **There are 15 chapters in the NCERT Solutions for Class 10 Maths.

**Q2. Can I get answers for miscellaneous exercises in the NCERT Solutions for Class 10 Maths?Answer:** Yes, the Class 10 Mathematics NCERT Solutions include answers for the miscellaneous exercises as well.

**Q3. Is Class 10 Mathematics NCERT Solutions the best source of reference materials for the students?Answer: **Yes, the Class 10 Mathematics NCERT Solutions are considered one of the best sources of reference materials for students because they provide detailed and accurate answers that align with the CBSE curriculum.

**Q4. Where can I download the NCERT Solutions for Class 10 Maths?Answer: **You can download the NCERT Solutions for Class 10 Maths from various educational websites, the official NCERT website, or apps that provide educational resources for students.

**Q5. What type of questions are asked in Class 10 maths?Answer:** In Class 10 maths, questions range from multiple-choice and short answer questions to long answer and problem-solving questions, covering topics like algebra, geometry, trigonometry, and statistics.

**Q6. Are NCERT solutions important for Class 10?Answe:** Yes, Class 10 Mathematics NCERT Solutions are important as they provide detailed, step-by-step explanations of textbook problems, helping students understand and master the concepts effectively.

**Q7. How to solve Class 10 Mathematics NCERT Solutions** **easily?Answer:** To solve Class 10 Mathematics NCERT Solutions easily in Class 10, regularly practice problems, understand the concepts thoroughly, and use Class 10 Maths NCERT solutions to clarify doubts and learn the correct methods.

**Q8. Which is the hardest Class 10 maths chapter?Answer: **Many students find the chapter on “Quadratic Equations” to be the hardest in Class 10 maths due to its complex problem-solving and abstract concepts.