# NCERT Solutions for Class 10 Maths

## NCERT Solutions for Class 10 Maths

Maths is a revered topic for engineering students pursuing professions through competitive exams such as JEE Main and JEE Advanced. It is one of those disciplines where a flawless centum can be obtained if the right preparation schedule and time are followed.

Over the last three to four years, CBSE has shifted away from regular NCERT questions and has focused more on application-based questions. This has made the paper rather tough to score if students just prepare for the questions that are expected to appear in the exam.

## NCERT Solutions for Class 10 Maths Chapter-wise

Maths is a compulsory component in Class 10. Therefore, all CBSE students need to use the CBSE Class 10 Maths NCERT Solutions for complete understanding of the concepts to ace their preparation. These solutions cover all key mathematical ideas and assist students in developing critical problem-solving skills.

### NCERT Solutions for Class 10 Maths

The solutions consist of 15 chapters, all of which are crucial for study. Students need to complete all of the exercises, even the optional ones to score well in the exam. NCERT solutions for class 10 Maths will assist you in thoroughly understanding each question. You can easily do well in board exams if you solve the NCERT Maths and practice the previous 5 years’ questions.

#### NCERT Solutions for Class 10 Maths Chapter 1 – Real Numbers

Using Euclid’s Lemma, the Fundamental Theorem of Arithmetic. Real Numbers explains the notion of properties of real numbers in great detail. Exercises 1.1 and 1.2 require the use of division procedure to determine the divisibility of integers.  Exercises 1.3 and 1.4, on the other hand, feature a question about proving the roots of any irrational number and decimal expansions of rational numbers.

#### NCERT Solution for Class 10 Maths Chapter 2 – Polynomials

This chapter covers advanced polynomial terms such as degree, coefficient, and zeroes for any type of polynomials. The chapter offers four exercises, with Exercises 2.1 and 2.2 requiring the use of a graph. Exercise 2.3 focuses on the division algorithm, and exercise 2.4 covers all subjects covered in the chapter.

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

This chapter discusses the concept of linear equation pairs. It begins with linear equations in two variables and their solutions using the graphical approach, as well as algebraic conditions for linear equations. The chapter goes on to explain how to solve a pair of linear equations in two variables algebraically using substitution, elimination, and cross-multiplication.

#### NCERT Solutions for Class 10 Maths Chapter 4 – Quadratic Equations

In this chapter, the learner will learn how to write quadratic equations in standard form. The chapter also covers the nature of roots, such as whether they are real and distinct, real and equal, or non-real roots. It also includes four exercises in which you must determine whether an equation is a quadratic one or not.

#### NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions

Students will learn in  greater detail about arithmetic progression, which is a series in which two consecutive terms have a constant difference. The chapter serves as the foundation for other complex concepts that will be introduced in later classes. They will develop the skills to solve issues with sequences and series.

#### NCERT Solutions for Class 10 Maths Chapter 6 – Triangles

The Triangles chapter covers the concepts of similarity and congruence. The basics of triangles are covered in Exercise 6.1. Problems from the topic of triangular similarity and a related theorem appear in exercises 6.2, 6.3, and 6.4. Exercises 6.5 and 6.6 focus on triangular congruency and application.

#### NCERT Solutions for Class 10 Maths Chapter 7 – Coordinate Geometry

Students will learn how to find the coordinates of a point that splits a line segment connecting two given sites in a specified ratio. The Distance formula and Section formula are key to the chapter in 10th grade maths. Sections on the area of the triangle are also included.

#### NCERT Solutions for Class 10 Maths Chapter 8 – Introduction to Trigonometry

This chapter is about the ratio of right angles to acute angles in any right-angled triangle. The questions in this chapter cover trigonometric ratios of specific angles, trigonometric identities, and trigonometric ratios of complementary angles are used. There are four exercises in this chapter: Exercise 8.1 introduces the trigonometric ratio and its calculation using Pythagoras’ theorem. Exercise 8.2 uses the trigonometric table to calculate specific angles. Exercise 8.3 is about complementary angles; and Exercise 8.4 is about trigonometric identities.

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

Trigonometry is the study of how to calculate the heights and distances of various things without having to measure them. This chapter explains how trigonometry is used in everyday life. Other such topics included in this chapter are the angle of deviation and elevation, and the line of sight.

#### NCERT Solutions for Class 10 Maths Chapter 10 – Circles

Students have a fundamental understanding of circles and associated terminology such as chord, segment, arc, and so on. They become familiar with the concepts of Tangent to a Circle and Number of Tangents from a Point on a Circle. The chapter discusses circle theorems which aid in the solution of many geometry problems.

#### NCERT Solutions for Class 10 Maths Chapter 11 – Constructions

This chapter teaches students how to build various geometrical figures. Methods and processes for construction are presented in simple language. This chapter also discusses Thales Theorem, often known as the Basic Proportionality Theorem. It ends with tasks that will teach pupils how to generate tangents to a circle.

#### NCERT Solutions Class 10 Maths Chapter 12 – Areas Related to Circles

This chapter includes three exercises, as well as real-life difficulties and cost-related questions about the circular territory. It also introduces the concepts of circle perimeter and area. Students will be able to compute the area of a sector and a segment of a circular region.

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

This chapter discusses calculating the areas and volumes of several solids such as the cube, cuboid, and cylinder. Questions are based on determining the volume of objects generated by merging several solid figures or converting one shape to another. NCERT Solutions for Class 10 Maths provide answers to both easy and difficult questions on the topic.

#### NCERT Solutions for Class 10 Maths Chapter 14 – Statistics

Students will learn how to convert individual data into grouped data and calculate the Mean, Mode, and Median. This chapter serves as the foundation for data science and analytics. The chapter teaches students how to create a graphical representation of raw, unorganised data from which tangible results can be generated.

#### NCERT Solutions for Class 10 Maths Chapter 15 – Probability

The final chapter is about Probability, which is the study of determining the likelihood of success or failure in a specific experiment. There are numerous examples provided to clearly explain probability and to help students understand it. Students must first solve the textbook examples before attempting to solve the exercise problems.

### CBSE Class 10 Maths Exam Pattern for 2022-2023

The exam is worth 100 marks, with the theory worth 80 marks and the internal assessment worth 20 marks. The CBSE Board releases sample papers and grading schemes well in advance of the board exams to help students clear up any confusion. According to the CBSE’s revised design, 25% of theoretical questions would be objective. The number of questions has been raised, but the marks assigned to each question have been reduced. There are four parts to this paper. There are 30 questions for a total of 80 marks.

#### Internal Assessment Marking Scheme

 Sr. No Activity Marks 1 Pen Paper Test 10 2 Portfolio 05 3 Lab Practical 05 TOTAL 20

#### Class 10 Maths Chapter-Wise Marks Weightage

 Sr. No Chapter Name Marks 1 Number System 6 2 Algebra 20 3 Coordinate Geometry 6 4 Geometry 15 5 Trigonometry 12 6 Mensuration 10 7 Statistics and Probability 11

#### CBSE Class 10 Maths Question Paper Design 2022-23

 Sr. No Type of Questions Total Marks Weightage 1 Memory: Terms, answers, basic concepts and recalling of facts. Understanding: Compare, organise, interpret, translate, describe and stating main ideas. 43 54 2 Apply: Solving problems by applying the knowledge, facts, theorems and rules in different ways 19 24 3 Analyse: Analyse the information provided and make inferences. Evaluate: Opine about the validity of quality of work and validity of ideas. Create: Creating alternative solutions to the given problem and grouping the elements. 18 22 TOTAL 80 100

### How will CBSE Class 10 Maths Solutions Help You to Score High Marks in Board Exams?

Deeper Understanding of Topics: More than knowing the answer to a problem or how to solve a specific type of question, it is critical to comprehend the ideas of algebra, geometry, statistics, and trigonometry in order to score well in Class 10 Maths. Extramarks 10th CBSE Maths solutions make it easy to understand the underlying concepts while answering questions.

Ready Reference for Practice: Students should make it a point to practice Maths exercises on a regular basis. As a result, anytime you intend to practice after having previously solved exercises, you may not recall everything, which is why having a ready reference for practice is vital.

Creating a Solid Foundation: While answering exercise questions is important, it is also necessary to have a good conceptual understanding. There are two reasons behind this – 1) Exam questions may be difficult to answer, but possessing conceptual understanding makes them simple to solve. 2) As you proceed to the following level, the same concepts are utilized to explain more complicated subjects, emphasizing the need for a solid foundation in Maths.

No Delay in Understanding: When students face a challenge, they may have to wait for some time with teachers to properly understand the problems and clear their questions. Class 10 Maths NCERT Solutions, on the other hand, assist students in quickly grasping key topics and avoiding delays in comprehending Maths.

### Why Refer NCERT Maths Class 10 Solutions for Board Exams?

Class 10 is a critical time in a student’s life since the grades they obtain influence their future career route. Getting the top results on the board exams may be difficult if you do not have the correct study resources. The experts at Extramarks create NCERT solutions for class 10 Maths on a subject-by-subject basis for this purpose.

NCERT Solutions will guide you in dealing with the concepts that you find difficult to solve. These solutions use step-by-step procedures to ensure that you grasp each topic and perform well on your Class 10 board exams.

### Important Tips for Scoring Well in the Board Exams

• You should be familiar with the Class 10 maths test pattern, such as the number of very short answer questions, short answer questions, and long answer questions.
• Before you begin your test preparation, familiarise yourself with the CBSE class 10 Maths syllabus. It will assist you in developing a better study strategy for yourself. You will also learn how many topics and chapters must be finished during the full session.
• Remember the key formulas from each chapter. Keep a separate notebook for the formulas and revise it on a regular basis. This will save you time while answering questions throughout the exam.
• Make a schedule before you begin studying. Keeping timetables will keep you on track and allow you to study at a consistent pace. You can modify them according to your strengths in the subject and topics.
• Try solving questions from the NCERT Solutions for Class 10 Maths about whatever is taught in class. You can also consult other books, such as RD Sharma, for additional practice, but first complete the NCERT textbook’s exercise questions.
• Take a walk or exercise for a few minutes during your study breaks. In between your studies, doing 10-20 minutes of exercise will help you keep fit and psychologically prepared for future studies.
• As the exam approaches, try not to be stressed. The night before the exam, get a decent night’s sleep. Before the exam, do not study any new topics. Be calm and relaxed.
• When revising, pay careful attention to the topics from which most questions are usually asked and carry more marks. Also, before the exam, answer the important questions.