Ncert Maths Solution Class 6 for Chapter14 4
NCERT Solutions for Class 8 Maths
NCERT solutions for class 8 maths comprise the solutions to NCERT textbook problems that are explained in detail helping students to grasp a concept easily and effectively. If a student has a doubt while attempting a sum, she can easily overcome it by using these solutions as a reference. These class 8 maths NCERT solutions are prepared by math wizards who find the best possible techniques to solve a particular question enabling students to easily apply concepts to similar types of sums.
NCERT solutions class 8 maths are extremely helpful for students preparing for competitive exams such as Olympiads and school exams such as units, half-yearlies, and finals. They also allow students to revise all concepts taught to them in previous middle school classes. CBSE NCERT solutions for class 8 maths help students strengthen their practical skills and theoretical knowledge so that they can apply it to real-life examples.
NCERT Solutions for Class 8 Maths PDF Download
Class 8 maths NCERT solutions are easy to understand as they are created for an audience with varying learning styles. Thus, students can use these solutions to structure a lesson plan and study accordingly to get the best results. These NCERT solutions for class 8 maths are also available for free pdf download. You can find the links to all the pdfs listed below.
Class 8 Maths NCERT Solutions Chapter 1 to 16
| Download NCERT Solutions of Class 8 Maths Chapter-wise PDF | |
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| Chapter 1 Rational Numbers | |
| Chapter 2 Linear Equations In One Variable | |
| Chapter 3 Understanding Quadrilaterals | |
| Chapter 4 Practical Geometry | |
| Chapter 5 Data Handling | |
| Chapter 6 Squares And Square Roots | |
| Chapter 7 Cubes And Cube Roots | |
| Chapter 8 Comparing Quantities | |
| Chapter 9 Algebraic Expressions And Identities | |
| Chapter 10 Visualising Solid Shapes | |
| Chapter 11 Mensuration | |
| Chapter 12 Exponents And Powers | |
| Chapter 13 Direct And Inverse Proportions | |
| Chapter 14 Factorisation | |
| Chapter 15 Introduction To Graphs | |
| Chapter 16 Playing With Numbers | |
It is always advisable to study any topic by regularly practicing sums. Hence, you must revisit these chapter-wise NCERT solutions for class 8 maths to develop a good understanding of the subject. To improve your knowledge of different topics such as linear equations, geometry, data handling, exponents, etc. use the class 8 NCERT maths textbook given below.
☛ Download Class 8 Maths NCERT Book
NCERT Solutions for Class 8 Maths Chapter 1
NCERT solutions for class 8 maths chapter 1 rational numbers introduce young minds to the concept of rationals. Students learn about the various properties that can be applied to arithmetic operations while dealing with different classes of numbers and number line representation.
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Class 8 Maths Chapter 1 Rational Numbers
Topics Covered: Representation of numbers on a number line, closure property, commutativity, associativity, distributive property, negative numbers, reciprocals, multiplicative and additive identities are topics covered.
Total Questions: The chapter has a total of 18 questions. 8 are very easy, 6 slightly more difficult and 4 are tough sums.
NCERT solutions for class 8 maths chapter 1 gives students an idea of how to use the number line to represent rationals. It also teaches students how to find a rational number between two given rationals.
Class 8 Maths NCERT Solutions Chapter 2
Class 8 maths NCERT solutions chapter 2 linear equations in one variable introduces the concepts of linear equations and solving them using simple algebraic equations. In this chapter, students learn to convert a problem sum into a mathematical linear equation. Students must instill a good understanding of this chapter as the concepts learned are used in upcoming classes.
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Class 8 maths NCERT solutions chapter 2 linear equations form the basis of many chapters taught in higher grades thus, students can use the following study tips to improve their understanding of the topic.
- Develop in-depth knowledge of the topic by constant practice
- Read the question carefully before forming the linear equation
Class 8 Maths Chapter 2 Linear Equations in One Variable
Topics Covered: Transposing expressions between LHS (left-hand side) and RHS (right-hand side) to solve a linear equation, deriving expressions from word problems, reducing equations to a simpler form are some of the most important topics.
Total Questions: Chapter 2 linear equations in one variable have 65 well-structured questions that can be split into 20 simple calculation sums, 38 intermediate levels, and 7 tough problems.
NCERT Solutions Class 8 Maths Chapter 3
NCERT solutions class 8 maths chapter 3 understanding quadrilaterals comprise classification of polygons, types of quadrilateral and their elements, angles of specific quadrilaterals, and properties of special parallelograms.
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Class 8 Maths Chapter 3 Understanding Quadrilaterals
Topics Covered: Concave, convex polygons, questions on calculating the exterior angle, and determining the length of diagonals of a parallelogram.
Total Questions: There are a total of 31 questions in class 8 maths chapter 3 understanding quadrilaterals. 8 are tough problems, 7 are easy and 16 are of medium level.
NCERT Solutions for Class 8 Maths Chapter 4
NCERT solutions for class 8 maths chapter 4 practical geometry equip students with the tools necessary to construct quadrilaterals when different restraints such as lengths of sides, diagonals, or measures of angles are given.
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Class 8 Maths Chapter 4 Practical Geometry
Topics Covered: Constructing quadrilaterals when two diagonals and three sides are given, three sides and two included angles are mentioned as well as two adjacent sides and three angles are known are the topics that fall under the scope of class 8 maths NCERT solutions.
Total Questions: Chapter 4 practical geometry has 7 questions in total. Each problem is divided into 3-4 subparts with easy, moderate, and hard sums.
Once students finish practicing these NCERT solutions for class 8 maths chapter 4 they will be able to use a ruler and compass to successfully construct different quadrilaterals such as squares.
Class 8 Maths NCERT Solutions Chapter 5
Class 8 maths NCERT solutions chapter 5 data handling teaches to organize data using graphical methods, introduction to probability, and real-life applications of probability.
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Class 8 Maths Chapter 5 Data Handling
Topics Covered: Class 8 maths NCERT Solutions comprise of topics such as data representation using pictograph, bar graph, pie chart, probability, and how to determine the outcome of an event.
Total Questions: Chapter 5 data Handling has a total of 16 sums that can be divided into 3 simple questions, 8 moderate and 5 tough problems.
NCERT Solutions Class 8 Maths Chapter 6
NCERT solutions class 8 maths chapter 6 squares and square roots help students to get an insight into what are squares of a number, their properties, Pythagorean triplets, introduction to square roots, and division method to find a square root.
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NCERT Solutions Class 8 Maths Chapter 6 Study Tips:
Squares and square roots can be a difficult topic due to the computations involved. The following are some pointers to improve your skills in solving questions.
- Practicing regularly enables a student to improve her speed and accuracy in solving questions.
- Try to find patterns within questions to attempt the problem faster.
Class 8 Maths Chapter 6 Squares and Square Roots
Topics Covered: Identifying the square of a number, patterns formed by squares, determining square roots using different techniques, perfect square, and finding the square roots of decimals are some important topics covered.
Total Questions: There are 30 questions covered in class 8 maths chapter 6 squares and square roots, 10 of which are difficult problems, 11 are easy and 9 are medium level.
NCERT Solutions for Class 8 Maths Chapter 7
NCERT solutions for class 8 maths chapter 7 cubes and cube roots build on the previous chapter for introducing students to the concept of cube root.
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Class 8 Maths Chapter 7 Cubes and Cube Roots
Topics Covered: Identification of perfect cubes, and determining cube roots by prime factorization. Chapter 7 cubes and cube roots have 7 questions. 3 are easy such as true-false sums, 2 are tough and 2 are medium level.
Class 8 Maths NCERT Solutions Chapter 8
Class 8 maths NCERT solutions chapter 8 comparing quantities help students amass the tools required to calculate the ratio and proportion of quantities, percentage increase or decrease in a quantity, profit and loss, taxation, and determining the interest annually or semi-annually.
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Important Formulas:
- Cost Price = Buying price + Overhead expenses
- Discount = Marked Price - Sale Price
- Sales tax = Tax% of Bill Amount
- Annually Compounded Interest = P(1 + R/100)n
- Semi-annually Compounded Interest = P(1 + R/200)2n
Class 8 Maths Chapter 8 Comparing Quantities
Topics Covered: Class 8 maths NCERT solutions cover topics such as finding the ratio and proportion, determining the percentage, measuring the cost price, selling price, profit or loss incurred from a transaction, and determining the corresponding compound interest.
Total Questions: Chapter 8 comparing quantities has 29 questions. 13 are long answer types, 10 are intermediate and 6 are simple sums.
NCERT Solutions for Class 8 Maths Chapter 9
NCERT solutions for class 8 maths chapter 9 algebraic expressions and identities explain the basic terms associated with algebra. Students learn about the different categories of algebraic expressions and how to perform addition, subtraction, and multiplication on them.
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Important Algebra Formulas :
- (a + b) (a - b) = a2 - b2
- (a - b)2 = a2 - 2ab + b2
- (a + b)2 = a2 + 2ab + b2
- (x + a) (x + b) = x2 + (a + b)x + ab
Class 8 Maths Chapter 9 Algebraic Expressions and Identities
Topics Covered: Applying arithmetic operations to algebraic expressions, multiplying different polynomials, and solving questions using algebraic identities are essential topics covered in this chapter.
Total Questions: Chapter 9 algebraic expressions and identities have a pool of 25 well-structured questions out of which 8 are simple identity-based problems, 12 are intermediate and 5 are challenging sums.
NCERT Solutions for Class 8 Maths Chapter 10
NCERT solutions for class 8 maths chapter 10 visualizing solid shapes prepare students to develop the powers required to identify a solid shape and its attributes. This chapter is very useful for upcoming lessons such as mensuration. The most crucial benefit of this chapter is that it helps students in augmenting their visualization powers and analytical skills.
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Class 8 Maths Chapter 10 Visualising Solid Shapes
Topics Covered: Class 8 maths NCERT solutions chapter 10 encompass topics to determine the different features of a 3D object such as the number of faces as well as applying Euler's formula that gives a relationship between the faces, edges, and vertices of a solid shape.
Total Questions: There are a total of 15 sums in chapter 10 visualizing solid shapes. 10 are simple problems, 2 are difficult and 3 are moderate level sums.
Class 8 Maths NCERT Solutions Chapter 11
Class 8 maths NCERT solutions for chapter 11 mensuration are designed to help students calculate the areas of the different 2D shapes and 3D shapes. It also includes formulas and methods to determine the volume of basic solid figures. This chapter is very scoring and makes its way on several exams.
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NCERT Solutions Class 8 Maths Chapter 11 Preparation Tips:
Mensuration is one of the most important chapters necessary for a student's educational career. It can be a confusing topic thus, students can follow the tips listed below to enhance their learning.
- Develop visualization skills.
- Understand the formulas before memorizing them.
- Try to apply the concepts learned to daily-life objects such as finding the surface area of a cylindrical water bottle.
Class 8 Maths Chapter 11 Mensuration
Topics Covered: Determining the area of triangles, rhombuses, rectangles, circles, and other special figures, finding the total surface area, as well as the volume of cubes, cuboids, and cylinders, are the topics that are a part of class 8 maths NCERT solutions.
Total Questions: Chapter 11 incorporates 34 exemplar problem sums. 7 are short answer questions, 10 are moderately complex and 17 are complicated sums that required advanced thinking on a student's part.
Class 8 Maths NCERT Solutions Chapter 12
Class 8 maths NCERT solutions chapter 12 exponents and powers provide a detailed analysis of exponents and their laws that can be used to simplify the representation of very small or large numbers. Exponents are required as they greatly reduce the time taken in working with a number having colossal digits.
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Important Formulas in NCERT Solutions Class 8 Maths Chapter 12
- am × an = am+n
- am ÷ an = am-n
- (am)n = amn
- a0 = 1
Class 8 Maths Chapter 12 Exponents and Powers
Topics Covered: Class 8 maths NCERT solutions chapter 12 incorporates topics such as expressing numbers in the form of exponents and applying the laws of negative exponents.
Total Questions: There are 11 questions in class 8 maths chapter 12 exponents and powers wherein 4 are based on laws of exponents, 3 are medium level and 2 are complicated problems.
NCERT Solutions for Class 8 Maths Chapter 13
NCERT solutions for class 8 maths chapter 13 direct and inverse proportions have a step-wise explanation of problems to introduce students to the concept of proportions. It helps students get comfortable in establishing a correspondence between two related quantities.
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Class 8 Maths Chapter 13 Direct and Inverse Proportion
Topics Covered: Different formats of questions on direct proportion, identifying inverse proportion, and determining the value of quantities following this relationship, are the essential topics covered under class 8 maths NCERT solutions chapter 13.
Total Questions: Chapter 13 direct and inverse proportion has 21 well-structured problems. 5 are straightforward relationship identification questions, 10 are moderately difficult and 6 are long answer type sums.
NCERT Solutions for Class 8 Maths Chapter 14
NCERT solutions for class 8 maths chapter 14 factorization give students a clear understanding of how to use various techniques to factorize algebraic expressions and the steps required to divide the different types of polynomials. Factorization forms an integral part of mathematics and hence, is a very important topic.
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Class 8 Maths Chapter 14 Factorisation
Topics Covered: Factorisation by methods such as common factors, regrouping terms, using identities to solve problems fall under this chapter. Additionally, division of polynomials, and correcting errors is also part of this chapter.
Total Questions: Chapter 14 factorization has 31 questions that can be further categorized as 13 easy, 8 medium, and 10 long answer sums.
NCERT Solutions Class 8 Maths Chapter 15
NCERT solutions for class 8 maths chapter 15 introduction to graphs is a chapter that is needed to make statistical computations. Students can also develop crystal clear concepts on linear graphs using the coordinate system and their applications.
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Preparation Tips:
NCERT solutions for class 8 chapter 15 introduction to graphs give students a pictorial representation of data. The points listed below can further facilitate the process of learning this lesson.
- Draw the graphs and plot the data.
- Understand the relation between the variables before making a graph.
Class 8 Maths Chapter 15 Introduction to Graphs
Topics Covered: A detailed description of pie charts, bar graphs, histograms, and line graphs are given in the Class 8 maths NCERT solutions. Other topics include linear graphs and how to apply them to daily life problems. Chapter 15 introduction to graphs has 13 sums. 7 are complex analytical questions, 2 are intermediate and 4 are easy problems.
NCERT Solutions Class 8 Maths Chapter 16
NCERT solutions class 8 maths chapter 16 playing with numbers gives a fun way to students for exploring the attributes of numbers. This chapter helps students to identify the divisibility of numbers by listing certain pointers and tricks that can be used to increase calculation speed.
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Class 8 Maths Chapter 16 Playing with Numbers
Topics Covered: The general form of numbers, creating interesting games by digit reversal, and forming numbers based on a few constraints are topics in NCERT solutions class 8 maths. This chapter also includes divisibility tests for 10, 9, 3, 5, and 2. Chapter 16 playing with numbers has 14 sums. 5 are simple problems based on games, 7 are medium-level based on divisibility tests, and 2 are tough.
Class 8 Maths NCERT Solutions Important Formulas
Formulas are expressions that give the relationship between two or more quantities. These are constructed using some logical rules and aid students in reducing the time taken to solve questions. Students must develop a good understanding of the concept behind math formulas before memorizing them. Some of the vital formulas covered in NCERT solutions for class 8 maths are given below:
TSA of Solid Shapes
- Cuboid = 2(lb + bh +lh)
- Cube = 6a2
- Right Circular Cone = πr (l + r)
LSA/CSA of Solid Shapes
- Cuboid = 2(l + b)
- Cube = 4a2
- Right Circular Cone = πrl
Volume
- Cuboid = lbh
- Cube = a3
- Right Circular Cone = ⅓ × πr2h
Algebra
- (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
Importance of NCERT Solutions for Class 8 Maths
Class 8 Maths NCERT Solutions are extremely helpful for CBSE students because they provide a step-wise and detailed analysis of all NCERT sums. There are several advantages of using these well-curated class 8 maths NCERT solutions a few of which are listed below.
- Clear Concept Formation: When students solve a sum they are bound to have doubts and may not be able to proceed further. The detailed explanation of class 8 maths NCERT solutions helps students to understand the underlying concepts and improve in the problematic areas. Also, they give the steps in an easy format to combat any confusion. Thus, these solutions help to build a robust mathematical foundation.
- Organized Studying: These NCERT class 8 maths solutions help students to create a schedule wherein they can cover the entire syllabus well within the given time limit. Additionally, it also gives them ample time to revise all questions. The solutions give a quick overview to students on how to solve problems. During the examination days, students can quickly skim through the solutions helping them recall how to attempt different categories of questions.
- Exam Preparation: The NCERT solutions for class 8 maths give students an insight into how to solve a question with great skill and efficiency. They provide students with tips and tricks that can be used to score the best possible grade.
FAQs on NCERT Solutions Class 8 Maths
Why are NCERT Solutions for Class 8 Maths Important?
NCERT Solutions for class 8 maths are important as they give students a means to cross-check their answers to exercise questions. These class 8 maths NCERT solutions are self-explanatory and provide students with a detailed description of the steps they need to follow to get the right answer by using the most efficient method.
Do I Need to Practice all Questions Provided in Class 8 Maths NCERT Solutions?
The CBSE school exams are based on the syllabus in the NCERT textbooks hence, it becomes vital for students to practice all questions solved in class 8 maths NCERT solutions. Regular revision and conscientious effort will go a long way in scoring good marks during any examination be it a school test or a competitive paper.
Do I Need to Make Notes while Referring to NCERT Solutions Class 8 Maths?
It is always advisable to make notes while studying the NCERT Solutions Class 8 Maths as they act as guides for students when they revise those sums. In addition to this, notes help students recall concepts used in a problem at a glance. This drastically reduces the time taken to go over a problem during examination time.
How are NCERT Solutions for Class 8 Maths Promoting Problem Solving in Students?
NCERT solutions for class 8 maths explain how to decipher a question by breaking it down into smaller parts. By using these techniques students can not only develop a problem-solving mindset but can also enhance their mathematical acumen.
What are the Best Ways to Learn Concepts Covered in NCERT Solutions Class 8th Maths?
The best way to learn any concept covered in the NCERT solutions class 8 maths is by practicing it. The first step is to build a strong conceptual foundation of that topic by thoroughly studying the theory. The next step is to solve numerous sums on the same till a student gains confidence in working with it. Thus, he can breeze through exams without getting flustered.
How Many Chapters are there in Class 8 Maths NCERT Solutions?
There are 16 chapters in the class 8 maths NCERT solutions . The topics such as mensuration, graphs, factorization, exponents, etc lay the groundwork for higher classes. As mathematics is a subject where all topics are interlinked thus, it is important to be well versed in all these chapters to avoid any confusion in higher classes.
What are the Important Formulas in NCERT Solutions for Class 8 Maths?
Formulas covered in the NCERT solutions for class 8 maths based on mensuration and algebraic expressions are vital for a student's knowledge. However, it is necessary to give equal importance to other formulas as well because if not studied they can cause a gap in a student's educational journey. Also, to crack a question and solve it expeditiously, knowledge of formulas is a must.
Why Should I Practice NCERT Solutions for Class 8 Maths Regularly?
The only way to score a good grade in examinations is by practicing these NCERT solutions for class 8 maths regularly. Practice helps a student to master the subject within no time to get the best possible grades. It also brings about an improvement in his mathematical skills and abilities.
Are Class 8 Maths NCERT Solutions Sufficient for CBSE Exams?
Class 8 maths NCERT solutions are sufficient for students to clear the CBSE exams as they provide explanations to the well-researched NCERT questions. In addition to this, the CBSE exam's paper pattern is based on the syllabus given in the NCERT textbooks. However, to enhance a student's learning abilities, consulting other reference books on the same topic is also advisable.
Why Choose Cuemath for Class 8 Maths NCERT Solutions?
Cuemath is an amazing online educational platform that provides reliable, precise, and well-thought-out class 8 maths NCERT solutions. These solutions have been given by math experts and IIT graduates ensuring that students have a holistic learning experience.
Ncert Maths Solution Class 6 for Chapter14 4
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