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CBSE Class 9 Maths Case Study Questions PDF Download

Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams.

Case study questions play a pivotal role in enhancing students’ problem-solving skills. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

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CBSE Class 9th MATHS: Chapterwise Case Study Questions

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of Class 9 Maths

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadrilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

Checkout: Class 9 Science Case Study Questions

And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net

The above  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (18 Periods)

1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.

2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.

3. Definition of nth root of a real number.

4. Rationalization (with precise meaning) of real numbers of the type

(and their combinations) where x and y are natural number and a and b are integers.

5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)

UNIT II: ALGEBRA

1. POLYNOMIALS (26 Periods)

Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:

RELATED STORIES

and their use in factorization of polynomials.

2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)

Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.

UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.

UNIT IV: GEOMETRY

1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)

History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)

1. Given two distinct points, there exists one and only one line through them. (Theorem)

2. (Prove) Two distinct lines cannot have more than one point in common.

2. LINES AND ANGLES (15 Periods)

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.

2. (Prove) If two lines intersect, vertically opposite angles are equal.

3. (Motivate) Lines which are parallel to a given line are parallel.

3. TRIANGLES (22 Periods)

1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).

2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).

3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)

5. (Prove) The angles opposite to equal sides of a triangle are equal.

6. (Motivate) The sides opposite to equal angles of a triangle are equal.

4. QUADRILATERALS (13 Periods)

1. (Prove) The diagonal divides a parallelogram into two congruent triangles.

2. (Motivate) In a parallelogram opposite sides are equal, and conversely.

3. (Motivate) In a parallelogram opposite angles are equal, and conversely.

4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.

5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.

6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.

5. CIRCLES (17 Periods)

1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.

2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.

4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

5. (Motivate) Angles in the same segment of a circle are equal.

6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.

7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.

UNIT V: MENSURATION 1.

1. AREAS (5 Periods)

Area of a triangle using Heron’s formula (without proof)

2. SURFACE AREAS AND VOLUMES (17 Periods)

Surface areas and volumes of spheres (including hemispheres) and right circular cones.

UNIT VI: STATISTICS & PROBABILITY

STATISTICS (15 Periods)

 Bar graphs, histograms (with varying base lengths), and frequency polygons.

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF

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CBSE Class 9 Maths exam 2022-23 will have a set of questions based on case studies in the form of MCQs. CBSE Class 9 Maths Question Bank on Case Studies given in this article can be very helpful in understanding the new format of questions.

Each question has five sub-questions, each followed by four options and one correct answer. Students can easily download these questions in PDF format and refer to them for exam preparation.

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Class 9 Social Science Case Study Questions

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If you’re seeking Class 9 Social Science Case Study Questions, you’ve come to the correct spot. Students can use Class 9 Social Science Case Study Questions to help them answer a variety of questions about the Class 9 Social Science case study.

The CBSE Board has included case study questions in Class 9 Social Science examination pattern. As a result, it becomes an indispensable study tool.

The need for a student-friendly app to explain and facilitate the understanding of the social sciences subject has been felt for a long. Especially for students who do not have a strong foundation in Class 9 Social Science. With myCBSEguide , class 9 social science students now have a place where they can find resources that are student-friendly, interesting and easy to understand.

Class 9 Social Science Case Study questions are intended to assess student’s abilities to apply their learning to practical scenarios. You’ll need to employ your critical thinking and problem-solving skills to come up with the best solution. Class 9 Social Science case study questions are designed to test your knowledge and help you improve your skills.

Class 9 Social Science Case Study Questions Samples

myCBSEguide has identified the essential themes connected to CBSE case study questions for Class 9 Social Science that every student should be aware of following a comprehensive examination of CBSE Sample Papers and Marking Scheme. Students in Class 9 Social Science will benefit from this information in understanding the changes in the Class 9 Social Science. For a better understanding and analysis, students should refer to the example of Class 9 Social Science case study questions attached below:

Class 9 Social Science Case Study Question 1

Read the source given below and answer the questions that follow: On the morning of 14 July 1789, the city of Paris was in a state of alarm. The king had commanded troops to move into the city. Rumours spread that he would soon order the army to open fire upon the citizens. Some 7,000 men and women gathered in front of the town hall and decided to form a peoples’ militia. They broke into a number of government buildings in search of arms. Finally, a group of several hundred people marched towards the eastern part of the city and stormed the fortress-prison, the Bastille, where they hoped to find hoarded ammunition. In the armed fight that followed, the commander of the Bastille was killed and the prisoners released – though there were only seven of them. Yet the Bastille was hated by all because it stood for the despotic power of the king. The fortress was demolished and its stone fragments were sold in the markets to all those who wished to keep a souvenir of its destruction. The days that followed saw more rioting both in Paris and the countryside. Most people were protesting against the high price of bread. Much later, when historians looked back upon this time, they saw it as the beginning of a chain of events that ultimately led to the execution of the king in France, though most people at the time did not anticipate this outcome. Answer the following MCQs by choosing the most appropriate option:

On 14th July, 1789 the people of the ________ estate attacked the Bastille prison and freed all the prisoners signalling the start of the _________.

• first, civil war
• fourth, Russian war
• second, movement
• third, revolution

Which of the following statement is incorrect?

• The Bastille was the fortress-prison.
• The Bastille stood for the democratic power of the king.
• On the morning of 14 July 1789, the people of Paris stormed Bastille
• All are correct

In the question given below, there are two statements marked as Assertion (A) and Reason (R). Read the statements and chose the correct option: Assertion (A): The people of France storm the Bastille. Reason (R): They were hopeful to find King Louis XIV and commander of the Bastille there.

• Both A and R are correct and R is the correct explanation of A.
• Both A and R are correct but R is not the correct explanation of A.
• A is correct but R is wrong.
• Both A and R are wrong.

What was the immediate cause of rioting in Paris?

• Atrocities by the commander
• The high price of bread
• The killing of women and children
• All of these

Answer Key:

• (d) third, revolution
• (b) The Bastille stood for the democratic power of the king. [Explanation: The Bastille stood for the despotic power of the king.]
• (c) A is correct but R is wrong. [Explanation: The people of France stormed the fortress-prison, the Bastille because they were hopeful to find hoarded ammunition there.]
• (b) high price of bread

Class 9Social Science Case Study Question 2

Read the extracts and answer the question that follows:

The Himalayas, geologically young and structurally fold mountains stretch over the Himalayas northern borders of India. These mountain ranges run in a west-east direction from the Indus to the Brahmaputra. The Himalayas represent the loftiest and one of the most rugged mountain barriers of the world. They form an arc, which covers a distance of about 2,400 Km. Their width varies from 400 Km in Kashmir to 150 Km in Arunachal Pradesh. The altitudinal variations are greater in the eastern half than those in the western half. The Himalaya consists of three parallel ranges in its longitudinal extent. A number of valleys lie between these ranges. The northern most range is known as the Great or Inner Himalayas. It is the most continuous range consisting of the loftiest peaks with an average height of 6,000 metres. It contains all the prominent Himalayan peaks.

The folds of Great Himalayas are asymmetrical in nature. The core of this part of Himalayas is composed of granite. It is perennially snow bound, and a number of glaciers descend from this range.

• The Great or Inner Himalayas is also known as?
• Give two features of the folds of Great Himalayas.
• Give two features of the Inner Himalayas.
• The Great or Inner Himalayas is also known as the ‘Himadri’.
• (Any two relevant points)
• The folds of Great Himalayas are asymmetrical in nature.
• The core of this part of Himalayas is composed of granite.
• It is perennially snow bound, and a number of glaciers descend from this range.
• Features of the Inner Himalayas:
• It is the most continuous range consisting of the loftiest peaks with an average height of 6,000 metres.
• It contains all the prominent Himalayan peaks.  

Class 9 Social Science Case Study Question 3

Read the source given below and answer the questions that follow: In Pakistan, General Pervez Musharraf led a military coup in October 1999. He overthrew a democratically elected government and declared himself the ‘Chief Executive’ of the country. Later he changed his designation to President and in 2002 held a referendum in the country that granted him a five-year extension. Pakistani media, human rights organisations and democracy activists said that the referendum was based on malpractices and fraud. In August 2002 he issued a ‘Legal Framework Order’ that amended the Constitution of Pakistan. According to this Order, the President can dismiss the national and provincial assemblies. The work of the civilian cabinet is supervised by a National Security Council which is dominated by military officers. After passing this law, elections were held to the national and provincial assemblies. So Pakistan has had elections, elected representatives have some powers. But the final power rested with military officers and General Musharraf himself. Clearly, there are many reasons why Pakistan under General Musharraf should not be called a democracy. People may have elected their representatives to the national and provincial assemblies but those elected representatives were not really the rulers. They cannot take the final decisions. The power to take final decision rested with army officials and with General Musharraf, and none of them were elected by the people. This happens in many dictatorships and monarchies. They formally have an elected parliament and government but the real power is with those who are not elected. In a few countries, the real power was with some external powers and not with locally elected representatives. This cannot be called people’s rule. Answer the following MCQs by choosing the most appropriate option:

What is the meaning of Referendum?

• Direct vote in which the entire electorate is asked to either accept or reject a particular proposal
• A form of government in which the rulers are elected by the people
• A system where the majority or elected representatives are allowed to take decisions on behalf of all the people

In the question given below, there are two statements marked as Assertion (A) and Reason (R). Read the statements and chose the correct option: Assertion (A): Pakistan not considered a democratic country even after having elections Reason (R): Despite elections to the national and provincial assemblies, the final powers rested with General Musharraf and military officers.

• Both A and R are true and R is the correct explanation of A.
• Both A and R are true but R is not the correct explanation of A.
• A is wrong but R is correct.

After the passage of the ________, elections were held to the national and state assemblies.

• Military rule
• Legal Framework Order
• Both (b) and (c)

Does the given source explain the significance of which feature of democracy?

• Democracy must be based on a free and fair election
• In a democracy, the final decision-making power must rest with those elected by the people
• In a democracy, each adult citizen must have one vote
• Democratic government rules within limits set by constitutional law and citizens’ rights
• (a) Direct vote in which the entire electorate is asked to either accept or reject a particular proposal
• (a) Both A and R are true and R is the correct explanation of A.
• (c) Legal Framework Order
• (b) In a democracy, the final decision-making power must rest with those elected by the people

Steps to Master Class 9 Social Science Case Study Questions

Class 9 Social Science case study questions can be daunting, but there are some strategies you can use to ace them. There is no one-size-fits-all answer to Class 9 social science case study questions. The best way to solve a social science case study will vary depending on the specific case in question. However, there are some general tips that can be followed in order to improve your chances of success while answering class 9 social science case study questions.

• First, make sure to read the question carefully and understand what is being asked. It is often helpful to re-read the question after gathering all of your information.
• Next, organize your thoughts and create an outline of your answer. This will help you to stay on track and include all relevant information.
• Finally, write your answer in a clear and concise manner.

Class 9 Social Science Content Structure

Class 9 social science content is divided into four parts: History, Geography, Economics and Political Science. Each part is further divided into smaller themes/chapters.

Each of these topics given in Class 9 Social Science is important in its own right, and together they provide a comprehensive overview that affect our world today. The content is structured in such a way as to provide Class 9 Social Science students with a broad understanding of each issue, while also allowing them to focus on specific areas that are of particular interest to Class 9 Social Science students.

Class 9 Social Science COURSE CONTENT 

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CBSE Class 9 Maths Most Important Case Study Based Questions With Solution

Cbse class 9 mathematics case study questions.

In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are preparing for their final class 9 maths exam.

All these questions provided in this article are with solution which will help students for solving the problems. Dear students need to practice all these questions carefully with the help of given solutions.

As you know CBSE Class 9 Maths exam will have a set of cased study based questions in the form of MCQs. CBSE Class 9 Maths Question Bank given in this article can be very helpful in understanding the new format of questions for new session.

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Case studies in class 9 mathematics.

The Central Board of Secondary Education (CBSE) has included case study based questions in the Class 9 Mathematics paper in current session. According to new pattern CBSE Class 9 Mathematics students will have to solve case based questions. This is a departure from the usual theoretical conceptual questions that are asked in Class 9 Maths exam in this year.

Each question provided in this post has five sub-questions, each followed by four options and one correct answer. All CBSE Class 9th Maths Students can easily download these questions in PDF form with the help of given download Links and refer for exam preparation.

There is many more free study materials are available at Maths And Physics With Pandey Sir website. For many more books and free study material all of you can visit at this website.

Given Below Are CBSE Class 9th Maths Case Based Questions With Their Respective Download Links.

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CBSE Class 9 Science Important Case Study Questions with Answers for Term 2 Exam 2022 (PDF)

Check important case study questions of cbse class 9 science to prepare for the cbse term 2 exam 2022. all these questions have been put together by subject experts..

CBSE Class 9 Term 2 Exam 2022:  Important case based questions for CBSE Class 9 Science are provided here students to prepare for the upcoming Term 2 Exam 2022. All the questions provided below are curated by the subject experts. These questions are really helpful to revise important concepts and prepare the case study questions for the exam. Answers to all questions have been provided for reference. So, students should practice the chapter-wise questions to clearly understand the right way to attempt the case based questions. Download the chapter-wise questions in PDF.

Check some of the important case study questions below:

Q. Read the following and answer the questions :

A student was asked by his teacher to verify the law of conservation of mass in the laboratory. He prepared 5% aqueous solutions of NaCl and Na 2 SO 4 . He mixed 10 mL of both these solutions in a conical flask. He weighed the flask on a balance. He then stirred the flask with a rod and weighed it after sometime. There was no change in mass.

• Was the student able to verify the law of conservation of mass?
• If not, what was the mistake committed by him?
• In your opinion, what he should have done?
• What is the molar mass of Na 2 SO 4 ?
• No, he could not verify the law of conservation of mass in-spite of the fact that there was no change in mass.
• No chemical reaction takes place between NaCl and Na 2 SO 4 . This means that no reaction actually took place in the flask.
• He should have performed the experiment by using aqueous solutions of BaCl 2 and Na 2 SO 4 . A chemical reaction takes place in this case and a white precipitate of BaSO 4 is formed.
• Will the weight of the precipitate be the same as that of the reactants before mixing?
• If not, what she should have done?
• Which law of chemical combination does this support?
• State the law of conservation of mass.
• No, it will not be the same.
• She should have weighed the total contents of the beaker after the reaction and not the precipitate alone.
• It supports the law of conservation of mass.
• Mass can neither be created nor destroyed during a chemical reaction.

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CBSE Case Study Questions for Class 9 Maths Circles Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 9 Maths Circles  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 9 Maths Circles PDF

Checkout our case study questions for other chapters.

• Chapter 8 Quadrilaterals Case Study Questions
• Chapter 9 Areas of Parallelograms and Triangles Case Study Questions
• Chapter 11 Constructions Case Study Questions
• Chapter 12 Heron’s Formula Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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Case Study Questions Class 9 Science Sound

Case study questions class 9 science chapter 12 sound.

CBSE Class 9 Case Study Questions Science Sound. Important Case Study Questions for Class 9 Exam. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Sound.

At Case Study Questions there will given a Paragraph. In where some Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks or 4 marks.

CBSE Case Study Questions Class 9 Science – Sound

(1) Sound is produced by vibrating objects. The matter or substance through which sound is transmitted is called a medium. It can be solid, liquid or gas. Sound moves through a medium from the point of generation to the listener. When an object vibrates, it sets the particles of the medium around it vibrating. The particles do not travel all the way from the vibrating object to the ear. Sound waves are characterized by the motion of particles in the medium and are called mechanical waves.When a vibrating objectmoves forward, it pushes and compresses theair in front of it creating a region of highpressure; this region is called a compression(C).When the vibrating object moves backwards,it creates a region of low pressure calledrarefaction (R). Hence sound is longitudinal wave.

(i) Sound waves are

(a) Mechanical waves

(b) Electromagnetic wave

(c) Transverse waves

(d) None of these

(ii) Sound travel in medium with

(a) Compression and rare fraction

(b) Crest and trough

(c) Both can be possible

(iii) Compression is the region of

(a) High pressure

(b) Low pressure

(c) Medium pressure

(iv) What is sound and how is it produced?

(v) Why sound wave is called as longitudinal wave?

Answer key 1

(iv) Sound is vibrations created by object. When body vibrates, it forces the adjacent particles of the medium to vibrate. This results in disturbance in the medium, which travels as waves an reaches the ear hence sound is produced.

(v) The vibration of medium that travels parallel to direction of wave or along in the direction of the wave is called longitudinal wave. The direction of particles of medium vibrates parallel to direction of propagation of disturbance. Therefore a sound is called longitudinal waves.

(2) The individual particlesof the medium move in a direction parallel tothe direction of propagation of thedisturbance. The particles do not move fromone place to another but they simply oscillateback and forth about their position of rest.This is exactly how a sound wave propagates;hence sound waves are longitudinal waves.There is also another type of wave, calleda transverse wave. In a transverse waveparticles do not oscillate along the direction of wave propagation but oscillate up and downabout their mean position as the wave travels.Thus, a transverse wave is the one in whichthe individual particles of the medium move about their mean positions in a directionperpendicular to the direction of wavepropagation.

(a) Transverse waves

(b) Longitudinal  wave

(c) Both a and b

(ii) Light is

(iii) In case of Longitudinal waves

(a) The particles do not move fromone place to another but they simply oscillateback and forth about their position of rest

(b) The particles move fromone place to another

(c) The particles move up and down.

(iv) When stone is dropped in water; waves are generated of which types?

(v) Differentiate between longitudinal wave and transverse waves.

Answer key-2

(iv) When stone is dropped in water. Waves are generated where water particles are moving up and down and propagated away from dropping point .hence this is sign of transverse waves. Hence transverse waves are produced when stone is dropped in water.

(v) Following are differentiated points

• The distance between two consecutivecompressions (C) or two consecutiverarefactions (R) is called the wavelength.The wavelength is usually represented by λ (Greek letter lambda). Its SI unit is meter (m). • If we can count the number of the compressions or rarefactions that cross us per unit time, we will get the frequency of the sound wave. It is usually represented by υ (Greek letter, nu). SI unit is hertz (symbol, Hz). • The time taken for one complete oscillation is called the time period of the sound wave. It is represented by the symbol T. Its SI unit is second (s).Frequency and time period are related asfollows: υ=1/λ • The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time.

speed, v = distance / time

v= λ/T = υλ

(i ) SI unit of wavelength

(ii)SI unit of Frequency

(iii) Relation between frequency and time is given by

(a) frequency and time are directly proportional

(b) frequency and time are inversely  proportional

(c) There is no relation between them

(iv) Define speed of sound. Give its formula in terms of wavelength and frequency

(v) Define wavelength frequency and time period of longitudinal wave

answer key-3

(iv) The speed of sound is defined as the distance which a point on a wave, such as a compression or a rarefaction, travels per unit time.

v= λ/T = υλ.

(v) The distance between two consecutive compressions (C) or two consecutive rarefactions (R) is called the wavelength.The wavelength is usually represented by λ (Greek letter lambda). Its SI unit is meter (m).

If we can count the number of the compressions or rarefactions that cross us per unit time, we will get the frequency of the sound wave. It is usually represented by υ (Greek letter, nu). SI unit is hertz (symbol, Hz).

The time taken for one complete oscillation is called the time period of the sound wave. It is represented by the symbol T. Its SI unit is second (s).Frequency and time period are related as follows:  υ= 1/λ.

(4) A violin and a flute may both be played the same time in an orchestra. Bothsounds travel through the same medium,that is, air and arrive at our ear at the sametime. Both sounds travel at the same speedirrespective of the source. But the soundswe receive are different. This is due to thedifferent characteristics associated with thesound. Pitch is one of the characteristics.How the brain interprets the frequency ofan emitted sound is called its pitch. The fasterthe vibration of the source, the higher is the frequency and the higher is the pitch. The magnitude of the maximumdisturbance in the medium on either side ofthe mean value is called the amplitude of thewave. It is usually represented by the letter (A).

The loudness or softness of a sound isdetermined basically by its amplitude. Theamplitude of the sound wave depends uponthe force with which an object is made tovibrate. If we strike a table lightly, we hear asoft sound because we produce a sound waveof less energy (amplitude).

The quality or timber of sound is thatcharacteristic which enables us to distinguishone sound from another having the same pitchand loudness. The sound which is morepleasant is said to be of a rich quality. A sound of single frequency is called a tone. The sound which is produced due to a mixture of several frequencies is called a note and is pleasant to listen to. Noise is unpleasant to the ear! Music is pleasant to hear and is of rich quality.

(i) Pitch of sound is higher when

(a) Vibration of source of sound is higher

(b) Vibration of source of sound is Lower

(c) Independent of vibration of source of sound

(ii) Loudness and softness of sound depends upon

(a) Frequency of sound

(b) Amplitude of sound

(c) Wavelength of sound

(iii) Sound of single frequency is called

(iv)If we strike a table lightly, we hear asoft sound. If we hit the tablehard we hear a louder sound up to large distance. Why?

(v) Determine which of the following has higher pitch railway horn or guitar?

Answer key-4

(iv) If we hit the table hard we hear a louder sound because A sound wave spreads out from its source. As it moves away from the source its amplitude as well as its loudness decreases. Louder sound can travel a larger distance as it is associated with higher energy.

(v) Pitch of sound depends on the frequency of vibration of waves and if the frequency of vibration is higher we say that the sound has higher pitch. Pitch of the sound is the response of our ear. So, basically guitar has 6 strings and the sharpness of each string increases on going below. On the other hand in car horns, there is flat pitch with high noise which can affect anyone’s heart too. As guitar has higher frequency than car horn as number of vibrations per unit time of guitar string are more than car.

(5) Sound bounces off a solid or a liquid like a rubber ball bounces off a wall. Like light, sound

gets reflected at the surface of a solid or liquid and follows the same laws of reflection. The directions in which the sound is incident and is reflected make equal angles with the normal to the reflecting surface at the point of incidence, and the three are in the same plane. If we clap near a suitable reflecting object such as a tall building or a mountain, we will hear the same sound again a little later. This sound which we hear is called an echo. The sensation of sound persists in our brain for about 0.1 s. To hear a distinct echo the time interval between the original sound and the reflected one must be at least 0.1s. Hence, for hearingdistinct echoes, the minimum distance of theobstacle from the source of sound must be 17.2 m. Thisdistance will change with the temperature ofair. Another phenomenon of reflection of sound is reverberation.A sound created in a big hall will persist byrepeated reflection from the walls until it isreduced to a value where it is no longeraudible. The repeated reflection that resultsin this persistence of sound is called reverberation. Excessive reverberation is highly undesirable.

(i) Which of the following is true related to reflection of sound?

(a) Directions in which the sound is incident and is reflected make equal angles with the normal to the reflecting surface at the point of incidence.

(b) Incident wave reflected wave and normal lies in same plane

(c) Both a and b are true.

(ii)For hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be

(iii) Excessive reverberation is 

(a) Desirable phenomenon

(b) Undesirable phenomenon

(c) Does not exist

(iv) A person makes sound near a obstacle and heard the echo after 1 s. What is the distance of the obstacle from the person if the speed of the sound, v is taken as 346 m/s?

(v) State law of reflection of sound.

Answer key-5

(iv) Given,

Speed of sound, v = 346 m/s

Time taken for hearing the echo, t = 1 s

Distance travelled by the sound= v × t = 346 m/s × 1 s = 346 m

In 1 s sound has to travel twice the distance between the obstacle and the person.

Hence, the distance between the obstacle and the person= 346/2 = 173 m.

(v) Law of reflection states that The directions in which the sound is incident and is reflected make equal angles with the normal to the reflecting surface at the point of incidence, and the three  that is reflected wave, incident wave and normal to surface are in the same plane.

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CBSE Class 9

The CBSE Class 9 can be called as the foundation for higher classes and thus it is very important for students to learn the topics thoroughly. For example, if a student takes up science after their board exams, topics like mechanics and waves, etc. would also be included in higher classes. So, learning the topics properly from an early stage is very crucial. The curriculum is designed in a way that the students learn and develop their sense of individuality which naturally shapes their future. The guidelines for CBSE Class 9 are issued by the board and the NCERT. So, the schools affiliated to the CBSE board follows the NCERT syllabus . It is important that subjects like science and maths are learnt properly by understanding each concept and topic as these topics would be included in higher standards. For proper preparation, knowing the syllabus is very important along with solving various sample questions.

Note : As per the latest notification dated 6th April 2023 , there are a few changes in the CBSE Class 9 Examination and Assessment practices for the academic session 2023-24 to align assessment to Competency Focused Education. The changes are as mentioned below,

CBSE Class 9 Subjects

The CBSE Board make education accessible for each and every student. CBSE 9th Class can be called as the foundation of higher classes and thus it is important for students to learn and understand the concepts thoroughly. So, to help you with Class 9 subjects below we have listed the subjects included in the respective academic year.

Social Science

CBSE syllabus for Class 9

The CBSE Board designs the syllabus of Class 9 and each and every subject syllabus is structured in such a way that it conveys the subject matter clearly and concisely to students. A well-evaluated syllabus describes each and every topic of textbooks with marking scheme.

CBSE class 9 Syllabus All Subject 

CBSE Class 9 Maths Syllabus

CBSE Class 9 Science Syllabus 

CBSE Class 9 English Syllabus 

CBSE Class 9 Social Science Syllabus 

CBSE study materials for class 9

CBSE study materials for Class 9 will help students to prepare well for the exam. Understand the concepts in an easy and interesting way and finish your studies weeks before the exam so that you have enough time to revise. So to help you with the same, below we have provided the notes for class 9 maths and science syllabus.

CBSE Class 9 Science Detailed Notes

CBSE Class 9 Maths Detailed Notes

CBSE Class 9 English Notes

CBSE Unseen Passages for Class 9

CBSE Essays

CBSE Class 9 Social Science Notes

CBSE Class 9 History Notes

CBSE Class 9 Geography Notes

CBSE Class 9 Political Science Notes

CBSE Class 9 Economics Notes

CBSE Class 9 Science Revision Notes

CBSE Class 9 Maths Revision Notes

NCERT Class 9 Maths Notes

NCERT Class 9 Science Notes

CBSE Class 9 Books

CBSE books of Class 9 are provided below for students of the CBSE board. The CBSE books are selected such that they cover the CBSE syllabus. Class 9 books are listed in such a way that the complete requirements of the CBSE syllabus are contained in the textbooks in an easy to understand way.

CBSE 9th Class Science Book

CBSE 9th Class Maths Book

CBSE 9th Class Hindi Book

CBSE 9th Class Social Science Book

CBSE class 9 English Book

CBSE Class 9 Textbooks Solutions

Class 9 textbook solutions give invaluable help to the students when they are in need of help with their exam preparation and when learning. So to help you with the same, below we have provided the CBSE Class 9 Textbook Solutions for Maths and Science.

NCERT Solutions for Class 9 Maths

NCERT Solutions for Class 9 Science

NCERT Solutions for Class 9 Social Science

NCERT Solutions for Class 9 Histroy

NCERT Solutions for Class 9 Geography

NCERT Solutions for Class 9 Political Science

NCERT Solutions for Class 9 Economics

RD Sharma Solutions for class 9

CBSE Class 9 Important Questions

Important questions of Class 9 gives an idea of questions that can be framed in an examination, marking scheme, important topics, etc. So, we have listed below the important questions of CBSE Class 9 as per the marking scheme for Maths and Science.

CBSE class 9 Science Important Questions

CBSE class 9 Science 2 Marks Important Questions

CBSE class 9 Science 3 Marks Important Questions

CBSE class 9 Science 5 Marks Important Questions

CBSE Class 9 Maths Important Questions

CBSE class 9 Maths 2 Marks Important Questions

CBSE class 9 Maths 3 Marks Important Questions

CBSE class 9 Maths 5 Marks Important Questions

CBSE class 9 Social Science Important Questions

CBSE Class 9 Sample Papers

Class 9 sample papers for all the subjects will help students to get an idea of the marking scheme, important questions, difficulty level of the paper, time management, etc. Students of 9th Class are advised to practice the below-mentioned sample paper before the final exam.

CBSE Sample Paper for Class 9 Maths CBSE Sample Paper for Class 9 Science CBSE Sample Paper for Class 9 English CBSE Sample Paper for Class 9 Social Science

CBSE Class 9 Exam Papers

Class 9 exam papers is a fruitful resource for the students as it will provide students a brief structure of the questions asked in the examination which will in return help them study accordingly. It is advised to add these exam papers in your preparation checklist.

CBSE Class 9 Sciecne Exam Papers

CBSE Class 9 Maths Exam Papers

CBSE Class 9 Science Experiments

For Class 9 students, science is an important subject as it gives the basic understanding of the topics to be covered in Class 9. Along with the theory, practicals are also important part of the syllabus. So, we have provided below a few of the practical experiments which might come in your final practical exam. Along with this, we have also provided the Class 9 Science Lab Manual which contains the activities, science experiments and project works.

Wave Particle Duality of Light Acid Test – How to spot minerals separately Elastic Collision of Equal Masses Using Pool How to make a Fireproof balloon CBSE Class 9 Science Lab Manual

We have also provided the Maths Lab Manual to help students in performing the Maths activities and making the projects.

CBSE Class 9 Maths Lab Manual

CBSE Class 9 Science Projects

For Class 9 students science project is a part of their curriculum. It’s mandatory to do a science project as it is a part of the syllabus. Here on the list, we have provided two science projects to help students to get an idea about what kind of project they can expect.

Observations of Magnetic Permeability

Science Project on Water Pollution

CBSE Class 9 working Models

Working models for Class 9 will help students in terms of learning and preparing for their exam. By going through the below-listed working models students will understand the concepts clearly and can also try making at it home.

Make a Buzzer

How to make a Wooden Generator

How to Make a model of Seasons

How to Make a Lifter

CBSE Class 9 Videos

Video learning has become a trend in today’s educational field. Learning through video will help students of Class 9 to understand the concepts and topics clearly and can also get the idea of how the concepts are practically used in our day to day life.

How to Study in CBSE class 9 (Preparation Tips )

Class 9 CBSE is an important year in the life of a student. It forms the foundation of everything that follows. Given below are few points about CBSE Class 9 preparation. Read on to find out.

• It is essential for CBSE 9th Class students to follow a proper timetable and ensure that you study every subject evenly throughout the week.
• Make proper notes while studying and highlight the important points. These important points will help you remember important concepts faster.
• Practicing past year question papers or sample papers will help you to get an idea of the type of questions you will face. Even you will get an idea of the time required for can question to solve.
• Never ignore any topic and understand each and every topic and concepts clearly so that at the time of exam you don’t have any doubt.
• Apart from study material, refer NCERT textbooks because most of the questions are directly asked from these NCERT textbooks.

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Class 9 Maths Case Study Questions of Chapter 1 Real Numbers

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Case study Questions in Class 9 Mathematics Chapter 1  are very important to solve for your exam. Class 9 Maths Chapter 1 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 1 Real Numbers

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Real Numbers Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 1 Real Numbers

Case Study/Passage-Based Questions

Case Study 1: A Mathematics Exhibition is being conducted in your school and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

1. What will be the value of x?

Answer: b) 13915

2. What will be the value of y?

Answer: c) 11

3. What will be the value of z?

Answer: b) 23

4. According to the Fundamental Theorem of Arithmetic 13915 is a

a) Composite number

b) Prime number

c) Neither prime nor composite

d) Even number

Answer: a) Composite number

5. The prime factorization of 13915 is

a) 5 × 11 3  × 13 2

b) 5 × 11 3  × 23 2

c) 5 × 11 2  × 23

d) 5 × 11 2  × 13 2

Answer: c) 5 × 112 × 23

Case Study 2: Srikanth has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

Answer: (d) no value of n3

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, an is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

Answer: (c) for all n > 1

(iii) If x and y are two odd positive integers, then which of the following is true?

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2   is odd (d) both (a) and (b)

Answer: (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

(a) always true (b) always false (c) sometimes true (d) None of these

Answer:(a) always true

(v) If n is any odd integer, then n 2 – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

Answer: (d) 8

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 1 Real Numbers with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Real Numbers Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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