# CBSE Class 8 Maths Notes

• Difficulty Level : Easy
• Last Updated : 04 Jul, 2022

Class 8 is that turning point in the life of students when subjects start to get difficult and it becomes harder for students to cope. It’s important that students learn the basic foundation of subjects like Maths from a young age and Class 8 seems the best time to start. CBSE students find it hard to understand NCERT Maths problems and finding solutions that are easy to understand is as hard as practically doing them. This is where GeeksforGeeks put its foot down to create the easy-to-understand CBSE Class 8 Maths Notes that are well prepared for quick revision of all the important concepts that will help the students to score good marks in board exams. These CBSE notes will help students to understand the tough maths problems without any worries.

These class 8th maths revision notes are prepared in an order to provide good knowledge of all the chapters based on the updated syllabus for Class 8th provided by the CBSE in their NCERT textbooks.

These notes are prepared by our experts and are available for free at GeeksforGeeks. CBSE Class 8 Maths Notes cover all the important chapters given in the revised NCERT textbooks that include some Important topics of Class 8 Maths like Rational Numbers, Direct and Inverse proportions, Algebraic Expressions and Identities, Practical Geometry, Polygons, etc.

Class 8 Maths Notes cover some more important topics like Cubes and Cube roots, Linear equations, Playing with numbers, Surface area, and Volumes from Class 8 Maths NCERT. Our experts have also covered Class 8 Maths Solutions like NCERT Solutions for Class 8, and RD Sharma Solutions for Class 8.

To improve the basic knowledge of students, we have also covered 1500+ Most asked Questions of Mathematics, Chapterwise Important Formulas, and many more based on the new Class 8th CBSE curriculum. These notes and other study materials provide a helping hand for students to prepare for their Final Examinations.

## CBSE Class 8 Maths Topic-wise Revision Notes

All the Chapters covered in Class 8 Maths NCERT textbooks are listed below. Here is the detailed chapter-wise information about the Class 8 Maths syllabus provided by CBSE. Additionally, this also contains all the major topics that have been covered in Class 8 Maths NCERT textbooks and Class 8 CBSE Maths Syllabus.

## Chapter 1: Rational Numbers

Any number that can be described in p/q form where q is not equal to zero is called a rational number. A rational number is a kind of real number. Or in other words, Any fraction with non-zero denominators is a rational number. Examples of rational numbers are 1/2, 1/5, 3/4,  and so on. The number “0” is also a rational number, as we can define it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values.

In this chapter, you will learn more about Rational Numbers, the representation of rational numbers on the number line, and rational numbers between two rational numbers. To represent rational numbers on a number line, we need to streamline and write in the decimal form first.

Important formulas and Properties used in Class 8 Maths Chapter 1- Rational Numbers,

For any rational numbers a, b and c,

Want to know more about these topics??? We have covered them here:

More resources for CBSE Class 8 Maths Chapter 1

## Chapter 2: Linear Equations in One Variable

The linear equation in one variable is an expression that is denoted as ax+b = 0, where a and b are any two integers, and x is a variable and consists of only one solution. A linear equation is a simple technique to convey a mathematical proposition. Any variable or symbol can be used to represent unknown values, however, in most cases, a variable ‘x’ is used to represent the unknown number in a linear equation with only one variable. A linear equation can be solved using a variety of basic approaches. To acquire the final value of the unknown quantity, the variables are isolated on one side of the equation and the constants are isolated on the other. An algebraic equation is an equality involving variables. The expression on the left of equality is called LHS (Left Hand Side) and on the right is called RHS (Right Hand Side).

Some methods to solve algebraic equations like addition or subtraction and multiplication or division and transposing can be learned in this chapter. Other significant methods to solve linear equations are, solving equations having variables on both sides and reducing equations to a simpler form.

Important points covered in Class 8 Maths Chapter 2- Linear Equations in One Variable

• A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable.
• A simple example of a linear equation with only one variable, x, may be written in the form:

ax + b = 0

where a and b are constants and a ≠ 0.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 2

## Chapter 3: Understanding Quadrilaterals

Geometrically, a quadrilateral is defined as a closed, 2-D shape that has four linear sides. The different types of quadrilaterals according to their number of edges and vertices are square, rectangle, parallelogram, trapezium, kite, and rhombus.

Chapter 3 of CBSE Class 8 Maths Notes covers a wide range of characteristics and kinds of quadrilaterals. However, the solutions and explanations provided in these answers aid in the learning process by ensuring that students shave a solid geometrical basis.

Special quadrilaterals such as squares, rectangles, parallelograms, kites, and rhombuses are explained in detail in Class 8th math notes. Some important theorems can also be learned in this chapter like the Angle sum property and the Exterior angle property

Another section covered in this chapter is Quadrilaterals. Like Polygons, Quadrilateral are also classified on the basis of the nature of their sides and angle. Examples of Quadrilaterals are Trapezium, Kite, Parallelogram, etc.

Major points and formulas can be studied in Class 8 Maths Chapter 3- Understanding Quadrilaterals,

• A simple closed curve made only of line segments is called a Polygon. Polygons are classified based on various factors like the number of their sides or vertices, part of the diagonals in exteriors, and the size and angle between the vertices.
• Some examples of Polygons are Triangle, Quadrilateral, Pentagon, Hexagon, Heptagon, Octagon, Decagon, … , n-gon, Convex Polygons, concave Polygons, regular Polygons, Irregular Polygons, etc.
• Angle Sum Property: This property states that the sum of all angles of a quadrilateral is 360°.
• Sum of the Measures of the Exterior Angles of a Polygon: Regardless of the number of sides in the polygons, the total of the measurements of the exterior angles equals 360 degrees.
• The parallelogram is the four-sided geometrical figure in which the pair of two opposite sides of it are parallel to each other. The main types of parallelograms are, Rhombus, rectangle, square, etc.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 3

## Chapter 4: Practical Geometry

This is the chapter where students can gain extra marks if they understand the detailed explanations. Chapter 4 of CBSE Class 8 Maths Notes covers practical geometry which simply means constructing geometrical figures like squares, triangles, quadrilaterals, etc. using a scale, and compass when different parameters of it are known.

The main concept that is learned in this chapter is the Construction of a Quadrilateral under different cases. These cases depend on the given factors of the quadrilateral to determine the unknown one.

Hence, the major points covered in Class 8 Maths Chapter 4- Practical Geometry,

• Geometry is a branch of mathematics that deals with the problems of size, shape, volume, locations, and positions of the figures, and the properties of space. Geometry gives us a practical way of working with Volumes and areas of the figures.
• To construct a quadrilateral uniquely, five measurements are required.
• A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal are given.
• A quadrilateral can be constructed uniquely if its two diagonals and three sides are known.
• A quadrilateral can be constructed uniquely if its two adjacent sides and three angles are known.
• A quadrilateral can be constructed uniquely if its three sides and two included angles are given.

In this chapter, you’ll be introduced to only 1 topic:

More about CBSE Class 8 Maths Chapter 4

## Chapter 5: Data Handling

If you want to understand What is Data Handling? and How does it work? and Why it’s needed? then read chapter 5 of CBSE Class 8 Maths Notes. Data handling refers to the process of collecting, organizing, and presenting any raw information. Data handling is an important maths concept that ensures the integrity of the study data. Whatever subject we choose, we have knowledge in the form of a numerical figure. Every value of this kind is referred to as an observation. Typically, data refers to the collection of all observations. in a way that is helpful to others like in graphs or charts, etc.

The sub-topics covered in this chapter are Organising Data, Grouping Data, Bars with a difference, Circle Graph or Pie Chart, and Chance And Probability. In the Class 8 syllabus, Data Handling also includes some basic concepts of probability like Equally likely Outcomes, Linking chance to Probability, Outcomes as events, and some real-life examples of Chances and Probability.

Some Important methods are used to organize and represent Data in Class 8 Maths Chapter 5- Data Handling,

• Graphical representation of data:
1. Pictograph: Pictorial representation of data using symbols.
2. Bar Graph: A display of information using bars of uniform width, their heights proportional to the respective values.
3. Double Bar Graph: A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data.
4. Histogram: a graphical representation of frequency distribution in the form of rectangles with class intervals as bases and heights proportional to corresponding frequencies such that there is no gap between any successive rectangles.
5. Circle Graph or Pie Chart: A pictorial representation of the numerical data in the form of sectors of a circle such that area of each sector is proportional to the magnitude of the data represented by the sector.
• Probability = Number of outcomes making up an event / Total number of outcomes, if the outcomes are equally likely.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 5

## Chapter 6: Squares and Square Roots

Chapter 6 of CBSE Class 8 Maths Notes covers the concepts of squares and square roots that are opposite to each other. As the squares are used for the numbers come after multiplying the number by itself. However, the square root of a number is the value obtained when multiplied by itself to give the original value. For instance, the square of 5 is 25 and the square root of 25 is 5.

This chapter is divided into two parts: Squares and Square roots. The first section of this chapter consists of the Properties of Square Numbers, Interesting Patterns, and Finding the square of a number, also the Pythagorean triplets.

Another section covered in this chapter is Square Roots, which explains Finding square roots through different methods like Repeated Subtraction, Prime Factorization, and Division Method. This section not only discusses the Square Roots of simple numbers but even the methods to Determine the square roots of Decimals and Estimating Square Roots.

Important points learned in Class 8 Maths Chapter 6- Squares and Square Roots,

If q is a natural number such that p2= q then,

√q = p and –p

Some of the important properties of Squares and Square roots are listed below:

• There are 2n non-perfect square numbers between n2 and (n+1)2.
• If a perfect square is of n digits then its square root will have n/2 digits if n is even, or (n+1)/2, if n is odd.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 6

## Chapter 7: Cubes and Cube roots

Chapter 7 of CBSE Class 8 Maths Notes again talks about the concepts of cubes and cube roots opposite to each other. As the cubes are used for the numbers come after multiplying the number by itself thrice. However, the cube root of a number is the value obtained when multiplied by itself thrice to give the original value. For instance, the cube of 5 is 125 and the cube root of 125 is 5.

This chapter thus provides the introduction to Cubes, Some interesting patterns to find cubes, Smallest multiple that is a perfect cube. Also, the introduction to concepts of Cube Roots, the methods to determine the Cube roots through the prime factorization method, and the Cube root of a cube number can also be learned in this chapter.

Important concepts learned in Class 8 Maths Chapter 7- Cubes and Cube roots,

Consider any number m, which can be expressed as the product of any number three times as m = n × n × n = n3. n3 is so known as the cube of n and m is now known as cube root of n:

3√m = n

Method of finding a Cube Root: There are two different ways to determine the cube root of a number, that are:

1. Prime Factorization Method
2. Estimation Method

Here, we’ll solely focus on:

More about CBSE Class 8 Maths Chapter 7

## Chapter 8: Comparing Quantities

In chapter 8 of CBSE Class 8 Maths Notes, we’ll cover Comparing quantities which is the most basic everyday-life application of Mathematics that deals with quantities. Students can understand how the market works at a young age. This includes the concepts like percentage, ratio, market price, selling price, cost price, discount and discount price, profit or loss, interest, etc.

The sub-topics in this chapter are: Ratios and Percentages, Finding the Increase or Decrease Percentage and Finding Discounts. Also, the Estimation in percentages, Prices Related To Buying And Selling (Profit And Loss), and Finding cost price/selling price, are thoroughly explained in this chapter.

Students can also learn Compound Interest along with deducing a Formula for Compound Interest, Rate Compounded Annually or Half Yearly (Semi-Annually), and Applications of Compound Interest formulas in Comparing Quantities.

Important formulas covered in Class 8 Maths Chapter 8- Comparing Quantities,

• Profit = Selling price – Cost price
• Loss = Cost price – Selling price
• If SP > CP, then it is profit.
• If SP = CP, then it is neither profit nor loss.
• If CP > SP, then it is loss.
• Discount = Marked Price – Sale Price
• Discount % = Discount × 100 / MP
• Profit Percentage = (Profit / Cost Price) × 100
• Loss Percentage = (Loss / Cost Price) × 100
• Percentage Increased = Change in Value / Original Value
• Simple Interest = ( Principal × Rate × Time )/100
• Compound Interest Formula = Amount – Principal
• Sales tax or VAT =  Tax of  Selling price = (Cost Price × Rate of Sales Tax) / 100
• Billing Amount = Selling price + VAT

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 8

## Chapter 9: Algebraic Expressions and Identities

Chapter 9 – Algebraic Expressions and Identities provides information about the basics of monomials, binomials, and polynomials in an algebraic expression.

Here we’ll learn about some basic terminologies like Expressions, Terms, Factors, Coefficients, Monomials, Binomials, and Polynomials. Along with these basics operations like Addition, Subtraction, and Multiplication of Algebraic Expressions are covered in this chapter. Standard Identities, and Applying Identities from this chapter are the most important and scoring sections of this chapter.

Important formulas covered in Class 8 Maths Chapter 9- Algebraic Expressions and Identities are,

• (a + b)2 = a2 + 2ab + b2
• (a – b)2 = a2 – 2ab + b2
• (a + b) (a – b) = a2 – b2
• (x + a) (x + b) = x2 + (a + b)x + ab
• (x + a) (x – b) = x2 + (a – b)x – ab
• (x – a) (x + b) = x2 + (b – a)x – ab
• (x – a) (x – b) = x2 – (a + b)x + ab
• (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – b3 – 3ab(a – b)

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 9

## Chapter 10: Visualising Solid Shapes

Visualizing Solid Shapes is a concept that provides the understanding of different solids shapes when visualized in different dimensions and various terms used to describe their properties.

This is one of the easiest scoring chapters in Class 8 maths. Thus, this chapter helps to understand the interesting topics related to solid shapes. These topics are Views of 3D-Shapes, explanation of Faces, Edges, and Vertices, and Regular polyhedrons. However, Euler’s formula is the most important topic in this chapter.

Important formula that is covered in the Class 8 Maths Chapter 10- Visualising Solid Shapes,

A polyhedron has a certain number of planar faces, edges, and vertices that meet the formula:

F + V – E = 2

where F is the number of faces. The letters V and E stand for the number of vertices and edges, respectively.

The above formula is called as Euler’s formula.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 10

## Chapter 11: Mensuration

Mensuration is the chapter that deals with the measurement or the calculations related to determining the area, perimeter, volume of various geometrical figures like squares, cubes, rectangles, cuboids, cylinders, and triangles, etc.

The chapter consists of the calculation of area and volume for trapezium, quadrilateral, polygons, cube, cuboid, etc., by understanding the formulas. Thus, the major topics explained in this chapter are only related to Surface areas and Volumes. The area of the Trapezium, some general quadrilaterals, polygons, etc are covered in the first section. While the surface areas and volumes of different solid shapes like cubes, cuboids, cones, etc are covered in the next section of the chapter.

Here is the list of major formulas covered in Class 8 Maths Chapter 11- Mensuration,

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 11

## Chapter 12: Exponents and Powers

The chapter Exponents and powers cover the primary concepts such as laws of exponents and their applications. The chapter deals with the problems using the applications of power to write large numbers in exponents and vice-versa.

In this chapter, we will learn to calculate negative exponents and negative power values. The sub-topics in this chapter explained are Powers with Negative Exponents, Laws of Exponents along with the use of Exponents to Express small numbers in Standard Form.

Important Laws covered in Class 8 Maths Chapter 12- Exponents and Powers are,

• Law of Product: am × an = am + n
• Law of Quotient: am/an = am – n
• Law of Zero Exponent: a0 = 1
• Law of Negative Exponent: a-m = 1/am
• Law of Power of a Power: (am)n = amn
• Law of Power of a Product: (ab)n = ambm
• Law of Power of a Quotient: (a/b)m = am/bm

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 12:

## Chapter 13: Direct and Inverse Proportions

This chapter gives a detailed explanation of inverse and direct proportions through word problems. Any two quantities a and b can be said to be in direct proportion if they variate (increase or decrease) together with each other in such a way that the ratio of their corresponding values remains the same. However, two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant.

Major points covered in Class 8 Maths Chapter 13- Direct and Inverse Proportions,

• Proportionality is represented by the symbol ∝. For example, if we claim that p is proportional to q, this implies p ∝ q and if we say that p is inversely proportional to q, then this implies “p∝1/q.”
• Direct Proportion: If a/b = k, where k is any positive number, then a and b are said to be in direct proportion. e.g. If the number of things bought increases, then the total cost of purchase also increases.
• Inverse Proportion: If xy = k, then x and y are said to vary inversely. e.g. If the number of people increases, the time is taken to finish the food decreases. Or If the speed will increase the time required to cover a given distance will decrease.

In this chapter, we’re solely focusing on:

More about CBSE Class 8 Maths Chapter 13

## Chapter 14: Factorisation

This chapter comprises the problems on the factors of natural numbers and algebraic expressions, factorization by regrouping terms, factorization using identities, and division of algebraic expressions

Major topics and subtopics that can be understood in-depth are, Factors and How to do Factorisation? Some common methods for performing factorization are, Factorisation by regrouping terms, Factorisation using identities, and Factors of the form (x+a) (x+b) is also part of this chapter. Most important and scoring topic in this unit is the Division of Algebraic Expressions- monomial by another monomial, polynomial by a monomial. Thus, this will help students to understand all about factorization.

Important formulas explained in Class 8 Maths Chapter 14- Factorisation,

• A number of factorable expressions are of the form or may be factored into the form: a2 + 2ab + b2, a2 – 2ab + b2, a2 – b2 and x2 + (a + b)x + ab. These expressions can be easily factorized using below mentioned identities as,
• a2 + 2ab + b2 = (a + b)2
• a2 – 2ab + b2 = (a – b)2
• a2 – b2 = (a + b) (a – b)
• x2 + (a + b)x + ab = (x + a)(x + b)
• We have divisions of algebraic expressions in the case of divisions of algebraic expressions that we discussed in this chapter.

Dividend = Divisor × Quotient

or

Dividend = Divisor × Quotient + Remainder

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 14

## Chapter 15: Introduction to Graphs

This chapter is all about the basic understanding of the graphs, kinds of graphs, etc. Lately, this chapter provided an emphasis on the construction of different types of graphs and their applications.

Introduction to graphs like – Bar Graph, Pie Graph, Histogram, Line Graph, and Linear Graphs are some important terms that are majorly covered in this chapter.

Important terms that are discussed in Class 8 Maths Chapter 15- Introduction to Graphs,

• Bar Graph: When comparing categories, the bar graph is the most appropriate tool.
• Pie charts: The pie charts are the best way to compare sections of a whole.
• Histogram: A histogram may be used to make data simpler to interpret when it is presented in intervals.
• Line Graph: A line graph will be beneficial in the situation of data that changes constantly over time.

CBSE Class 8 Maths Topicwise Notes Chapter 15

More about CBSE Class 8 Maths Chapter 15

## Chapter 16: Playing with Numbers

All the above-mentioned chapters basically helped to learn about various kinds of numbers and their different properties likewise in this chapter the concept of numbers is discussed in a more general way.

Numbers in General Form, Games with Numbers, and Letters for Digits are covered in this chapter. However, Divisibility tests like Divisibility by 10, Divisibility by 5, Divisibility by 7, Divisibility by 9, and 3 are also covered.

Here is the list of some important points that are covered in Class 8 Maths Chapter 16- Playing with Numbers,

• Divisibility by 2: A number is divisible by 2 when its one’s digit is 0, 2, 4, 6 or 8.
• Divisibility by 3: A number is divisible by 3 when the sum of its digits is divisible by 3.
• Divisibility by 4: A number is divisible by 4 when the number formed by its last two digits is divisible by 4.
• Divisibility by 5: A number is divisible by 5 when its ones digit is 0 or 5.
• Divisibility by 6: A number is divisible by 6 when it is divisible by both 2 and 3.
• Divisibility by 9: A number is divisible by 9 when the sum of its digits is divisible by 9.
• Divisibility by 10: A number is divisible by 10 when its one digit is 0.
• Divisibility by 11: A number is divisible by 11 when the difference of the sum of its digits in odd places and the sum of its digits in even places is either o or a multiple of 11.

In this chapter, you’ll be introduced to these topics:

More about CBSE Class 8 Maths Chapter 16:

## Frequently Asked Questions (FAQs)

Question 1: How to Score Good Marks in CBSE Class 8th Maths?

Getting good grades in Class 8 Math is not hard. You may become one of the best scores in your class if you implement the appropriate approach and pick the right study materials. The most important aspect of maths performance is practise. You should prioritise completing NCERT in the test prep. You should begin studying your test syllabus after completing NCERT.

Question 2: What is a rational number in CBSE Class 8 Maths?

Any number that can be written in the form of ab, where, a and b are integers (positive or negative number) and b is not equal to zero can be called a rational number. For example, -21, 76 etc.

Question 3: What are some most important chapters in maths class 8?

The important chapters in maths class 8 for exams as well as for further classes are-

1. Comparing Quantities,
2. Algebraic identities and expressions,
3. Mensuration,
4. Exponents and Powers, and
5. Factorisation.

Question 4: How to remember math formulas easily?

Some of the best tips to memorize the maths formulas are listed below:

• Develop an interest in the concept you are studying. Because it is always easier for a student to understand and memorize something that interests you.
• While learning these concepts relate them to visuals. Simply attaching a visual to every maths formula, will help you to save and memorize it for a long.
• Before going through any result one must its process first, that how the conclusion arrives. Therefore, the same happens with memorizing maths formulas also.
• Always solve problems using your maths formulas repeatedly, because repetition leads to memorization.

Question 5: What are the benefits of referring to GFG’s Class 8 Maths Notes available here?