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CBSE Class 9 Mathematics Case Study Questions

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Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

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.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

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All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

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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.

CBSE Class 9 All Students can also Download here Class 9 Other Study Materials in PDF Format.

• NCERT Solutions for Class 12 Maths
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• CBSE Syllabus 2023-24
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• CBSE Class 9th 2023-24 : Science Practical Syllabus; Download PDF 19 April, 2023, 4:52 pm
• CBSE Class 9 Maths Practice Book 2023 (Released By CBSE) 23 March, 2023, 6:16 pm
• CBSE Class 9 Science Practice Book 2023 (Released By CBSE) 23 March, 2023, 5:56 pm
• CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF 10 February, 2023, 6:20 pm
• CBSE Class 9th Maths 2023 : Important Assertion Reason Question with Solution Download Pdf 9 February, 2023, 12:16 pm
• CBSE Class 9th Exam 2023 : Social Science Most Important Short Notes; Download PDF 16 January, 2023, 4:29 pm
• CBSE Class 9th Mathematics 2023 : Most Important Short Notes with Solutions 27 December, 2022, 6:05 pm
• CBSE Class 9th English 2023 : Chapter-wise Competency-Based Test Items with Answer; Download PDF 21 December, 2022, 5:16 pm
• CBSE Class 9th Science 2023 : Chapter-wise Competency-Based Test Items with Answers; Download PDF 20 December, 2022, 5:37 pm

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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

Cbse case study questions for class  9 maths.

CBSE Case Study Questions for Class 9 Maths are a type of assessment where students are given a real-world scenario or situation and they need to apply mathematical concepts to solve the problem. These types of questions help students to develop their problem-solving skills and apply their knowledge of mathematics to real-life situations.

Chapter Wise Case Based Questions for Class 9 Maths

The CBSE Class 9 Case Based Questions can be accessed from Chapetrwise Links provided below:

Chapter-wise case-based questions for Class 9 Maths are a set of questions based on specific chapters or topics covered in the maths textbook. These questions are designed to help students apply their understanding of mathematical concepts to real-world situations and events.

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

• Case Based Questions: Linear Equations - 1
• Case Based Questions: Linear Equations -2

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

• Case Based Questions: Quadrilaterals - 1
• Case Based Questions: Quadrilaterals - 2

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

• Enhance critical thinking:  Case study questions require students to analyze a real-life scenario and think critically to identify the problem and come up with possible solutions. This enhances their critical thinking and problem-solving skills.
• Apply theoretical concepts:  Case study questions allow students to apply theoretical concepts that they have learned in the classroom to real-life situations. This helps them to understand the practical application of the concepts and reinforces their learning.
• Develop decision-making skills:  Case study questions challenge students to make decisions based on the information provided in the scenario. This helps them to develop their decision-making skills and learn how to make informed decisions.
• Improve communication skills:  Case study questions often require students to present their findings and recommendations in written or oral form. This helps them to improve their communication skills and learn how to present their ideas effectively.
• Enhance teamwork skills:  Case study questions can also be done in groups, which helps students to develop teamwork skills and learn how to work collaboratively to solve problems.

In summary, case study questions are important in Class 9 because they enhance critical thinking, apply theoretical concepts, develop decision-making skills, improve communication skills, and enhance teamwork skills. They provide a practical and engaging way for students to learn and apply their knowledge and skills to real-life situations.

Class 9 Maths Curriculum at Glance

The Class 9 Maths curriculum in India covers a wide range of topics and concepts. Here is a brief overview of the Maths curriculum at a glance:

• Number Systems:  Students learn about the real number system, irrational numbers, rational numbers, decimal representation of rational numbers, and their properties.
• Algebra:  The Algebra section includes topics such as polynomials, linear equations in two variables, quadratic equations, and their solutions.
• Coordinate Geometry:  Students learn about the coordinate plane, distance formula, section formula, and slope of a line.
• Geometry:  This section includes topics such as Euclid’s geometry, lines and angles, triangles, and circles.
• Trigonometry: Students learn about trigonometric ratios, trigonometric identities, and their applications.
• Mensuration: This section includes topics such as area, volume, surface area, and their applications.
• Statistics and Probability:  Students learn about measures of central tendency, graphical representation of data, and probability.

The Class 9 Maths curriculum is designed to provide a strong foundation in mathematics and prepare students for higher education in the field. The curriculum is structured to develop critical thinking, problem-solving, and analytical skills, and to promote the application of mathematical concepts in real-life situations. The curriculum is also designed to help students prepare for competitive exams and develop a strong mathematical base for future academic and professional pursuits.

Students can also access Case Based Questions of all subjects of CBSE Class 9

• Case Based Questions for Class 9 Science
• Case Based Questions for Class 9 Social Science
• Case Based Questions for Class 9 English
• Case Based Questions for Class 9 Hindi
• Case Based Questions for Class 9 Sanskrit

Frequently Asked Questions (FAQs) on Case Based Questions for Class 9 Maths

What is case-based questions.

Case-Based Questions (CBQs) are open-ended problem solving tasks that require students to draw upon their knowledge of Maths concepts and processes to solve a novel problem. CBQs are often used as formative or summative assessments, as they can provide insights into how students reason through and apply mathematical principles in real-world problems.

What are case-based questions in Maths?

Case-based questions in Maths are problem-solving tasks that require students to apply their mathematical knowledge and skills to real-world situations or scenarios.

What are some common types of case-based questions in class 9 Maths?

Common types of case-based questions in class 9 Maths include word problems, real-world scenarios, and mathematical modeling tasks.

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CBSE Case Study Questions for Class 9 Maths - Pdf Free PDF Download

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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

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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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NCERT Solutions Class 9 Maths Chapter 1 Number Systems

NCERT solutions for class 9 maths chapter 1 number systems consists of an introduction about the number system and the different kinds of numbers in it. The number system has been classified into different types of numbers like natural numbers, whole numbers , integers, rational numbers, irrational numbers , etc. The NCERT solutions class 9 maths chapter 1 covers all the basics of the number system which will be helpful in forming the basic foundation of mathematics.

Class 9 maths chapter 1 number systems will help the students in differentiating between rational and irrational numbers, wherein irrational numbers cannot be expressed in the form of a ratio, and also about real numbers. Class 9 maths NCERT solutions chapter 1 number systems sample exercises can be downloaded from the links below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.4
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.5
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.6

NCERT Solutions for Class 9 Maths Chapter 1 PDF

These NCERT solutions for class 9 maths involving the important concepts of real numbers , rational and irrational numbers, are available for free pdf download. The questions involving real numbers and their decimal form, the law of exponents are given below:

☛ Download Class 9 Maths NCERT Solutions Chapter 1 Number Systems

NCERT Class 9 Maths Chapter 1   Download PDF

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

It is advisable for the students to practice the questions in the above links as this will give them better clarity on the kind of numbers and their properties. An exercise-wise detailed analysis of NCERT Solutions Class 9 Maths Chapter 1 number systems is given below for reference.

• Class 9 Maths Chapter 1 Ex 1.1 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.2 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.3 - 9 Questions
• Class 9 Maths Chapter 1 Ex 1.4 - 2 Questions
• Class 9 Maths Chapter 1 Ex 1.5 - 5 Questions
• Class 9 Maths Chapter 1 Ex 1.6 - 11 Questions

☛ Download Class 9 Maths Chapter 1 NCERT Book

Topics Covered: The important topics focussed upon are irrational numbers, real numbers, and real numbers when expanded in the decimal form. The class 9 maths NCERT solutions chapter 1 covers the representation of real numbers on a number line, methods to perform operations on real numbers, and laws of exponents when dealing with real numbers.

Total Questions: Class 9 maths chapter 1 Number Systems consists of total 35 questions of which 30 are easy, 2 are moderate and 3 are long answer-type questions.

List of Formulas in NCERT Solutions Class 9 Maths Chapter 1

NCERT solutions class 9 maths chapter 1 covers important facts about the number systems which will help strengthen the math foundation. Like if a number ‘a’ is rational, and ‘b’ represents an irrational number, then ‘a+b’, and ‘a-b’ are irrational numbers, and ‘ab’ and ‘a/b’ are supposed to be irrational numbers, and ‘b’ is not equal to zero. For ‘a’ and ‘b’ positive real numbers the following formula or entities will be true:

• √ab = √a √b
• √(a/b) = √a / √b

Important Questions for Class 9 Maths NCERT Solutions Chapter 1

Video solutions for class 9 maths ncert chapter 1, faqs on ncert solutions class 9 maths chapter 1, do i need to practice all questions provided in ncert solutions class 9 maths number systems.

Practicing the NCERT solutions class 9 maths number systems and exercises on real numbers, rational numbers will help in exploring the number systems in a better way. The NCERT Solutions Class 9 Maths Number Systems will also provide a good insight into the solving of problems.

Why are Class 9 Maths NCERT Solutions Chapter 1 Important?

Since the number systems chapter deals with rational and irrational numbers, real numbers, and their expansion, their decimal form, also covering the law of exponents. Hence, this makes the NCERT solutions class 9 maths important for examinations.

What are the Important Formulas in NCERT Solutions Class 9 Maths Chapter 1?

There are several formulas or entities for positive real numbers which will be helpful in learning mathematics even for higher grades. Like if one wants to rationalize the denominator of 1/ ( √a + b ), then we can multiply and divide by its algebraic conjugate which is √a - b

How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 1 Real Numbers?

The questions in the NCERT Solutions Class 9 Maths Chapter 1 are a great way for learning real numbers. There are around 35 questions dealing with number systems with 25 of them being simple and have straightforward logic, 6 of them are with medium complexity and 4 are elaborative questions.

What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 1?

The NCERT Solutions Class 9 Maths Chapter 1 deal with integers, real numbers, rational and irrational numbers. Apart from these the important topics covered are the real numbers, and what happens when they are expanded in decimal form, the law of exponents in the case of real numbers, how to differentiate between rational and irrational numbers etc.

How CBSE Students can utilize NCERT Solutions Class 9 Maths Chapter 1 effectively?

The students should first practice all the examples to understand the logic and problem solving technique and should try to solve all the exercise questions. The CBSE itself recommends the NCERT Solutions Class 9 Maths for the board exam studies.

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 1 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 1 Number Systems NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.3

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.4

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.6

NCERT Solutions for Class 9 Maths Chapter 1 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter. As Number System is one of the important topics in Maths, it has a weightage of 6 marks in class 9 Maths exams. 

• Introduction of Number Systems
• Irrational Numbers
• Real Numbers and Their Decimal Expansions
• Representing Real Numbers on the Number Line.
• Operations on Real Numbers
• Laws of Exponents for Real Numbers

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Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

Himanshu 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

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

(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)

(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

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

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

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• CBSE Class 9 Maths Worksheet Chapter 1 Number System

CBSE Class 9 Maths Worksheet Chapter 1 Number System - Download Free PDF with Solution

When it comes to Maths as a whole, not many people excel in this subject as it is a subject that solely relies on the logical reasoning functions of the brain. That is why the number system can be intimidating to most students. In Chapter 1, Number System for Class 9, students will learn the number system and their types and how to solve the equations. 

So, what is the number system, and what does the number system syllabus contain? A number system can be defined as an arithmetic system or practice of writing numbers to express them. It is the mathematical notation for continuously representing numbers of any given set by using a certain set of digits, symbols, or other characters. It offers a unique representation of every number. It signifies the arithmetic and algebraic structure of the given figures, permitting us to carry out mathematical calculations such as addition, subtraction, and division. 

All these figures carry their values, which can be determined by looking at the digit, the position in the number, and the base of the number. A number is a mathematical value used to count, measure, or label objects. Regarding the number system, these numbers are used as digits. 

With the help of worksheets such as the Number System Class 9 worksheet, Class 9 Maths Chapter 1 worksheet pdf, and worksheet for Class 9 Maths Chapter 1 with solutions and the operations on Real Numbers Class 9 worksheet, students will have a better understanding of what number systems are and how to solve them accurately.

Access Worksheet for Class 9 Maths Number System

1. It is impossible to represent a rational number in decimal form.

Terminating

Non- terminating

Repeating or Non- Terminating

Non-repeating or Non- terminating

2. Between two rational numbers

There is no rational number.

There is exactly one rational number.

There are infinitely many rational numbers.

There are only rational numbers and no irrational numbers.

3. The product of any two irrational numbers,

is always an irrational number.

is always a rational number.

is always an integer.

can be rational or irrational.

4. Which of the following is irrational?

$\sqrt{81}$

$\dfrac{\sqrt{12}}{\sqrt{3}}$

$\dfrac{\sqrt{4}}{9}$

5. What is the value is $\sqrt{4} \times \sqrt{81}$?

6. Fill in the blanks;

Any two integers are separated by a finite number of others …..

There are an ….. amount of rational numbers between 15 and 18.

X+Y is a rational number if x and y are both ……

Value of $\sqrt[3]{8}$ …….

7. Match the Column:

8. Using two irrational numbers as an example:

Product is an irrational number.

Difference is an irrational number.

Division is an irrational number.

9. Simplify; $(\sqrt{5}+\sqrt{6})(\sqrt{5}-\sqrt{6})$.

10. Simplify; $\sqrt[3]{1331}-\sqrt{100}+\sqrt{81}$.

11. Calculate the value of $\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}$.

12. Calculate the $\dfrac{x}{y}$ form of $0.777 . . . . .$, where $\mathbf{x}$ and $\mathbf{y}$ are integers and $\mathbf{y}$ does not equal to zero.

13. Find three rational number between $\dfrac{9}{11}$ and $\dfrac{5}{11}$.

14. The value of $\dfrac{\sqrt{8}+\sqrt{12}}{\sqrt{32}+\sqrt{48}}$.

15. The value of $a^b+b^a$, if $\mathbf{a}=2$ and $\mathbf{b}=3$

16. Simplify; $2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}$

17. Find the value of $\dfrac{1}{a^b+b^a}$, where $a=5, \mathbf{b}=2$

18. Arrange in ascending order $\sqrt[3]{2}, \sqrt{3}, \sqrt[6]{5} \text {. }$

19. Simplify $(4 \sqrt{5}+3 \sqrt{7})^2$

20. Find the value of a, If $\left(\dfrac{y}{x}\right)^{2a-8}=\left(\dfrac{x}{y}\right)^{a-1}$.

21. Rationalize the denominators of $\dfrac{1}{\sqrt{7}}$.

22. Recall, $\pi$ is defined as the ratio of circumference (say c) to its diameter (say d). That is $\pi=\dfrac{c}{d}$. This seems to contradict the fact that $\pi$ is irrational. How will you resolve this contradiction?

23. Express $0 . \overline{001}$ in the form of $\dfrac{p}{q}$, where $\mathrm{p}$ and $\mathrm{q}$ are integers and $\mathrm{q} \neq 0$.

24. Find five rational numbers between $\dfrac{3}{4}$ and $\dfrac{4}{5}$

25. Find six rational numbers between 3 and 4.

Answers to the Worksheet:

A rational number cannot have a non-terminating or non-repeating decimal form.

2. (c) 

Between two rational numbers, there are infinitely many rational numbers. 

E.g. $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are two rational numbers, then $\dfrac{31}{50} \dfrac{32}{50} \dfrac{33}{50} \dfrac{34}{50} \dfrac{35}{50} \ldots$ are infinite rational number between them.

3. (d) 

The product of two irrational numbers can be rational or irrational depending on the two numbers.

For example, $\sqrt{3} \times \sqrt{3}$ is 3 which is a rational number whereas $\sqrt{2} \times \sqrt{4}$ is $\sqrt{8}$ which is an irrational number. As $\sqrt{3}, \sqrt{2}, \sqrt{4}$ are irrational.

Hence, option D is correct.

4. (a) $\sqrt{7}$ is an irrational number.

5. (b) 

$\sqrt{4} \times \sqrt{81}$ $= \sqrt{2^2} \times \sqrt{9^2}$ $= 2 \times 9$ = 18

6. Fill in the blanks.

Any two integers are separated by a finite number of other integers .

There are an endless amount of rational numbers between 15 and 18 .

$\mathrm{X}+\mathrm{Y}$ is a rational number if $\mathrm{x}$ and $\mathrm{y}$ are both rational numbers .

Value of $\sqrt[3]{8}$ is $\underline{2}$

7. Match The Column:

Explanation:

8. Given an example of two irrational numbers whose;

Product is an irrational number $\sqrt{6} \times \sqrt{3}=\sqrt{6 \times 3}=\sqrt{18}=3 \sqrt{2}$

Difference is a irrational number $\sqrt{6}-\sqrt{3}$ = $\sqrt{3}$

Division is an irrational number $\dfrac{\sqrt{6}}{\sqrt{3}}=\sqrt{\dfrac{6}{3}}=\sqrt{2}$

9. Simplify; $(\sqrt{5}+\sqrt{6})(\sqrt{5}-\sqrt{6})$ 

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

= $\left((\sqrt{5})^2-(\sqrt{6})^2\right)$

10. $\sqrt[3]{1331}-\sqrt{100}+\sqrt{81}$

= $\sqrt[3]{11^3}-\sqrt{10^2}+\sqrt{9^2}$

= $11-10+9$

11. $\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}$

$\dfrac{11^{\dfrac{1}{2}}}{11^{\dfrac{1}{4}}}=11^{\dfrac{1}{2}-\dfrac{1}{4}}$

$=11^{\dfrac{2-1}{4}}$

$=11^{\dfrac{1}{4}}$

12. Let, 

$p= 0.777…$ ....   (1)

Multiply both side in above equation 10

Then, 

$10p= 7.777…$ ….(2)

Subtracting equation (1) from (2), we get;

$10p-p= 7.777… - 0.777…$

$p= \dfrac{7}{9}$

13. Three rational number between $\dfrac{9}{11}$ and $\dfrac{5}{11}$

Rational number of $\dfrac{9}{11}$ and $\dfrac{5}{11}$ is denominator same

$= \dfrac{9}{11}, \dfrac{8}{11}, \dfrac{7}{11}, \dfrac{6}{11}, \dfrac{5}{11}$

14. $\dfrac{\sqrt{8}+\sqrt{12}}{\sqrt{32}+\sqrt{48}}$

$= \dfrac{\sqrt{2^3}+\sqrt{4 \times 3}}{\sqrt{8 \times 4}+\sqrt{8 \times 6}}$

$= \dfrac{2 \sqrt{2}+2 \sqrt{3}}{4 \sqrt{2}+4 \sqrt{3}}$

$= \dfrac{2(\sqrt{2}+\sqrt{3})}{4(\sqrt{2}+\sqrt{3})}$

$= \dfrac{(\sqrt{2}+\sqrt{3})}{2(\sqrt{2}+\sqrt{3})}$

$= \dfrac{1}{2}$

15. If $a=2$ and $b=3$

The value of $a^b+b^a$

$= 2^3+3^2$

16. $2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}$

$2^{\dfrac{2}{3}} \cdot 2^{\dfrac{1}{5}}=2^{\dfrac{2}{3}+\dfrac{1}{5}} \quad \because a^p \cdot a^q=a^{p+q}$

$=2^{\dfrac{10+3}{15}}$

$=2^{\dfrac{13}{15}}$

17. Value of $\dfrac{1}{a^b+b^a}$, where $a=5, b=2$

$= \dfrac{1}{5^2+2^5}$

$= \dfrac{1}{25+32}$

$= \dfrac{1}{57}$

18. Here we have : $\sqrt[3]{2}, \sqrt{3}, \sqrt[5]{5}$

We can also write the expression in simpler form as follows:

$2^{\dfrac{1}{3}}, 3^{\dfrac{1}{2}}, 5^{\dfrac{1}{6}}$

Now we can see that in the denominators of the exponents we have: $3,2,6$

We will now take the LCM of $3,2,6$, which is 6 .

Now we will make all the denominators equal to 6 , so we have to multiply by the multiples in both numerator and denominator.

We can write the numbers as:

$2^{\dfrac{1}{3}} \times \dfrac{2}{2}=2^{\dfrac{2}{6}}$

For the second number we can write:

$3 \dfrac{1}{2} \times \dfrac{3}{3}=3 \dfrac{3}{6}$

Since in the third number we already have the desired denominator, so the third number is

$5^{\dfrac{1}{6}}$

Now we will again write the numbers in the root under, but we have to keep in mind that the numerator will turn as the exponential powers inside the root.

So we have the numbers as:

$\sqrt[6]{2^2}, \sqrt[5]{3^3}, \sqrt[5]{5}$

We will simplify the values inside the root, so we have:

$\sqrt[5]{4}, \sqrt[6]{27}, \sqrt[5]{5}$

From this we can write the smaller value in the front and then the larger value:

$\sqrt[5]{4}, \sqrt[6]{5}, \sqrt[5]{27}$

Hence the original numbers in ascending form are:

$\sqrt[3]{2}, \sqrt[6]{5}, \sqrt{3}$

19. $(4 \sqrt{5}+3 \sqrt{7})^2$

We know that,

$(a+b)^2=a^2+b^2+2 a b$

$=(4 \sqrt{5})^2+(3 \sqrt{7})^2+2 \times (4 \sqrt{5}) (3 \sqrt{7})$

$=80+63+24 \sqrt{5 \times 7}$

$=143+24 \sqrt{35}$

20. $\left(\dfrac{y}{x}\right)^{2 a-8}=\left(\dfrac{x}{y}\right)^{a-1}$

$\left(\dfrac{y}{x}\right)^{2 a-8}=\left(\dfrac{x}{y}\right)^{8-2 a}$   $ \because (x)^{-a}=\dfrac{1}{x^a}$

$\left(\dfrac{x}{y}\right)^{8-2 a}=\left(\dfrac{x}{y}\right)^{a-1}$

When the bases of both sides of an equation are the same, then their exponents are also equal.

$\Rightarrow 8-2 a=a-1$

$\Rightarrow 2 a+a=8+1$

$\Rightarrow 3 a=9$

$\Rightarrow a=\dfrac{9}{3}$

$\Rightarrow a=3$

21. $\dfrac{1}{\sqrt{7}}=\dfrac{1}{\sqrt{7}} \times \dfrac{\sqrt{7}}{\sqrt{7}}$

(Dividing and multiplying by $\sqrt{7}$ )

$=\dfrac{\sqrt{7}}{7}$

22. Writing $\pi$ as $\dfrac{22}{7}$ is only an approximate value and so we can't conclude that it is in the form of a rational. In fact, the value of $\pi$ is calculating as non-terminating, non-recurring decimal as $\pi=3.14159$ Whereas

If we calculate the value of $\dfrac{22}{7}$ it gives $3.142857$ and hence $\pi \neq \dfrac{22}{7}$

In conclusion $\pi$ is an irrational number.

23. Let $x=0.001001 \ldots \ldots$ (1)

Since 3 digits are repeated multiply both the sides of (1) by 1000

$1000 x=1.001001 \ldots$

$1000 x=1+0.001001 \ldots$

$1000 x=1+x$

$1000 x-x=1$

$x=\dfrac{1}{999}$

$\therefore 0 . \overline{001}=\dfrac{1}{999}$

24. Since we make the denominator the same first, then

$\dfrac{3}{4}=\dfrac{3 \times 5}{4 \times 5}=\dfrac{15}{20}$

$\dfrac{4}{5}=\dfrac{4 \times 4}{5 \times 4}=\dfrac{16}{20}$

Now we need to find 5 rational no.

$\dfrac{15}{20}  =\dfrac{15 \times 6}{20 \times 6}=\dfrac{90}{120}$

$\dfrac{16}{20}=\dfrac{16 \times 6}{20 \times 6}=\dfrac{96}{120}$

$\therefore$ Five rational numbers between $\dfrac{3}{4}$ and $\dfrac{4}{5}$ are $\dfrac{91}{120}, \dfrac{92}{120}, \dfrac{93}{120}, \dfrac{94}{120}$ and $\dfrac{95}{120}$

25. We can find any number of rational numbers between two rational numbers. First of all, we make the denominators same by multiplying or dividing the given rational numbers by a suitable number. If denominator is already same then depending on number of rational no. we need to find in question, we add one and multiply the result by numerator and denominator.

$3=\dfrac{3 \times 7}{7} \text { and } \quad 4=\dfrac{4 \times 7}{7}$

$3=\dfrac{21}{7} \quad \text { and } \quad 4=\dfrac{28}{7}$

We can choose 6 rational numbers as: $\dfrac{22}{7}, \dfrac{23}{7}, \dfrac{24}{7}, \dfrac{25}{7}, \dfrac{26}{7}$ and $\dfrac{27}{7}$

Benefits of Learning Number System in Class 9 Chapter 1 Maths Worksheet The Class 9 Maths Chapter 1 worksheet pdf contains more than enough material to help students better understand what number systems are and how to solve them. The worksheets come with extensive questions, attempting to clear any doubts the students might have about the number system and their types.

The Maths assignment for Class 9 Number System list of questions and answers provide thorough insights on the topic’s resources and offers easy tricks to identify quicker ways to solve the questions faster while also being more aware and making sure students don’t go wrong or commit any silly mistakes in their solutions.

All of these worksheets have been developed by the best mathematicians and experienced arithmetic representatives who are very aware of the needs and requirements of the students of Class 9.

Examples of Usage of Number System for Class 9

These are a few examples of Maths assignments for Class 9 Number System exercises’ examples :

Answer the following.

Find two irrational numbers and two rational numbers between 0.7 and 0.77.

Every integer is not a whole number. True or false?

Find at least 7 rational numbers between 2 and 9.

Write down 4567 in the decimal and binary number systems.

Is 0 a rational number? State your reasons based on your answer.

Interesting Facts About Number System for Class 9

There are nine types of number systems in mathematics. They are :

Natural numbers

Whole numbers

Rational numbers

Irrational numbers

Real numbers

Imaginary numbers

Prime and composite numbers

Natural numbers are the root forms of numbers between 0 to infinity. They are also named “positive numbers” or “counting numbers” and are represented by the symbol N. (1, 2, 3, 4, 5 and so on)

Whole numbers are natural numbers, with the only difference being the inclusion of 0. They are represented by the symbol W. (0, 1, 2, 3, 4, 5 and so on)

Integers contain whole numbers and the negative values of natural numbers and don’t include fractions, so their numbers can’t be written in the “a/b” format. It ranges from infinity at the negative end to infinity at the positive end, including 0 and is represented by Z. (...-3, -2, -1, 0, 1, 2, 3… and so on)

Fractions are numbers written in the “a/b” format, where “a” (numerator) is a whole number, and “b” (denominator) is a natural number. Hence, the denominator can never be 0. (2/4, 0/10, 5/7, etc.)

Rational numbers can be written in fractions where “a” and “b” are both integers and b ≠ 0. All fractions are rational numbers, but all rational numbers are not fractions.(-5/9, 3/9, -8/14, etc)

Irrational numbers are numbers that can’t be written in fractional forms. (√8, √.127, √3.209, etc)

Real numbers can be written in decimals, including whole numbers, integers, fractions, etc. All integers belong to real numbers, but not all real numbers belong to integers. (1.25, 0.467, 8.9, etc.)

Imaginary numbers are not real numbers, resulting in negative numbers when squared or put together. They are also named complex numbers and are represented by the symbol i. (√-3, √-16, √-1, etc.)

Numbers that don’t have other factors except 1 are called prime numbers, and the rest of the numbers - except 0 - are called composite numbers, as 0 is neither a prime nor a composite number. ( 2, 3, 5… are prime numbers whereas 4, 6, 8… are composite numbers)

Other definitions and elaborated explanations will be provided in the operations on real numbers class 9 worksheet pdf and more .

Important Topics for Class 9 Number System

The important topics students will have to learn in the number system syllabus for Class 9 are as follows :

What are number systems, and how to solve them?

What are the four types of number systems?

How to convert one number system to another number system.

Solving the problems and choosing the correct answer.

Various other exercises in the Number System Class 9 worksheet

What does the PDF Consist of?

Most schools have syllabuses that don’t include just spoon-feeding the information to the students.

It only means that the students must learn by themselves, with the teachers guiding and aiding them throughout their learning process.

With technology being part of most school curriculums, a huge part of their assignments, tests, and worksheets are online, favoured as pdfs.

Vedantu’s pdf format is highly sought-after as it is used for creating, editing, highlighting, saving, and sharing content.

The worksheet for Class 9 Maths Chapter 1 with Solutions pdfs is free for download at Vedantu’s website.

Rest assured, all the worksheets adhere to the CBSE guidelines' strict, updated, and revised rules.

Many other Number Systems Class 9 worksheet pdfs are present at Vedantu’s platform, created by their own arithmetic subject matter experts, ensuring that the students receive the best training and exercises needed to test their skills and excel in their examinations.

FAQs on CBSE Class 9 Maths Worksheet Chapter 1 Number System

1. Which number system is frequently used?

The decimal number system is the most widely used.

2. How are the values of various figures calculated?

All these figures carry their values, and these values can be determined by: 

looking at the digit 

the position in the number 

the base of the number. 

3. Can rational numbers be whole numbers?

No, since rational numbers may be fractional and whole numbers are not.

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CBSE Class 9 Maths: Extra Questions - Chapter 1 - Number System (with Answers)

Check cbse class 9 maths extra questions for chapter 1 - number system (with answers). these questions are based on 9th maths ncert textbook & important for the preparation of upcoming cbse 9th maths exam 2020-21..

CBSE Class 9 Maths  extra Questions for Chapter 1 - Number System (with Answers). These questions are NCERT based important for the preparation of the upcoming CBSE 9th Maths Exam 2020-21. Most of the questions given here are very simple and can be solved in less than 5 minutes. If someone is facing problems in solving these questions then more clarity of basic concepts is required. These extra questions from Class 9 Maths Chapter 1 - Number System are also expected to be asked in CBSE Class 9 Maths test.

CBSE Class 9 Maths Extra Questions from Chapter 1 - Number System (with Answers):

1: Simplify: [{(8 2  + 9 2 ) 2 } 0 ] 2  = ____

Answer:  1.

2: 2 (2/3)  x 2 (1/3)  

Answer:  2.

3: [2 + (3) 1/2 ] [2 - (3) 1/2 ] = ______

Answer:  1.

CBSE Class 9 Maths Syllabus 2020-2021 (Reduced) - Download in PDF

4: Let  a  > 0 be a real number and p and q be rational numbers. Then which of the following statement(s) is/are correct?

(i) a p  . a q  = a p + q

(ii) a p   b p   = (ab) p

(iii) (a p ) q  = a pq  

(iv) All of these

Answer:  (iv) All of these.

5: Find the value of 1/(4) 3  ÷ 1/(4) 3  + 1/(1) 3

Answer:  2.

6: Divide 10 √15 by 5 √3 .

Answer:  2√5.

7.  Which of the following given statement(s) is/are correct?

(i) The sum or difference of a rational number and an irrational number is irrational.

(ii) The product or quotient of a non-zero rational number with an irrational number is

irrational.

(iii)  If we add, subtract, multiply or divide two irrationals, the result may be rational or

(iv) All of these statements are correct

Answer: 

(iv) All of these statements are correct.

8. [1/(2 + √5)] can also be written as

(a) (2 - √5)

(b) (√5 - 2)

(c) [1/(2 ÷ √5)]

(d) [1 + (2 + √5)]

[1/(2 + √5)] can be rationalised and can be written as (√5 - 2).

9. π (Pi) is a rational number or irrational number?

π (Pi) is an irrational number.

10. The value of π = 22/7. 22/7 is a rational number then how come π is an irrational number?

It is true that 22/7 is a rational number but π is irrational. Please note that 22/7 is an approximate value of π. 

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• Math Article
• Number System For Class 9

Number System for Class 9

Number system for class 9 which is the first chapter has been given here for students to get a reference for the same. Here you will learn about the Number System with its definition and types of numbers. Also, learn the definition of all the types along with their properties. Students who are preparing for the exam could use these materials as a source of learning and have revision at the time of the final exams. Get some example questions and practice questions to understand the number system.

Introduction to number system class 9

The collection of numbers is called the number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers. Let us see the table below to understand with the examples.

Natural Numbers

All the numbers starting from 1 till infinity are natural numbers, such as 1,2,3,4,5,6,7,8,…….infinity. These numbers lie on the right side of the number line and are positive.

Whole Numbers

All the numbers starting from 0 till infinity are whole numbers such as 0,1,2,3,4,5,6,7,8,9,…..infinity. These numbers lie on the right side of the number line from 0 and are positive.

Integers are the whole numbers which can be positive, negative or zero.

Example: 2, 33, 0, -67 are integers.

Rational Numbers

A number which can be represented in the form of p/q is called a rational number. For example, 1/2, 4/5, 26/8, etc.

Irrational Numbers

A number is called an irrational number if it can’t be represented in the form of ratio.

Example: √3, √5, √11, etc.

Real Numbers

The collection of all rational and irrational numbers is called real numbers. Real numbers are denoted by R.

Every real number is a unique point on the number line and also every point on the number line represents a unique real number.

Difference between Terminating and Recurring Decimals

Some special characteristics of rational numbers.

• Every Rational number is expressible either as a terminating decimal or as a repeating decimal.
• Every terminating decimal is a rational number.
• Every repeating decimal is a rational number.
• The non-terminating, non-repeating decimals are irrational numbers.

Example: 0.0100100001001…

• Similarly, if m is a positive number which is not a perfect square, then √m is irrational.

Example: √3

• If m is a positive integer which is not a perfect cube, then 3 √m is irrational.

Example:  3 √2

Properties of Irrational Numbers

• These satisfy the commutative, associative and distributive laws for addition and multiplication.
• Sum of two irrationals need not be irrational.

Example: (2 + √3) + (4 – √3) = 6

• Difference of two irrationals need not be irrational.

Example: (5 + √2) – (3 + √2) = 2

• Product of two irrationals need not be irrational.

Example: √3 x √3 = 3

• The quotient of two irrationals need not be irrational.
• Sum of rational and irrational is irrational.
• The difference of rational and irrational number is irrational.
• Product of rational and irrational is irrational.
• Quotient of rational and irrational is irrational.

A number whose square is non-negative is called a real number.

• Real numbers follow Closure property, associative law, commutative law, the existence of an additive identity, existence of additive inverse for Addition.
• Real numbers follow Closure property, associative law, commutative law, the existence of a multiplicative identity, existence of multiplicative inverse, Distributive laws of multiplication over Addition for Multiplication.

Rationalisation

If we have an irrational number, then the process of converting the denominator to a rational number by multiplying the numerator and denominator by a suitable number is called rationalisation.

3/√2 = (3/ √2) x (√2/√2) = 3 √2/2

Laws of Radicals

Let a>0 be a real number, and let p and q be rational numbers, then we have:

i) (a p ).a q = a (p+q)

ii) (a p ) q = a pq

iii)a p /a q = a (p-q)

iv) a p x b p = (ab) p

Example: Simplify (36) ½

Solution: (6 2 ) ½ = 6 (2 x ½) = 6 1 = 6

Class 9 Number system Extra questions

Q2) Write the irrational numbers between √2 and √3.

Q3) Give an example of two irrational numbers whose sum as well as the product is rational.

To understand the mathematical topics of Class 9 more clearly, visit us at BYJU’S.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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there must be some more questions

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

By QB365 on 08 Sep, 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

QB365 - Question Bank Software

Coordinate geometry case study questions with answer key.

9th Standard CBSE

Final Semester - June 2015

Mathematics

(b) What are the coordinates of C and D respectively?

(c) What is the distance between B and D?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?  

(b) What are the coordinates of A and B respectively?

(c) The coordinates of point O in the sketch -2 is

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is 

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

*****************************************

Coordinate geometry case study questions with answer key answer keys.

(a) (iii) A(3, 5); B(7, 9) (b) (i) C(11, 5); D(7, 1) (c) (iii) 8 units (d) (iii) 8 units (e) (i) (7, 5)

(i) (b) (2, 3) (ii) (a) (2, -1) (iii) (a) 4 (iv) (d) (6, 2) (v) (b) II

(a) (ii) A(13, 10); B(19, 10) (b) (iv) A(19, 6); B(13, 6) (c) (ii) (16, 8) (d) (i) (0, 8) (e)  (ii) (16, 0)

(a) (iv) C(10, 6) (b) (iii) R(5, 6) (c) (ii)   \(\sqrt{34}\)  units PS 2 = AS 2 + AP 2 = 5 2 + 3 2 = 25 + 9 = 34 ⇒ PS =  \(\sqrt{34}\) (d) (iv) Rhombus (e) (i) 30 sq. units Area of rhombus =  \(1 / 2\)  x product of diagonals =  \(1 / 2\)  x 6 x 10  = 30 sq. units

(i) (d) (-4, 3)  (ii) (b) (-3, -2) (iii) (b) (8, 4.5) (iv) (d) IV (v) (b) 10 units

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