NCERT Solutions For Class 8 Maths

Mathematics is the subject most students would like to run away from. This is not because the subject is tough but due to the complexity of the presentation. Maths is the subject that needs interest in the numbers and application of mind in the proper direction. Mathematics involves proving and discovering numbers. The objects in maths are either abstract from nature like natural numbers or in modern mathematics entities are stipulated with certain properties.

The mathematics syllabus in class 8 has some chapters which are tough to understand for the average student but they are essential to building the formation for the next two schooling years. Moreover, the syllabus is selected based on the capacity of an average student only so it is good if the students are learning it by heart. Ambitious students will usually make it good in all subjects but maths is of prime importance as it helps to decide the career path at an earlier stage of life. Studying NCERT Solutions for Class 8 Maths apart from textbooks will be an ideal step to go forward.    

Chapter-wise summary: –

Chapter 1 – Rational Numbers

This chapter covers everything from basic to advanced concepts of rational numbers. in this introductory chapter on rational numbers, students can learn about whole numbers and natural numbers as whole numbers are denoted with ‘W’ and natural numbers with ‘N’. A rational number is represented as a fraction of two integers in the form of p/q.

Students can also learn about integers, closure property of rational numbers, commutative property of rational numbers, associative property of rational numbers, distributive property of rational numbers, negatives & reciprocals, representation of rational numbers on the number line, and rational numbers between two rational numbers.

Chapter 2 – Linear Equations in One Variable

The variables can also be transposed from one side of the equation to the other side just like numbers. The equation can be brought into a linear form by equating the expression by multiplication with the help of suitable techniques. The students can learn to perform mathematical operations on an equation, solve a linear equation on one side and numbers on the other side, equations with variables on both sides, applications, variables & constants, algebraic equations, and linear equations in one variable. 

Chapter 3 – Understanding Quadrilaterals

Quadrilaterals are a type of polygon that has four sides, four angles, and four vertices along with two diagonals. Students, from this chapter, can understand types of quadrilaterals like rhombus, rectangle, kite, square, parallelogram, and trapezium. In the section on revising geometry, students can learn an introduction to curves, polygons, classification of polygons basis of a number of sides/vertices, polygons on the basis of shape, polygons on the basis of regularity, angle sum property of a polygon, properties of parallelograms, elements of a parallelogram, angles of a parallelogram, diagonals of a parallelogram, rectangle, and square.  

Chapter 4 – Practical Geometry

This chapter explains the various dimensions of learning about geometry. The students can understand the concepts of construction of a quadrilateral, four sides and one diagonal, construction of a quadrilateral with different measures of sides and angles, SSS construction, construction of a quadrilateral when one diagonal and four sides are given, construction of a quadrilateral when three sides and two diagonals are given, construction of a quadrilateral when three angles and two adjacent sides are given, construction of a quadrilateral when two included angles and three sides are given, special quadrilaterals, and necessary numbers for construction of a unique quadrilateral.

Chapter 5 – Data Handling

Data handling is the procedure to organize the information given to perform mathematical operations on them. From this chapter, students will get the knowledge of Pie charts, how to create different Pie charts, raw data, pictographs & bar graphs, grouped data, tally marks, histograms, random experiments, experiments & outcomes, equally likely outcomes, probability of an event, and experimental probability.

Chapter 6 – Squares and Square Roots

Square is the most common term and concept in maths to understand. In this chapter, students will get to know about perfect squares, properties of square numbers, finding the square of a number with unit’s place 5, square roots, square root of a number, estimating the number of digits in the square root of a number, estimating the square root, introduction to square numbers, finding the square of a number, finding the square of a number using identity, interesting patterns, adding triangular numbers, numbers between square numbers, the addition of odd numbers, a square of an odd number as a sum, product of two consecutive even or odd natural numbers, random interesting patterns followed by square numbers, Pythagorean triplets, finding square root through repeated subtraction, finding square root by long division method, and finding Pythagorean triplets for any given number.

Chapter 7 – Cubes and Cube Roots

If a natural number m is expressed as n3 then m denotes the cube of number n. The numbers 1, 8, and 27 are cube numbers 1, 2, and 3 respectively. From this chapter, students will learn cubes relation with cube numbers, units digits in cube numbers, the addition of consecutive odd numbers, the prime factorization method to find a cube, cube roots, cube root using prime factorization, cube root of a cube number using estimation, and differences of squares of triangular numbers & converse.     

Chapter 8 – Comparing Quantities

In this chapter, students will learn the comparing quantities in various forms. They will know about fractions & ratios, finding increase or decrease percentages in situations, finding SP without finding discount percentage, finding discounts, estimation of amounts in percentage, prices/charges related to buying & selling, sales tax VAT, Simple & compound interest, calculating compound interest, a formula for compound interest, rate compounded annually/half-yearly, finding CI when rate compounded annually/half-yearly, and application of formula of CI.

Chapter 9 – Algebraic Expressions and Identities

The expressions made up of variables and constants along with mathematical operations are called algebraic expressions. It does not have sides or equal to signs like algebraic equations. From this chapter, students can learn about terms, factors, coefficients, like terms, monomial, binomial, polynomial, addition & subtraction of algebraic expressions, multiplication of monomials, distributive property of monomials, and multiplication of any polynomial.   

Chapter 10 – Visualising Solid Shapes

A shape with only two dimensions (length and width) and no thickness is called a two-dimensional shape, for eg, squares, circles, triangles, etc are two-dimensional shapes. In this chapter, students will understand the concept of various shapes and their features. They can learn about the area and volume of 2D shapes, three-dimensional solid objects, formation of solids, hexagon, non-polyhedrons, polyhedrons, solid cuboid, solid triangular prism, solid hexagonal prism, solid cylinder, solid sphere, solid cone, hollow cuboid, hollow triangular prism, hollow hexagonal prism, hollow cylinder, hollow cone, pyramid, and types of polyhedrons.

Chapter 11 – Mensuration

Mensuration is a study of different types of geometrical shapes along with their volume, length, area, and perimeter. It is based on algebraic equations and geometric calculations. Mensuration gives the most accurate results. The students, in this chapter, can understand the volume of a 3D object, the volume of a cube, the volume of a cylinder, introduction to Mensuration, and identify the shapes and areas of different regular figures. Area of trapezium by division into shapes of known area, area of trapezium by finding the area of a triangle of the same area, area of a general quadrilateral, area of rhombus, area of polygons, the surface area of solids (cuboid, cube, cylinder), and solids with a pair or more of identical faces. 

Chapter 12 – Exponents and Powers

The power of a number indicates the number of times it is multiplied. It is denoted as ‘ab’ where ‘b’ indicates the number of times ‘ a is multiplied. Here, ‘a’ is called the base, and ‘b’ is called the exponent. This chapter explains the theory of exponents and power in mathematical equations. The students will get to know powers with negative exponents, visualize powers and exponents, expand a rational number using power, exponents with like bases, power of a power, exponents with unlike bases and same exponents, inter-conversion between standard and normal forms, and comparison of quantities using exponents.

Chapter 13 – Direct and Inverse Proportions

The students can learn the concept of proportions from this chapter, a well-described study material is provided in the chapter. The students will be introduced to inverse & direct proportions, relation for inverse proportion, and time & work. Students will understand that if the value of variable increases or decreases upon a relevant decrease or increase in the value of the variable then the relation between the two is inversely proportional.  

Chapter 14 – Factorisation

An expression can be factorized into the product of its factors. These factors may be variables, algebraic expressions, and numbers too. In this chapter, the students can learn about the division of a monomial by another monomial, division of a polynomial by a monomial, division of a polynomial by a polynomial, factors of natural numbers, factors of algebraic expressions & factorization, method of common factors, method of identities, factorization using algebraic identities, and visualization of factorization.

Chapter 15 – introduction to Graphs

This chapter explains the different types of graphical representations of data. Any data can be very effectively organized to understand it better. Here, the students can learn about bar graphs, Pie charts, histograms, linear graphs, applications of graphs, Cartesian plane & coordinate axes, and representation of points on the plane.

Chapter 16 – Playing with Numbers

This chapter will teach the students how numbers are important and play a critical role in mathematics. The chapter states what is numbers, numbers in general form, reversing the two-digit numbers & adding them, reversing the two-digit numbers & subtracting them, reversing the three-digit numbers & subtracting them, a combination of three numbers, letters for digits, and divisibility.

Scope for maths in the future: –

Studying maths in school and graduating in it are two different things because of the results one would get. A good score in maths at the school level along with other subjects will help one to opt for the desired stream, mostly medical or engineering. However, students can also opt to take maths as a special subject and do graduation in it. to build the basics strong students can rely on NCERT Solutions for Class 8 Maths.

Either way, there are a lot of opportunities for a high-profile student in the outside world. Let us what are the job opportunities and requirements laid down for the appropriate candidates –

• Statistician – Bachelors’ in Mathematics/Statistics, Master’s in Statistics
• Mathematician – Masters’ in Mathematics
• Operations Research Analyst – Bachelors’ in Mathematics/Statistics/Engineering followed by an MBA in Operations Management
• Actuary – Bachelors in Mathematics/Statistics/Economics, B.Com or Actuarial Science followed by clearance of Actuarial Common Entrance Test (ACET) and Actuarial Science 15 stages.
• Data Analyst/Business Analyst/Big Data Analyst – Bachelors’ in Mathematics/Statistics/Engineering. Masters’ in Data Analytics/Big Data Analytics/Business Intelligence.
• Economist – bachelors’ in Economics followed by master’s in Economics/Econometrics/Applied Economics
• Market Researcher – Graduate in Mathematics/Statistics/Economics or Psychology
• Psychometrician – Bachelors’ in Psychology followed by Masters’ in Psychology/Statistics

Apart from these, if you are an engineering graduate or medical graduate you can have big salary jobs or can start a business or practice medicine.

Sources of Class 9 Maths NCERT solutions: –

• Students can download the solutions from the official website of NCERT in PDF format.
• They will be available on other educational websites to which students can refer and make notes from them.
• Search on any SEO with relevant keywords to find out more study material.
• One can avail of it from a nearby book store.
• Class 8 students can also get them with the help of their school.

Importance of Mathematics: –

All subjects are an integral part of the school syllabus except a few. A bright and ambitious student needs to understand the right time to pick up on studies and plan the future. Some students are fortunate to get a good guide in a subject like maths but not all are that lucky. Such students must refer to and study NCERT Solutions for Class 8 Maths which can make their concepts clear.

Simply reciting and getting a good score will help a student to get a high percentage but it won’t help in practical life which is otherwise. India has seen some great mathematicians who are well-known across the globe for their valued contribution. Such personalities can be an idol for most aspiring bright students. Sir C.V. Raman, Great Abdul Kalam sir, and founder of ‘zero’ Aryabhatta are only a few names.

Some interesting facts about Mathematics: –

• This information is off-syllabus but worth knowing as there are some maths involved –
• Conversely ‘one’ is the only number that is spelled with letters arranged in descending order.
• The markings on animal bones indicate that humans are doing maths since around 30,000 BC.
• The word ‘Mathematics’ only appears in one Shakespearean play “The Taming of the Shrew”.
• By shuffling a deck of cards properly it is more likely that the exact order of the cards you get has never been seen before in the whole history of the universe. (That’s crazy)
• The symbol for division is called an obelus.
• There are thirteen letters in both “twelve plus one” and “eleven plus two”.
• “Eleven plus two” is an anagram of “twelve plus one” in which the answer is 13.  
• Every odd number has an ‘e’ in it.
• From 0 to 1000 the only number that has ‘a’ is ‘one thousand’.
• Most mathematical symbols were not invented till the 16^th century and before that the equations were written in words.
• ‘Forty’ is the only number that is spelled with letters arranged in alphabetical order.
• In a room of 23 people, there is a 50 percent chance of two people having the same birthday.
• Zero is not represented in Roman numerals.
• The word ‘hundred’ comes from the Old Norse term ‘hundredth’ which actually means 120 and not 100.
• -40 deg C is equal to -40 deg F.
• 2 and 5 are only prime numbers that end in 2 and 5.
• In France, a Pie chart is sometimes referred to as a ‘camembert’.
• A ‘jiffy’ is a unit of time and indicates 1/100^th of a second.

Conclusion

Mathematics may seem a tough subject to many but in reality; it is a very interesting subject. It is the magic of numbers, formulae, and operations of equations that makes it amazing. If the teachers can convert students’ minds regarding maths it will be fun to learn it during school and college. Well-known scientists and mathematicians have got success in solving the puzzles around us and more than that they have invented a lot of good things with the help of maths. It is advised to learn maths as a guide that as a subject. In this, NCERT Solutions for Class 8 Maths is going to help students in many ways.

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