maths case study questions for class 8

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CBSE 8th Standard CBSE all question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 8th Standard CBSE all books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

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• Rational Numbers Class 8 Case Study Questions Maths Chapter 1

Last Updated on April 30, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 8 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 8 maths. In this article, you will find case study questions for CBSE Class 8 Maths Chapter 1 Rational Numbers. It is a part of Case Study Questions for CBSE Class 8 Maths Series.

Table of Contents

Case Study Questions on Rational Numbers

Passage 1: Aditya who is working in a multinational company earns ₹150000 per month. Out of his earnings he spend 1/10th on food items, 1/4th on shopping with family, 1/5th of remaining on education of his two kids and rest of his money he puts in his savings.

Difficulty Level: Easy

On basis of this information given in passage answer the following questions.

Q. 1. How much money he spends on food items? (a) 15000 (b) 1500 (c) 1050 (d) 10500

Q. 2. How much money he spend on shopping? (a) 32000 (b) 37500 (c) 25000 (d) 27500

Q. 3. How much money was left with him after spending on food and shopping? (a) 90000 (b) 95000 (c) 98500 (d) 97500

Ans. Option (d) is correct. Explanation: Total earning = ₹ 150000 Money spent on food and shopping = ₹ 15000 + ₹ 37500 = ₹ 52500 Money left after food and shopping = ₹ 150000 – ₹ 52500 = ₹ 97500

Q. 4. Calculate the amount spend by Aditya on education of children?

Sol. Total money earn by Aditya = ₹150000 Total amount spend by him on shopping and food = ₹52500 Money left = ₹150000 – ₹52500= ₹97500 Money spend on education of children $=\frac{1}{5}$ of Money left $\quad=\frac{1}{5}$ of 97500 = ₹19500

Q. 5. How much money he saved?

Sol. Saving = Total earning – total expenditure = 150000 – (15000 + 37500 + 19500) = 150000 – 72000 = ₹78000. Thus money saved by Aditya is ₹78000.

Understanding Quadrilaterals Class 8 Case Study Questions Maths Chapter 3

Linear equations in one variable class 8 case study questions maths chapter 2, download ebooks for cbse class 8 maths rational numbers.

• Rational Number Topicwise Worksheet for CBSE Class 8 Maths

Topics from which case study questions may be asked

• Rational Number and its identification.
• Whole Number, Natural Number and their Properties.
• Difference between Rational and Irrational Number.

Case study questions from the above given topic may be asked.

Frequently Asked Questions (FAQs) on Rational Numbers Case Study

Q1: what is the significance of rational numbers in mathematics.

A1: Rational numbers play a crucial role in mathematics as they represent quantities that can be expressed as fractions of integers. They include both integers and fractions, making them essential for various mathematical operations and real-life applications.

Q2: How are rational numbers defined, and what are their properties?

A2: Rational numbers are defined as numbers that can be expressed in the form p/q ​, where p and q are integers and q≠0. They possess properties such as closure under addition, subtraction, multiplication, and division, as well as the commutative, associative, and distributive properties.

Q3: Can you provide real-life examples where rational numbers are used?

A3: Real-life examples of rational numbers include measurements such as length, mass, and time, as well as quantities like money, fractions of a whole, and ratios in cooking recipes or construction projects.

Q4: What are the key concepts covered in Chapter 1 of CBSE Class 8 Maths regarding rational numbers?

A4: Chapter 1 of CBSE Class 8 Maths covers concepts such as understanding rational numbers, representation on the number line, operations on rational numbers, and solving problems involving rational numbers. More Precisely, (i) Rational Number and its identification. (ii) Whole Number, Natural Number and their Properties. (iii) Difference between Rational and Irrational Number.

Q5: Can you explain the operations (addition, subtraction, multiplication, division) involving rational numbers with examples?

A5: Addition, subtraction, multiplication, and division of rational numbers follow specific rules. For example, to add or subtract rational numbers, we find a common denominator, while for multiplication and division, we multiply or divide the numerators and denominators.

Q6: What are the common misconceptions students have about rational numbers, and how can they be clarified?

A6: Common misconceptions include confusion between rational and irrational numbers, misunderstanding the concept of fractions, and errors in performing operations. These can be clarified through hands-on practice, visual representations, and providing clear explanations of concepts.

Q7: Are there any online resources or tools available for practicing rational number case study questions?

A7: We provide case study questions for CBSE Class 8 Maths on our website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

Q8: What are the important keywords for CBSE Class 8 Maths Rational Numbers?

A8: List of important keywords given below – Natural Numbers: Positive Counting number starting from 1. Whole Number: All natural number together with 0. Rational Number: Numbers which can be expressed in p/q form, where q ≠ 0 and p and q are integers. Fraction: Numbers which can be expressed in form of p/q but are only positive

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CBSE Class 8th Maths Value Based Questions PDF Download

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CBSE Class 8th Maths Value Based Questions are the easiest questions which you see in your question paper and the scoring one all student who attempt it surely get they are just little bit difficult and examine your basic knowledge regarding the particular chapter. Maths Value Based Questions for Class 8th are available here at Free of cost. These questions are expected to be asked in the Class 8th board examination. These Maths Value Based Questions are from complete CBSE Syllabus.

CBSE Class 8th Maths Value Based Questions

Most of these Maths Value Based Questions are quite easy and students need only a basic knowledge of the chapter to answer these questions. Download CBSE Maths Value Based Questions for board examinations. These Maths Value Based Questions are prepared by Directorate of Education, Delhi.

CBSE Maths Value Based Questions Class 8th PDF

The purpose of the Maths Value Based Questions is to make students aware of how basic values are needed in the analysis of different situations and how students require to recognize those values in their daily lives. Some questions are subject related. But even if they are not, that one-minute awareness of what we write about value without any specific preparation is a good step indeed.

CBSE Maths Value Based Questions for Class 8th download here in PDF format. The most CBSE Maths Value Based Questions for annual examination are given here for free of cost. The additional questions for practice the Class 8th exam are collected from various sources. It covers questions asked in previous year examinations.

CBSE Maths Value Based Questions for Class 8th Free PDF

Class 8th books have many questions. These questions are regularly asked in exams in one or other way. Practising such most CBSE Maths Value Based Questions certainly help students to obtain good marks in the examinations. 

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Important Questions for CBSE Class 8 Maths 2023-24

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Maths Important Questions for Class 8

Maths is a vast subject. The concept students learn in the lower classes helps in developing skills for higher classes. Thus, solving important questions for class 8 Maths helps students to score good marks.

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Class 8 Maths gives the student a chapter-wise plan to prepare the student for the CBSE class 8 examination. Important questions for class 8 Maths will help the students with practice for exam preparation. The questions are prepared by expert teachers of the subject so that all the topics and concepts are covered.

The important questions for class 8 Mathes will help students to gauge their understanding of the major concepts that are taught in class 8 Maths. By practising them, students will get an idea of what type of questions will be asked in the exam. Solving the important questions of Maths for class 8 CBSE will help students understand the concept well.

To access the important questions for class 8 Maths, students may register at Extramarks.

Class 8 Maths Important Questions – Chapters Covered

There are 16 Chapters and sub-topics that have important questions for class 8 Maths. The list here is created as per the NCERT books and the latest CBSE syllabus and is mentioned below.

 Chapter 1: Rational Numbers

Rational numbers are the numbers that can be represented in the form of p/q, where p and q are integers, and q is not equal to 0.

• Ex 1.1 Introduction to Rational Numbers
• Ex 1.2 Properties of Rational Numbers
• Ex 1.3 Representation of Rational Numbers on the Number Line
• Ex 1.4 Rational Numbers between Two Rational Numbers

Chapter 2: Linear Equations in One Variable

Linear equations in one variable are algebraic expressions that have only one variable.

• Ex 2.1 Introduction to Linear Equations in One Variable
• Ex 2.2 Solving Equations which have Linear Expressions on one Side and Numbers on the Other Side
• Ex 2.3 Some Applications
• Ex 2.4 Solving Equations having the Variable on Both Sides
• Ex 2.5 Some More Applications
• Ex 2.6 Reducing Equations to Simpler Form
• Ex 2.7 Equations Reducible to the Linear Form

Chapter 3: Understanding Quadrilaterals

Understanding quadrilaterals teaches different types of quadrilaterals and their properties.

• Ex 3.1 Introduction to Quadrilaterals
• Ex 3.2 Polygons
• Ex 3.3 Sum of the Measures of the Exterior Angles of a Polygon
• Ex 3.4 Kinds of Quadrilaterals
• Ex 3.5 Some Special Parallelograms

Chapter 4: Practical Geometry

In this chapter, students will learn to construct the quadrilaterals based on certain given conditions, such as when the dimensions are given for its sides and diagonals or for angles.

• Ex 4.1 Introduction to Practical Geometry
• Ex 4.2 Constructing a Quadrilateral
• Ex 4.3 Some Special Cases

Chapter 5: Data Handling

Students will understand the significance of data and its management in small and large industries.

• Ex 5.1 Looking for Information – Data Handling
• Ex 5.2 Organising Data
• Ex 5.3 Grouping Data
• Ex 5.4 Circle Graph or Pie Chart
• Ex 5.5 Chance and Probability

Chapter 6: Squares and Square Roots.

Students will learn how to find squares and square roots for different numbers.

• Ex 6.1 Introduction to Square and Square Roots
• Ex 6.2 Properties of Square Numbers
• Ex 6.3 Some More Interesting Patterns
• Ex 6.4 Finding the Square of a Number
• Ex 6.5 Square Roots
• Ex 6.6 Square Roots of Decimals
• Ex 6.7 Estimating Square Root

Chapter 7: Cubes and Cube Roots

In this chapter, students will learn to find cube and cube roots for different numbers.

• Ex 7.1 Introduction to Cubes and Cube Roots
• Ex 7.2 Cubes
• Ex 7.3 Cube Roots

Chapter 8: Comparing Quantities

This chapter is based on finding percentage, cost price, selling price, profit, loss, and compound interest.

• Ex 8.1 Recalling Ratios and Percentages
• Ex 8.2 Finding the Increase or Decrease in percent
• Ex 8.3 Finding Discounts
• Ex 8.4 Prices Related to Buying and Selling (Profit and Loss)
• Ex 8.5 Sales Tax/Value Added Tax/Goods and Services Tax
• Ex 8.6 Compound Interest
• Ex 8.7 Deducing a Formula for Compound Interest
• Ex 8.8 Rate Compounded Annually or Half Yearly (Semi-Annually)
• Ex 8.9 Applications of Compound Interest Formula

Chapter 9: Algebraic Expressions and Identities

The chapter teaches students to find the degree of the polynomial, dividing a monomial by monomial, dividing a polynomial by a monomial, and dividing polynomial by polynomial. It also teaches the students to divide the algebraic expression employing factorisation.

• Ex 9.1 What are Expressions?
• Ex 9.2 Terms, Factors and Coefficients
• Ex 9.3 Monomials , Binomials and Polynomials
• Ex 9.4 Like and Unlike Terms
• Ex 9.5 Addition and Subtraction of Algebraic Expressions
• Ex 9.6 Multiplication of Algebraic Expressions: Introduction
• Ex 9.7 Multiplying a Monomial by a Monomial
• Ex 9.8 Multiplying a Monomial by a Polynomial
• Ex 9.9 Multiplying a Polynomial by a Polynomial
• Ex 9.10 What is an Identity?
• Ex 9.11 Standard Identities
• Ex 9.12 Applying Identities

Chapter 10: Visualising Solid Shapes

The chapter introduces some very interesting concepts, such as visualising solid shapes, and views of 3d-shapes like cubes, cylinders, cones, spheres, etc.

• Ex 10.1 Introduction to Visualising Solid Shapes
• Ex 10.2 Views of 3D-Shapes
• Ex 10.3 Mapping Space Around Us
• Ex 10.4 Faces, Edges and Vertices

Chapter 11: Mensuration

This chapter deals with the measurement of area, perimeter, surface area and volume of different types of shapes.

• Ex 11.2 Introduction to Mensuration
• Ex 11.2 Let us Recall
• Ex 11.3 Area of Trapezium
• Ex 11.4 Area of a General Quadrilateral
• Ex 11.5 Area of a Polygon
• Ex 11.6 Solid Shapes
• Ex 11.7 Surface Area of Cube, Cuboid and Cylinder
• Ex 11.8 Volume of Cube, Cuboid and Cylinder
• Ex 11.9 Volume and Capacity

Chapter 12: Exponents and Powers

Here students will learn how to write large numbers easily using exponents and powers.

• Ex 12.1 Introduction to Exponents and Powers
• Ex 12.2 Powers with Negative Exponents
• Ex 12.3 Laws of Exponents
• EX 12.4 Use of Exponents to Express Small Numbers in Standard Form

Chapter 13: Direct and Inverse Proportions.

A direct and inverse proportion are applied to determine how the quantities and amounts are correlated with each other.

• Ex 13.1 Introduction to Direct and Inverse Proportions
• Ex 13.2 Direct Proportion
• Ex 13.3 Inverse Proportion

Chapter 14: Factorisation

This chapter deals with writing a given expression as the product of two or more factors is called factorisation.

• Ex 14.1 Introduction to Factorisation
• Ex 14.2 What is Factorisation?
• Ex 14.3 Division of Algebraic Expressions
• Ex 14.4 Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)
• Ex 14.5 Can you Find the Error?

Chapter 15: Introduction to Graphs 

This chapter deals primarily with the representation of data using different graph diagrams.

• Ex 15.1 Introduction
• Ex 15.2 Linear Graphs
• Ex 15.3 Some Applications

Chapter 16: Playing with Numbers

Playing with Numbers, introducing Numbers in General Form, Games with Numbers and Divisibility test by some numbers.

• Ex 16.1 Introduction
• Ex 16.2 Numbers in General Form
• Ex 16.3 Games with Numbers
• Ex 16.4 Letters for Digits
• Ex 16.5 Tests of Divisibility

Important Questions For Class 8 Maths Weightage

Practicing important questions for class 8 Maths will build the student’s confidence which will help them to score better during examinations. It will help in building a strong foundation for students. While class 8 Maths’ important questions are crucial, it is also vital to revise all topics under the chapter before trying to solve the important questions. 

All important questions for class 8 Maths are prepared according to the latest syllabus and follow the guidelines set by CBSE, India. Solving these Maths questions for class 8 will assist the students in judging their understanding of the chapter.

Important Questions for Class 8 Maths Chapter Wise

Extramarks important questions for class 8 Maths are equipped with chapter-wise plans for the students to prepare well for the CBSE class 8 examination. The solutions provided for the Maths important questions for class 8 are prepared by subject experts who have got very good teaching experience. These questions are compiled with reference to NCERT Books, several years of examination papers and based on how crucial the topic is for higher studies.

Students can click on the link for chapter-wise important questions for class 8 Maths with solutions.

• Chapter 1. Rational Numbers
• Chapter 2. Linear Equation 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

Maths Questions for Class 8 with Answers – Types of Questions

The important questions for class 8 Maths include MCQs, short answer type questions, long answer type questions, and case study-based questions. These questions are a vital part of the study schedule. The chapter-wise important questions are good for students for self-study, which will help them in preparing for examinations. In addition to it, solving sample papers will be a great help for students.

Along with important questions for class 8 Maths, students can use various study materials during revision by clicking the link below.

Important Questions For Class 8 Maths With Solutions

• CBSE revision notes
• CBSE Sample papers
• CBSE previous year question papers
• CBSE extra questions

Benefits Of Solving Maths Questions for Class 8

Some of the benefits of Extramarks important questions for class 8 Maths include the following.

• Solving these questions increases the confidence in the student, which in turn helps them to score good marks.
• Practicing important questions for class 8 Maths helps students to improve in their weak topics.
•  Solving them helps students to learn the formulae and understand the concepts well.
• It covers all the important topics that will be asked in the exam.
• Solving important questions for class 8 Maths increases students’ problem-solving skills and critical thinking abilities.
• Students will understand the pattern of the question paper and the marking scheme of the exam.
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CBSE Class 8 Maths Important Questions

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, faqs (frequently asked questions), 1. how are chapter-wise important questions for class 8 maths helpful for students.

The chapter-wise important questions for class 8 Maths can help the students to clear their doubts, improve in their weak topics and prepare themselves for the exam in a better way. They also help with board exam preparation.

2. Which chapter is interesting in class 8 Maths?

Playing with numbers is an interesting chapter in class 8 Mathcs. Students will enjoy puzzles of missing numbers.

3. How to score the highest marks in class 8 Maths?

One can score 90% and above in class 8 Maths by practising important questions for class 8 Maths, solving past  years’ question papers, revision notes, and sample papers.

CBSE Related Links

ebookpublisher.in

Case Study Questions for CBSE Class 8 Maths

Here we are providing case study questions for CBSE Class 8 Maths. The list of chapters is given below. Student can access the question by clicking on the chapter link.

Chapter List

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 Indirect proportions Chapter 14 Factorisation Chapter 15 Introduction to Graphs Chapter 16 Playing with Numbers

Deleted Chapter for Session 2023-24

Chapter 4, Chapter 10 and Chapter 16 are not in syllabus for session 2023-24.

What are Case Study Questions in CBSE Class 8 Maths?

Case based questions are questions that require students to analyze a hypothetical situation or scenario. These types of questions are designed to test a student’s ability to apply their knowledge and understanding of a particular topic to a real-life situation.

How to Solve Case Study Questions for CBSE Class 8 Maths?

To tackle Case Study-Based Questions in Class 8 Maths, students need to carefully observe and analyze the provided information or data. When approaching these questions, it’s crucial to read the passage thoroughly and then proceed to solve them.

When dealing with Class 8 Maths Case Study questions, an effective strategy is to identify and highlight key information or given data. This practice will prove beneficial when formulating the final answers.

A Case Study in Class 8 Maths usually consists of 4 to 5 questions that are answered in a multiple-choice question (MCQ) format. While addressing these MCQs, it’s advisable for students to closely read the paragraph, as it might contain hints related to the discussed topics.

Prior to solving Case Study type questions, it’s recommended to refer to the CBSE Syllabus. This helps in revisiting and reinforcing previous learnings, enhancing preparation and confidence.

By following these simple yet effective steps, students can approach Class 8 Maths Case Study questions with a clearer understanding and better problem-solving skills. This approach not only aids in academic success but also contributes to a deeper grasp of mathematical concepts.

Understanding Case Study Questions in CBSE Class 8 Maths

Case study questions have emerged as a dynamic and engaging approach within the CBSE Class 8 Maths curriculum. These questions deviate from traditional problem-solving by presenting students with real-world scenarios that require the application of mathematical concepts. In essence, case study questions bridge the gap between theoretical knowledge and practical application, fostering a deeper understanding of mathematics.

Exploring the Concept of Case Study Questions

Case study questions involve presenting students with contextualized problems that mimic situations they might encounter in their daily lives. These scenarios are designed to challenge students to think critically, analyze data, and formulate solutions using mathematical principles. By immersing students in such scenarios, educators aim to nurture their ability to solve complex problems in various contexts.

Importance of Case Study Questions in Mathematics Learning

The significance of case study questions lies in their ability to cultivate practical problem-solving skills. Unlike traditional exercises that often focus solely on mathematical manipulation, case studies require students to apply their knowledge to authentic situations. This application not only enhances their comprehension of mathematical concepts but also equips them with valuable life skills, as they learn to approach challenges systematically and logically.

How Case Study Questions Differ from Traditional Problems

The fundamental distinction between case study questions and conventional math problems lies in their context-driven nature. While traditional problems tend to be abstract and formulaic, case study questions introduce variables, uncertainty, and real-world relevance. This dynamic approach encourages students to think multidimensionally, as they must consider factors beyond the mathematical equations themselves.

Benefits of Using Case Study Questions for CBSE Class 8 Maths

The adoption of case study questions in CBSE Class 8 Maths curriculum brings forth a multitude of benefits that extend beyond traditional teaching methods. These advantages stem from the unique nature of case study questions, which encourage active engagement, real-world application, and the development of analytical skills.

Fostering Critical Thinking and Problem-Solving Skills

Case study questions compel students to approach problems from various angles, dissecting complex scenarios and extracting pertinent information. This process cultivates critical thinking by encouraging students to analyze, evaluate, and synthesize data to arrive at well-considered solutions. By navigating through intricate case studies, students hone their ability to tackle multifaceted problems that mirror real-life challenges.

Real-world Application of Mathematical Concepts

One of the paramount advantages of case study questions is their relevance to everyday situations. Students encounter mathematical concepts in action, witnessing firsthand how these principles are embedded in various scenarios. This exposure not only deepens their understanding of theoretical concepts but also helps them appreciate the practical utility of mathematics in diverse contexts.

Enhancing Analytical Abilities through Practical Scenarios

Case study questions promote the development of analytical skills by requiring students to interpret data, identify patterns, and derive meaningful insights. As students engage with intricate case studies, they refine their ability to discern crucial information from irrelevant details, strengthening their capacity to make informed decisions—a skill applicable not only in mathematics but also in various aspects of life.

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• Important Questions for CBSE Class 8 Maths Chapter 13 - Direct and Inverse Proportions

CBSE Class 8 Maths Important Questions for Direct and Inverse Proportions - Free PDF Download

Free PDF download of Important Questions with solutions for CBSE Class 8 Maths Chapter 13 - Direct and Inverse Proportions prepared by expert Mathematics teachers from latest edition of CBSE(NCERT) books. Register online for Maths tuition on Vedantu.com to score more marks in your examination.

Vedantu is a platform that provides free (CBSE) NCERT Solution and other study materials for  Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 8 Science , Maths solutions and solutions of other subjects.

Download Class 8 Maths NCERT Solutions to help you to revise complete syllabus ans score more marks in your examinations.

Study Important Questions for Class 8 Maths Chapter 13 – Direct and Inverse proportions

Very short answer type questions.

1. If two quantities x and y are in direct proportion with each other, then:

(a) $\dfrac{{\text{x}}}{{\text{y}}}$ remains constant

(b) $x\times y$ remains constant

(c) ${\text{x}}\,{\text{ - }}\,{\text{y}}$ remains constant

(d) None of these

Ans: (a) $\dfrac{{\text{x}}}{{\text{y}}}$ remains constant. 

2. The cost of 5 metres of a particular quality of cloth is Rs.210. Find the cost of 2 metres of cloth of the same type.

(d) Rs. 100

Ans: Cost of 5 metre cloth = Rs. 210

Thus, cost of 2 metre cloth = $\dfrac{{2 \times 210}}{5}\, = \,{\text{Rs}}{\text{.84}}$

3. If X = 5Y, then X and Y vary ______ with each other.

Ans: They are directly proportional.

${\text{X }} \propto {\text{ Y}}$

$\dfrac{{\text{X}}}{{\text{Y}}}\, = \,5$

4. If XY = 10 then X and Y vary _____ with each other.

Ans: Indirectly proportional.

5. Time taken to cover a distance by car and speed of the car are said to be in _______ variation.

Ans: Inversely

${\text{Speed  =  }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$

${\text{speed }} \propto \,\dfrac{1}{{{\text{time}}}}$

6. In the table state whether x and y vary directly or indirectly.

Ans: Since, as ‘x’ increases, ‘y’ also increases. 

Therefore, ‘x’ and ‘y’ vary directly.

7. If a car covers 80km in 5 litres of petrol, how much distance will it cover in 3 litres of petrol?

Ans: Given: In 5 litres of petrol, distance covered = 80km

Thus, in 1 litre of petrol, distance covered = $\dfrac{{80}}{5} = {\text{ 16km}}$

In, 13 litres of petrol, distance covered = $16\, \times \,13\, = \,{\text{208km}}$

Short  Answer Type Questions                                                         2 Mark

8. If 32 men can reap a field in 15 days. In how many days can 40 men reap the same field?

Ans: This situation is inverse variation (less men, more days)

Let $x=$ men,$y=$ no. of days $x_{1}=32, y_{1}=15$ $x_{2}=40, y_{2}=?$

Formula is $x_1 y_1=x_2 y_2$

$(32)(15)=(40) \mathrm{y} 2$

$\mathrm{y}_{2}=\dfrac{32 \times 15}{40}$

$\mathrm{y}_{2}=12$

Therefore, number of days $=12$

9. If 4 kg potatoes cost Rs. 60. What is the cost of 12kg of potatoes?

Ans: Given: cost of 4 kg potatoes = Rs. 60

Therefore, 1 kg potatoes cost Rs = $\dfrac{{60}}{4} = 15$

Thus, 12kg potatoes cost = $15\, \times \,12\, = \,{\text{Rs}}{\text{.180}}$

10. Find the value of x and y if x : y = 2 : 3 and 2 : x = 1 : 2.

Ans: Given: 2 : x = 1 : 2

$\Rightarrow {\text{ }}\dfrac{2}{{\text{x}}} = \dfrac{1}{2}$

 $\Rightarrow \,{\text{x  =  2}} \times {\text{2}} $

 $\Rightarrow {\text{x = 4}} $

  ${\text{x : y  =  2 : 3}} $

 $ {\text{4 : y  =  2 : 3}} $

  $\dfrac{4}{{\text{y}}}\, = \,\dfrac{2}{3} $

  ${\text{y  =  }}\dfrac{{4 \times 3}}{2} $

  ${\text{y  =  6}} $ 

11. If 2 : 3 = x : 51. Find ‘x’.

Ans: $\dfrac{2}{3}\, = \,\dfrac{{\text{x}}}{{51}} $

   $\Rightarrow \,{\text{x  =  }}\dfrac{{2 \times 51}}{3} $

   $\Rightarrow {\text{x  =  34}} $ 

Short  Answer Type Questions                                                         3 Mark

12. if x and y are in inverse proportion. find the value of a, b and c in the table..

$\mathrm{x} \propto \dfrac{1}{\mathrm{y}} \Rightarrow \mathrm{x_1} \mathrm{y_1}=\mathrm{x_2} \mathrm{y_2}$

$25 \times 3=15 \times \mathrm{a} \Rightarrow \mathrm{a}=\dfrac{75}{15}=5$

$25 \times 3=\mathrm{b} \times 4 \Rightarrow \mathrm{b}=\dfrac{75}{4}=18.75$

$25 \times 3=10 \times \mathrm{c} \Rightarrow \mathrm{c}=\dfrac{75}{10}=7.5$

13. The scale of a map is given as 1 : 80000000. Two places A and B on the map are 3 cm apart. What is the actual distance between A and B? If C and D are at a distance of 3200 km, then find the distance between them on map?

Ans: Given: scale of map = 1 : 80000000

Thus, 1 unit on map shows 80000000 units in the real world.

If A and B are 3 cm apart on map,

Actual distance =

 ${\text{3cm }} \times {\text{ 80000000}} $

  ${\text{ =  240000000}} $

  ${\text{ =  2400 km}} $ 

If C and D are at a distance of 32km apart, then

${\text{3200km  =  3200 }} \times {\text{ 1000 }} \times {\text{ 100cm}} $

  ${\text{ =  320000000 cm}} $ 

Therefore, on the map it should be $ = \,\dfrac{{320000000}}{{80000000}}\, = \,{\text{4cm}}$

14. There are 50 students in a hostel. The food provision for them is for 15 days. How long will their provision last if 5 students leave the group?

Ans: It is inverse variation since no. of students increases as no. of days food provision provided increases.

Let ' $x$ ' be the no. of students And ' $\mathrm{y}$ ' be the number of days 

Given: $\mathrm{x}_{1}=50, \mathrm{y}_{1}=15$

$\mathrm{x}_{2}=50-5=45, \mathrm{y}_{2}=? $

$\mathrm{x_1} \mathrm{y_1}=\mathrm{x_2} \mathrm{y_2}$

$50 \times 15=45 \times \mathrm{y_2}$

$\mathrm{y}_{2}=\dfrac{50 \times 15}{45}$

$\mathrm{y}_{2}=16.66=17$ days

15. A workforce of 210 men with a supervisor can finish a certain piece of work in 5 months. How many extra men must he employ if he want to complete job in just 2 months?

Ans:   Let the extra men employed be ‘x’

Number of men(x):       210           x

Months(y):                         5             2

Since, men hired and time required are inversely proportional, we have

$\mathrm{x_1} \mathrm{y_1}=\mathrm{x_2}\mathrm{y}_{2}$

$210 \times 5=\mathrm{x} \times 2 $

$\mathrm{x}=\dfrac{210 \times 5}{2}=525$

Thus, extra men needed $=525-210=315$.

16. Ranjith has enough money to buy 75 machines worth Rs. 200 each. How many machines can he buy if he gets a discount of Rs.50 on each machines?

Ans: Let the no. of machines he can buy if a discount of Rs. 50 is offered on each machine be ‘x’.

Number of Machines(x):                         75                             x

Price of Each Machine(y):                       200                           150

Since the discount is Rs.50, the cost of each machine will be 200 – 50  = 150.

It is the inverse proportion as if the price of a machine is less, the more machines he can buy.

$75\, \times \,200\, = \,{\text{x}}\, \times {\text{ 150}} $

$\Rightarrow \,{\text{x  =  }}\dfrac{{75\, \times \,200}}{{150}}\, = \,\dfrac{{15000}}{{150}} $

 $\Rightarrow \,{\text{x  =  100}} $ 

17. A worker is paid Rs. 420 for 2 days work. If his total income of the month is Rs. 1750, For how many days did he work?

Ans: It is direct variation. More wages, more days of work.

Let ‘x’ be the amount paid and ‘y’ be the number of days.

Amount paid(x)     :   Rs.420       Rs.1750     

Number of days(y):   12                ?

$\dfrac{\mathrm{x}_1}{\mathrm{y}_1}=\dfrac{\mathrm{x}_2}{\mathrm{y}_2}$

$\dfrac{420}{12}=\dfrac{1750}{\mathrm{y}_2} $

$\mathrm{y}_{2}=\dfrac{1750 \times 12}{420} $

$\mathrm{y}_{2}=50 \text { days }$

18. Abdul takes 75 steps to cover a distance of 50m. How much distance will it cover in 375 steps?

Ans: It is direct variation as the number of steps increases, the distance covered will be more.

Let ‘x’ be the number of steps and ‘y’ be the distance covered.

Number of steps(x):     75      375

Distance covered(y):   50m     ?

$\dfrac{75}{50}=\dfrac{375}{\mathrm{y}_2} $

$\mathrm{y}_{2}=\dfrac{375 \times 50}{75} $

$\mathrm{y}_{2}=250 \mathrm{~m}$

19. If the weights of 8 sheets of paper be 45 grams. How many sheets would weigh $1\dfrac{1}{2}$kg?

Ans: It is direct variation as more number of sheets implies more weight.

Number of sheets(x):   6       ?

Number of hours(y):   45     $1\dfrac{1}{2}$kg = 1500g [1 Kg = 1000g, 1.5Kg = 1500g]

$\dfrac{\mathrm{x}_1}{\mathrm{y}_1}=\dfrac{\mathrm{x}_2}{\mathrm{y}_{2}} $

$\dfrac{6}{45}=\dfrac{\mathrm{x}_2}{1500}$

$\mathrm{x}_{2}=\dfrac{6 \times 1500}{45}$

$\mathrm{x}_{2}=200$

20. 20 pumps can empty a reservoir is 12 hours. In how many hours can 45 such pumps do the same work?

Ans: It is inverse variation as it takes less hours if the number of pumps are more.

Number of pumps(x):   20      45

Number of hours(y):     12       ?

$x_1 y_{1}=x_2 y_2 $

$20 \times 12=45 \times y_2 $

$y_{2}=\dfrac{20 \times 12}{45} $

$y_{2}=5.33=5 \dfrac{1}{3} \text { hours }$

Long  Answer Type Questions                                                                          5 Mark  

21. A water tanker can finish a certain journey in 10 hours at the speed of 38 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance?

Ans: Given: speed = 38 km/hr, time = 10 hours.

Distance covered = speed $ \times $ time = $38\, \times \,10\, = \,380\,{\text{km}}$

Speed(x)            :     38km/hr          ?

Time taken(y)   :     10 hours        8 hours

It is an inverse variation.

$\mathrm{x}_1 \mathrm{y}_1=\mathrm{x}_2 \mathrm{y}_2 $

$38 \times 10=\mathrm{x}_2 \times 8 $

$\mathrm{x}_{2}=\dfrac{38 \times 10}{8} $

$\mathrm{x}_{2}=47.5 \mathrm{~km} / \mathrm{hr}$

Thus, the speed is increased by $47.5-38=9.5 \mathrm{~km} / \mathrm{hr}$.

22. 1000 children in a hostel had enough food for 28 days. After 4 days, some children were shifted to other hostel. As a result, the food now lasted for 32 days. How many students were shifted?

Ans: Given: 1000 students in a hostel had enough food for 28 days.

Let ‘x’ be the number of students shifted.

Number of students(x):   1000      1000-x

Number of days:                 28           32

It is an inverse variation: as the number of students increases, food remains for less number of days.

${x_1 y_1  =  x_2 y_2} $

$1000\times 28=(1000-x)\times 32 $

$1000-x = \dfrac{1000\times 28}{32}=875 $

$x = 1000-875=125 $ 

Therefore, the number of students shifted = 125.

23. The amount of extension in the length of the elastic string directly varies as the weight hung on it. If a weight of 500 gm produces an extension of 3 cm, then what weight would produce an extension of 36.2 cm. Write the solution in Kg.

Ans: Weight(x)                      :   200gm      7

Extension in length(y) :    3 cm        36.2 cm

It is a direct variation.

$\dfrac{x_1}{y_1}= \dfrac{x_2}{y_2} $

$\dfrac{{200}}{3}\, = \,\dfrac{{{\text{x2}}}}{{36.2}} $

$x_2 = \dfrac{{200\, \times \,36.2}}{3} $

$x_2 = \dfrac{{7240}}{3} $

$x_2 = 2.41kg  $ 

24. Find ‘a’ in the following table when

x, y vary directly

(b)  x, y vary inversely.

when x and y vary directly.

$ \dfrac{x_1}{y_1}= \dfrac{x_2}{y_2} $

$ \dfrac{2}{{10}}\, = \,\dfrac{5}{{\text{a}}} $

 $ {\text{a  =  }}\dfrac{{50}}{2}\, = \,25 $ 

When x and y vary inversely

$ {x_1 y_1  =  x_2 y_2} $

 $ 2\, \times \,10\, = \,5\, \times \,{\text{a}} $

  ${\text{a  =  }}\dfrac{{20}}{5} $

 $ {\text{a  =  4}} $ 

25. Which of the following quantities vary directly or indirectly with each other

Number of pens and their cost

Distance travelled (at constant speed) and petrol used.

Number of men available and time taken to do a job.

Area of land and its price.

wages y and hours of work x.

As pens increase, cost increases – direct variation.

As distance travelled increases, the amount of petrol increases – direct variation.

Number of men decreases, time taken increases – Inverse variation.

Direct variation.

Common Mistakes Students Make While Solving Class 8 Maths Chapter 13 - Direct and Inverse Proportions Problems:

Here are common mistakes students make while solving problems in Class 8 Maths Chapter 13 - Direct and Inverse Proportions:

1. Confusing Direct and Inverse Proportions: Students often mix up the concepts of direct and inverse proportions. It's crucial to grasp when one variable increases with the other (direct) and when it decreases (inverse).

2. Misinterpreting Proportionality Constants: Students sometimes miscalculate or misinterpret the constant of proportionality. Pay attention to its role in maintaining the relationship between variables.

3. Skipping Units in Ratios: Ignoring units while setting up ratios can lead to errors. Always include units to ensure accurate proportionality.

4. Overlooking Cross Multiplication: When solving proportions, students may forget to cross-multiply. This step is essential for finding the value of unknowns correctly.

5. Neglecting Unitary Method: Forgetting to apply the unitary method to solve problems related to proportions can hinder accurate solutions. Ensure consistency in units throughout.

6. Not Verifying Answers: Students might forget to check their solutions back into the original problem. Always verify answers to confirm their correctness in the given context.

Being mindful of these common pitfalls can help students navigate Direct and Inverse Proportions with greater accuracy and understanding.

Tips and Tricks to Solve Chapter 13 - Direct and Inverse Proportions with Ease!

Here are 8 tips and tricks to solve "Chapter 13 - Direct and Inverse Proportions" with ease:

1. Understand the Concept: Grasp the difference between direct and inverse proportions. In direct, one variable increases as the other increases, and in inverse, one decreases as the other increases.

2. Identify the Proportionality Constant: Pay attention to the constant that relates the two variables. It's crucial for setting up accurate proportions.

3. Include Units in Ratios: Always include units when setting up ratios. This helps in maintaining consistency and ensuring correct proportionality.

4. Cross-Multiply Carefully: When dealing with proportions, cross-multiplication is key. Double-check your calculations to avoid errors.

5. Apply Unitary Method: Use the unitary method to solve problems related to proportions. It simplifies calculations and ensures accuracy.

6. Verify Answers: After finding solutions, don't forget to check them back into the original problem. This step ensures the correctness of your answers in the given context.

7. Practice Regularly: Practice solving various problems regularly to reinforce your understanding of direct and inverse proportions. It builds confidence and familiarity.

8. Use Real-Life Examples: Relate problems to real-life situations to enhance your understanding. This makes the concepts more tangible and relatable.

By incorporating these tips, you can approach "Direct and Inverse Proportions" with confidence and tackle problems with ease!

What are the Benefits of Important Questions from Vedantu for Class 8 Maths Chapter 13 - Direct and Inverse Proportions 

Focus on key topics for efficient studying.

Prepares students for exams and reduces anxiety.

Reinforces understanding of fundamental concepts.

Teaches effective time management.

Enables self-assessment and progress tracking.

Strategic approach for higher scores.

Covers a wide range of topics for comprehensive understanding.

Supports exam preparation and boosts confidence.

Reviewing all the crucial questions for Class 8 Maths Chapter 13 - Direct and Inverse Proportions provides students with a solid grasp of the chapter's topics. The extra and important questions for Class 8 Maths Chapter 13 - Direct and Inverse Proportions engage in a concept-focused discussion, encompassing all chapter themes. This question-and-answer method proves time-saving during exam prep, offering an efficient way to revise the chapter and enhance understanding. Practising these important questions streamlines preparation and boosts confidence for the upcoming exams.

FAQs on Important Questions for CBSE Class 8 Maths Chapter 13 - Direct and Inverse Proportions

1. What is the direct proportion?

A mathematical comparison between two numbers in which the ratio of the two numbers equals a fixed value is known as direct proportion. When two ratios are equal, they are in proportion, according to the proportion definition. When two quantities are split in a direct proportion, the ratio between them remains the same. (They divide into equal portions). Daily hours are an example of a directly proportional relationship. We can find other examples of direct proportion in our day to day life.

2. Where can I avail myself of the Solutions of Class 8 Maths Chapter 13?

The solutions are easily available on the Vedantu site. 

Visit the page NCERT Solutions for Class 8 Maths Chapter 13.

The webpage with Vedantu’s solutions for Class 8 Maths Chapter 13 will open.

To download this, click on the Download PDF button and you can view the solutions offline. 

You can browse through the solutions of the other exercises and chapters as well on the Vedantu website and on the Vedantu app at free of cost.

3. What do you mean by inverse proportion?

When one quantity rises, the other decreases in an indirect (or inverse) proportion. The product of the matching amounts remains the same in an inverse proportion. When one number grows while the other drops, the inverse proportion occurs. Adding additional workers to a task, for example, might speed up completion. That means that they're inversely proportional to each other. Practice all the problems related to inverse proportion to learn each topic concerned with inverse proportions. Important questions are easily available on Vedantu. 

4. Is direct proportion always linear?

A linear connection that is exactly proportionate or directly proportional is a specific form of a linear relationship. When one variable equals 0, the second variable has the same value as the first. On a graph, the "origin" would be represented by a straight line. The graph of a proportionate connection is always a straight line since the two variables always change by the same multiple and one cannot observe any bends, curves or open spots. 

5. How do I find out proportionality?

You might write several ratios as fractions, decrease them and then compare them to determine if they are proportionate. Proportional ratios exist when the reduced fractions are all the same. This is one of the most efficient ways to find out the proportionality of comparatively simpler quantities. Practice all of the direct proportion problems to become proficient in each concept of direct proportions.

Chapterwise Important Questions for CBSE Class 8 Maths

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Case Study Questions for Class 8 Maths Chapter 16 Playing with Numbers

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Here we are providing Case Study questions for Class 8 Maths Chapter 16 Playing with Numbers .

Playing with Numbers Class 8 Maths Case Study Questions

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• CBSE Maths Important Questions
• Class 8 Maths
• Chapter 15: Introduction to Graphs

Important Questions Class 8 Maths Chapter 15: Introduction to Graphs

Important questions with solutions for Class 8 Maths Chapter 15 (Introduction to Graphs) has been provided here by our subject experts. The extra questions are available here to help students score better marks in final exam 2022 – 2023 . The materials provided at BYJU’S for CBSE students are as per the latest syllabus and in reference with NCERT book .

In this chapter, students will go through plotting the graph for the different given situations. For example, change in temperature with respect to the number of days can be plotted in an XY plane. The problems and solutions for graphs will consist of such scenarios. To prepare for Maths exam practice Class 8 Maths Important questions for all the chapters here.

Also Check:

• Important 2 Marks Questions for CBSE 8th Maths
• Important 3 Marks Questions for CBSE 8th Maths
• Important 4 Marks Questions for CBSE 8th Maths

Important Questions With Solutions For Maths Class 8 Chapter 15 (Introduction to Graphs)

Q.1: The following line graph shows the yearly sales figures for a manufacturing company.

(a) What were the sales in (i) 2002 (ii) 2006?

(b) What were the sales in (i) 2003 (ii) 2005?

(c) Compute the difference between sales in 2002 and 2006.

(d) In which year was there the greatest difference between the sales as compared to its previous year?

(a) The sales in (i) 2002 were Rs. 4 crores and (ii) 2006 was Rs. 8 crores

(b) The sales in (i) 2003 was Rs. 7 crores and (ii) 2005 was Rs.10 crores.

(c) The difference of sales in 2002 and 2006 = Rs. 8 crores – Rs. 4 crores = Rs. 4 crores

(d) In the year 2005, there was the greatest difference between the sales and compared to its previous year, which is (Rs. 10 crores – Rs. 6 crores) = Rs. 4 crores.

Q.2: Use the tables below to draw linear graphs:

(a) The number of days a hillside city received snow in different years.

(b)Population (in thousands) of men and women in a village in different years.

a) Consider “Years” along the x-axis and “Days” along the y-axis. Using the given information, the linear graph will look like:

b) Consider “Years” along the x-axis and “No. of Men and No. of Women” along the y-axis (2 graphs). Using the given information, the linear graph will look like:

Q.3: Plot the point (4, 3) on a graph sheet. Is it the same as the point (3, 4)?

Locate the x, y axes, (they are actually number lines!). Start at O (0, 0). Move 4 units to the right; then move 3 units up, you reach the point (4, 3). From Fig 15.13, you can see that the points (3, 4) and (4, 3) are two different points.

Q.4: Plot the following points on a graph sheet. Verify if they lie on a line:

(a) A(4,0), B(4, 2),C(4,6), D(4, 2.5)

(b) P(1, 1), Q(2, 2), R(3,3), S(4, 4)

(c) K(2, 3), L(5, 3), M(5,5), N(2, 5)

Plot all the points on the graph.

(a) All points A, B, C and D lie on a vertical line.

(b) P, Q, R and S points also make a line. It verifies that these points lie on a line.

(c) Points K, L, M and N do not lie in a straight line

Q.5: Draw the line passing through (2,3) and (3,2). Find the coordinates of the points at which this line meets the x-axis and y-axis.

Graph for the Line passes through points (2, 3) and (3, 2) is:

The coordinates of the points at which this line meets the x-axis at (5, 0) and Y axis at (0, 5).

Q.6: Draw the graphs for the following table of values, with suitable scales on the axes.

Interest on deposits for a year.

(i) Does the graph pass through the origin?

(ii) Use the graph to find the interest on Rs 2500 for a year.

(iii) To get an interest of Rs. 280 per year, how much money should be deposited?

Represent “Deposit” on y-axis and “simple interest” on x-axis.

(i) Yes, the graph passes through the origin.

(ii) Interest on Rs. 2500 is Rs. 200 for a year.

(iii) Rs. 3500 should be deposited for the interest of Rs. 280

Extra Questions For Class 8 Maths Chapter 15

• Plot the following points and verify if they lie on a line. If they lie on a line, name it.

(i) (0, 2), (0, 5), (0, 6), (0, 3.5)

(ii) A (1, 1), B (1, 2), C (1, 3), D (1, 4)

(iii) K (1, 3), L (2, 3), M (3, 3), N (4, 3)

(iv) W (2, 6), X (3, 5), Y (5, 3), Z (6, 2)

• State whether True or False. Correct that is false.

(i) A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.

(ii) A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

(iii) The coordinates of the origin are (0, 0)

• A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph

(a) the annual interest obtainable for an investment of ` 250.

(b) the investment one has to make to get an annual simple interest of ` 70.

• Draw a graph for the following.

Is it a linear graph?

5. Write the coordinates of each point shown is the graph.

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