 # Ncert Solutions For Class 8 Maths

NCERT Solutions for Class 8 Maths are provided here to help you clear all your doubts and boost your exam preparations. We bring you comprehensive NCERT Solutions for Class 8 Maths. Our highly experienced Mathematics teachers have designed these detailed chapter-wise NCERT solutions for Class 8 Mathematics for your better understanding. In addition, the solutions for each practice are organized in separate PDF files. These maths PDF files of NCERT Solutions Class 8 can be downloaded for free from the official website of Utopper. These NCERT solutions are based on the updated CBSE syllabus and guidelines.

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#### NCERT Solutions for Class 8 Maths

The Class 8 Maths NCERT book 16 contains Chapters:

#### Class 8 Maths Ncert Solutions and main points of all chapters

##### Chapter 1: Rational Numbers

Class 8 Mathematics Chapter 1 is based on ration numbers, which are a collection of integers, natural numbers, whole numbers, decimals, and fractions. We will examine the closure property under addition, multiplication, division, and subtraction for rational numbers here. Class 8 Mathematics practice 1.1 is involving questions on multiplier inverse and other properties of rational numbers. Exercise 1.2 In Class 8 mathematics, we will draw rational numbers on the number line.

##### Chapter 2: Linear Equations in a Variable

Class 8 Mathematics Chapter 2 describes how to solve a linear equation in a variable. In Exercise 2.1, simple linear equations of variables are given to simplify and solve them, while in Exercise 2.2 there are questions based on the application of linear equations. Class 8 Mathematics Practice 2.3 has some complex linear equations to solve by simplification. A variable concept in 8th mathematics practice 2.4 has some applications in daily life based on linear equations. In Exercise 2.5, we have to convert the given equation to linear before solving and in Exercise 2.6 there are various questions from Chapter 2 of class 8 mathematics.

##### Chapter 3: Understanding the Quadrilateral

Class 8 Mathematics Chapter 3 deals with plane curves like different types of polygons such as triangles, quadrilateral, pentagon, hexagon, heptagon, etc. Exercise 3.1 summarizes the inner and outer parts of a closed shape, the diagonal, convex and, polygon. Angle sum properties of concave polygons and polygons. All the questions in Exercise 3.2 follow the properties of measurements of the external angles of a polygon. Exercise 3.3 is based on types of quadrilaterals such as trapezoid, kite, a parallel quadrilateral with angles, and diagonals. We will discuss some special types of quadrilaterals in Exercise 3.4. These quadrilaterals are rhombus, rectangle, and square.

##### Chapter 4: Practical Geometry

In Class 8 Mathematics Chapter 4, we will discuss how to construct a unique quadrilateral under the given measurements. All the questions in Exercise 4.1 are on the condition that 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 terms are two adjacent sides and three angles, and in Exercise 4.4, it is three sides, and two quadrilateral angles of a quadrilateral are given. The final exercise, which is Exercise 4.5, involves the formation of quadrilaterals when other special properties are known.

##### Chapter 5: Data Handling

Class 8 Mathematics Chapter 5 starts with the concepts of class interval, lower and upper limit, range, square width, and square shape. This is an introduction to the histogram. Therefore, we have to study the histogram in class 5.1 mathematics practice 5.1. The second exercise, which is Exercise 5.2, represents another method of graphical representation, which is a pie chart or circle graph. The third and final topic in Exercise 5.3 is probability. It describes the concepts of events, outcomes, total favorable events, and a total number of events. Probability is an important subject even in higher classes.

##### Chapter 6: Square and Square root

In class 8 mathematics chapter 6 we will learn how to find the square root or square root of a number. In practice 6.1, most of the questions are based on the hit and trial method or the sequential addition method. Exercise 6.2 deals with finding the square of a number simply by multiplying it by itself or by using the binomial formula of the expansion. A brief introduction about the Pythagoras triplets is also given in the second exercise. In Exercise 6.3, we have to find the square root of a number using the ordinal subtraction or prime factorization method. Exercise 6.4 is designed to find the square root by division methods as well as an approximation. Here we can also find the square root of decimal numbers.

##### Chapter 7: Cube and Cube root

In class 8 mathematics chapter 7 we will also discuss the cubes of a number and its cube root. Exercise 7.1 Explain the method of finding a cube by adding consecutive odd numbers or using prime factors. Questions related to cube root are given in Exercise 7.2 for Class 8 mathematics. We can also find the cube root of a number by using its prime factor.

##### Chapter 8: Comparison of Quantities

Class 8 Mathematics Chapter 8 contains questions related to ratios and ratios. In Exercise 8.1, there are questions on proportions and percentages with some practical application. Class 8 Maths Practice 8.2 has questions related to increase and decrease the percentage, profit and loss percentage, rebate, sales tax, and VAT. Practice 8.3 covers questions based on simple and compound interest when the interest is compounded yearly, semiannually, or quarterly. It also includes compound interest based on daily life.

##### Chapter 9: Algebraic Expressions and Identities

In class 8 mathematics chapter 9, concepts of algebraic expressions with terms, factors, and coefficients of monomial, binomial, and tripod are given. Questions in Exercise 9.1 are based on the same and odd terms and addition or subtraction of the algebraic expression. Practices of 8th Mathematics 9.2 introduce multiplication of algebraic expressions. Most questions have the property of monomial. Exercise 9.3 includes questions in which we multiply a polynomial with a monomial, while in Exercise 9.4 we learn to multiply one polynomial with another. Questions based on common questions are given in Class VII Maths Exercise 9.5.

##### Chapter 10: Imagining Solid Shapes

Mathematics chapter 10 of class 8 states that a 3-dimensional object looks different when viewed from different positions. In Exercise 10.1, we will learn to plot a 3-D object using its lateral view, front view, top view, or some other factor. Mapping locations and locations are described in Exercise 10.2 of Class 8 mathematics. In Exercise 10.3, we will learn to find the edges, faces, and corners or vertices of a 3-D object. Euler’s formula (F + V – E = 2) is important in this practice. Most of the time, school exams ask questions based on Euler’s formula.

##### Chapter 11: Mensuration

Class 8 Mathematics Chapter 11 Mensuration is not only the main subject for Class 8, but it is also important for further classes. Exercise 11.1 has only five questions, of which the fifth question is difficult. In Exercise 11.2, we will talk about areas related to the trapezium and another quadrilateral, when given vertically on the arm or diagonal. The next step is to find the surface area of ​​solid figures in Class 11 Maths Exercise 11.3. Here, we will learn to find the area of ​​a cube, cuboid, cylinder, sphere, semi-sphere, or cone. The volume of these 3-D digits can be obtained using the formulas used for Exercise 11.4 in 8th Mathematics.

##### Chapter 12: Exponents and powers

In Class 8 mathematics chapter 12, we will study numbers that have negative or positive powers. Practice 12.1 is based on exponential rules. Questions 5, 6, and 7 are important for the exam. The second practice refers to the scientific form or standard form. In Exercise 12.2, we convert numbers into standard form with the help of exponents.

##### Chapter 13: Direct and Inverse Proportion

Class 8 Mathematics Chapter 13, we have to check whether the values ​​of both quantities are increasing or one is increasing and the other is decreasing. Exercise 13.1 has direct proportionality questions, where two quantities increase or decrease simultaneously. Similarly, Exercise 13.2 also deals with the inverse ratio, where one value is increasing, but the other is decreasing. The second exercise also includes questions where Direct and Inverse are applied to the same question.

##### Chapter 14: Factors

In class 8 mathematics chapter 14, we will study factors of natural numbers as well as algebraic expressions. In Exercise 14.1, we will regroup factors by regrouping terms, while in Exercise 14.2, identities are the main tool for factorization. It is important for class 8 students to divide the algebraic expression by a monomial or polynomial. Exercise 14.3 contains questions based on the division of polynomials by another polynomial. Finally, in Exercise 14.4, some errors are given in the equations. Students must correct these errors to make the equations or identities true.

##### Chapter 15: Introduction to Graphs

Class 8 Mathematics Chapter 15 describes the methods of plotting a bar graph, a pie chart or circle graph, histogram, 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 mathematics. Here, we learn how the points of x-coordinates and y-coordinates are taken on a plain sheet of paper. Eighth mathematics exercises 15.3 contain articles related to two variables. These are questions based on the application of linear equations in two variables.

##### Chapter 16: Playing with Numbers

In class 8 mathematics chapter 16, we have to present numbers in a general form. Exercise 16.1 is based only on the addition, subtraction, and multiplication of numbers in the form of a puzzle. This is the most exciting practice to solve questions in a fun way. We will discuss the divisibility test from 2, 3, 5, 6, and 10 in class 4 maths exercises 14.2. This practice is also entertaining. Class 8 Mathematics Chapter 16 Doing these exercises of playing with numbers did not make any sense.