NCERT Solution for Class 8 Maths: Download PDF

The NCERT Solution for Class 8 Maths provides comprehensive answers to all exercises and questions from the Class 8 Maths textbook. These NCERT solutions are designed to help students build a strong understanding of mathematical concepts, from basic arithmetic to more complex topics like algebra, geometry, and data handling. By downloading the PDF, students can access a well-structured guide that simplifies problem-solving and prepares them for exams. Get Free NCERT Solutions for Class 8 Maths with detailed explanations, step-by-step solutions, and PDF downloads for all chapters. Updated for CBSE syllabus.

NCERT Solutions for Class 8 Maths - All Chapters

NCERT Solutions for Class 8 Maths are essential for building a strong foundation in mathematics and preparing for future competitive exams. These step-by-step solutions are prepared according to the latest CBSE guidelines (2025-26) and help students strengthen conceptual clarity while ensuring accuracy in problem-solving.

Detailed Chapter-wise NCERT Solution for Class 8 Maths

NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 – Rational Numbers explain the fundamental concepts of rational numbers in a step-by-step manner. This chapter builds on the basics you studied earlier and helps strengthen your understanding of number systems. The introduction should not be skipped, as it revises important concepts that are essential for solving higher-level problems. In this chapter, you will solve 2 exercises (Exercise 1.1 and Exercise 1.2) from your NCERT textbook. These exercises cover properties of rational numbers, representation on the number line, and identifying rational numbers between two given numbers.

Exercises in Chapter 1 Rational Numbers

• Exercise 1.1 (11 Questions):
  Focuses on the properties of rational numbers like closure, commutative, associative, distributive laws, identity, and inverse properties. Students also learn about additive and multiplicative inverses.
• Exercise 1.2:
  Covers representation of rational numbers on the number line and finding rational numbers between two rational numbers. This helps in developing visualization skills and understanding the density property of rational numbers.

Important Topics Covered in Chapter 1 – Rational Numbers

1. Properties of Rational Numbers (Closure, Commutativity, Associativity, Distributivity, Identity, Inverse)
2. Representation of Rational Numbers on the Number Line
3. Finding Rational Numbers Between Two Rational Numbers
4. Concept of Additive and Multiplicative Inverses

Additional Study Resources for Class 8 Maths Chapter 1

To strengthen your preparation, you can refer to the following resources for Class 8 Rational Numbers:

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable introduce you to the basics of equations and their applications. A linear equation in one variable is an equation that can be written in the form ax + b = 0, where x is the variable and a and b are integers. This chapter is an important foundation for Algebra and higher-level mathematics. It contains 6 exercises designed to help students understand how to form, simplify, and solve linear equations step by step.

Exercises in Chapter 2 Linear Equations in One Variable

• Exercise 2.1 (12 Questions):
  Focuses on operations involving fractions and decimals. Students practice simplification and solving equations that contain rational numbers.
• Exercise 2.2 (16 Questions):
  Involves comparing and ordering fractions and decimals along with addition, subtraction, multiplication, and division. These problems build numerical skills needed for algebraic equations.

Important Topics Covered in Chapter 2

1. Solving Equations with Linear Expressions on One Side and Numbers on the Other
2. Solving Equations that Involve Applications (Word Problems)
3. Solving Equations with the Variable on Both Sides
4. More Real-Life Applications of Linear Equations
5. Reducing Equations to a Simpler Form
6. Equations Reducible to Linear Form

Other Important Study Resources for Chapter 2 Linear Equations 

To make learning easier, students can use additional resources along with NCERT Solutions for Class 8 Maths Chapter 2:

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals explain the properties of polygons and quadrilaterals in a structured way. This chapter contains 5 exercises that help students learn how to identify, classify, and apply properties of quadrilaterals and polygons. It also covers special cases like parallelograms, rhombuses, and rectangles, which form the foundation for higher geometry.

Exercises in Chapter 3 Understanding Quadrilaterals

• Exercise 3.1 :
  Focuses on identifying and classifying quadrilaterals based on properties such as sides, angles, and diagonals. Students also learn about convex and concave polygons.
• Exercise 3.2:
  Tests understanding of diagonals in quadrilaterals—how many diagonals are formed and their properties.
• Exercise 3.3:
  Explores special quadrilaterals like squares, rectangles, parallelograms, and rhombuses, highlighting their unique characteristics and relationship to the broader family of quadrilaterals.
• Exercise 3.4:
  A mix of true/false and application-based questions that require classifying quadrilaterals, explaining overlapping properties, and recognizing special diagonals.

Key Topics Covered in Class 8 Maths Chapter 3

1. Polygons and their classification
2. Sum of the Measures of Exterior Angles of a Polygon
3. Different Kinds of Quadrilaterals
4. Properties of Parallelograms and Special Quadrilaterals

Other Chapter 3 Understanding Quadrilaterals Study Resources 

Students can also download additional study materials along with NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals:

NCERT Solutions for Class 8 Maths Chapter 4 – Data Handling

NCERT Solutions for Class 8 Maths Chapter 4 – Data Handling help students learn how to collect, organize, represent, and interpret data effectively. This chapter is very important from the examination point of view, as it generally carries around 11 marks in Class 8 Maths exams. The chapter contains 4 exercises that cover data organization, grouping, bar graphs, histograms, pie charts, and the basics of chance and probability. By practicing these exercises thoroughly, students can build a strong understanding of statistics and probability concepts.

Exercises in Chapter 4 Data Handling

• Exercise 4.1 (5 Questions):
  Focuses on representing data visually using bar graphs and histograms. Students also learn how to select the most suitable graph for a given dataset.
• Exercise 4.2 (6 Questions):
  Covers data interpretation. Questions involve reading information from tables, graphs, or charts and solving problems like finding totals, averages, and most frequent values.
• Exercise 4.3 & 4.4 (if included):
  Extend concepts to circle graphs (pie charts) and introduce chance and probability, helping students apply data handling in real-life contexts.

Key Topics Covered in Class 8 Maths Chapter 4 Data Handling

1. Looking for Information in Data
2. Organising and Grouping Data
3. Representation through Bar Graphs and Histograms
4. Circle Graph or Pie Chart
5. Basics of Chance and Probability

Other Chapter 4 Study Resources

Students can access the following resources along with NCERT Solutions for Class 8 Maths Chapter 4 Data Handling for better preparation:

NCERT Solutions for Class 8 Maths Chapter 5 – Squares and Square Roots

NCERT Solutions for Class 8 Maths Chapter 5 – Squares and Square Roots explain the concepts of perfect squares, square numbers, and methods of finding square roots. This chapter is widely applied in construction, area calculation, financial mathematics, and interest-related problems, making it an important topic for exams as well as real-life applications. The chapter contains 4 exercises that help students understand patterns of squares, properties of square numbers, and systematic methods to calculate square roots.

Exercises in Chapter 5 Squares and Square Roots

• Exercise 5.1 (9 Questions):
  Based on patterns involving perfect squares. Students practice identifying perfect squares and completing missing patterns.
• Exercise 5.2 (2 Questions):
  Focuses on expressing perfect squares as the sum of consecutive odd numbers, strengthening the number system concept.
• Exercise 5.3 (10 Questions):
  Introduces different techniques for finding the square of a number, including shortcut methods and algebraic identities.
• Exercise 5.4 (10 Questions):
  Covers methods of finding square roots, such as prime factorization and long division.

Key Topics Covered in Class 8 Maths Chapter 5

1. Properties of Square Numbers
2. Interesting Patterns of Squares
3. Finding the Square of a Number
4. Methods of Finding Square Roots (Prime Factorization & Long Division)

NCERT Solutions for Class 8 Maths Chapter 5 Other Study Resources

Students can also use the following additional materials along with NCERT Solutions for Class 8 Maths Chapter 5 Squares and Square Roots:

Chapter 6 – Cubes and Cube Roots (Class 8 Maths)

The NCERT Class 8 Maths Chapter 6 – Cubes and Cube Roots helps students understand how to work with numbers in the form of cubes and cube roots. These concepts are widely used in finding volumes of 3D objects, solving exponents, and even in real-life cases like calculating interest rates. This chapter is a step ahead of the previous ones as it introduces students to the properties of cubes and cube roots in detail.

Exercises in Chapter 6 – Cubes and Cube Roots

• Exercise 6.1 – Focuses on cubes of numbers and their patterns.
• Exercise 6.2 – Deals with finding cube roots of perfect cubes.

Class 8 Maths Chapter 6 Exercises with Solutions (PDF)

• Exercise 6.1 – 4 Questions & Solutions
• Exercise 6.2 – 2 Questions & Solutions

Students can download NCERT Class 8 Maths Chapter 6 Solutions in PDF format for free and practice them for exams.

Additional Study Resources for Chapter 6

Along with NCERT solutions, students can access the following important resources for revision and exam preparation:

NCERT Solutions for Class 8 Maths Chapter 7 – Comparing Quantities 

The NCERT Class 8 Maths Chapter 7 – Comparing Quantities introduces students to the skill of comparing two or more quantities and understanding their relationships. This chapter is very useful in real life because it teaches students how to work with percentages, ratios, proportions, profit & loss, discounts, simple interest, and compound interest. It acts as a foundation for higher classes, especially for topics in algebra, commercial mathematics, and data interpretation.

Exercises in Chapter 7 – Comparing Quantities

• Exercise 7.1 – Focuses on percentages. Students practice converting percentages into fractions/decimals and solving problems related to finding part of a whole.
• Exercise 7.2 – Deals with ratios and proportions, helping students understand proportional relationships between quantities.
• Exercise 7.3 – Introduces compound interest. Students learn the formula for compound interest and apply it to practical problems like calculating future investment values.

Class 8 Maths Chapter 7 Exercises with Solutions

All solutions are explained step by step, making it easy for students to follow and apply in exams. Free NCERT Solutions PDF for Class 8 Maths Chapter 7 can also be downloaded for practice.

Additional Study Resources for Chapter 7

NCERT Solution for Class 8 Chapter 8 – Algebraic Expressions and Identities

The NCERT Class 8 Maths Chapter 8 – Algebraic Expressions and Identities introduces students to the world of algebra. By learning about expressions and identities, students can find unknown values, simplify problems, and apply formulas in real-life mathematical situations. This chapter explains important terms in algebra and shows how to perform operations on expressions. It also covers standard identities and their applications, which form the base for higher-level algebra in Class 9 and 10.

NCERT Solutions for Chapter 8 Algebraic Expressions and Identities

• Exercise 8.1 & 8.2 – Focus on identifying terms, coefficients, and types of polynomials such as monomials, binomials, and trinomials.
• Exercise 8.3 & 8.4 – Teach operations on polynomials, including addition, subtraction, and multiplication using rules of exponents.

Each exercise includes step-by-step NCERT solutions to help students practice and revise with ease.

Additional Study Resources for Chapter 8

NCERT Solutions for Class 8 Maths Chapter 9 – Mensuration

Mensuration is a branch of mathematics that deals with calculating the area, perimeter, surface area, and volume of 2D and 3D figures. In NCERT Class 8 Maths Chapter 9 – Mensuration, students learn how to measure the area of trapeziums, quadrilaterals, polygons, and find the surface area and volume of solid figures like cubes, cuboids, and cylinders. This chapter builds on earlier knowledge and is highly useful for solving real-life problems such as painting walls, fencing land, or finding the capacity of tanks.

Class 8 Chapter 9 – Mensuration Exercises Overview

1. Exercise 9.1 compares the areas of a square and a rectangle with the same perimeter. It helps solidify the understanding that a square often encloses a larger area compared to a rectangle with the same boundary length.
2. Exercise 9.2 This exercise might involve finding the area of a square plot or solving for the side length of a square given its area. It reinforces the formula for area of a square (side x side).

Additional Study Resources for Chapter 9 – Mensuration

NCERT Solutions for Class 8 Maths Chapter 10 – Exponents and Powers

The NCERT Class 8 Maths Chapter 10 – Exponents and Powers introduces students to the concepts of powers, exponents, and their rules. Exponents help simplify very large or very small numbers and make mathematical expressions easier to write and understand. In this chapter, students learn about positive and negative exponents, apply the laws of exponents, and express small decimal numbers in standard form (scientific notation). These concepts are useful in higher mathematics and also in science subjects like Physics and Chemistry.

NCERT Solutions for Chapter 10 – Exponents and Powers

• Exercise 10.1 – Evaluating expressions with exponents having positive whole numbers as powers.
• Exercise 10.2 – Comparing expressions with exponents, including simplification before comparison.

Topics Covered in Chapter 10 – Exponents and Powers

1. Powers with Negative Exponents
2. Laws of Exponents
3. Use of Exponents to Express Small Numbers in Standard Form

Additional Study Resources for Chapter 10 – Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 11 – Direct and Inverse Proportions

The NCERT Class 8 Maths Chapter 11 – Direct and Inverse Proportions helps students understand how two quantities are related to each other. These concepts are widely used in real-life situations such as speed and distance, number of workers and time taken to complete work, or cost and quantity.

• In a direct proportion, when one quantity increases, the other also increases proportionally.
• In an inverse proportion, when one quantity increases, the other decreases proportionally so that their product remains constant.

This chapter is highly practical and improves students’ ability to apply mathematics in day-to-day problem-solving.

Exercises in Chapter 11 – Direct and Inverse Proportions

• Exercise 11.1 – Questions on direct proportion, where both quantities increase or decrease together in the same ratio.
• Exercise 11.2 – Questions on inverse proportion, where one quantity increases and the other decreases proportionally.

Additional Study Resources for Chapter 11 – Direct and Inverse Proportions

NCERT Solutions for Class 8 Maths Chapter 12 – Factorisation

The NCERT Class 8 Maths Chapter 12 – Factorisation teaches students how to simplify mathematical expressions by breaking them into factors. Factorisation is a key concept that helps in solving quadratic equations, algebraic problems, and higher-level mathematics. In this chapter, students learn different methods of factorisation such as using identities, regrouping terms, and division of expressions. They also practice dividing a monomial by another monomial and a polynomial by another polynomial. With 34 questions across the exercises, this chapter provides extensive practice for exams.

Exercises in Chapter 12 – Factorisation

• Exercise 12.1 – Finding factors of given numbers.
• Exercise 12.2 – Representing a number as a product of prime factors.
• Exercise 12.3 – Problems on Highest Common Factor (HCF).

Topics Covered in Chapter 12 – Factorisation

1. What is Factorisation?
2. Factorisation of Algebraic Expressions
3. Division of Algebraic Expressions
4. Division of Polynomial by Polynomial
5. Error Identification in Factorisation

Additional Study Resources for Chapter 12 – Factorisation

NCERT Solutions for Class 8 Maths Chapter 13 – Introduction to Graphs

The NCERT Class 8 Maths Chapter 13 – Introduction to Graphs helps students understand how data can be represented visually using different types of graphs. Graphs are powerful tools to present information in a clear and easy-to-read format. In this chapter, students extend their learning from data handling and explore various graph types such as bar graphs, pie charts, histograms, and linear graphs. They also learn how to plot points on a graph, locate coordinates, and interpret real-world data. Regular practice of the exercises in this chapter will help students gain confidence in handling graph-based problems.

Exercises in Chapter 13 – Introduction to Graphs

• Exercise 13.1 – Reading and interpreting real-world data from graphs, such as temperature variations or distance-time records.
• Exercise 13.2 – Answering questions based on the graphs, including identifying intervals, plotting points, and analyzing trends.

Additional Study Resources for Chapter 13 – Introduction to Graphs

Key Features of Class 8 Maths NCERT Solutions

The NCERT Solutions for Class 8 Maths are designed to help students learn concepts in a simple, step-by-step manner. These solutions are well-structured, easy to understand, and exam-focused, making them one of the best study resources for students. Some key features of Class 8 Maths NCERT Solutions include:

• Well-structured explanations – Each concept and exercise question is solved in a detailed, step-by-step way.
• Topic-wise preparation – Students can study chapter by chapter, download separate sections, and revise them along with important questions.
• Free availability – The NCERT solutions are available to download in PDF format anytime, free of cost.
• Expert-designed content – All solutions are prepared by experienced subject experts and reviewed for accuracy, ensuring 100% reliable material.
• Useful for revision – Students can use these solutions for last-minute exam preparation, quick concept recall, and practice.

Download NCERT Solutions for Class 8 Maths PDF

The chapter-wise NCERT Solutions for Class 8 Maths are available for free download. Students can use them to:

• Strengthen their understanding of key concepts.
• Practice exercise questions with step-by-step answers.
• Revise quickly before exams with ready-to-use notes.
• Clarify doubts and improve overall preparation.

With these solutions, students can complete their syllabus effectively, practice thoroughly, and score higher marks in their Class 8 Maths exams.

Why Choose Infinity Learn's NCERT Solutions for Class 8 Maths?

Infinity Learn provides comprehensive NCERT solutions for Class 8 Maths that are specifically designed to help students master mathematical concepts with confidence. Our NCERT textbook solutions for Class 8 Maths cover all 16 chapters with detailed step-by-step solutions, making complex mathematical problems easy to understand.

Key Features of NCERT Solution for Class 8 Maths:

• Complete Coverage: All chapters from the NCERT solution for Class 8 Maths book
• Step-by-step Solutions: Detailed explanations for every exercise question
• Free PDF Downloads: Downloadable NCERT solutions for Class 8 Maths PDF format
• Exam-Focused: Aligned with CBSE examination patterns and marking schemes
• Visual Learning: Diagrams, graphs, and illustrations for better understanding