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# CBSE Class 8th Maths Notes

CBSE Class 8th Maths Notes cover all chapters from the updated NCERT textbooks, including topics such as Rational Numbers, Algebraic Expressions, Practical Geometry, and more. Class 8 is an essential time for students as subjects become harder to cope with. At GeeksforGeeks, we provide easy-to-understand Class 8th Maths Notes for quick revision of important concepts.

Additionally, there are solutions for NCERT and RD Sharma problems, as well as 1500+ Most Asked Questions and Chapterwise Important Formulas to improve students’ basic knowledge. These study materials are an excellent resource to prepare for the final exams.

## CBSE Class 8th Maths Notes Chapters List (2023)

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

## Deleted Chapters from NCERT Class 8th Maths Notes (2023-2024)

The most recent CBSE Class 8th Mathematics syllabus has been changed and reduced by 30% for the upcoming annual assessment in the academic year 2023-2024, you can find the list of all deleted chapters/topics in the table below:

## 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 Rules Used in CBSE Class 8 Maths Notes Chapter 1 Rational Numbers:

For any rational numbers a, b, and c,

• Multiplicative Inverse: (a ⁄ b) × (b/a) = 1.
• Additive Inverse: a + (-a) = (-a) + a = 0.
• Closure Property – Addition: a + b is also a rational number.
• Closure Property – Multiplication: a × b is also a rational number.
• Commutative Property – Addition: a + b = b + a.
• Commutative Property – Multiplication: (a × b) = (b × a).
• Associative Property – Addition: (a + b) + c = a + (b + c).
• Associative Property – Multiplication: (a x b) x c = a x (b x c).
• Distributive Property: a × (b + c) = (a × b) +( a × c).

## Chapter 2: Linear Equations in One Variable

A linear equation in one variable is represented as ax+b = 0, where a and b are integers and x is a variable with one solution. The unknown quantity is usually represented by ‘x’ in a linear equation. There are various basic approaches to solving a linear equation, such as isolating variables and constants on separate sides of the equation.

In addition to addition, subtraction, multiplication, and division, the chapter also covers other techniques for solving algebraic equations. To solve linear equations, one must learn to solve equations with variables on both sides and simplify equations

### Important Points Covered in Class 8th Maths Notes 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.

A quadrilateral is a closed, 2-D shape with four linear sides, and there are several types based on their edges and vertices, including squares, rectangles, parallelograms, trapeziums, kites, and rhombuses. CBSE Class 8 Maths Notes Chapter 3 covers various characteristics and types of quadrilaterals, including special ones like squares, rectangles, parallelograms, kites, and rhombuses.

The chapter also includes essential theorems such as the Angle sum property and Exterior angle property. Quadrilaterals, like polygons, are classified by their sides and angles, and trapeziums, kites, and parallelograms are among the examples.

### Major Points and Formulas can be Studied in Class 8th Maths Notes 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.

## 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 8th 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.

### Major Points Covered in Class 8th Maths Notes 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.

## 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.

### Important Methods are Used to Organize and Represent Data in Class 8th 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.

## Chapter 6: Squares and Square Roots

CBSE Class 8 Maths Notes, Chapter 6 covers squares and square roots, where squares represent the numbers obtained after multiplying a number by itself, while square roots represent the value obtained after multiplying a number by itself to give the original value. This chapter is divided into two parts: Squares and Square Roots. The first section includes the Properties of Square Numbers, Interesting Patterns, and Finding the square of a number, while the second section explains Finding square roots through different methods like Repeated Subtraction, Prime Factorization, and Division Method.

### Important Points Learned in Class 8th Maths Notes 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.

## 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 that 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 an 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 be learned in this chapter.

### Important Concepts Learned in Class 8th Maths Notes 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

## 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.

### Important Formulas Covered in Class 8 Maths Notes 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

## 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 scoring sections of this chapter.

### Important Algebraic Identities:

• (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)

## 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, explanations of Faces, Edges, and Vertices, and Regular polyhedrons. However, Euler’s formula is the most important topic in this chapter.

### Important Formula Covered in Class 8th Maths Notes 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.

## 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.

## Chapter 12: Exponents and Powers

The chapter Exponents and Powers cover the primary concepts such as the 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 Notes Chapter 12 Exponents and Powers:

• 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

## 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 Notes 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.

## 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. The 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 8th Maths Notes 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

## Chapter 15: Introduction to Graphs

This chapter is all about the basic understanding of 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 Graphs, Pie Graph, Histogram, Line Graph, and Linear Graphs are some essential terms that are majorly covered in this chapter.

### Important Terms in Class 8th Maths Notes 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.

## 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.

### List of Important Points Covered in Class 8 Maths Notes 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.

## FAQs on CBSE Class 8th Standard Maths Notes

### Q1: 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.

### Q2: What is a rational number in CBSE Class 8th 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.

### Q3: What are some most important chapters in maths class 8th?

The important chapters in maths class 8th 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.

### Q4: 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.