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Class 8 - Maths

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Updated according to new NCERT - 2023-24 NCERT Books.

NCERT Solutions of all exercise questions and examples have been solved for Class 8 Maths. Answers to all questions have been solved without missing a step, with detailed explanation of the concepts as well.

In teachoo, each chapter is divided into - Serial Order Wise, and Concept Wise

In Serial Order Wise, the chapter is taught according to the NCERT Book - divided into exercises and examples.

You can check it if you have a doubt in a particular question, click on an exercise link under Serial Order Wise

The Teachoo way of doing a chapter is from Concept Wise.

Each chapter is divided into concepts, first the concept is explained, and then the questions of that concept. Easiest question first, difficult questions later.

This is a great method to do the chapter when you're studying it for the first time, or revising.

In Class 8, the chapters and its topics include

  • Chapter 1 Rational Numbers - What are Natural Numbers, Whole Numbers, Integers, Rational numbers. How are they related. Properties of rational numbers like Closure, Commutativity, Associativity, Distributivity. Additiving Identity and Additive Inverse. Multiplicative Identity and Multiplicative inverse. Rational numbers on the number line, Rational numbers between two rational numbers 
  • Chapter 2 Linear Equations in One Variable  - What are Equations, What are linear Equations in one variable, Solving Linear Equations, Making equations from Statements and then solving
  • Chapter 3 Understanding Quadrilaterals - Curves - Simple, Closed, Polygons - Convex, Concave, Diagonal of a polygon, Regular and Irregular polygons, Angle sum property of polygons, Sum of exterior angle of a polygon, Interior and Exterior Angle of a Regular Polygon.Type of Quadrilaterals - Trapezium, Kite, Parallelogram, Rhombus, Rectangle, Square and their properties
  • Chapter 4 Practical Geometry - Using the properties studied in Chapter 3, we will learn how to construct Quadrilaterals - When four sides and one diagonal are given,  When two diagonals and three sides are given, When two adjacent sides and three angles are given, When three sides and two included angles are given, When other special properties are known
  • Chapter 5 Data Handling  - We learn what is Data, how to represent data - pictograph, bar graph, double bar graph, How to draw a frequency distribution table, drawing a grouped frequency distribution table, reading a histogram, drawing a histogram, Reading a Pie chart (Circle Graph), Drawing a circle graph, Chance, Probability, Finding Probability 
  • Chapter 6 Squares and Square Roots - What are square numbers, Properties of square number, Unit digit of square numbers, Solving Patterns, Finding squares without multiplication (using properties (a + b) 2 , (a - b) 2 ), What is a Pythagorean triplet, What is square root, Symbol for Square root, Finding Square root through repeated subtraction, Finding Square root through prime factorisation, Finding Square root by division method (of numbers, as well as decimal numbers) 
  • Chapter 7 Cubes and Cube Roots - What is a cube, What are Hardy-Ramanujan Numbers, Unit digit of Cubes, Properties of cube numbers, Checking if number is a perfect cube, What is cube root, Symbol for cube root, Finding cube root through prime factorization, Finding cube root through estimation
  • Chapter 8 Comparing Quantities - Recalling what are ratios and percentages, how to convert ratio into percentage, finding percentage, Finding increase or decrease percent, Finding discount, discount percentage, Selling Price, Cost Price, Profit or Loss, Profit percentage or Loss percentage, What is simple interest, Compound Interest, Compound Interest Formula, Compound Interest when interest is compounded half yearly, Compound Interest for Fraction years
  • Chapter 9 Algebraic Expressions and Identities - What is expression; Terms, Factors and Coefficients of Expressions, What are monomials, binomials, trinomials, polynomials; Like and unlike terms, Addition, Subtraction,Multiplication and Division of Algebraic Expressions, Some Algebra Identities
  • Chapter 10 Visualising solid shapes  - We learn what is a 3 Dimensional Shape, Front View, Top View, Side View of 3D Objects, How to read a map, and what is scale in a map, Faces, Edges and Vertices of Polyhedrons, and Euler's Formula
  • Chapter 11 Mensuration - Perimeter and Area of different Shapes like Rectangle, Square, Triangle, Parallelogram, Circle, Finding Area of Trapezium, Finding Area of a General Quadrilateral, Area of Rhombus, Finding Area of Polygons by dividing it into different parts, Solid  Shapes, Lateral (or Curved) Surface Area, Total Surface Area, Volume of Cube, Cuboid and Cylinder
  • Chapter 12 Exponents and Powers - What is exponent and base of a number like 10 24 , Numbers with negative exponents, Law of Exponents with positive and negative powers, Converting very small, and very big numbers into standard form
  • Chapter 13 Direct and Inverse Proportions - What is Direct Proportion, examples of things in direct proportion, and some questions on it. Similarly, what is indirect proportion and solving questions with indirect proportion
  • Chapter 14  Factorization  - We factorise algebra expressions using different methods like - Method of Common Factors, By Regrouping Terms, Using Identities, Using Splitting the middle term method, Dividing Algebra Expressions, Finding Errors in some questions
  • Chapter 15 Introduction to Graphs  - We remember common graphs like Bar Graph, Double Bar Graph, Circle Graph (Pie Chart), Histogram, We study what is a line graph, How to read a line graph, then what is linear graph, What is a point in the graph, coordinates of a point in the graph, and plotting a linear graph
  • Chapter 16 Playing with Numbers - In this chapter, we will do some questions where we need to find letters while doing addition or multiplication, and then we will study divisibility of numbers and solve some questions
Note : When you click on a link in the chapter, the first question will be opened. To check other questions and concepts, you can click on next or check the arrowed list which has the list of questions. Important Questions have also been marked

Click on a chapter below to get started.

Chapter 1 Class 8 Rational Numbers

Chapter 2 class 8 linear equations in one variable, chapter 3 class 8 understanding quadrilaterals, practical geometry, chapter 4 class 8 data handling, chapter 5 class 8 squares and square roots, chapter 6 class 8 cubes and cube roots, chapter 7 class 8 comparing quantities, chapter 8 class 8 algebraic expressions and identities, visualising solid shapes, chapter 9 class 8 mensuration, chapter 10 class 8 exponents and powers, chapter 11 class 8 direct and inverse proportions, chapter 12 class 8 factorisation, chapter 13 class 8 introduction to graphs, playing with numbers.

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NCERT Solutions for Class 8 Maths

math question solve class 8

Class 8 Maths ncert solutions: Simplified and Updated for 2023-24 exams Tiwari Academy presents user-friendly ncert solutions for Class 8 Maths in PDF and videos, perfectly tailored to the Class 8 Maths textbooks from NCERT. Our guides, available in both Hindi and English, are freshly updated for the 2023-24 academic year, offering the latest and most effective Class 8 Maths Solutions for students. Chapter Wise Class 8 Maths NCERT Solutions It covers all the questions and even the extra Try These ones. NCERT is a big group that makes school books for Bharat and good news: for 2023-24, there are just 13 chapters in the 8th Maths book, and we’ve got them all covered.

Chapter 1. Rational Numbers Chapter 2. Linear Equations in one Variable Chapter 3. Understanding Quadrilaterals Chapter 4. Data Handling Chapter 5. Square and Square Roots Chapter 6. Cube and Cube Roots Chapter 7. Comparing Quantities Chapter 8. Algebraic Expressions and Identities Chapter 9. Mensuration Chapter 10. Exponents and Powers Chapter 11. Direct and Inverse Proportions Chapter 12. Factorization Chapter 13. Introduction to Graphs

NCERT solutions for class 8 Maths are designed to help students understand and solve the exercises and problems presented in the NCERT class 8 mathematics textbook. Rate and Review these solutions for further improvement. These solutions provide step-by-step explanations and answers for each exercise and chapter, making it easier for students to grasp mathematical concepts and improve their problem-solving skills.

Class 8 ncert solutions App Download

Class 8 is a crucial year in mathematics education, and ncert solutions are widely used by students and teachers in Bharat to prepare for class 8 mathematics exams and build a strong foundation in mathematics. These solutions are available in various formats, including printed books, online platform like Tiwari Academy, PDFs, and digital resources. Students often use NCERT solutions alongside their textbooks to practice and understand mathematical concepts thoroughly.

How to perform well in 8th Maths

The effectiveness of any educational resource like class 8 ncert solutions at Tiwari academy can vary depending on individual learning styles and needs, so it’s important for students to explore different resources at website or app and choose the ones that best suit their preferences and goals.

Etymology and Evolution of Mathematical Terms The term “mathematics” comes from the Ancient Greek “máthēma,” meaning “that which is learnt” or “study.” Its meaning evolved over time, and by the 17th century, it began to acquire its current meaning. Interestingly, the term “mathematics” in English was once more commonly associated with astrology rather than the study of numbers and shapes.

Class 8 Maths Solution

8th Maths NCERT solutions are prepared by experts and provide step-by-step explanations. 8th Maths Textbook from NCERT (ncert.nic.in) website and Solutions are described completely showing all steps with formulae. If someone is still facing a problem to understanding the sums please see the videos given here or specify through the “Discussion Forum” section.

With the help of Class VIII Maths NCERT solution , students can understand the concepts better and score good marks in their exams. Get NCERT Solutions for class 8 Maths in PDF file format Hindi medium as well as English medium to download. All the solutions are updated for the academic session 2023-24 based on the latest NCERT Books .

Best way to prepare Class 8 Maths for Exams For Class 8, excelling in Maths involves a well-organized and dedicated approach to learning. Begin by getting a firm grasp of the Class 8 Maths syllabus, which includes diverse topics like Rational Numbers, Linear Equations, Data Handling, Squares and Square Roots, Cubes and Cube Roots, Comparing Quantities, Algebraic Expressions and Identities, Visualizing Solid Shapes, Mensuration, Exponents and Powers, Direct and Inverse Proportions, Factorization, Introduction to Graphs, and Playing with Numbers. Establish a consistent study routine, setting aside specific times each day for Maths. This helps in building a solid foundation in basic concepts, making it easier to understand more complex topics. Use your textbooks, particularly NCERT, as primary study resources since they offer detailed explanations and a variety of practice problems. Break down the syllabus into smaller sections for focused and manageable study sessions.

Practicing a wide range of mathematical problems is crucial. This should include exercises from your textbook, additional problems from other books, and online resources. Regular practice not only reinforces the concepts but also sharpens your problem-solving skills. If you find certain topics challenging, don’t hesitate to ask for help from teachers or consider joining study groups for collaborative learning. Practice with past papers or sample questions to get used to the exam format and question types, which also helps in improving time management skills. Pay attention to common mistakes and work on correcting them to enhance accuracy.

Balancing your studies with relaxation is important. Make sure to take regular breaks and engage in activities that you enjoy, like sports, music, or any hobby. This helps in keeping your mind fresh and focused. Maintain a positive attitude towards learning and believe in your capability to improve. Regular quizzes or timed practice sessions can be very helpful for self-assessment. They not only aid in identifying areas that need more focus but also boost your confidence. Remember, with consistent effort, a clear understanding of mathematical concepts, and effective time management, you can excel in Class 8 Maths.

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. To download class 8 Maths, just follow the links given below. There are solutions in Hindi as well as English Medium free to use.

Class 8 Maths Exercise 1.1

Class 8 Maths Exercise 1.1 in Hindi

We will learn 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.

Chapter 2: Linear Equations in one Variable

Class 8 Maths Chapter 2 describes how to solve a linear equation in one variable. There are seven main points given in chapter 2 of 8th Mathematics. Get here topics separately the two exercises.

Class 8 Maths Exercise 2.1 Class 8 Maths Exercise 2.2

Class 8 Maths Exercise 2.1 in Hindi Class 8 Maths Exercise 2.2 in Hindi

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.

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. There are total four exercises in class 8 Maths chapter 3. Students can get there solutions from the links given here.

Class 8 Maths Exercise 3.1 Class 8 Maths Exercise 3.2 Class 8 Maths Exercise 3.3 Class 8 Maths Exercise 3.4

Class 8 Maths Exercise 3.1 in Hindi Class 8 Maths Exercise 3.2 in Hindi Class 8 Maths Exercise 3.3 in Hindi Class 8 Maths Exercise 3.4 in Hindi

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. Learn here about different types of quadrilaterals in Exercise 3.4 . These quadrilaterals are Rhombus, Rectangle and Square.

Chapter 4: Data Handling

Class 8 Maths Chapter 4 starts with the concepts of Class Intervals, Lower and Upper Limits, Range, Class Width and Class Size. There are only two exercises in chapter 4 of class 8th Maths. Solutions links of these exercises are given here.

Class 8 Maths Exercise 4.1 Class 8 Maths Exercise 4.2

Class 8 Maths Exercise 4.1 in Hindi Class 8 Maths Exercise 4.2 in Hindi

Here students of class VIII will learn about Histogram. The first exercise that is Exercise 4.1 represents another way of graphical representation, which is Pie Chart or Circle Graph. The second and last topic in Exercise 4.2 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 5: Square and Square Roots

In Class 8 Maths Chapter 5 , we will learn how to find square or square roots of a number. Square and square roots is one of the most important chapters of class 8th Math. This chapter is useful not only in class 8 but in next classes also. Practice well to learn it better using the solutions given here.

Class 8 Maths Exercise 5.1 Class 8 Maths Exercise 5.2 Class 8 Maths Exercise 5.3 Class 8 Maths Exercise 5.4

Class 8 Maths Exercise 5.1 in Hindi Class 8 Maths Exercise 5.2 in Hindi Class 8 Maths Exercise 5.3 in Hindi Class 8 Maths Exercise 5.4 in Hindi

In Exercise 5.1 , most of the questions are based on hit and trial method or successive addition method. Exercise 5.2 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 5.3 , the simple method is given to find square roots of a number by successive subtraction or using Prime Factorisation method. Exercise 5.4 is designed to find the square roots using division methods as well as by estimation.

Chapter 6: Cube and Cube Roots

In Class 8 Maths Chapter 6 , we will discuss with the cubes of a number and its cube root also. There are only two exercises in class 8th Maths NCERT (https://ncert.nic.in/) chapter 6, which are given below with the complete solutions.

Class 8 Maths Exercise 6.1 Class 8 Maths Exercise 6.2

Class 8 Maths Exercise 6.1 in Hindi Class 8 Maths Exercise 6.2 in Hindi

Exercise 6.1 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 6.2 of Class 8 Mathematics. Students can learn here to find the cube root of a number using its Prime Factors.

Chapter 7: Comparing Quantities

Class 8 Maths Chapter 7 includes the questions related to ratio and proportion. Find the links given below to practice all the questions of Class 8 Maths chapter 7 in English and Hindi Medium .

Class 8 Maths Exercise 7.1 Class 8 Maths Exercise 7.2 Class 8 Maths Exercise 7.3

Class 8 Maths Exercise 7.1 in Hindi Class 8 Maths Exercise 7.2 in Hindi Class 8 Maths Exercise 7.3 in Hindi

In Exercise 7.1 , questions are on ratios and percentage with some practical application. Increasing or decreasing of the percentage of given number, profit and loss percentage, discount, sell tax and VAT related questions are there in Exercise 7.2 of Class 8 Maths. Exercise 7.3 covers the questions on Simple (SI) and Compound Interest (CI).

Chapter 8: Algebraic Expressions and Identities

In Class 8 Maths Chapter 8 , the concepts of algebraic expression with terms, factors and coefficient of Monomial, Binomial and Trinomials are given. 8th Maths chapter 8 is one of the most important chapters for exam.

Class 8 Maths Exercise 8.1 Class 8 Maths Exercise 8.2 Class 8 Maths Exercise 8.3 Class 8 Maths Exercise 8.4

Class 8 Maths Exercise 8.1 in Hindi Class 8 Maths Exercise 8.2 in Hindi Class 8 Maths Exercise 8.3 in Hindi Class 8 Maths Exercise 8.4 in Hindi

Questions of Exercise 8.1 are based on like and unlike terms and addition or subtraction of algebraic expression. Introduction of multiplication of algebraic expression is given in Exercise 8.2 of 8th Maths. Most of the questions carry the product of monomials. Exercise 8.3 provides an overview of the questions in which we multiply a polynomial by a monomial, whereas in Exercise 8.4 , we learn how to multiply a polynomial by another one.

Chapter 9: Mensuration

Class 8 Maths Chapter 9 Mensuration is not only the main topic for class 8, but it is important for further classes also. Get here the solutions, and start practicing.

Class 8 Maths Exercise 9.1 Class 8 Maths Exercise 9.2 Class 8 Maths Exercise 9.3

Class 8 Maths Exercise 9.1 in Hindi Class 8 Maths Exercise 9.2 in Hindi Class 8 Maths Exercise 9.3 in Hindi

The Exercise 9.1 , deals with the areas related to Trapezium and another quadrilateral. In the next step of this chapter, we have to find the surface area of solid objects in Exercise 9.2 of Class 8th NCERT Maths. The volume of these 3D figures can be obtained using the formulae in Exercise 9.3 of 8th Maths.

Chapter 10: Exponents and Powers

In Class 8 Maths Chapter 10 , students will study the numbers having negative or positive powers. The exercise 10.1 takes little bit more time as compare to exercise 10.2, get the solutions in link during practice, to help yourself during practice.

Class 8 Maths Exercise 10.1 Class 8 Maths Exercise 10.2

Class 8 Maths Exercise 10.1 in Hindi Class 8 Maths Exercise 10.2 in Hindi

Exercise 10.1 is based on the Laws of Exponents. The second exercise explains about the Scientific Form or Standard Form. In 8th mathematics Exercise 10.2 , we learn to convert the numbers in the standard form with the help of exponents.

Chapter 11: Direct and Inverse Proportions

Class 8 Maths Chapter 11 , we have to check whether the value of both the quantities are increasing or one is increasing and other is decreasing. To practice all the NCERT questions follow the solutions links given below.

Class 8 Maths Exercise 11.1 Class 8 Maths Exercise 11.2

Class 8 Maths Exercise 11.1 in Hindi Class 8 Maths Exercise 11.2 in Hindi

Exercise 11.1 contains the basic and easy questions of Direct Proportion, where the two quantities increase or decrease together. Similarly, Exercise 11.2 also deals with Inverse Proportion, where one value is increasing, but other is decreasing.

Chapter 12: Factorization

In Class 8 Maths Chapter 12 , we will study about factors of natural numbers as well as algebraic expressions. For any difficulty, first try yourself. If the problem persist just get the solutions and find the systematic way to solve.

Class 8 Maths Exercise 12.1 Class 8 Maths Exercise 12.2 Class 8 Maths Exercise 12.3

Class 8 Maths Exercise 12.1 in Hindi Class 8 Maths Exercise 12.2 in Hindi Class 8 Maths Exercise 12.3 in Hindi

In Exercise 12.1 , we will make factors by regrouping the terms, whereas, in Exercise 12.2 , identities are the main tool to get simple factors of any polynomial. Exercise 12.3 contains questions based on the division of polynomials by another polynomial.

Chapter 13: Introduction to Graphs

Class 8 Maths Chapter 13 describes the methods to plot a Bar Graph, a Pie Chart or Circle Graph, Histograms and a Line Graph. Here the sums are based on formation as well as observation of the graphs.

Class 8 Maths Exercise 13.1 Class 8 Maths Exercise 13.2

Class 8 Maths Exercise 13.1 in Hindi Class 8 Maths Exercise 13.2 in Hindi

Most of the questions in Exercise 13.1 are of Line Graphs. Graphs related to two variables are present in Exercise 13.2 based on the application of linear equations in two variables.

Provide your feedback about the content quality and website user experience. Download Class 8 Maths Solutions App , which work offline without internet also. All the Solutions and explanation for 2023-24 for class 8 Maths are done properly with full care, if you still find any mistake please notify us, so that we can remove it to provide the best study material for the students.

NCERT Solution for Class 8 Maths

Class 8 Solutions Android and iOS Apps for iPhone, iPad)

Get the Assignment and test papers for the preparation of exams. This page is rebuilt on the basis to suggestions received by parents as well as students. We always respect all the user and try to maintain our website as per their requirements. Give your feedback and Suggestions to improve this website to get best for class 8 Maths solutions.

Tiwari Academy apps allow users to download NCERT solutions and related content for offline use. This feature is especially beneficial for students who may not have a consistent internet connection.

Apps often provide search functionality and well-structured navigation, making it easier for users to find specific solutions or topics quickly. This can save valuable study time.

How to use Class 8 Maths NCERT Solutions to get good Marks in Exam?

The NCERT Solutions for Class 8 Maths are modified for academic session 2023-24. Studying class 8 mathematics using NCERT solutions is a great way to ensure a strong foundation in the subject. Start by obtaining a copy of the NCERT textbook for class 8 mathematics. NCERT Solutions for class 8 Mathematics are a valuable resource available on https://www.tiwariacademy.com for students, offering guidance, clarity, and practice to help them excel in their math studies. They are designed to support the NCERT curriculum, making them an ideal tool for students following this educational board’s syllabus in Bharat. This is the primary resource you’ll be working with. Here’s a step-by-step guide on how to do it effectively.

Step 1: Understand the Syllabus and Focus on NCERT Textbooks for practice.

Step 2: solve examples and use class 8 maths ncert solutions for practicing exercises., step 3: follow class 8 maths ncert, take notes to clear doubts., step 4: use ncert solutions for class 8 mathematics to ensure accuracy of answers., step 5: use technology for better revision and take mock tests to test yourself..

Step 1: Understand the Syllabus and Focus on NCERT Textbooks for practice.

How many chapters are ther in Class 8 Maths?

According to revised syllabus for CBSE 2023-24, there are total 13 Chapters in Class 8 Maths NCERT Book. All chapters are compulsory for the exams. All the chapters are related to each other. Student can get the solutions of each questions of 8th Mathematics here in Hindi and English Medium. The tricky chapters are explained well in video also. The class 8 Maths Solutions are easy to use and understand. Follow the following steps to solve the questions: 1. Read the lesson and examples given before exercise. 2. Try to solve each question with the help of examples . 3. For the difficult questions, take help from PDF solutions . 4. To understand better the concepts, use the video solutions given here.

Which is the most interesting chapter in Class 8 Maths?

The most interesting chapter of class 8 is Chapter 13. To describe in better format videos related to this chapter is also given here. Students of 8th standard can easily understand it using class 8 Maths NCERT Solutions in Hindi or English Medium. Follow the steps to solve the questions of this chapter: 1. Spend time to find out the answer of these questions without taking any help from solutions given on websites. 2. Apply different tricks to solve the puzzles. 3. Discuss the exercise questions with family and friend for fun. 4. Make more similar questions of own to enjoy and learn more.

How can I score good marks in 8th Maths?

There are some easy as well as difficult chapters in all the subjects. Its all varies from student to student. Some student enjoy doing all the time Maths but some get tired and bored in the same calculations. If a student who is somehow weak in Maths, he should start that chapter of Maths, which is most easier for him. Gradually practicing will increase the level of confidence and the interest towards Maths will be generated automatically.

What is better for class 8 Mathematics online or offline mode?

Studying offline through books is always better than any website or other online portals. Offline study using latest NCERT Books for class 8 Maths generates interest to do hard work whereas online portals are good only if you have any doubt in questions. Studying through Phone, laptops, computers, tablets make us mentally tired where studying offline compel us to think more and more about the fact we are studying.

How to score 90% or more marks in class 8 Maths exams?

Mathematics, as we all know, is a practice oriented subject. The more you practice, the more you will understand that will help you score good in the examinations . In Class 8 Maths, everyone should carefully read the examples given in each chapter of mathematics and then solve each question given in the exercises on its own. If the question is not solved or answered, then you should try and try again. Solving the questions by various methods help us to learn many different ways of doing each question. If you have no idea about a question in the exam or do not have complete confidence in any question, then this practice of solving help you here to find proper solutions. We see that even the toughest question gets solved by trying once or twice. In this way. Students will feel that their performance in day to day examinations gets better and easily get 90% or even more marks in the annual examination of Class 8 Maths.

How can I easily pass the Class 8 Maths exam?

There are a total of 13 chapters in the class 8 Maths NCERT Textbook. According to the interest of the students, they find that some chapters are simple but few are difficult one. By solving all the questions of the easy chapters we can easily manage passable marks in 8th Maths. For example, linear equations with one variable, rational numbers, Data Handling, and introduction to graphs are easy.

Which is the easiest chapter of class 8 Maths NCERT?

The easiest chapter in Class 8 Mathematics is chapter 2 Linear Equations in One Variable. It has a total of 2 exercises. Chapter 2 of 8th Maths is easy as well as very useful for examinations. By practicing this chapter, we can score better marks even in less practice. Class 8 Chapter 2 is one of the very important chapters in next classes also.

Which lesson is the most difficult chapter of Class 8 Maths?

Which chapter is difficult and which is simple, generally it can vary from student to student. But most of the students find difficulty in Chapter 9 algebraic expressions and identities of Class 8 Maths. Most of the students face difficulties during implementation of identities in questions. Even after solving each question repeatedly, one is not able to get the confidence which is easily found in the rest of the chapters.

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NCERT Solutions for Class 8 Maths Free PDF Download

Ncert solutio ns for class 8 maths.

NCERT Solutions for Class 8 Maths will help you to ace the unsolved problems in the maths book prescribed by the CBSE. NCERT Solutions for Class 8 breaks down the solutions into detailed steps to increase your score in exams.

NCERT Solutions are prepared by our team of highly professional, qualified and experienced faculties. These NCERT Solutions for Class 8 Maths helps you to quickly grasp all the concepts and formulas of maths. In case you have a doubt while you are studying NCERT Solutions for Class 8 Maths which we are providing, for this, we have a team of teachers who are just a click away to solve your doubt any time.

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Download NCERT Solutions for other subjects here .

Download NCERT Solutions for Class 8 here.

ncert solutions for class 8 maths

NCERT Solutions for Class 8 Maths Chapter-wise

  • 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 – Square and Square Roots
  • Chapter 7 – Cube 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

CBSE Class 8 Maths Chapter-wise NCERT Solutions

Ncert solutions for class 8 maths chapter 1 – rational numbers.

In this chapter will learn the properties of real numbers, rational numbers, representation of a rational number on number line, additive and multiplicative identity.

NCERT Solutions for Class 8 Maths Chapter 2 – Linear Equations in One Variable

In this chapter you will learn the concept of linear equation and methods to solve them, reducing equations to a simpler form and their applications.

NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals

In this chapter, you will learn the basics of a quadrilateral, polygon, kinds of quadrilateral and polygon, the measure of external angle of polygons.

NCERT Solutions for Class 8 Maths Chapter 4 – Practical Geometry

This chapter includes drawing 4 sides in a quadrilateral with 2 adjacent sides, 3 angles, and 1 diagonal area given.

NCERT Solutions for Class 8 Maths Chapter 5 – Data Handling

In this chapter you will learn to organize the data in a systematic method, represent the data in a pictograph, a bar graph, double bar graph, pie chart, and histogram.

NCERT Solutions for Class 8 Maths Chapter 6 – Square and Square Roots

In this chapter, you will learn about the squares of numbers and their properties, various patterns of squares, and square roots of numbers.

NCERT Solutions for Class 8 Maths Chapter 7 – Cube and Cube Roots

In this you will study about cubes of different numbers, cubes of numbers by adding consecutive odd numbers pattern, cube roots of a number, solving cube roots by prime factorization method.

NCERT Solutions for Class 8 Maths Chapter 8 – Comparing Quantities

In this chapter you will compare quantities, increase or decrease of percentage, discount, profit and loss, vat tax, sales tax, computing interest.

NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

In this chapter, you will learn about the algebraic expressions and their types, like and unlike terms, addition and subtraction, multiplication of algebraic expressions, standard identities and their implementation.

NCERT Solutions for Class 8 Maths Chapter 10 – Visualizing Solid Shapes

In this chapter, you will study the cubes, cuboids, cones, cylinders, spheres, hemispheres and their area, triangular pyramids, triangular and square base prisms, application of Euler’s formula.

NCERT Solutions for Class 8 Maths Chapter 11 – Mensuration

In this chapter, you will learn about the perimeter and areas of plane closed figure and surface area, the volume of a solid figure, transform the quantity into other units.

NCERT Solutions for Class 8 Maths Chapter 12 – Exponents and Powers

In this chapter you will study powers with negative exponents, laws of exponents, express the numbers in standard form and comparison of extremely large numbers.

NCERT Solutions for Class 8 Maths Chapter 13 – Direct and Inverse Proportions

In this chapter, you will solve the problems related to direct and inverse proportion and their identification based on relative increase or decrease of a quantity with respect to the first one.

NCERT Solutions for Class 8 Maths Chapter 14 – Factorization

In this chapter, you will learn methods of factorization, division of algebraic expression, error finding in algebraic equations.

NCERT Solutions for Class 8 Maths Chapter 15 – Introduction to Graphs

In this, you will study the representations of data by a bar graph, histogram, pie chart, line graph, and linear graph, application based on the graph using the dependent & independent variable.

NCERT Solutions for Class 8 Maths Chapter 16: Playing with Numbers

In this chapter, you will deal with numbers in a general form, puzzles related to numbers, divisibility tests.

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Solved Questions For You:

Question 1. For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by  5  companies. (d) The number of passengers boarding trains from  7 : 0 0  a.m. to  7 : 0 0  p.m. at a station. Give reasons for each.

(a) We can’t use the histogram in this case because we cannot define the class intervals for this data.

(b) We can use histogram here because it will be easy to divide the data into class intervals.

(c) We do not have approximate data we won’t use a histogram. We do not know about the number of cassettes produced by companies.

Question 2. List the outcomes you can see in these experiments.

question

(a) Possible outcomes would be:  A , B , C , D

Question 3. When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than  5

Possible outcomes:  1 , 2 , 3 , 4 , 5 , 6 (i) (a) Prime numbers:  2 , 3 , 5 It represents the outcomes of Prime numbers (b) Not a prime number:  1 , 4 , 6 It represents the outcomes of not prime numbers. (ii) (a) A number greater than  5 : Only when  6  comes (b) Number not greater than  5 : Only when outcomes:  1 , 2 , 3 , 4  and  5

Question 4. A survey was made to find the type of music that a certain group of young people liked in a city. The adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: (i) If  2 0  people liked classical music, how many young people were surveyed? (ii) Which type of music is liked by the maximum number of people? (iii) If a cassette company were to make  1 0 0 0  CDs, how many of each type would they make?

question

The light chart represents the maximum number as it is  4 0 % of the total.  ∴  Light music is liked by max. people.

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  • Important Questions for CBSE Class 8 Maths Chapter 9 - Algebraic Expressions and Identities

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CBSE Class 8 Maths Important Questions for Algebraic Expressions and Identities - Free PDF Download

Important questions for Algebraic Expressions Class 8 are now available on Vedantu’s website. The important questions are compiled by our experts keeping in mind the syllabus given by the board and the previous years question papers. Important questions of algebraic expressi ons class 8 maths will help the students to understand the topic thoroughly. It will help them to get a good grasp of the chapter, prepare properly by solving the given questions, and familiarize themselves with the question patterns. The important questions also include questions from the latest edition of CBSE NCERT books which will help the students keep up with the current syllabus. 

Vedantu is a platform that provides free (CBSE) NCERT Solution and other study materials for students.You can also download NCERT Solutions f or Class 8 Science to help you to revise complete syllabus and score more marks i n your examinations. 

The important questions of algebraic expressions class 8 are now available on our website in downloadable, PDF format along with pdfs of other subjects and chapters from the current year’s maths syllabus. Students can deliver these PDFs anytime and anywhere they want and practice them accordingly. 

Study Important Questions for Class 8 Mathematics Chapter 9 - Algebraic Expressions and Identities

Very short answer questions (1 mark).

1. Identify the coefficient of x in the expression

(a) 1 

(b) -1 

(c) -2 

(d) None of these

Ans: Given: \[x\]

We need to find the coefficient of the given expression.

We know that coefficient is the number before any variable. 

So, the expression \[x\] can be written as $ 1\times x $ . 

So, the coefficient will be $ 1. $ 

2. The expression for sum of numbers p and q subtracted from their product is

(a) p+q-pq  

(b) pq-p+q  

(c)  pq-(p+q)  

(d)  pq+p-q  

Ans: Given: variables $ p,q $ 

To find: the expression for sum of numbers $ p $ and $ q $ subtracted from their product

The product of the numbers will be

$ \begin{align} & p\times q \\ & =pq \\ \end{align} $

Sum of numbers will be

 $ p+q $ 

Therefore, the required answer will be

$pq-(p+q) $ 

3. Sum of \[\mathbf{ab,}\] \[\mathbf{a\text{ }+\text{ }b,}\] and \[\mathbf{b\text{ }+\text{ }ab}\] is

(a) 2ab+2a+b

(d)2ab+a+2b

Ans: Given: $ab, a+b, b+ab $ 

We need to find the sum of the given terms.

Therefore, the sum will be

$ \begin{align} & ab+a+b+b+ab \\ & =2ab+a+2b \\ \end{align} $

4. The value of expression $ \mathbf{5{{x}^{2}}-2} $ when $\mathbf{ x=3 }$ is

 (a)-12 

 (b) 8 

 (c) 43 

 (d) 36 

Ans: Given: $ 5{{x}^{2}}-2 $ , $ x=3 $ 

We need to find the value of $ 5{{x}^{2}}-2 $ at $ x=3 $ 

We will put $ 3 $ in place of $ x $ in the expression $ 5{{x}^{2}}-2 $ 

Therefore, the value of the expression will be

$ \begin{align} & 5{{x}^{2}}-2 \\ & =5{{(3)}^{2}}-2 \\ & =5(3)-2 \\ & =45-2 \\ & =43 \\ \end{align} $

5. On simplifying the result is $\mathbf{ (a+b-2)-(b-a+2)+(a-b+2)} $

 (a) $\mathbf{ a-b+2} $ 

 (b) $ \mathbf{a-b-2 }$ 

 (c) $ \mathbf{3a-b-2 }$ 

 (d) $\mathbf{ 3a+b+2 }$ 

Ans: Given: $ (a+b-2)-(b-a+2)+(a-b+2) $ 

We need to simplify the given expression.

So, the expression will be simplified as

$ \begin{align} & (a+b-2)-(b-a+2)+(a-b+2) \\ & =a+b-2-b+a-2+a-b+2 \\ & =3a-b-2 \\ \end{align} $

6. What is the statement for the expression $\mathbf{ 2(y-9)} $ 

 (a)  2y  subtracted from  9  

 (b)  9  subtracted from  y  and multiplied by  2  

 (c)  9  subtracted from  9  

 (d) Three of  y  minus  9 $ 

Ans: Given: $ 2(y-9) $ 

We need to find the statement of the given expression.

We can write the expression as $ 9 $ subtracted from $ y $ and multiplied by $ 2 $.

7. The factors of $\mathbf{ 7{{a}^{2}}+14a} $ is

 (a) $ \mathbf{7(a+2) }$ 

 (b) $\mathbf{ 21a } $ 

 (c) $ \mathbf{7(a+1) }$ 

 (d) $\mathbf{ 7a(a+2) }$ 

Ans: Given: $ 7{{a}^{2}}+14a $ 

We need to factorize the given expression

The factors of $ 7{{a}^{2}}+14a $ will be

 $ 7{{a}^{2}}+14a $ 

Take $ 7a $ as a common factor, we get

 $ 7a(a+2) $ 

Therefore, these will be the factors of the given expression.

Short Answer Questions (2 Mark)

8. The volume of a rectangular box where length, breadth, and height are $ \mathbf{2a,4b,8c} $ respectively.

Ans: Given: length of rectangular box, $ l=2a $ 

Breadth of rectangular box, $ b=4b $ 

Height of rectangular box, $ h=8c $ 

We need to find the volume of the rectangular box with given dimensions.

We know, Volume of a cuboid $ =l\times b\times h $ 

Therefore, the volume of the rectangular box will be

$ \begin{align} & =2a\times 4b\times 8c \\ & =64abc \\ \end{align} $

9. Simplify $\mathbf{ (p+{{q}^{2}})({{p}^{2}}-q) } $ 

Ans: Given: $ (p+{{q}^{2}})({{p}^{2}}-q) $ 

To simplify, we will open the brackets by multiplying the terms in it with each other.

Therefore, the expression will become

\[\begin{align} & \left( p+{{q}^{2}} \right)\left( {{p}^{2}}-q \right) \\ & =p\left( {{p}^{2}}-q \right)+{{q}^{2}}\left( {{p}^{2}}-q \right) \\ & ={{p}^{3}}-pq+{{q}^{2}}{{p}^{2}}-{{q}^{3}} \\ \end{align}\]

10. If $ \mathbf{pq=3 } $ and $\mathbf{ p+q=6, } $ then $\mathbf{ ({{p}^{2}}+{{q}^{2}})} $ is

Ans: Given: $ pq=3 $ , $ p+q=6, $ 

We need to find $ ({{p}^{2}}+{{q}^{2}}) $ 

We know that, 

$ \begin{align} & {{(p+q)}^{2}}={{p}^{2}}+{{q}^{2}}+2pq \\ & \left( {{p}^{2}}+{{q}^{2}} \right)={{(p+q)}^{2}}-2pq \\ \end{align} $

Substituting the values, $ pq=3 $ , $ p+q=6, $ in above equation we get

$ \begin{align} & \left( {{p}^{2}}+{{q}^{2}} \right) \\ & ={{(6)}^{2}}-2(3) \\ & =36-6 \\ & =30 \\ \end{align} $

11. Simplify $\mathbf{ x(2x-1)+5 }$ and find its value at $ \mathbf{x=-3} $ 

Ans: Given: $ x(2x-1)+5 $ 

We need to find the value of the given expression at $ x=-3 $ 

We will substitute $ x=-3 $ in the given expression. Therefore, the expression after simplifying will be

$ \begin{align} & 2{{(-3)}^{2}}-(-3)+5 \\ & =2(9)+3+5 \\ & =18+8 \\ & =26 \\ \end{align} $

Short Answer Questions (3 Mark)

12. Find the value of $ \mathbf{{{\left( \frac{2}{3}x-\frac{3}{2}y \right)}^{2}}+2xy }$ 

Ans: Given: $ {{\left( \frac{2}{3}x-\frac{3}{2}y \right)}^{2}}+2xy $ 

We need to find the value of the given expression

We know that, $ {{(a-b)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab $ 

Therefore, using the formula, we will get the value of the expression as:

\[\begin{align} & ={{\left( \frac{2}{3} \right)}^{2}}{{x}^{2}}+{{\left( \frac{3}{2} \right)}^{2}}{{y}^{2}}-2\left( \frac{2}{3} \right)x\left( \frac{3}{2} \right)y+2xy \\ & =\frac{4}{9}{{x}^{2}}+\frac{9}{4}{{y}^{2}}-2xy+2xy \\ & =\frac{4}{9}{{x}^{2}}+\frac{9}{4}{{y}^{2}} \\ \end{align}\]

13. Find $\mathbf{ (m+n)(m-n)\left( {{m}^{2}}+{{n}^{2}} \right)\left( {{m}^{4}}+{{n}^{4}} \right)} $ 

Ans: Given: $ (m+n)(m-n)\left( {{m}^{2}}+{{n}^{2}} \right)\left( {{m}^{4}}+{{n}^{4}} \right) $ 

We need to simplify the given expression. 

Formula Used: $ (a+b)(a-b)={{a}^{2}}-{{b}^{2}} $ 

Simplifying the expression, we get

$ \begin{align} & (m+n)(m-n)\left( {{m}^{2}}+{{n}^{2}} \right)\left( {{m}^{4}}+{{n}^{4}} \right) \\ & =\left( {{m}^{2}}-{{n}^{2}} \right)\left( {{m}^{2}}+{{n}^{2}} \right)\left( {{m}^{4}}+{{n}^{4}} \right) \\ & =\left[ {{\left( {{m}^{2}} \right)}^{2}}-{{\left( {{n}^{2}} \right)}^{2}} \right]\left( {{m}^{4}}+{{n}^{4}} \right) \\ & =\left[ {{m}^{4}}-{{n}^{4}} \right]\left[ {{m}^{4}}+{{n}^{4}} \right] \\ & ={{m}^{8}}-{{n}^{8}} \\ \end{align} $

14. From the sum of $\mathbf{ 3a-b+9} $ and $\mathbf{ -b-9} $ , subtract $\mathbf{ 3a-b-9} $ 

Ans: Given: expressions $ 3a-b+9 $ , $ -b-9 $ , $ 3a-b-9 $ 

We need to subtract $ 3a-b-9 $ from the sum of $ 3a-b+9 $ and $ -b-9 $ 

The sum of the first two terms, $ -b-9 $ and $ 3a-b+9 $ will be

$ \begin{align} & 3a-b+9+(-b-9) \\ & =3a-b+9-b-9 \\ & =3a-2b \\ \end{align} $

Now subtracting $ 3a-b+9 $ from $ 3a-2b $ , we get

$ \begin{align} & 3a-2b-(3a-b-9) \\ & =3a-2b-3a+b=9 \\ & =-b+9 \\ \end{align} $

15. Find $ \mathbf{194\times 206 }$ using suitable identity

Ans: Given: $ 194\times 206 $ 

We need to find the value of the given expression using an identity.

We can write,

$ \begin{align} & 194=(200-6) \\ & 206=(200+6) \\ \end{align} $

Using identity, $ (a-b)(a+b)={{a}^{2}}-{{b}^{2}} $ , the given expression can be simplified as:

$ \begin{align} & (200-6)(200+6) \\ & ={{(200)}^{2}}-{{(6)}^{2}} \\ & =40000-36 \\ & =39964 \\ \end{align} $

16. If $\mathbf{ x+\frac{1}{x}=9, }$ find the value of $\mathbf{ \left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right). }$ 

Ans: Given: $ x+\frac{1}{x}=9 $ 

To find: $ \left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right) $ 

Let $ x+\frac{1}{x}=9\text{ }..............(1) $ 

Square both sides, we will get

$ \begin{align} & \left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)={{(9)}^{2}} \\ & \left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=81 \\ \end{align} $

Now, we know that $ {{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab $ 

$ \begin{align} & {{\left( x+\frac{1}{x} \right)}^{2}}={{x}^{2}}+{{\left( \frac{1}{x} \right)}^{2}}+2x\times \frac{1}{x} \\ & {{\left( x+\frac{1}{x} \right)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}+2 \\ & 81={{x}^{2}}+\frac{1}{{{x}^{2}}}+2 \\ & {{x}^{2}}+\frac{1}{{{x}^{2}}}=81-2 \\ & {{x}^{2}}+\frac{1}{{{x}^{2}}}=79 \\ \end{align} $

17. Simplify $\mathbf{ \left( {{x}^{2}}-3x+2 \right)(5x-2)-\left( 3{{x}^{2}}+4x-5 \right)(2x-1) }$ 

Ans: Given: $ \left( {{x}^{2}}-3x+2 \right)(5x-2)-\left( 3{{x}^{2}}+4x-5 \right)(2x-1) $ 

First simplifying, $ \left( {{x}^{2}}-3x+2 \right)(5x-2), $ we will get

$ \begin{align} & \left( {{x}^{2}}-3x+2 \right)(5x-2) \\ & =5{{x}^{3}}-15{{x}^{2}}+10x-2{{x}^{2}}+6x-4 \\ & =5{{x}^{3}}-17{{x}^{2}}+16x-4\text{ }...................(1) \\ \end{align} $

Now simplifying, $ \left( 3{{x}^{2}}+4x-5 \right)(2x-1) $ , we will get

$ \begin{align} & \left( 3{{x}^{2}}+4x-5 \right)(2x-1) \\ & =6{{x}^{3}}+8{{x}^{2}}-10x-3{{x}^{2}}-4x+5 \\ & =6{{x}^{3}}+5{{x}^{2}}-14x+5\text{ }..................(2) \\ \end{align} $

Subtract $ (1)-(2) $ to get the result

$ \begin{align} & \left( {{x}^{2}}-3x+2 \right)(5x-2)-\left( 3{{x}^{2}}+4x-5 \right)(2x-1) \\ & =5{{x}^{3}}-17{{x}^{2}}+16x-4-\left[ 6{{x}^{3}}+5{{x}^{2}}-14x+5 \right] \\ & =5{{x}^{3}}-17{{x}^{2}}+16x-4-6{{x}^{3}}-5{{x}^{2}}+14x-5 \\ & =-{{x}^{3}}-22{{x}^{2}}+30x-9 \\ \end{align} $

18. Find the following product $\mathbf{ (a-3b)(a+3b)\left( {{a}^{2}}+9{{b}^{2}} \right) }$ 

Ans: Given: $ (a-3b)(a+3b)\left( {{a}^{2}}+9{{b}^{2}} \right) $ 

We need to find the product of the given expression.

Formula Used: $ (a-b)(a+b)={{a}^{2}}-{{b}^{2}} $ 

Solve the given expression using the identity, we will get

$ \begin{align} & (a-3b)(a+3b)\left( {{a}^{2}}+9{{b}^{2}} \right) \\ & =\left[ {{(a)}^{2}}-{{(3b)}^{2}} \right]\left( {{a}^{2}}+9{{b}^{2}} \right) \\ & =\left( {{a}^{2}}-9{{b}^{2}} \right)\left( {{a}^{2}}+9{{b}^{2}} \right) \\ & ={{\left( {{a}^{2}} \right)}^{2}}-{{\left( 9{{b}^{2}} \right)}^{2}} \\ & ={{a}^{4}}-81{{b}^{4}} \\ \end{align} $

Long Answer Questions (5 Mark)

19. Find $\mathbf{ {{(3st+4t)}^{2}}-{{(3st-4t)}^{2}} }$ 

Ans: Given: $ {{(3st+4t)}^{2}}-{{(3st-4t)}^{2}} $ 

We know that,

$ \begin{align} & {{(a+b)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab \\ & \therefore {{(3st+4t)}^{2}}={{(3st)}^{2}}+{{(4t)}^{2}}+2(3st)(4t) \\ & =9{{s}^{2}}{{t}^{2}}+16{{t}^{2}}+24s{{t}^{2}}.................(1) \\ \end{align} $

We also know that,

$ \begin{align} & {{(a-b)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab \\ & \therefore {{(3st-4t)}^{2}}={{(3st)}^{2}}+{{(4t)}^{2}}-2(3st)(4t) \\ & {{(3st-4t)}^{2}}=9{{s}^{2}}{{t}^{2}}+16{{t}^{2}}-24s{{t}^{2}}............(2) \\ \end{align} $

Therefore, using equations $ (1) $ and $ (2) $ , the given expression will become

$ \begin{align} & =9{{s}^{2}}{{t}^{2}}+16{{t}^{2}}+24s{{t}^{2}}-\left[ 9{{s}^{2}}{{t}^{2}}+16{{t}^{2}}-24s{{t}^{2}} \right] \\ & =9{{s}^{2}}{{t}^{2}}+16{{t}^{2}}+24s{{t}^{2}}-9{{s}^{2}}{{t}^{2}}-16{{t}^{2}}+24s{{t}^{2}} \\ & =48s{{t}^{2}} \\ \end{align} $

20. The area of a rectangle is uv where u is length and v is breadth. If the length of rectangle is increased by \[\mathbf{5\text{ units}}\] and breadth is decreased by \[\mathbf{3\text{ units}\text{.}}\]. The new area of rectangle is?

Ans: Given: Area of the old rectangle $ =uv $ 

Length of the old rectangle $ =u $ 

Breadth of told rectangle $ =v $ 

Length of the ew rectangle $ =u+5 $ 

Breadth of the new rectangle $ =v-3 $ 

We need to find the area of the new rectangle.

We know that, Area of rectangle $ =length\times breadth $ 

Therefore, the area of the new rectangle will be 

$ \begin{align} & =(u+5)(v-3) \\ & =uv-3u+5v-15 \\ \end{align} $

21. If \[\mathbf{\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=27}\], find $\mathbf{ x-\frac{1}{x} }$ 

Ans: Given: \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=27\]

We need to find $ x-\frac{1}{x} $ Use identity, $ {{(a-b)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab $ 

Substitute, $ a=x,b=\frac{1}{x} $ , we get

$ \begin{align} & {{\left( x-\frac{1}{x} \right)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}-2x\times \frac{1}{x} \\ & \Rightarrow {{\left( x-\frac{1}{x} \right)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}-2 \\ \end{align} $

We know that, \[\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)=27\], therefore,

$ \begin{align} & \Rightarrow {{\left( x-\frac{1}{x} \right)}^{2}}=27-2 \\ & \Rightarrow {{\left( x-\frac{1}{x} \right)}^{2}}=25 \\ & \Rightarrow \left( x-\frac{1}{x} \right)=\sqrt{25} \\ & \Rightarrow \left( x-\frac{1}{x} \right)=5 \\ \end{align} $

22. Simplify using identity, $\mathbf{ \frac{2.3\times 2.3-0.3\times 0.3}{2.3\times 2.3-2\times 2.3\times 0.3+0.3\times 0.3} }$ 

Ans: Given: 0 $ \frac{2.3\times 2.3-0.3\times 0.3}{2.3\times 2.3-2\times 2.3\times 0.3+0.3\times 0.3} $ 

We need to simplify the given expression using an identity.

Identity used: 

$ \begin{align} & 1.{{a}^{2}}-{{b}^{2}}=(a+b)(a-b) \\ & 2.{{(a-b)}^{2}}={{a}^{2}}+{{b}^{2}}-2ab \\ \end{align} $

Using these identities, the given expression can be written as:

$ \begin{align} & =\frac{2.3\times 2.3-0.3\times 0.3}{2.3\times 2.3-2\times 2.3\times 0.3+0.3\times 0.3} \\ & =\frac{{{(2.3)}^{2}}-{{(0.3)}^{2}}}{{{(2.3)}^{2}}-2(2.3)(0.3)+{{(0.3)}^{2}}} \\ & =\frac{(2.3+0.3)(2.3-0.3)}{{{(2.3-0.3)}^{2}}} \\ & =\frac{(2.3+0.3)}{(2.3-0.3)} \\ & =\frac{2.6}{2} \\ & =1.3 \\ \end{align} $

23. The sum of \[\mathbf{\left( x\text{ }+\text{ }3 \right)}\] observations is $\mathbf{ ({{x}^{4}}-81).} $ Find the mean of the observations.

Ans: Given: 

Number of observations $ =\left( x\text{ }+\text{ }3 \right) $ 

Sum of observations $ =({{x}^{4}}-81) $ 

We know that $ \text{Mean=}\frac{\text{Sum of all observations}}{\text{Total number of observations}} $ 

Therefore, mean of the observations will be

$ \begin{align} & =\frac{\left( {{x}^{4}}-81 \right)}{(x+3)} \\ & =\frac{{{x}^{4}}-{{3}^{4}}}{x+3} \\ & =\frac{{{\left( {{x}^{2}} \right)}^{2}}-{{\left( {{3}^{2}} \right)}^{2}}}{(x+3)} \\ \end{align} $

We know that, $ {{a}^{2}}-{{b}^{2}}=(a+b)(a-b) $ 

$ \begin{align} & =\frac{\left( {{x}^{2}}+{{3}^{2}} \right)\left( {{x}^{2}}-{{3}^{2}} \right)}{(x+3)} \\ & =\frac{\left( {{x}^{2}}+{{3}^{2}} \right)(x-3)(x+3)}{(x+3)} \\ & =\left( {{x}^{2}}+9 \right)(x-3) \\ & ={{x}^{3}}+9x-3{{x}^{2}}-27 \\ & ={{x}^{3}}-3{{x}^{2}}+9x-27 \\ \end{align} $

24. Abhishek is \[\mathbf{6}\] years older than Jagadish. Six years ago Abhishek was twice as old as Jagadish. Write down the situation in algebraic expression and find how old is each now?

Ans: Given: Age of Abhishek \[=6\] years older than Jagadish

Six years ago Abhishek age $ =2 $ times of Jagadish age

We need to write the algebraic expression and find the age of both.

Let, present age of Jagadish $ =x $ 

Abhishek is \[6\] years older than Jagadish. 

Therefore, age of Abhishek $ =x+6 $ 

Jagadish age \[6\] years ago $ =x-6 $

Age of Abhishek \[6\] years ago $ =(x+6)-6 $ 

According to the question, Six years ago Abhishek was twice as old as Jagadish. So,

$ \begin{align} & (x+6)-6=2(x-6) \\ & \Rightarrow x+6-6=2x-12 \\ & \Rightarrow -x=-12 \\ & \Rightarrow x=12 \\ \end{align} $

We can conclude that present age of Jagadish $ =12\text{ years} $ 

The present age of Abhishek will be

$ \begin{align} & =x+6 \\ & =18\text{ years} \\ \end{align} $

25. Rohit mother gave him $ \mathbf{\text{Rs}\text{. }4x{{y}^{2}} }$ and his father gave him Rs. $\mathbf{ (5x{{y}^{2}}+3) }$ . Out of this total money he spent Rs. $\mathbf{ (10-3x{{y}^{2}}) }$ on his birthday party. How much money is left with him?

Ans: Given: Mother gives Rohit amount $ =4x{{y}^{2}} $ 

Father gives Rohit amount $ =(5x{{y}^{2}}+3) $ 

Total amount spent by Rohit $ =(10-3x{{y}^{2}}) $ 

We need to find how much money is left with him.

Total Amount Received by Rohit is,

$ \begin{align} & =4x{{y}^{2}}+(5x{{y}^{2}}+3) \\ & =9x{{y}^{2}}+3 \\ \end{align} $

Total amount spent by Rohit is

 $ =(10-3x{{y}^{2}}) $ 

Therefore, Amount left with him will be

$ \begin{align} & =\left( 9x{{y}^{2}}+3 \right)-\left( 10-3x{{y}^{2}} \right) \\ & =9x{{y}^{2}}+3-10+3x{{y}^{2}} \\ & =12x{{y}^{2}}-7 \\ \end{align} $

Why is it Necessary for Students to Solve Important Questions of Algebraic Expressions Class 8?

Students must solve the important questions of algebraic expressions class 8. This will help them to keep up with what is being taught in class and what might appear in the exams. These questions are carefully curated based on the current syllabus, and curriculum, previous years question papers. They contain only the questions which are most likely to appear in the examinations. This allows the students to study in-depth and prepare well in advance.

How the Chapter 9 Maths Class 8 Important Questions Are Going to Help Students 

The chapter 9 class 8 important questions are going to help the students immensely because - 

These solutions provide step by step explanations helping the students to answer questions better.

These solutions contain a list of important formulas that will help the students remember them during exam time.

The questions and solutions are written based on the current syllabus.

These questions and solutions will further help students during competitive exam revisions.

Questions are compiled by experts who have in-depth knowledge about the subject. 

Relevance of Chapter 9 Algebraic Expressions

This chapter is crucial for students because this chapter will create the base for many future chapters and problems. In higher studies and mathematics, algebraic expressions are utilised in several situations. Algebraic expressions play a vital role in the mathematics curriculum and mathematics in general. If any student wishes to pursue mathematics in higher studies it will be very important for them. Students will be required to understand, read, write expressions, as well as be skilled in computations and usage of algebraic expressions.  Apart from that, even students who do not pursue maths but have basic mathematics in their syllabus will have to use algebraic expressions in various fields. 

Algebraic expressions will be used to decipher relationships between variables and constants, between people, elements, thoughts, and structures. This chapter will help students see the relation and role of variables and constants in a real-life context and also help them implement these expressions in real life. 

Also, this chapter will help students in all competitive examinations later on in life. So it is important that students properly learn, clear their basics, and understand this chapter from a fairly young age. 

What Students will Learn from Class 8 Maths Chapter 9 Important Questions

Students will learn how to identify variable and constants in algebraic expressions given to them

It helps them to develop an idea about algebraic expressions and see their purpose.

It helps them to construct algebraic expressions from given real-life situations and solve them.

It helps students to learn about algebraic expression concepts which would help them in later years in various chapters and examinations. 

Introduction to Algebraic Expressions 

What are algebraic expressions.

Algebraic Expression refers to an expression that is constructed from integer constants, variables, and algebraic operations like addition, subtraction, multiplication, and division. 

For example, 5m + 8 is an algebraic expression where the two terms are 5m and 8 and m is the variable. The two terms are separated by the arithmetic sign +. 

Examples of Algebraic Expressions 

30x + 4y, 6x + 10y etc are basic examples of algebraic expressions. The expressions are being represented with the help of variables, constants, and arithmetic symbols. The combination of these terms is known as algebraic expressions.

This is different from algebraic equations because algebraic expressions do not have any sides or equal to signs. 

Types of Algebraic Expressions 

There are mainly three types of Algebraic Expressions, namely - 

Monomial Expression

Binomial Expression

Polynomial Expression 

Monomial Expression - Monomial Algebraic Expression refers to the expression which has only one term in it. 

For example, 3x, 5x, 5xy, etc, are monomial expressions.

Binomial Expression - Binomial Algebraic Expression refers to the expression which has two terms in it. 

For example, 5x+y, 10z- 5x, 20x+ 10, etc, are binomial expressions.

Polynomial Expression - Polynomial Expression refers to the expression which has more than one term with non-negative integral exponents of a variable in it. 

For example, ax - by - cz, x + 2x - 3y, etc are polynomial expressions. 

Other Types of Algebraic Expressions 

Apart from the above mentioned three types of algebraic expressions, there are two more classifications, namely -

Numeric Expression 

Variable Expression

Numeric Expression - A Numeric Expression is an expression that consists of numbers and operations but does not contain any variables. 

For example, 10 + 2, 11 - 5, etc are examples of numeric expressions.

Variable Expression - A variable Expression is an expression that consists of numbers as well as variables.

For example, 4x + 4y, 5xy - 5y, etc are variable expressions.

Some Important Terms of Algebraic Expressions

Some important terms that students will come across while studying the chapter Algebraic Expressions are -

Coefficient of the Term

Constant 

Factors of a Term

Terms of Equations

Like and Unlike terms

For example, in the expression 2xy + 14y, 2xy and 14y are the two terms.

Coefficient of the term xy is 2 

Constant term is 2. 

Examples of Like Terms are 3x and 2x 

Examples of Unlike Terms are 2x and 5y.

Suppose, 4xy is a term, then 4,x, and y are its factors.

Addition and Subtraction of Algebraic Expressions 

We can also add or subtract algebraic expressions easily. 

For example, if we are asked to add 3x + 10y - 5z and x + 2y + 2z,

We add the expressions and get 

(3x + 10y - 5z) + ( x + 2y + 2z) and get 4x + 12y - 3z. 

Important Formulas 

Some of the important algebraic formulas that we need to keep in mind are - 

(a + b) 2 = a 2 + 2ab + b 2

(a – b) 2 = a 2 – 2ab + b 2

a 2 – b 2 = (a – b)(a + b)

(a + b) 3 = a 3 + b 3 + 3ab(a + b)

(a – b) 3 = a 3 – b 3 – 3ab(a – b) 

a 3 – b 3 = (a – b)(a 2 + ab + b 2 )

a 3 + b 3 = (a + b)(a 2 – ab + b 2 )

How to Derive Algebraic Expressions

An algebraic expression is a combination of constants and variable and arithmetic symbols like + or - or * or /. We can use these combinations to derive algebraic expressions from given problems. 

Suppose it is given that Ram has thrice the number of apples as Rita does. The total number of apples between Ram and Rit is 40. Express this problem in an appropriate algebraic expression. 

We will write this as - 3x + x = 40 where x is the number of apples Rita has. 

Why Study from Vedantu?

Vedantu is one of the leading online education platforms which helps students learn their study materials in a better way. Vedantu provides notes on every chapter in the syllabus complete with notes, revision notes, important questions, and solves solutions.

The notes, questions, and solutions are prepared by trained experts who have ample knowledge in those particular chapters. They come up with necessary notes, important questions that might appear in the examinations after careful and close analysis of the syllabus and guidelines as provided by the board.

The notes and solutions are given in such a manner that it is fairly easy for students to understand and learn from. They also come in downloadable PDFs so that students can study from these notes on any device, from anywhere without facing any difficulties. 

Vedantu makes sure that the notes are available to every student so these downloadable PDFs are free. They help students to practice before their examinations as much as possible so that they can score the best possible marks. 

We also make sure that Vedantu is the one-stop destination for all students looking for notes and solved questions and solutions so that they do not face any difficulty before their school exams or any competitive exams. 

Conclusion 

To conclude, we would advise our beloved students to study hard, go through the given study and revision notes thoroughly, write down the important formulas to remember them better, and practice the given important questions of algebraic expressions class 8 from our website. This will help the students to get to know the chapter well, be familiar with the various types of questions thus saving valuable time during the exams and fetch good marks in the final examinations.

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FAQs on Important Questions for CBSE Class 8 Maths Chapter 9 - Algebraic Expressions and Identities

1. How many sums are there in the Important Questions for CBSE Class 8 Maths Chapter 9- Algebraic Expressions and Identities?

There are 25 sums solved in the Important Questions for CBSE Class 8 Maths Chapter 9- Algebraic Expressions and Identities. This list of important questions along with their solutions are curated and prepared by the highly experienced faculty at Vedantu.

2. Are the Important Questions for CBSE Class 8 Maths Chapter 9- Algebraic Expressions and Identities helpful for exam preparation?

Yes, the Important Questions for CBSE Class 8 Maths Chapter 9- Algebraic Expressions and Identities are very helpful for the exam preparation. Every sum is solved and explained in a step by step manner to facilitate an easy learning experience for all students. Students can download and refer to these Important Questions and their solutions to learn the most effective problem-solving techniques for the sums from this topic. Furthermore, the marks weightage for every type of sum is provided in this PDF file. Hence, students can get a clear idea of the expected question pattern from this chapter and prepare accordingly for their exams.

3. What are algebraic identities?

Certain algebraic equations hold good irrespective of the values of the variables in them. Such algebraic equations are called algebraic identities. There are 4 such algebraic equations that are called standard algebraic identities. These algebraic identities happen to be very useful for solving the factorization of algebraic polynomials and sums of quadratic equations. Also, these algebraic identities can be derived by multiplying one binomial to another.

4. What are the 4 standard algebraic identities?

The 4 standard algebraic identities are as follows.

(a + b) 2 = a 2 + b 2 + 2ab

(a - b) 2 = a 2 + b 2 - 2ab

(x + a) (x - b) = x 2 + (a + b) x + ab

a 2 - b 2 = (a + b) (a - b)

5. What are algebraic expressions?

An algebraic expression is a mathematical expression composed of variables, algebraic operations, and integer constants. Expressions and Identities in Algebra are the basics of this chapter. To comprehend these words, we must first grasp the concepts of terms, factors, and coefficients. You will learn to deal with variables and constants both along with algebraic expressions. This chapter goes through several different sorts of expressions and identities in depth. To understand algebraic equations thoroughly, you can check the Class 8 Chapter 9 Important Questions on Vedantu website (vedantu.com) free of cost.

6. How do you add algebraic expressions?

There are two methods for solving the addition of algebraic expressions.

Horizontal Method: All phrases are put in a horizontal line, and then the elements are sorted to gather all the groupings of like words, which are then added.

Each phrase is written in a distinct row in this approach, such that elements are placed one under the other in a column. The adding of terms is then done column by column. To learn more about algebraic equations, you can check the Class 8 Chapter 9 Solutions on Vedantu app.

7. What is the formula for algebraic expression?

Numeric expressions are a type of expression that allows you to perform operations on numbers. A number expression, for example, is 5 (6 + 4) When variables and algebraic terms are included in expressions, the result is an algebraic expression. As a result, algebraic expressions have one variable and only one operation, such as addition, subtraction, multiplication, division, and so on. An algebraic expression is, for example, 6 (a + 7b).

8. What is Algebra?

In eighth grade, students learn about algebraic words, algebraic identities, variables, constants, algebraic expressions, monomial, binomial, and trinomial expressions. This chapter also covers algebraic expressions' mathematical operations such as addition, subtraction, multiplication, and division. Algebra and its applications in real life are essential elements of the math curriculum. In Chapter 9 Maths, students are given a variety of exercises to do and become comfortable with algebra.

9. Where can I find important questions for class 8 Maths Algebraic Expressions?

On Vedantu's website, important questions for Algebraic Expressions Class 8 are now available. Our specialists have developed a list of significant questions based on the board's syllabus and prior year's exam papers. Important algebraic expressions for Class 8 mathematics problems will aid pupils in fully comprehending the material. It will assist students in grasping the chapter, correctly preparing by answering the questions provided, and familiarizing themselves with the question patterns.

Chapterwise Important Questions for CBSE Class 8 Maths

Cbse study materials.

NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry

The NCERT solutions for class 8 maths chapter 4 practical geometry combine two concepts to teach children more about geometry. The first topic used is Construction that students have learned in previous classes and the second is quadrilaterals that kids might be familiar with from chapter 3 Understanding Quadrilaterals . This lesson is the perfect amalgamation of both the topics mentioned above to build on the concepts that kids have learned before. Additionally, it also shows them all the new ways in which they can implement these ideas. NCERT solutions class 8 maths chapter 4 focuses on constructing quadrilaterals when certain constraints are imposed on them for example, constructing a quadrilateral when four sides and one diagonal are given.

Class 8 maths NCERT solutions chapter 4 shows children how to correctly use a ruler and a compass to draw quadrilaterals. When the measure of four sides and a diagonal is given the first step is to construct a triangle using the SSS construction condition. Next, the fourth point is located with the help of two arcs using the given measurements to give the quadrilateral. NCERT solutions Chapter 4 practical geometry consists of many such techniques that give students holistic learning of how to construct quadrilaterals and also you can find some of these in the exercises given below.

  • NCERT Solutions Class 8 Maths Chapter 4 Ex 4.1
  • NCERT Solutions Class 8 Maths Chapter 4 Ex 4.2
  • NCERT Solutions Class 8 Maths Chapter 4 Ex 4.3
  • NCERT Solutions Class 8 Maths Chapter 4 Ex 4.4
  • NCERT Solutions Class 8 Maths Chapter 4 Ex 4.5

NCERT Solutions for Class 8 Maths Chapter 4 PDF

The entire chapter helps students to revise previous concepts while incorporating some new and unique topics. The NCERT solutions class 8 Maths have to-the-point, precise, and well-written solutions that use a simple language understandable by students of all intelligence quotas. Given below are the links to the solutions that kids can use to cross-reference their answers and get an insight into presenting their answers in a structured manner to get excellent marks in any examination.

☛ Download Class 8 Maths NCERT Solutions Chapter 4 Practical Geometry

NCERT Class 8 Maths Chapter 4   Download PDF

NCERT Solutions Class 8 Math Chapter 4 Practical Geometry 1

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry

Constructing quadrilaterals requires a high degree of exactness. This can only be achieved if kids revise the coursework at regular intervals. The solutions given above have a step-wise and detailed explanation of all problems in the NCERT textbook along with some exceptional tricks to streamline the process of solving questions. An in-depth analysis of the NCERT Solutions Class 8 Maths Chapter 4 practical geometry is given below that will help students in perfecting this lesson.

  • Class 8 Maths Chapter 4 Ex 4.1 - 1 Question
  • Class 8 Maths Chapter 4 Ex 4.2 - 1 Question
  • Class 8 Maths Chapter 4 Ex 4.3 - 1 Question
  • Class 8 Maths Chapter 4 Ex 4.4 - 1 Question
  • Class 8 Maths Chapter 4 Ex 4.5 - 4 Questions

☛ Download Class 8 Maths Chapter 4 NCERT Book

Topics Covered: Constructing quadrilaterals when four sides and one diagonal are given, two diagonals and three sides are known, two adjacent sides and three angles are mentioned as well as some special cases are the scope of the topics that fall under class 8 maths NCERT solutions chapter 4.

Total Questions: Class 8 maths chapter 4 Practical Geometry has a pool of 8 questions. 4 problems have sub-parts that range from easy to medium level sums while the remaining 4 are complex.

List of Formulas in NCERT Solutions Class 8 Maths Chapter 4

The NCERT solutions class 8 maths chapter 4 does not have any mathematical formulas for solving questions, rather they are based on the properties of quadrilaterals as well as steps that need to be followed for constructions . There will be a different technique employed when constructing quadrilaterals depending upon the given conditions. The steps to a few of these sub-topics available in the NCERT solutions for class 8 maths chapter 4 are given below:

Four sides and one diagonal are known:

  • Draw a triangle with the two given sides and one diagonal using a compass as well as a ruler.
  • Next, mark an arc from the point of intersection of the first and second sides equal to the length of the third side. Another arc is marked from the point of intersection of the first and third sides equal to the distance measure of the fourth side.
  • Complete the lines to get the quadrilateral.

Similarly, steps are given to solve questions on other criteria as well.

Important Questions for Class 8 Maths NCERT Solutions Chapter 4

Ncert solutions for class 8 maths video chapter 4, faqs on ncert solutions class 8 maths chapter 4, why are ncert solutions class 8 maths chapter 4 important.

NCERT Solutions Class 8 Maths Chapter 4 are extremely important because it lays the foundation for geometric construction skills within children. In practical geometry, the main focus lies in the steps of construction. These solutions present them in a well-organized form to help kids instill crystal clear concepts.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 8 Maths Practical Geometry?

The problems in the NCERT textbook are handpicked by mathematical geniuses to give students a complete understanding of the chapter. Each problem in the NCERT Solutions Class 8 Maths Practical Geometry serves a different purpose and hence, must be practiced. By revising all questions, kids will maximize the probability of getting a good score in their exams.

What are the Important Topics Covered in NCERT Solutions Class 8 Maths Chapter 4?

Each exercise in the NCERT Solutions Class 8 Maths Chapter 4 is based on a different way of constructing a quadrilateral. Questions in an examination paper can be based on any constraint imposed such as constructing a quadrilateral when three sides and two diagonals are known, three sides and two included angles are given, and so on. Hence, all topics need to be given equal importance and the same amount of practice time.

How Many Questions are there in NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry?

There are a total of 7 questions in NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry. 4 are based on a different construction constraint and have sub-parts while 4 are higher-order thinking problems that require kids to use their acumen and mathematical intellect.

How CBSE Students can utilize Class 8 Maths NCERT Solutions Chapter 4 effectively?

To effectively utilize the NCERT Solutions Class 8 Maths Chapter 4 it is highly advised to go through all the properties associated with the special types of quadrilaterals such as parallelograms , rectangles , rhombuses, and squares . This enables kids to progress through the solutions faster and helps them instill strong concepts.

Why Should I Practice NCERT Solutions Class 8 Maths Practical Geometry Chapter 4?

Practice equals perfection. The NCERT Solutions Class 8 Maths Practical Geometry Chapter 4 calls for precise and accurate measurements . This level of precision in drawing figures can only be achieved through regular practice and due diligence; thus, kids must periodically revise these sums and ensure that they do not skip any question.

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Maths Topics to be covered for Class 9

  • Real Numbers
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  • Linear Equations in Two Variables
  • Introduction to Euclid's Geometry
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  • Constructions
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What are CBSE Sample Papers?

Sample papers are mainly a kind of mock tests or model test papers which are prepared in accordance with the latest syllabus and guidelines that are issued by the central board. These examination test papers are designed as the replica of the actual papers that are asked in final examinations. All the marking schemes , number of questions , types of questions asked are followed as per board scheme and are issued to students two or three months before the examinations so that students get enough time to practice.

What is the importance of Sample Papers for Students?

In order to access the level of preparation done by any particular student he or she needs to solve CBSE Sample Papers. These papers are the perfect way to practise for the final board exam. If one wants to have a clear idea of how the final exam papers would be in terms of level of difficulty, time and other aspects then , all students must make sure that they do sample papers once their course revision is finished.

Few benefits of solving CBSE sample papers are given below:

  • Gauging Self Performance: Understanding and revising the subject is very good, but unless one attempts the sample paper in the lookalike environment as in board exam, seldom can the student identify and check whether the understanding of all concepts of the subject are complete or not. Once students try the question paper in the same time frame he or she is able to judge the capability of solving the paper in the stipulated time frame. It highlights the weak areas if any and gives students ample amount of time to work on those areas and be better prepared before exams.
  • Testing Time Criticality: Knowing is not everything as far as board papers are concerned. Sometimes it happens that in spite of knowing everything a student falls short of time to complete the entire paper and thus loses marks. Generally CBSE sample papers are generally of 3 hour duration. So while practicing sample papers it is imperative to create a board like environment at home and ensure that sample paper is attempted only in 3 hours and then check whether it was possible to complete the paper in the desired amount of time. Often at first students take longer than expected, and thus they get early warning to practice more and increase the speed.
  • Exam Anxiety: Sometimes sensitive students feel anxious to sit in the examination hall with a 3 hour length paper and for them it becomes a more intense requirement to practice prior to main exams and get rid of any kind of fear. Since they do not know what questions will be asked in the CBSE board they create panic in their mind due to this fear of the unknown and get scared with the idea that they might not be able to do well in exams. Thus such students needs to complete at-least 7-10 sample papers prior to the exams, to gain confidence and get into better frame of mind.

Best Time to Practice Sample Papers

This mainly varies from student to student but in general students should start dealing with sample papers as soon as their book revisions are over. Infact along with sample papers students should also look for model test papers of various publishers and attempt them to get the idea of level of preparation. As the dates of exam are approaching near by that time only samples papers should be mainly considered for practice and in case of any shortcomings those should be thoroughly discussed with teachers freids and other concerned person so that one has clarity before attempting the final paper.

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CBSE Class 8 Maths Solved Sample Question Paper 2023-24

NCERT Solutions for Class 8 Maths Updated 2023-24

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Mathematics is an important subject, but it can be challenging for students. The Physics Wallah team has come the with NCERT solutions for Class 8 Math. We aim to make math clear and easy to understand, boosting your confidence. These solutions are valuable for improving your math scores. Students can easily access the NCERT Class 8 Maths Solutions PDF provided links below. We are dedicated to offering you the best possible support and help.

NCERT Solutions for Class 8 Maths Chapter-Wise List

Here are the chapter-wise NCERT Solutions for Class 8 Maths prepared by our experts at PW. These detailed solutions will help you understand all the concepts explained in each chapter. Check out the list of Class 8 Math chapters below.

NCERT Solutions for class 8 Maths

NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers

Rational numbers are crucial in describing quantities or measures that whole numbers alone cannot represent. These quantities, such as length, mass, time, and others, are effectively measured using rational numbers.

The initial chapter of the NCERT Class 8 textbook focuses on rational numbers. Within this chapter, students will explore the properties of integers, natural numbers, and whole numbers. Additionally, they will learn how to represent rational numbers on the number line and the significance of zero and one in addition and multiplication. A solid understanding of this chapter is essential for comprehending more advanced concepts. The chapter includes various exercises and questions to reinforce the learning process.

Also Check-

  • Important Questions for class 8 maths Chapter 1 Rational Numbers
  • RS Aggarwal Class 8 solutions for Maths Chapter 1 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 2 - Linear Equations in One Variable

Linear equations in one variable are highly useful in determining the value of an unknown integer when two or more integers are given.

In this chapter, students will be introduced to the concept of linear equations in one variable and learn various methods to solve them.The chapter includes exercises to test students' ability to solve these equations using different approaches.

  • Important Questions for class 8 maths Chapter 2 Linear Equations in One Variable
  • RS Aggarwal Class 8 solutions for Maths Chapter 2 Linear Equations in One Variable

NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals

Knowing about quadrilaterals is extremely beneficial in architecture and engineering as it assists in designing floor plans for buildings and other structures.

Students will comprehensively understand quadrilaterals in this chapter and learn about their properties. They will also explore the fascinating realm of polygons, like pentagons and hexagons, expanding their knowledge further.

  • Important Questions for class 8 maths Chapter 3 Understanding Quadrilaterals
  • RS Aggarwal Class 8 solutions for Maths Chapter 3 Understanding Quadrilaterals

NCERT Solutions for Class 8 Maths Chapter 4 - Practical Geometry

Practical geometry is essential for visualizing and applying geometric concepts in real-world situations. It finds applications in various fields like construction, sculpture, and computing dimensions.

Having learned about quadrilaterals, students will now explore Practical Geometry in this chapter. They will discover how to construct different quadrilaterals based on specific parameters such as side lengths, enclosing angles, and diagonals. By working through the exercises provided, students will learn to handle quadrilateral concepts and be better prepared to tackle more advanced problems.

Also Check- Important Questions for class 8 maths Chapter 4 Practical Geometry

NCERT Solutions for Class 8 Maths Chapter 5 - Data Handling

Data storage and security depend on the art and skill of data handling. Students must understand data handling to effectively manage their and others' important information securely and accurately.

In this chapter, students delve into the concept of data and its analysis. They learn how to organize data systematically, which forms the foundation of data handling. Additionally, students explore methods to represent organized data using bar graphs, pie charts, histograms, and more. These skills will enable them to better interpret and present data for various purposes.

  • Important Questions for class 8 maths Chapter 5 Data Handling
  • RS Aggarwal Class 8 solutions for Maths Chapter 5 Data Handling

NCERT Solutions for Class 8 Maths Chapter 6 - Squares and Square Roots

Squares and square roots are widely used for calculating areas of spaces, financial gains and losses, and interest rates, among other applications.

This chapter holds significant importance for Class 8 students, especially from an examination perspective. It offers interesting problem-solving opportunities once the concepts are well understood. Students will learn about squares, square roots, and the fascinating patterns related to them. Additionally, the chapter covers the concept and properties of Pythagorean triplets, which further enhances their knowledge in this area.

  • Important Questions for class 8 maths Chapter 6 Squares and Square Roots
  • RS Aggarwal Class 8 solutions for Maths Chapter 6 Squares and Square Roots

NCERT Solutions for Class 8 Maths Chapter 7 - Cubes and Cube Roots

Cubes and cube roots are essential for calculating volumes of objects, working with exponents, and understanding interest rates, among other practical uses.

In this chapter, students build upon their previous knowledge and explore the world of cubes and cube roots. They will learn about the properties and patterns related to these mathematical concepts, enriching their understanding as they progress through the chapter.

  • Important Questions for class 8 maths Chapter 7 Cube and Cube Roots
  • RS Aggarwal Class 8 solutions for Maths Chapter 7 Cube and Cube Roots

NCERT Solutions for Class 8 Maths Chapter 8 - Comparing Quantities

Comparing different quantities is a valuable approach to analyzing and studying two or more quantities, enabling us to comprehend their relationships and distinctions.

The chapter on Comparing Quantities will likely captivate students' interest, as they will become acquainted with concepts like percentages, discounts, and sales – terms encountered in our daily lives. Additionally, they will learn to calculate simple and compound interests, which have significant practical applications in various aspects of life. This chapter provides valuable knowledge and real-world skills to the students.

Also Check- Important Questions for class 8 maths Chapter 8 Comparing Quantities

NCERT Solutions for Class 8 Maths Chapter 9 - Algebraic Expressions and Identities

Understanding algebraic expressions and identities empowers students to discover unknown values and manipulate mathematical information, making it easier to solve problems.

This chapter introduces students to various terms related to Algebraic Expressions and Identities. They will learn about factors, coefficients, monomials, binomials, and polynomials and perform different operations on them. To master this chapter in CBSE Class 8 Maths, students must diligently practice all the exercise questions, ensuring a strong grasp of the concepts.

  • Important Questions for class 8 maths Chapter 9 Algebraic Expressions and Identities
  • RS Aggarwal Class 8 solutions for Maths Chapter 9 Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 10 - Visualising Solid Shapes

Understanding solid shapes and their dimensions is crucial for various aspects of our lives, from calculating volumes to constructing buildings and monuments, making it a rewarding study area.

Class 8 students find this Maths chapter particularly intriguing as it ignites their imagination. They explore the world of 3D geometry and learn to visualize solid shapes in different dimensions. In this chapter, students will learn about edges, faces, and vertices and how to represent three-dimensional solid shapes. A critical topic covered here is Euler's formula, which enriches their comprehension of solid shapes.

Also Check- Important Questions for class 8 maths Chapter 10 Visualizing Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 11 - Mensuration

Mensuration is a mathematical tool used to measure the area, perimeter, volume, and more of spaces or objects.

This chapter expands on the student's knowledge of quadrilaterals and triangles, focusing on measuring the area of these shapes. Moreover, using various formulas, students will be taught how to calculate the area and volume of cubes and cuboidal structures.

Also Check- Important Questions for class 8 maths Chapter 11 Mensuration

NCERT Solutions for Class 8 Maths Chapter 12 - Exponents and Powers

Exponents and powers play a significant role in simplifying and condensing large values, making them easier to read and understand.

In this chapter, students become familiar with the concepts of powers and exponents, including positive and negative exponents. They will also learn how to express numbers in standard form using exponents and explore comparisons of huge and tiny numbers. Understanding these concepts is an important part of this chapter.

Also Check- Important Questions for class 8 maths Chapter 12 Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 13 - Direct and Inverse Proportions

Direct and inverse proportions help us understand the relationships between quantities and amounts.

In direct proportion, when one quantity increases or decreases, the other quantity also changes in a manner that keeps its corresponding values constant. On the other hand, in inverse proportion, one quantity increases while the other decreases, and vice versa.

  • Important Questions for class 8 maths Chapter 13 Direct and Inverse Proportions
  • RS Aggarwal Class 8 solutions for Maths Chapter 13 Direct and Inverse Proportions

NCERT Solutions for Class 8 Maths Chapter 14 - Factorisation

Factorization is a crucial tool for solving quadratic equations as it simplifies complex problems and equations.

In this chapter, students explore the factorization of algebraic expressions and natural numbers. They learn various factorizing methods, such as using factorization identities and regrouping terms. Additionally, students discover how to divide a polynomial or a monomial by another monomial, among other valuable techniques. Mastering factorization will enable students to handle mathematical problems more effectively.

  • Important Questions for class 8 maths Chapter 14 Factorization
  • RS Aggarwal Class 8 solutions for Maths Chapter 14 Factorization

NCERT Solutions for Class 8 Maths Chapter 15 - Introduction to Graphs

Graphs are powerful visual tools that present data and information in an easy-to-understand way.

In this chapter, students build upon their knowledge of data handling and explore different types of graphs like pie charts, histograms, and linear graphs. They also learn how to locate and coordinate points on a graph, taking their understanding to a more advanced level. This chapter enhances students' ability to interpret and create graphs, making data representation more accessible and engaging.

Also Check- RS Aggarwal Class 8 solutions for Maths Chapter 15 Introduction to Graphs

NCERT Solutions for Class 8 Maths Chapter 16 - Playing with Numbers

Number sense is precious as it fosters flexible thinking in children.

This chapter serves as a comprehensive summary of the various number concepts students have learned. Here we cover the topics related to numbers and provide insights into justifying the test of divisibility using these concepts.

Also Check- RS Aggarwal Class 8 solutions for Maths Chapter 16 Playing with Numbers

NCERT Solutions For Class 8 Maths PDF

Check below the NCERT Solution for Class 8 Maths PDF

Benefits of Class 8 Math NCERT Books and Solutions

Class 8 Math NCERT books and solutions offer numerous benefits to students, making them an essential resource for learning and understanding mathematics. A few of the main advantages are:

  • Class 8 Math NCERT books and solutions offer comprehensive and well-structured content.
  • They follow a standardized syllabus, ensuring uniformity in education.
  • NCERT solutions provide step-by-step explanations for conceptual clarity.
  • Practice questions in the solutions reinforce understanding and improve problem-solving abilities.
  • They are designed with exams in mind, making them valuable resources for competitive exam preparation.
  • NCERT textbooks are known for their accuracy and minimal errors.
  • They support teachers in delivering effective lessons.
  • These books are cost-effective and accessible to a wider range of students.
  • Supplementary materials are available for enhanced learning.
  • They align with competitive exams like JEE and NEET, giving students an advantage in future preparations.

Why Physics Wallah is Best for NCERT Solutions for Class 8 Maths

Physics Wallah is a highly regarded platform for NCERT Solutions for Class 8 Maths, and there are several reasons why students prefer it:

  • Success-Oriented Strategy: Physics Wallah offers a winning strategy for excelling in Class 8 Maths exams with solutions that promote a thorough understanding of the subject.
  • Trusted by Toppers: Academic toppers consistently prefer Physics Wallah
  • Marked Important Questions: Physics Wallah highlights crucial questions in their solutions, helping students focus on essential topics and concepts for exam preparation.
  • Convenient PDF Format: The NCERT solutions are available in PDF format, making them easily accessible on different devices and shareable with friends for collaborative learning.
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  • Leading Education Portal: Physics Wallah is a reputable education portal known for delivering exceptional academic resources, and providing reliable support to students.

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NCERT Solutions For Class 8 Maths FAQs

Q1. What is the goal of NCERT Solutions for Class 8 Maths?

Ans. The goal of NCERT Solutions for Class 8 Maths is to make math clear and easy to understand, boosting students' confidence and improving their math scores.

Q2. What are the benefits of Class 8 Math NCERT books and solutions?

Ans. The benefits of Class 8 Math NCERT books and solutions include comprehensive and well-structured content, step-by-step explanations for conceptual clarity, practice questions to reinforce understanding, and preparation for competitive exams.

Q3. Why is Physics Wallah considered the best platform for NCERT Solutions for Class 8 Maths?

Ans. Physics Wallah is preferred for NCERT Solutions for Class 8 Maths because of its success-oriented strategy, trust by academic toppers, marked important questions, convenient PDF format, accessibility on multiple devices, and reputation as a leading education portal.

Q4. How can I best prepare for Class 8 Maths?

Ans. To prepare for Class 8 Maths, follow the NCERT Solutions, practice exercises, and understand the concepts thoroughly. Regular practice and understanding of fundamentals are key to success.

Q5. How do I sign up for Physics Wallah to access NCERT Solutions?

Ans. You can sign up for Physics Wallah on their platform by following a simple sign-up process. Once signed up, you can access the NCERT Solutions for Class 8 Maths and other resources.

Related Chapters

  • NCERT Solutions For Class 8 Science
  • NCERT Solutions For Class 8 Maths
  • NCERT solutions for class 8 Hindi
  • NCERT Solutions For Class 8 English

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Recent Concepts

  • 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

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ISC Class 12 Maths Exam 2024 Tomorrow: Solve Specimen Paper for Last Minute Revision, Download PDF

Isc maths specimen paper: class 12 maths specimen paper or sample paper for isc board exam 2024 has been released on the board’s website, cisce.org. get the direct link to download isc class 12 maths specimen paper 2024 in pdf here and check the latest paper pattern and marking scheme.  .

Gurmeet Kaur

ISC Specimen Paper 2024 Class 12 Maths: Students of ISC Class 12 can now download the sample papers or specimen papers by CISCE for the 2024 board exams. The same sample papers can be accessed from jagranjosh.com in PDF format. The latest ISC Class 12 sample papers will help you understand the exam pattern and marks distribution for the upcoming ISC Class 12 Board Exam 2024.

With this article, you will get the specimen paper of ISC Class 12 Mathematics to download in PDF format. The ISC Maths Specimen Paper reveals the question paper format, type and number of questions and marking scheme for the year-end board examination.

ISC Class 12 Mathematics Exam Pattern 2024

The ISC Class 12 Maths Annual Exam 2024 will include one theory paper of three hours duration. The paper will be of 80 marks.

  • Section A (Compulsory): 65 marks, 14 questions of 1, 2, 4, and 6 marks
  • Section B (Optional)*: 15 marks, 4 questions of 2, 4 and 5 marks
  • Section C (Optional)*: 15 marks, 4 questions of 2, 4 and 5 marks

*Candidates will have to choose any one of the sections C and B.

Format of Questions

  • Objective questions (1 mark each)
  • Short answer questions (2 marks each)
  • Long answer questions (4, 5, and 6 marks each)

ISC Class 12 Maths Specimen Paper 2024

In subparts (i) to (x) choose the correct options and in subparts (xi) to (xv), answer the questions as instructed.

math question solve class 8

(ii) If ∫ sin −1 (cosx)dx = g(x) − x 2 /2 + c, then g(x) will be:

(b) (−π/2)x

(iii) What is the value of cot (π/2 + tan −1 1/√2)?

(iv) For what value of n is the given a homogenous differential equation?

math question solve class 8

(v) Bhuvan is preparing chapati and curry for a dinner party at his home.

Let event A = Bhuvan prepares chapati well.

Let event B = Bhuvan cooks curry well.

Given P(A) = 0·40, P(B) = 0·30 and P(A and B) = 0·20

Which one of the following is true about the events A and B?

(a) They are mutually exclusive but not independent.

(b) They are independent but not mutually exclusive.

(c) They are both mutually exclusive and independent.

(d) They are neither mutually exclusive nor independent.

math question solve class 8

(vii) Given below are the graphs of f(x) along with the statements. Which one of the following statements is NOT correct about the graphs?

math question solve class 8

(viii) Shown below is the graph of a function, g(x).

math question solve class 8

Which of the following is true?

(a) g(x) is continuous and differentiable at x = 2

(b) g(x) is continuous but not differentiable at x = 2

(c) g(x) is not continuous but differentiable at x = 2

(d) g(x) is neither continuous nor differentiable at x = 2

(ix) Statement 1: The function f: N ⟶  N given by f(x) = 5x is one to one and onto.

Statement 2: The function f:R⟶  R given by f(x) = 5x is one to one and onto.

Which one of the following options is correct?

(a) Both the statements are true.

(b) Both the statements are false.

(c) Statement 1 is true and Statement 2 is false.

(d) Statement 1 is false and Statement 2 is true

(xi) The function f: X ⟶  Y is not invertible. State the reason.

math question solve class 8

(xiii) If a relation R on the set A = {1, 2, 3} be defined by R = {(1, 2), (2, 1)} then classify the function R.

(xiv) A company has estimated that the probabilities of success for three products introduced in the market are 1/3, 2/5 and 2/3 respectively. Assuming independence, find the probability that at least one product is successful.

  • Step 1: 30 out of every 990 chocolate bars are randomly picked for physical examination, where the shape of the bar is examined.
  • Step 2: For every 30 chocolate bars whose shape is examined, 1 chocolate bar is randomly picked for chemical examination, where the composition and taste of the chocolate is examined.

If one chocolate bar is randomly picked out of 990 bars, what is the probability that it was not chemically examined, provided it was physically examined?

The ISC Class 12 Maths Exam 2024 will be based on the format of the latest specimen paper. The paper will be a mix of objective and subjective questions, which will test the students’ knowledge of the concepts, as well as their ability to apply them in different situations. Hence, students must solve the sample paper thoroughly and practise solving similar questions to boost their preparation level and enhance confidence for the annual ISC Class 12 Board Exam 2024.

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ISC Class 12 Math Answer Key 2024, Important Math Questions_00.1

ISC Class 12 Math Answer Key 2024 PDF, Important Maths Questions

Students can use ISC Class 12 Math answer key 2024 to calculate marks. Access ISC Math Qusetion Paper 2024 after exam and Practice Important Questions below.

ISC Class 12 Math Answer Key 2024, Important Math Questions_20.1

Table of Contents

ISC Class 12 Math Answer Key 2024

The ISC Class 12 Math 2024 Examination held on 20th February 2024, by the Council of Indian School Certificate Examinations (CISCE). The ISC Class 12 Maths Syllabus for the academic year 2023-24 covers various mathematical topics, including relations and functions, algebra, calculus, three-dimensional geometry, integral, probability, vectors, calculus applications, linear regression, and linear programming.

This class 12 School Certificate exam is administered once a year. The Class 12 Math Paper 2024  concluded at 5 p.m. on Tuesday. The ISC Math Question Paper 2024 and ISC Class 12 Math Answer Key 2024 PDF Download Link is available here. Also Check out some important mathematics questions below, you can take it as an ISC Math 12th Suggestion 2024 for next year.

ISC Math Answer Key 2024

The ISC Class 12 Math Question Paper 2024 (theory paper) has a total weightage of 80 marks. The Class 12th Mathematics syllabus additionally features a 20-mark project work. The ISC Class 12 Math answer key 2024 contains the correct answers to all of the questions. The exams last three hours and are scheduled from 2 to 5 p.m. Students were given an additional 15 minutes to read the paper. Check out the ISC maths questions and answers for 2024 related information below.

Get Free Class 12 Science Study Materials

ISC Class 12 Math Answer Key 2024, Important Math Questions_30.1

ISC Class 12 Math Question Paper 2024: Analysis

Students can use the unofficial answer key, which posted soon in the space below. The full solution to ISC Maths paper 2024 is displayed here at the end of the exam on February 20th. The official ISC Math Answer Key 2024 and other Class 12 subjects will be published after all exams are completed on April 3, 2024.

SECTION A -65 MARKS

Question 1 In subparts (i) to (x) choose the correct options and in subparts (xi) to (xv), answer the questions as instructed. (i) Let L be a set of all straight lines in a plane. The relation Ron L defined as ‘perpendicular to’ is:[1] (a) Symmetric and Transitive (b) Transitive (c) Symmetric (ANS) (d) Equivalence

ISC Class 12 Math Answer Key 2024, Important Math Questions_40.1

(iii) Let A be a non-empty set. Statement 1: Identity relation on A is Reflexive. Statement 2: Every Reflexive relation on A is an Identity relation. (a) Both the statements are true. (b) Both the statements are false. c) Statement 1 is true and Statement 2 is false. (ANS) (d) Statement 1 is false and Statement 2 is true.

(iv) The graph of the function is shown below.

ISC Class 12 Math Answer Key 2024, Important Math Questions_50.1

More ISC Math Class 12 Questions 2024 with Answers is provided in the pdf

ISC Math 12th Questions with Answer Key 2024

After the exam students can match their answers from the table given below. Then they can predict how much they did correct, and the total score they can expect in the exam.

Students understand that we can use the ISC answer key to calculate their approximate marks. Students can use them to see which questions they answered correctly on the exam. Students who will write the paper next year can learn about the exam format by reviewing the Class 12 Math Question Paper 2024. Students can access the expert-provided answer key for ISC Math Paper 2024 through the links provided below.

ISC Class 12 Math Answer Key 2024, Important Math Questions_60.1

ISC Math Specimen Paper 2024: Important Questions

In the meantime, students must review the important concepts of all the important chapters the best way to do this is to revise the full ISC Maths specimen paper. Here we are providing the Class 12 maths specimen paper click the link below, download the question paper, and review all the problems of Section A and Section B, more important ICS maths 12th questions 2024 unloading soon.

ISC Maths Specimen paper 2024 Class 12 PDF Download Link with Answers

Check out some important maths questions for the ISC Class 12 Math exam –

ISC Class 12 Math Answer Key 2024, Important Math Questions_70.1

  •  Statement 1: The function 𝑓: 𝑁 ⟶ 𝑁 given by f(x) = 5x is one to one and onto. Statement 2: The function 𝑓: 𝑅 ⟶ 𝑅 given by f(x) = 5x is one to one and onto. [1] Which one of the following options is correct?

(a) Both the statements are true. (b) Both the statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

ISC Class 12 Math Answer Key 2024, Important Math Questions_80.1

  • Question 11                                        [6] Garima owns a cafe that serves burgers, samosas, and juice bottles. On a particular day, 100 items in total were sold. The number of burgers sold was thrice the number of samosas sold. Also, the number of samosas sold was 10 more than the number of juice bottles sold.(i) Form a set of simultaneous equations for the above information. (ii) Solve the set of equations formed in (i) by matrix method. (iii) Hence, find the number of items sold in each category.

ISC Class 12 Math Answer Key 2024, Important Math Questions_100.1

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The ISC Math Question Paper 2024 and ISC Class 12 Math Answer Key 2024 PDF Download Link is available here.

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math question solve class 8

Persona 3 Reload Classroom Answers

Persona 3 Reload has you assume the role of a new transfer student as you go about your everyday life. This includes regular school responsibilities like taking tests and quizzes, so we’re here to help any and all players who don’t want to study to pass. The questions in this remake are different from the ones in the original game, so here are all the new class answers in Persona 3 Reload , organized by date.

Persona 3 Reload Class Answers

P3R-Classroom-Quiz.png

April Class Answers

May class answers, first semester midterm exam answers, june class answers, july class answers, first semester final exam answers, september class answers, october class answers, second semester midterm exams, november class answers, december class answers, second semester final exam answers, january class answers, up next: persona 3 reload ending explained, top guide sections.

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Class 8 Maths MCQs

Class 8 Maths MCQs (Multiple Choice Questions) are presented here chapter-wise (from Chapter 1 to 16) with answers. The objective questions are prepared here, according to the  NCERT curriculum and the latest CBSE syllabus (2022-2023) . Practising these questions will guide students to do a quick revision of all the concepts present in each chapter and prepare for the final exams. We have also provided answers with detailed explanations to all the problems, so that students can cross-check their solutions.

At BYJU’S, get chapter-wise important questions for class 8 maths and practise them to score good marks in the examination.

MCQs with Solutions for Class 8 Maths

Chapter-wise MCQs for Class 8 Maths subject are provided here online for students. Below are the links given for particular chapters starting from 1 to 16. These multiple-choice questions comprise all the important topics explained in each chapter, so that students can cover their syllabus, as per their exams.

These online learning materials will not only help students to score better in the final exam but also perform exceptionally in the competitive exams. Therefore, students are advised to practise all these Maths MCQs with their own problem-solving methods and verify with the given answers here.

Below is the list of chapter-wise multiple-choice questions for 8th standard Maths. Click on the particular link to get the MCQs with answers.

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  1. NCERT Solutions for Class 8 Maths Updated for 2023-24

    NCERT Solutions Class 8 Maths Exercise 2.1 - 12 Questions (12 Short Answers) NCERT Solutions Class 8 Maths Exercise 2.2 - 16 Questions (6 Long Answers, 10 Short Answers) NCERT Solutions Class 8 Maths Exercise 2.3 - 10 Questions (3 Long Answers, 7 Short Answers)

  2. NCERT Solutions for Class 8 Maths

    Chapter 15 Introduction to Graphs Chapter 16 Playing with Numbers NCERT Solutions for Class 8 Maths NCERT Solutions for Class 8 Maths solved by Expert teachers from LearnCBSE.in. Class 8 Maths NCERT Solutions are created with utmost care and accuracy.

  3. NCERT Solutions Maths for Class 8

    View Details Chapter 1 Class 8 Rational Numbers Chapter 2 Class 8 Linear Equations in One Variable Chapter 3 Class 8 Understanding Quadrilaterals Practical Geometry Chapter 4 Class 8 Data Handling Chapter 5 Class 8 Squares and Square Roots Chapter 6 Class 8 Cubes and Cube Roots Chapter 7 Class 8 Comparing Quantities

  4. NCERT Solutions For class 8 maths

    1800-120-456-456 Sign In NCERT Solutions For class 8 Maths NCERT Solutions NCERT Solutions For class 8 Maths Last updated date: 17th Feb 2024 Total views: 800.1k Views today: 15.00k Book a Demo Session NCERT Solutions NCERT Solutions for Class 12 NCERT Solutions for Class 11 NCERT Solutions for Class 10 NCERT Solutions for class 9

  5. NCERT Solutions for Class 8 Maths

    Chapter 1. Rational Numbers Chapter 2. Linear Equations in one Variable Chapter 3. Understanding Quadrilaterals Chapter 4. Data Handling Chapter 5. Square and Square Roots Chapter 6. Cube and Cube Roots Chapter 7. Comparing Quantities Chapter 8. Algebraic Expressions and Identities Chapter 9. Mensuration Chapter 10. Exponents and Powers Chapter 11.

  6. NCERT Solutions for Class 8 Maths

    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.

  7. NCERT Solutions for Class 8 Maths Free PDF Download

    NCERT Solutions for Class 8 Maths Chapter 1 - Rational Numbers In this chapter will learn the properties of real numbers, rational numbers, representation of a rational number on number line, additive and multiplicative identity. NCERT Solutions for Class 8 Maths Chapter 2 - Linear Equations in One Variable

  8. CBSE Class 8 Maths Important Questions 2023-24

    Get here all the important questions for class 8 maths as free PDF downloads to enhance your exam preparation. These solutions are prepared by our subject matter experts with very vast teaching experience. The class 8 maths important questions have covered all the significant chapters and related important questions.

  9. CBSE Important Questions for Class 8 Maths

    49,604 Important questions for Class 8 Maths based on the NCERT syllabus are as follows: Important Questions for Class 8 Maths Chapter-wise Important Questions Chapter 1 - Rational Numbers Important Questions Chapter 2 - Linear Equations in One Variable Important Questions Chapter 3 - Understanding Quadrilaterals

  10. NCERT Solutions for Class 8 Maths (PDF)

    The NCERT Solutions Class 8 Maths is the collection of questions and their correct answers asked in exercises of all chapters of NCERT Book for Class 8 Maths. Therefore these NCERT Solutions for Class 8 contain chapter-wise answers of the book or books Mathematics. They are as follows. NCERT Solutions for Class 8 Maths PDF

  11. Free Class 8 NCERT Mathematics Solutions

    You can solve the Class 8 Maths Book Solutions CBSE textbook questions by using Shaalaa.com to verify your answers, which will help you practise better and become more confident. CBSE Class 8 Maths Textbook Solutions Questions and answers for the Class 8 Maths Textbook are on this page.

  12. 8th Grade Math

    Quiz Unit test Course challenge Test your knowledge of the skills in this course. Start Course challenge Unit 1: Numbers and operations 0/3000 Mastery points Repeating decimals Square roots & cube roots Irrational numbers Approximating irrational numbers Exponents with negative bases Exponent properties intro

  13. Simple equations

    Unit 6 Comparing quantities. Unit 7 Data handling. Unit 8 Simple equations. Unit 9 Algebraic expressions. Unit 10 Perimeter and area. Unit 11 Lines and angles. Unit 12 Triangles. Course challenge. Test your knowledge of the skills in this course.

  14. NCERT Solutions for Class 8 Maths Chapter 8 Comparing Quantities

    Ex 8.1 Class 8 Maths Question 1. Find the ratio of the following: (a) speed of a cycle 15 km per hour to the speed of scooter 30 km per hour. (b) 5 m to 10 km. (c) 50 paise to ₹ 5. Solution: (a) Speed of cycle : Speed of Scooter = 15 km per hour : 30 km per hour. = 15 30 = 12. Hence, the ratio = 1 : 2.

  15. NCERT Solutions for Class 8

    NCERT Solutions clear your concepts to the core ensuring to stay with you in the long run. These are created by experts in accordance with the CBSE curriculum. You can find 100% accurate step-by-step solutions for every question in all the latest NCERT books. Practice with these daily to perform better in boards. NCERT Solutions for Class 8 Maths.

  16. Important Questions for CBSE Class 8 Maths Chapter 9

    Important questions of algebraic expressi ons class 8 maths will help the students to understand the topic thoroughly. It will help them to get a good grasp of the chapter, prepare properly by solving the given questions, and familiarize themselves with the question patterns.

  17. Class 8 BLE Math Model Question Solve 2080

    Class 8 BLE Math Question Solve 2080 | BLE Book of Class 8 2080 | BLE Math Model Question SolutionPlease Follow Our Page 🙏https://www.facebook.com/profile.p...

  18. Rational Numbers Class 8 Practice Questions [Solved]

    Practice Questions on Rational Numbers Class 8. 1. State true or false for the following: (i) All integers are rational number. (ii) Multiplicative inverse does not exist for rational numbers. (iii) 1 is the additive identity for rational numbers. (iv) ⅔ lies in between the rational numbers ⅛ and 7/9.

  19. NCERT Solutions Class 8 Maths Chapter 4 Practical Geometry

    The NCERT solutions class 8 maths chapter 4 does not have any mathematical formulas for solving questions, rather they are based on the properties of quadrilaterals as well as steps that need to be followed for constructions. There will be a different technique employed when constructing quadrilaterals depending upon the given conditions.

  20. CBSE Class 8 Maths Solved Sample Question Paper 2023-24

    CBSE Sample Question Paper for Class 8 Maths. Maths for Class 8 is considered to be one of the most important and immensely scoring subjects. And the best way to prepare apart from completing NCERT and reference books is solving CBSE Sample Papers. Here on Ribblu one can get immense collection of Sample Question Papers for Class 8 Maths in PDF ...

  21. NCERT Solutions for Class 8 Maths Updated 2023-24

    Here are the chapter-wise NCERT Solutions for Class 8 Maths prepared by our experts at PW. These detailed solutions will help you understand all the concepts explained in each chapter. Check out the list of Class 8 Math chapters below. NCERT Solutions Class 8 Maths Chapter-wise List. Chapter 1 - Rational Numbers.

  22. ISC Class 12 Maths Paper Analysis 2024: Student Feedback, Difficulty

    ISC Class 12 Maths Exam Analysis 2024: The Council for the Indian School Certificate Examinations, CISCE conducted the ISC Maths Exam today from 2:00 pm to 5:00 pm. Mathematics being common to all ...

  23. Class 8 BLE Math Question Solve 2080

    Class 8 BLE Math Question Solve 2080 | BLE Model Question Math 2080 | Math MantraPlease Follow Our Page 🙏https://www.facebook.com/profile.php?id=10009458093...

  24. CBSE Sample Papers for Class 8 Maths

    1) Strengths And Weaknesses When students solve CBSE sample papers, they get a real status of their preparation. They get to know how well they are prepared for the Maths exam and rate themselves accordingly by solving the latest CBSE sample papers. Also, they experience a gradual improvement in their performance by working on weak areas.

  25. ISC Class 12 Maths Specimen Paper 2024 Exam, Download PDF

    The ISC Class 12 Maths Exam 2024 will be based on the format of the latest specimen paper. The paper will be a mix of objective and subjective questions, which will test the students' knowledge ...

  26. ISC Class 12 Math Answer Key 2024, Important Math Questions

    The ISC Class 12 Math Question Paper 2024 (theory paper) has a total weightage of 80 marks. The Class 12th Mathematics syllabus additionally features a 20-mark project work. ... Solve the set of equations formed in (i) by matrix method. (iii) Hence, find the number of items sold in each category. Sharing is caring! 0 shares.

  27. Persona 3 Reload Classroom Answers

    The questions in this remake are different from the ones in the original game, so here are all the new class answers in Persona 3 Reload, organized by date. ... Question Answer 4/8

  28. Important Questions For Class 8 Maths Chapter 9

    Solution: (i) x 2 y + xy 2 = Binomial (ii) 564xy = Monomial (iii) -8x + 4y = Binomial (iv) x 2 + x + 7 = Trinomial (iv) xy + yz + zp + px + 9xy = Polynomial 3. Identify terms and their coefficients from the following expressions:

  29. Class 8 Maths MCQs (With Answers)

    MCQs with Solutions for Class 8 Maths Chapter-wise MCQs for Class 8 Maths subject are provided here online for students. Below are the links given for particular chapters starting from 1 to 16. These multiple-choice questions comprise all the important topics explained in each chapter, so that students can cover their syllabus, as per their exams.