NCERT Solutions for Class 8 Maths

NCERT Solutions 2022-23 of all questions are described completely showing all steps with formulae. If someone is still facing a problem to understanding the solution to any question, please specify through the “Discussion Forum” section. Download 8 Maths Solutions App or 8 Ganit App, which work offline without internet also.

NCERT Solutions for class 8 Maths are given on this webpage. Please give feedback and suggestions to improve the contents and quality of 8th Maths if possible. Use Vedic Maths to make your calculations faster and better. We have started Holiday Homework section to help the students in solving holiday home work in summer vacation. Assignments, Notes, Sample Papers, Chapter test and other study material related to class 8 Maths will be uploaded for the session 2022-23.

Class 8 Maths NCERT Solutions & Main Points of All Chapters

Chapter 1: Rational Numbers

Class 8 Maths Chapter 1 is based on Rations Numbers, which is the collection of Integers, Natural Numbers, Whole Numbers, Decimal and Fractions. We will check here the closure property under Addition, Multiplication, Division and Subtraction for Rational Numbers. Exercise 1.1 of Class 8 Maths is covering the questions on Multiplicative Inverse and other properties of Rational Numbers. In Exercise 1.2 Class 8 Maths, we will draw the Rational Numbers on Number Line.

Chapter 2: Linear Equations in one Variable

Class 8 Maths Chapter 2 describes how to solve a linear equation in one variable. In Exercise 2.1, the simple linear equations in the variable are given to simplify and solve them, whereas Exercise 2.2 contains the questions based on the application of linear equations. Class 8 Maths Exercise 2.3 contains some tricky linear equations to solve them by simplification. Exercise 2.4 of 8th Maths contains some application on a day to day life based on linear equations in one variable concept. In Exercise 2.5, we have to reduce the given equation into linear before solution and Exercise 2.6 has the miscellaneous questions on Chapter 2 of Class 8 Maths.

Chapter 3: Understanding Quadrilaterals

Class 8 Maths Chapter 3 deals with the plane curves like various type of polygons as a triangle, quadrilateral, pentagon, hexagon, heptagon, etc. Exercise 3.1 briefs about the interior and exterior parts of a closed figure, diagonals of a polygon, convex and concave polygons and angle sum property of a polygon. All the questions in Exercise 3.2 are following the property of the Measures of the Exterior Angles of a Polygon. Exercise 3.3 is based on types of quadrilaterals like Trapezium, Kite, Parallelogram with its angles and diagonals. We will discuss some particular type of quadrilateral in Exercise 3.4. These quadrilaterals are Rhombus, Rectangle and Square.

Chapter 4: Practical Geometry

In Class 8 Maths Chapter 4, we will discuss how to construct a unique quadrilateral under the given measurements. All the questions of Exercise 4.1 are on the condition when four sides and one diagonal are given, whereas in Exercise 4.2, and we have to construct a quadrilateral when two diagonals and three sides are given. Similarly, in Exercise 4.3, the given conditions are two adjacent sides and three angles, and in Exercise 4.4, it is three sides, and two included angles of a quadrilateral are given. The last exercise that is Exercise 4.5 contains the constructions of quadrilateral when other special properties are known.

Chapter 5: Data Handling

Class 8 Maths Chapter 5 starts with the concepts of Class Intervals, Lower and Upper Limits, Range, Class Width and Class Size. This is an introduction to Histogram. So, we have to deal with Histogram in Exercise 5.1 of Class 8th Maths. The second exercise that is Exercise 5.2 represents another way of graphical representation, which is Pie Chart or Circle Graph. The third and last topic in Exercise 5.3 is Probability. It describes the concepts of events, outcomes, total favourable events and the total number of events. The Probability is an important topic, even in higher classes.

Chapter 6: Square and Square Roots

In Class 8 Maths Chapter 6, we will learn how to find square or square roots of a number. In Exercise 6.1, most of the questions are based on hit and trial method or successive addition method. Exercise 6.2 is related to find the square of a number by just multiplying the number to itself or using the Binomial Formula of expansion. A brief intro about Pythagoras Triplet is also given in the second exercise. In Exercise 6.3, we have to find square roots of a number by successive subtraction or using Prime Factorisation method. Exercise 6.4 is designed to find the square roots using division methods as well as by estimation. Here we can find the square roots of decimal numbers also.

Chapter 7: Cube and Cube Roots

In Class 8 Maths Chapter 7, we will discuss with the cubes of a number and its cube root also. Exercise 7.1 explain the method of finding cube by adding a consecutive odd number or by using prime factors. Questions related to cube roots are given in Exercise 7.2 of Class 8 Maths. We can also find the cube root of a number using its Prime Factorisation.

Chapter 8: Comparing Quantities

Class 8 Maths Chapter 8 includes the questions related to ratio and proportion. In Exercise 8.1, questions are on ratios and percentage with some practical application. Increase and decrease the percentage, profit and loss percentage, discount, sell tax and VAT related questions are there in Exercise 8.2 of Class 8 Maths. Exercise 8.3 covers the questions based on Simple and Compound Interest when the interest is compounded yearly, half-yearly or quarterly. It also includes the sums of compound interest based on daily life.

Chapter 9: Algebraic Expressions and Identities

In Class 8 Maths Chapter 9, the concepts of algebraic expression with terms, factors and coefficient of Monomial, Binomial and Trinomials are given. Questions of Exercise 9.1 are based on like and unlike terms and addition or subtraction of algebraic expression. Introduction of multiplication of algebraic expression is given in Exercise 9.2 of 8th Maths. Most of the questions carry the product of monomials. Exercise 9.3 includes the questions in which we multiply a polynomial by a monomial, whereas in Exercise 9.4, we learn how to multiply a polynomial by another one. The questions based on identities are given in Exercise 9.5 of Class 8 Maths.

Chapter 10: Visualizing Solid Shapes

In Class 8 Maths Chapter 10 states that the 3-dimensional object looks different when seen from different positions. In Exercise 10.1, we will learn to plot a 3-D object using its Side view, Front view, Top view or some other factors. The description of mapping places and spaces are given in Exercise 10.2 of Class 8 Maths. In Exercise 10.3, we will learn to find out the Edges, Faces and Corners or Vertices of a 3 – D object. Euler’s Formula (F + V – E = 2) is important in this exercise. Most of the time, a question based on Euler’s Formula is asked in school exams.

Chapter 11: Mensuration

Class 8 Maths Chapter 11 Mensuration is not only the main topic for class 8, but it is important for further classes also. Exercise 11.1 contains only five questions, in which the 5th question is tricky. In Exercise 11.2, we will deal with the areas related to Trapezium and another quadrilateral, when the perpendicular to the side or diagonal is given. Next step is to find the surface area of solid figures in Exercise 11.3 of Class 8 Maths. Here, we will learn to find out the areas of Cube, Cuboid, Cylinder, Sphere, Hemi-sphere or Cone. The volume of these 3 – D figures can be obtained using the formulae used for Exercise 11.4 in 8th Maths.

Chapter 12: Exponents and Powers

In Class 8 Maths Chapter 12, we will study the numbers having negative or positive powers. Exercise 12.1 is based on the Laws of Exponents. Questions 5, 6 and 7 are important for exams. The second exercise explains about the Scientific Form or Standard Form. In Exercise 12.2, we convert the numbers in the standard form with the help of exponents.

Chapter 13: Direct and Inverse Proportions

Class 8 Maths Chapter 13, we have to check whether the value of both the quantities are increasing or one is increasing and other is decreasing. Exercise 13.1 has the questions of Direct Proportion, where the two quantities increase or decrease together. Similarly, Exercise 13.2 also deals with Inverse Proportion, where one value is increasing, but other is decreasing. The second exercise also contains the questions where Direct and Inverse are implemented in the same question.

Chapter 14: Factorization

In Class 8 Maths Chapter 14, we will study about factors of natural numbers as well as algebraic expressions. In Exercise 14.1, we will make factors by regrouping the terms, whereas, in Exercise 14.2, identities are the main tool for Factorisation. Division of algebraic expression by monomial or polynomial is important for class 8th students. Exercise 14.3 contains questions based on the division of polynomials by another polynomial. At last, in Exercise 14.4, there some errors given in equations. Students have to remove these errors to make the equations or identities true.

Chapter 15: Introduction to Graphs

Class 8 Maths Chapter 15 describes the methods to plot a Bar Graph, a Pie Chart or Circle Graph, Histograms and a Line Graph. Most of the questions in Exercise 15.1 are based on Line Graphs. Concepts of the coordinate system, x-axis and y-axis are given in Exercise 15.2 of Class 8 Maths. Here, we learn how to take points of x – coordinates and y – coordinates on a plain sheet of paper. Graphs related to two variables are present in Exercise 15.3 of 8th Maths. These are the questions based on the application of linear equations in two variables.

Chapter 16: Playing with Numbers

In Class 8 Maths Chapter 16, we have to represent numbers in a general form. Exercise 16.1 is just based on addition, subtraction and multiplication of numbers in the form of a puzzle. This the most exciting exercise to solve the questions with fun. In Exercise 16.2 of Class 8 Maths, we will discuss the test of divisibility by 2, 3, 5, 9 and 10. This exercise is also enjoyable. No one bore doing these exercises of Class 8 Maths Chapter 16 Playing with Numbers.

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