NCERT Solutions for Class 10 Maths, Best Books for Maths

Physics Wallah Academic Expert
January 27, 2024

Candidates, gear up for Class 10 Maths exams with our user-friendly NCERT Solutions. Our expert faculty has crafted solutions for all exercises in Chapters 1 to 15, available in easy-to-download PDFs. These solutions, designed for the 2023-24 academic year, not only help candidates prepare effectively but also deepen their understanding of textbook concepts. By practising these solutions, candidates can assess their preparation level and quickly clear any doubts they may have about the questions in the NCERT books. Don't miss out on this valuable resource to boost confidence and excel in Class 10 Maths exams.

NCERT Solutions for Class 10 Maths Overview

Mathematics is an important subject, but it can be tough for some students. That's why the Physics Wallah team made special solutions for Class 10 Maths. We want to make math easy to understand, so students feel more confident. These solutions are helpful guides to improve math grades and do better in school overall. Thus, for proper NCERT Solutions for Class 10 Maths candidates. 

NCERT Maths Class 10 Chapters

Here are the chapters that students need to study and hold a proper grip on the concept of the chapters. Thus, candidates can go through the NCERT Maths Class 10 Chapters from the below table:- 

Class 10 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 Circle

Chapter 12 – Surface Areas and Volumes

Chapter 13 – Statistics

Chapter 14 – Probability

Class 10 Maths Solutions Chapter Wise:

NCERT Class 10 Chapter 1 – Real Numbers

In Chapter 1 of Class 10, candidates will explore real and irrational numbers. The chapter begins with Euclid’s Division Lemma, stating that "For any positive numbers a and b, there are special numbers q and r. They make a = bq + r, where 0 is less than or equal to r, and r is less than b." Euclid’s Division algorithm uses this idea to figure out the HCF of two positive numbers. Afterwards, candidates will encounter the Fundamental Theorem of Arithmetic, assisting in finding the LCM and HCF of two positive numbers. Then, the chapter covers irrational and rational numbers, demonstrating how to express rational numbers as decimals using the theorem. The chapter covers the following topics:

  1. Fundamental Theorem of Arithmetic – providing statements after reviewing the work done both before and after, and explaining through examples.

  2. Proofs of the irrationality of √2, √3, √5.

NCERT Class 10 Chapter 2 – Polynomials

In the Polynomials chapter, we start by learning about different types of polynomials like linear, quadratic, and cubic, and what we call the "degree" of a polynomial. There are four exercises to practice, and one is optional. In Exercise 2.1, we answer questions about the number of zeroes shown in a graph, understanding something called the "Geometric meaning of the Zeroes of a Polynomial." 

Exercise 2.2 is about figuring out the relationship between zeroes and coefficients of a polynomial, where we find the zeroes of a special kind of polynomial and even create one in some questions. Exercise 2.3 introduces a new concept called the division algorithm, and we solve problems related to it. The optional Exercise 2.4 includes questions covering all the ideas from Chapter 2. Key Ideas in Class 10 Maths Chapter 2 Polynomials:

  1. Understanding different types of polynomials.

  2. Figuring out the relationship between zeroes and coefficients of quadratic polynomials.

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

This chapter is all about figuring out pairs of math problems that involve two variables. There are seven sets of exercises to practice, and each set teaches us different ways to solve these problems. In Exercise 3.1, we learn how to show the problems using both numbers and pictures. Exercise 3.2 shows us how to solve these problems using pictures. Exercises 3.3, 3.4, 3.5, and 3.6 teach us different ways to solve problems using numbers. Exercise 3.7 is optional and has a mix of all kinds of problems. To get really good at solving these problems, it's important to practice all these exercises. Main Ideas in this Chapter:

  1. Understanding pairs of problems with two variables and solving them using both numbers and pictures.

  2. Figuring out if the solutions to these problems make sense or not.

  3. Using different ways like numbers and pictures to solve these problems.

  4. Solving these problems by trying different methods.

  5. Solving simple problems related to these pairs of problems.

NCERT Class 10 Chapter 4 – Quadratic Equations

In this chapter, we're going to learn the standard way of writing a special kind of math problem called a Quadratic Equation. We'll figure out how to solve these problems using two methods: one called completing the square and another called factorization. Towards the end, we'll talk about what kind of answers these problems can have. For these problems like ax² + bx + c = 0, we'll find out:

If there are two different real answers when b² – 4ac is more than 0.

If there are two equal answers when b² – 4ac is exactly 0.

If there are no real answers when b² – 4ac is less than 0.

Important Ideas in this Chapter:

  1. Learning the special way to write a quadratic equation.

  2. Figuring out how to solve these problems using different methods.

  3. Understanding what kind of answers these problems can have based on a special math calculation.

NCERT Class 10 Chapter 5 – Arithmetic Progressions

In this chapter, we're going to learn about something new called Arithmetic Progression or AP. There are four sets of exercises to practice what we learn. In Exercise 5.1, we'll answer questions about situations in AP, figure out the first number and the difference between numbers, and decide if a series is in AP. Moving on to Exercise 5.2, we'll work on questions about finding the nth number using a special formula:

To find the nth number (an), use this formula: an = a + (n-1) d

Exercise 5.3 is all about finding the total of the first n numbers in an AP. The last exercise brings some tricky questions to help us get better at solving problems using AP.

Main Ideas in this Chapter:

  1. Learning about Arithmetic Progression or AP.

  2. Figuring out different things about AP like the first number, the difference between numbers, and if a series is in AP.

  3. Using a formula to find the nth number in an AP.

  4. Working on problems related to finding the total of the first n numbers in an AP.

  5. Solving trickier problems based on AP to get better at solving problems.

NCERT Class 10 Chapter 6 – Triangles

Chapter 6 in Class 10 is all about triangles. It talks about triangles that look alike but can be different sizes. The chapter explains things like similarities in triangles and special rules for them. We also learn about triangles that are the same. The chapter also talks about the size of triangles, the Pythagorean theorem, and a rule connected to it.

For the exam, students need to know these special rules:

  1. Rule of Proportionality: If a line is drawn parallel to one side of a triangle and cuts the other side in certain places, the two sides are split in the same way.

  2. Parallel Line Rule: If a line cuts any two sides of a triangle in the same way, then the line is parallel to the third side.

  3. Similar Triangles Rule: If the angles of two triangles are the same, their sides are in the same order, making the triangles similar.

  4. Proportional Sides Rule: If the sides of one triangle are related to the sides of another triangle, their angles are equal, and the triangles are similar.

  5. Angle-Side Similarity Rule: If one angle of a triangle is equal to one angle of another triangle, and the sides, including these angles, are in the same order, then the two triangles are similar.

  6. Area Ratio Rule: The size ratio of two similar triangles is equal to the square of the ratio of their sides.

  7. Right Triangle Perpendicular Rule: In a right triangle, if a line is drawn straight down from the right-angle corner to the long side, the little triangles on both sides are similar to the whole triangle and each other.

  8. Pythagorean Theorem: In a right triangle, the square of the longest side equals the sum of the squares of the other two sides.

  9. Converse of the Pythagorean Theorem: In a triangle, if the square of one side equals the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

NCERT Class 10 Chapter 7 – Coordinate Geometry

In this chapter, candidates will explore cool stuff about coordinate geometry and graphs of lines. They'll figure out how far two points are from each other using the Distance Formula. Candidates will also learn a trick called the Section Formula, which helps find where a point is between two other points on a line. We'll also explore drawing triangles with three points. So, candidates will cover the Distance Formula, and Section Formula (how we split a line), and understand how to draw lines on graphs.

NCERT Class 10 Chapter 8 – Introduction to Trigonometry

This chapter will introduce students to Trigonometry. We'll explore special ratios in a right triangle related to its angles, called trigonometric ratios. The chapter defines these ratios for angles like 0 degrees and 90 degrees. Students will also learn how to calculate these ratios for certain angles and establish some relationships between them, known as trigonometric identities.

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

  1. Trigonometric ratios of an acute angle in a right-angled triangle. We'll prove that these ratios make sense and understand why they are defined at 0 degrees and 90 degrees. We'll also find the values of these ratios for angles like 30, 45, and 60 degrees.

  2. Trigonometric Identities: We'll prove and apply the identity sin²A + cos²A = 1. Only simple identities will be introduced.

NCERT Class 10 Chapter 9 – Some Applications of Trigonometry

In Chapter 8 of NCERT Solutions, students dive into trigonometry, exploring the ratios of right triangles based on their angles. These ratios, known as trigonometric ratios, are explained for angles like 0° and 90°, and students learn how to find them for other angles. The chapter introduces crucial trigonometric identities, setting a strong foundation not just for Class 10 but also for higher classes like 11 and 12.

This chapter serves as a vital introduction to trigonometry, providing students with introductory formulas that lay the groundwork for future studies. It delves into the relationship between trigonometric ratios and angles. Students encounter important complementary angle trigonometric ratios, such as 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, and cosec (90° – A) = sec A.

Additionally, students grasp fundamental trigonometric identities like sin² A + cos² A = 1, sec² A – tan² A = 1 for 0° ≤ A < 90°, and cosec² A = 1 + cot² A for 0° < A ≤ 90°. These concepts serve as essential tools, aiding students in solving trigonometry problems and understanding the connections between various trigonometric functions.

NCERT Class 10 Chapter 10 – Circles

Before, we learned about circles, chords, segments, and arcs. Now, in this chapter, we're looking at what happens when we have a circle and a line in the same space. It's like exploring a new adventure! We're getting the hang of something called Tangent to a Circle and figuring out how many tangents we can draw from a point on a circle.

Here's what we'll be doing in Class 10 Maths Chapter 10 Circles:

  1. Tangent to a circle at the point where it touches

  2. (Prove) Showing that the line touching the circle at any point always stands straight up like a superhero cape to the line going from that point to the centre.

  3. (Prove) Proving that if we draw lines from a point outside the circle to touch it, those lines will always be the same length.

NCERT Class 10 Chapter 11 – Areas Related to Circle

In Class 10 Maths, Chapter 10 continues our exploration of circles from earlier classes. This chapter introduces us to the idea of tangents and focuses on figuring out how many tangents we can draw from a point on a circle.

The chapter covers two important ideas:

  1. Idea 1: Whenever we draw a tangent at any point on a circle, it's always going to be like a superhero line that stands straight up, making a perfect angle with a radius that starts from the same point.

  2. Idea 2: If we draw tangents from a point outside the circle, those tangent lines will be the same length.

NCERT Class 10 Chapter 12 – Surface Areas and Volumes

In Chapter 13, there are 5 sets of problems to tackle. The first set involves figuring out how much surface covers an object made by sticking together two basic shapes like cubes, cuboids, spheres, hemispheres, cones, or cylinders. In the second set (Exercise 13.2), we'll be finding out how much space is inside objects created by combining any two of those shapes. Moving on to Exercise 13.3, the questions focus on when a solid transforms from one shape to another. Exercise 13.4 is all about calculating the inside and outside of a cone-shaped object called a frustum. The last set is an extra challenge with high-level questions covering everything we've learned in this chapter.

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

  1. Finding surface areas and volumes of mix-and-match combinations of cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

NCERT Class 10 Chapter 13 – Statistics

In this chapter, we're going to make numbers organized and find some cool stuff like the average (Mean), middle point (Median), and the most common number (Mode). We'll also learn about cumulative frequency, putting numbers in order, and even drawing some curves.

Key Topics in Class 10 Maths Chapter 14 Statistics:

  1. Figuring out the average, middle point, and most common number when our numbers are all grouped together. 

NCERT Class 10 Chapter 14 – Probability

In the last chapter, we're talking about Probability. First, we look at the theory of probability. Then, we figure out the difference between what should happen in theory (theoretical probability) and what actually happens in real life (experimental probability). There are lots of examples to make it easy to understand. So, before trying the practice problems, it's a good idea to work through the examples in CBSE Maths.

Important Things to Learn in Class 10 Maths Chapter 14- Probability:

  1. Understanding the basic idea of probability and solving simple problems to find the chance of something happening.

Best Books for NCERT Class 10 Maths

With the 10th-grade exams getting closer, choosing the right books for NCERT Class 10 Maths can be confusing. Buying different books can also cost a lot. To make it easier, the Physics Wala team has put together affordable combo books for the Best Books for NCERT Class 10 Maths in both English and Hindi. These books are designed to help Class 10 students prepare for their exams. To buy directly from the PW Store, click on the link below.

Class 10 Maths Solutions

Candidates can go through the Class 10 Maths Solutions from the below table:- 

Chapter

NCERT Solutions

Chapter 1 - Real Numbers

Solutions

Chapter 2 - Polynomials

Solutions

Chapter 3 - Pair of Linear Equations in Two Variables

Solutions

Chapter 4 - Quadratic Equations

Solutions

Chapter 5 - Arithmetic Progressions

Solutions

Chapter 6 - Triangles

Solutions

Chapter 7 - Coordinate Geometry

Solutions

Chapter 8 - Introduction to Trigonometry

Solutions

Chapter 9 - Some Applications of Trigonometry

Solutions

Chapter 10 - Circles

Solutions

Chapter 11 - Areas Related to Circles

Solutions

Chapter 12 - Surface Areas and Volumes

Solutions

Chapter 13 - Statistics

Solutions

Chapter 14 - Probability

Solutions

Other Books for Class 10 Maths

Candidates can go through the other important books for Class 10th if they wish to advance their knowledge in maths:- 

Book

Short Description

NCERT Mathematics Textbook for Class 10

Widely used primary source for CBSE board exams, covering essential concepts.

RD Sharma Mathematics for Class 10

Comprehensive coverage of mathematical concepts with a variety of practice problems.

RS Aggarwal Mathematics for Class 10

Clear explanations and extensive practice questions for effective exam preparation.

Together with Mathematics by Rachna Sagar

Additional practice questions, solved examples, and revision notes to support CBSE exam preparation.

CBSE Question Bank Class 10 Mathematics

Compilation of important questions, sample papers, and revision notes for exam readiness.

Arihant Publications - Class 10 Mathematics

Includes additional practice material, previous years' question papers, and solutions.

KC Sinha Mathematics for Class 10

Known for clarity in explaining mathematical concepts, suitable for exam preparation.

Benefits of NCERT Solutions for Class 10 Maths

  1. Easy Learning: These solutions make learning math easy for candidates by explaining problems in a way that's simple to understand.

  2. Everything Covered: All the problems in each chapter are explained, so candidates are ready for whatever shows up in exams.

  3. Step-by-Step Help: The solutions break down problems step by step, so candidates can follow along and understand each part.

  4. Pictures Help: There are pictures to help candidates see what's going on, making it easier to understand tricky math concepts.

  5. Follows a Plan: The solutions have a plan, so candidates know exactly how to tackle each problem and don't get confused.

  6. Gets You Ready for Exams: These solutions are designed for the exams candidates will be taking, so they're preparing in the right way.

  7. Good for Other Exams Too: Understanding math in Class 10 sets candidates up for success in other exams where math is important.

  8. Quick and Easy to Access: Candidates can easily find these solutions online, and they're in a format that's simple to use.

  9. Practice Makes Perfect: Candidates can use these solutions to practice, which is super important for getting better at math.

  10. Helps with Managing Time: Using these solutions helps candidates manage their study time better, so they're not stuck on one problem for too long.

NCERT Solutions for Class 10 Maths FAQs

Q1. What is the significance of NCERT Solutions for Class 10 Maths?

Ans. NCERT Solutions for Class 10 Maths are essential study materials that provide clear explanations, step-by-step guidance, and visual aids to help students understand and prepare for their exams effectively.

Q2. How are these solutions beneficial for exam preparation?

Ans. These solutions cover all chapters comprehensively, ensuring that students are well-prepared for their exams. The step-by-step approach and visual aids make exam preparation more effective.

Q3. Why are NCERT books recommended for Class 10 Maths preparation?

Ans. CBSE recommends NCERT books for exam preparation as they present concepts in a simple way, aiding in better understanding. NCERT Solutions align with the prescribed curriculum, ensuring students are on the right track.

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