Class 10^{th} is the biggest educational milestone for every student. That is why a lot of planning and study organization is necessary for getting good marks in these classes. If you have the best and most efficient resources of these classes by your side, then you will not get disappointed by your results at all. Having the right **NCERT Solutions For Class 10 Maths**, science, and other subjects is very important for getting good scores in not only your 10^{th} standard exams but also for the betterment of your future studies.

By logging into the official website of NCERT, you can either download the digital books or can learn from them online. This way, the cost of manual books will be reduced greatly and it will be easier to get all the knowledge of these books right at your home.

Table of Contents

## Marking Scheme for 10th Maths 1st Term Exam 2022-2023

Chapters | Marks |
---|---|

Chapter 1: Real Numbers | 6 |

Chapter 2: Polynomials and Chapter 3: Pair of Linear Equations in Two Variables | 10 |

Chapter 6: Triangles | 6 |

Chapter 7: Coordinate Geometry | 6 |

Chapter 8: Introduction to Trigonometry | 5 |

Chapter 12: Area Related to Circles | 4 |

Chapter 15: Probability | 3 |

Total | 40 |

Internal Assessment | 10 |

First Term Total Marks | 50 |

### Marking Scheme for 10th Maths 2nd Term Exam 2021-2022

Chapters | Marks |
---|---|

Chapter 4: Quadratic Equations and Chapter 5: Arithmetic Progression | 10 |

Chapter 9: Some Applications of Trigonometry | 7 |

Chapter 10: Circles and Chapter 11: Constructions | 9 |

Chapter 13: Surface Areas and Volumes | 6 |

Chapter 14: Statistics | 8 |

Total | 40 |

Internal Assessment | 10 |

Second Term Total Marks | 50 |

**NCERT Class 10 Mathematics Solutions Chapter-wise:-**

Following is a chapter-wise elaboration of mathematics subject for the class 10^{th} students-

**Chapter 1- Real Numbers:**

The proper definition of real numbers, which numbers should be considered as real numbers, and many other questions are answered with examples and problems in this chapter.

Exercise 1.1 | 5 Questions & Solutions (4 Long Answers, 1 Short Answer) |

Exercise 1.2 | 7 Questions & Solutions (4 Long Answers, 3 Short Answers) |

Exercise 1.3 | 3 Questions & Solutions (3 Short Answers) |

Exercise 1.4 | 3 Questions & Solutions (3 Short Answers) |

*Real Numbers Exercise Table***Chapter 2- Polynomials:**

An expression that contains more than 2 algebraic terms is called a polynomial. This definition is explained in much more detail in this chapter so that students can understand this concept very briefly. For this and many other concepts, **NCERT Solutions For Class 10 Maths **is the best guide that students will also love to use.

Exercise 2.1 | 1 Question & Solutions (1 Short Answer) |

Exercise 2.2 | 2 Questions & Solutions (2 Short Answers) |

Exercise 2.3 | 5 Questions & Solutions (2 Short Answers, 3 Long Answers) |

Exercise 2.4 | 5 Questions & Solutions (2 Short Answers, 3 Long Answers) |

*Polynomials Exercise Table***Chapter 3- Pair of Linear Equations in Two Variables:**

Linear equations in 2 variables have a special property that always gives a straight line graph whether whichever numbers are used in it. This is explained in detail In this chapter with numerous numerical problems so that students can get cleared in mind in this context. Just like other chapters, even for this chapter, **NCERT Solutions For Class 10 Maths **is undoubtedly a great choice for every student who wants to get good marks in their board exams.

Exercise 3.1 | 3 Questions & Solutions (2 Short Answers, 1 Long Answer) |

Exercise 3.2 | 7 Questions & Solutions (5 Short Answers, 2 Long Answers) |

Exercise 3.3 | 3 Questions & Solutions (2 Short Answers, 1 Long Answer) |

Exercise 3.4 | 2 Questions & Solutions (2 Long Answers) |

Exercise 3.5 | 4 Questions & Solutions (4 Short Answers) |

Exercise 3.6 | 2 Questions & Solutions (2 Long Answers) |

Exercise 3.7 | 8 Questions & Solutions (1 Short Answer, 7 Long Answers) |

*Pair of Linear Equations in Two Variables Exercise Table*

**Chapter 4- Quadratic Equations:**

Quadratic equations are one of the basic topics that help in making the mathematics subject strong for students. Various quadratic equations of different types are given for the students to solve in this chapter.

Exercise 4.1 | 2 Questions & Solutions (1 Short Answer, 1 Long Answer) |

Exercise 4.2 | 6 Questions & Solutions (6 Short Answers) |

Exercise 4.3 | 11 Questions & Solutions (8 Short Answers, 3 Long Answers) |

Exercise 4.4 | 5 Questions & Solutions (2 Short Answers, 3 Long Answer) |

*Quadratic Equations Exercise Table***Chapter 5- Arithmetic Progressions:**

When a number series either increase or decrease by the same amount every time it is asked to, these types of mathematical problems are called arithmetic progressions. These are explained numerically elaborately in this chapter of the NCERT solutions book.

Exercise 5.1 | 4 Questions & Solutions (1 Short Answer, 3 Long Answers) |

Exercise 5.2 | 20 Questions & Solutions (10 Short Answers, 10 Long Answers) |

Exercise 5.3 | 20 Questions & Solutions (7 Short Answer, 13 Long Answers) |

Exercise 5.4 | 5 Questions & Solutions (5 Long Answers) |

**Arithmetic Progressions**

*Exercise Table***Chapter 6- Triangles:**

Triangle may seem to us as just a type of shape but it has a lot of measurements and subtypes included in it. These are explained with numerical problems in this chapter.

Exercise 6.1 | 3 Questions & Solutions (3 Short Answers) |

Exercise 6.2 | 10 Questions & Solutions (9 Short Answers, 1 Long Answer) |

Exercise 6.3 | 16 Questions & Solutions (12 Short Answer, 4 Long Answer) |

Exercise 6.4 | 9 Questions & Solutions (7 Short Answers, 2 Long Answers) |

Exercise 6.5 | 17 Questions & Solutions (15 Short Answer, 2 Long Answer) |

Exercise 6.6 | 10 Questions & Solutions (5 Short Answers, 5 Long Answers) |

*Triangles Exercise Table*

**Chapter 7- Coordinate Geometry:**

All questions in this chapter include graphs and still, every question is unique in its way. That is why this chapter is a very important one from a mathematical point of view for every student to understand and practice for good marks.

Exercise 7.1 | 10 Questions & Solutions (3 Short Answers, 7 Long Answers) |

Exercise 7.2 | 10 Questions & Solutions (2 Short Answers, 8 Long Answers) |

Exercise 7.3 | 5 Questions & Solutions (2 Short Answers, 3 Long Answers) |

Exercise 7.4 | 8 Questions & Solutions (3 Short Answers, 5 Long Answers) |

*Coordinate Geometry Exercise Table*

**Chapter 8- Introduction to Trigonometry:**

Trigonometry is a concept that is not explained properly in a lot of guides and class 10^{th} solutions. However, **NCERT Solutions For Class 10 Maths **explains the whole trigonometry concept in specific detail to the students. This chapter is explained in such a way that students will not forget it for the whole of their life at all.

Exercise 8.1 | 11 Questions & Solutions (8 Short Answers, 3 Long Answers) |

Exercise 8.2 | 4 Questions & Solutions (2 Short Answers, 2 Long Answers) |

Exercise 8.3 | 7 Questions & Solutions (5 Short Answers, 2 Long Answers) |

Exercise 8.4 | 5 Questions & Solutions (3 Short Answers, 2 Long Answers) |

**Introduction to Trigonometry Exercise Table**### Chapter 9- Some Applications of Trigonometry:

Trigonometry has some specific applications in the field of mathematics and these applications are explained briefly and numerical problems related to that are asked by the students to be solved in this chapter.

Exercise 9.1 | 16 Questions & Solutions (16 Long Answers) |

**Some Applications of Trigonometry Exercise Table****Chapter 10- Circles:**

Just like triangles, the circle is also another type of shape and various aspects of this shape are explained for a better understanding of the students with numerical problems on every aspect individually.

Exercise 10.1 | 4 Questions & Solutions (2 Short Answers, 2 Long Answers) |

Exercise 10.2 | 13 Questions & Solutions (2 Short Answers, 14 Long Answers) |

**Circles Exercise Table**### Chapter 11- Constructions:

The construction of different shapes with the help of a geometrical box is explained in this chapter with numerous questions for the students to solve. All types of shapes such as triangles, squares, polygons, rectangles, circles, etc., are taught to construct in this chapter.

Exercise 11.1 | 7 Questions & Solutions (7 Long Answers) |

Exercise 11.2 | 7 Questions & Solutions (7 Long Answers) |

**Constructions**

*Exercise Table*### Chapter 12- Area Related to Circles:

What is an area of a circle, how to find it, and many other such questions are answered in detail in this chapter, and some important formulae for the same are also presented for the use of students to solve their numerical problems.

Exercise 12.1 | 5 Questions & Solutions (5 Short Answers) |

Exercise 12.2 | 14 Questions & Solutions (9 Short Answers, 5 Long Answers) |

Exercise 12.3 | 16 Questions & Solutions (9 Short Answers, 7 Long Answers) |

*Area Related to Circles Exercise Table*** Chapter 13- Surface Areas & Volumes**

Various problems on surface areas and volumes of different shapes are given for the students to solve in this chapter and some of their basic concepts are also cleared.

Exercise 13.1 | 9 Questions & Solutions (2 Short Answers, 7 Long Answers) |

Exercise 13.2 | 8 Questions & Solutions (1 Short Answer, 7 Long Answers) |

Exercise 13.3 | 9 Questions & Solutions (9 Long Answers) |

Exercise 13.4 | 5 Questions & Solutions (5 Long Answers) |

Exercise 13.5 | 7 Questions & Solutions (7 Long Answers) |

*Surface Areas & Volumes Exercise Table*

**Chapter 14- Statistics:**

Statistics is a very important branch of mathematics and has a lot of regular mathematical uses. Some important problems in this branch are given for the students to solve in this chapter of the class 10 NCERT mathematics book.

Exercise 14.1 | 9 Questions & Solutions (9 Long Answers) |

Exercise 14.2 | 6 Questions & Solutions (6 Long Answers) |

Exercise 14.3 | 7 Questions & Solutions (7 Long Answers) |

Exercise 14.4 | 3 Questions & Solutions (3 Long Answers) |

**Statistics Exercise Table****Chapter 15- Probability**

Just like a coin has 2 sides, there’s always a presence of 2 or more possibilities for a particular thing. How these possibilities work in the form of probability and how to detect the number of probabilities of a particular thing is what is better explained in this chapter. Also, the **NCERT Solutions For Class 10 **elaborately explains every step of these probability problems to the students for their better understanding.

Exercise 15.1 | 25 Questions & Solutions (22 Short Answers, 3 Long Answers) |

Exercise 15.2 | 5 Questions & Solutions (5 Short Answers) |

*Probability Exercise Table*

## How to Score Top Marks in NCERT Class 10 Maths?

Every student is trained to be the best academically right from the start of their educational life. Many parents expect that their children should score the highest marks in their academic education. However, every student has their capabilities and passions. Academically active students also face a lot of problems while studying but the only thing that helps them receive more marks is their consistency. Almost 90% of the students face trouble in mathematics subjects, especially when they are on their 10 & 12 boards.

Cracking your mathematics subject properly in 10 boards is possible with the help of amazing NCERT material mathematics that is available very freely in the market. However, making proper use of all the available material is also equally important because without proper usage knowledge, collecting any study material becomes just a waste of time for the students.

### Importance of NCERT Class 10 Mathematics in Educational Life of Students:-

Below are some points that prove the importance of NCERT Class 10 mathematics in the educational life of students for sure-

#### Teachers Students to organize their Plans properly & work accordingly always

Mathematics is a very procedural subject and this teaches students to always be organized in their life. This organization helps in bringing balance in their life ahead and they always remain consistent in all that they do lifelong.

**Improves the Reasoning Ability of Students**

Mathematics includes a lot of reasoning ability right from 1 standard education. That is why understanding mathematics properly in the 10 standards will help you in grasping a lot of reasoning ability for yourself & this will stay with you lifelong whichever career field you choose for yourself ahead.

#### Sharpens the Minds of Students & makes them much more Active

Mathematics is a subject that helps you in brainstorming your creativity and think out of the box always. This way, students’ minds get sharpened and then become much more active mentally without any doubt.

**Helps Students to think Rationally in Difficult Situations**

Rational thinking is very important, especially in tough and stressful situations. This thinking is facilitated with the knowledge of out-of-the-box thinking which strengthens with the help of mathematics subjects right from the start of your educational life.

All the above points related to the importance of NCERT class 10 mathematics are very crucial to be understood by every student. This way, students can improve their maths skills to a much greater extent and get very good marks in their board exams undoubtedly.

## Why does NCERT Class 10 Maths seem to be so difficult for many Students?

Below is a list of some important reasons why NCERT class 10 mathematics subject seems to be so difficult for many students in the beginning-

#### Maths needs a lot of Energy & Time:

Mathematics is a subject that needs a lot of time and energy to be properly understood initially. When students don’t give enough time to maths, the progress in those topics starts getting deposited more and more. This eventually becomes difficult for the students to cope with all at once.

**Concepts are a little difficult to Understand & Grasp:**

Mathematics concepts are a little tricky to be understood and need a lot of practice to be remembered properly. However, students don’t give maths enough time and this is where they fail miserably.

#### Maths Problems may seem Easier at the Beginning but becomes Complex Gradually:

Mathematics problems may seem very basic and easier at the beginning, but eventually, they start getting complicated and leads to major solution disasters. In such situations, students lose marks by doing very silly mistakes that they regret incredibly later on.

The above reasons why NCERT class 10 mathematics seems to be very difficult for the students and continues to be so if proper organization & planning is not implemented.

## Ways to Score Top Marks in NCERT Class 10 Maths:-

Following are some important ways to score top marks in NCERT Class 10 mathematics and achieve a good rank in their board exams very comfortably-

#### Don’t Skip your Practice even for a Single Day:

Mathematics needs regular practice and that too for a particular time. If you skip even a single day of your maths practice, then you are left behind, and coping becomes difficult for you from the next day onwards.

**Make a separate list of all the Formulae:**

Make a separate list of all the required formulae chapter-wise & then revise it regularly. This will help you in learning all the formulae properly and using them according to their requirements to solve problems quickly and rightly.

## Make proper NCERT Analysis:

NCERT books are the best source of knowledge for the Class 10^{th} students. That is why ignoring this will not be good for the students at all. Instead, students should analyze these NCERT books very wisely for a better understanding of all the mathematics topics, even very difficult ones.

#### Sort your Time according to the Topic Requirement:

Mathematics has a lot of topics included in it and that is why you should sort your time in such a way that the difficult ones get more time to be dealt with by you.

#### Revise your Every Topic at least 3-4 Times:

Every mathematics topic that is mentioned in your NCERT book and your syllabus should be revised by you at least 3 to 4 times. This will give you a larger hand on even your difficult topics and you will easily be able to crack your board exams with good grades.

All the above ways of scoring more in the NCERT 10 class are very reliable. If all these ways are implemented every day by students for at least 2-3 hours, then students can get a very speedy success in their Mathematics problems for sure.

**Conclusion**:-

Mathematics is surely a very crucial subject but paying close attention to it can improve your situation greatly. When you focus on your weak points in this subject, then you can improve your performance in it as well. Determination and hard work is the only way through which mathematics can be cracked and ultimate scores can be received by students in even a very little period.

Getting good performance is only possible when you focus on your weak points more and keep improving your strong points. This is the right way to get success and good scores in mathematics in your 10 board exams and use your valuable NCERT books rightly and most effectively.