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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 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

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)

Mycbseguide: blessing in disguise.

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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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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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
• NCERT Solutions for Class 10 Maths
• 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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Class 9 Maths Case Study Questions of Chapter 13 Surface Areas and Volumes

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Case study Questions in Class 9 Mathematics Chapter 13  are very important to solve for your exam. Class 9 Maths Chapter 13 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 9 Maths Case Study Questions  Chapter 13 Surface Areas and Volumes

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These case study questions challenge students to apply their knowledge of quadrilaterals in practical scenarios, enhancing their problem-solving abilities. This article provides the Class 9 Maths Case Study Questions of Chapter 13 Surface Areas and Volumes, enabling students to practice and excel in their examinations.

Surface Areas and Volumes Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 13 Surface Areas and Volumes

Case Study/Passage-Based Questions

Case Study 1: A class teacher brings some clay in the classroom to teach the topic of mensuration. First she forms a cylinder of radius 6 cm and height 8 cm and then she molds that cylinder into sphere.

Find the volume of the cylindrical shape. (a) 288 π cm 3 (b) 244 π cm 3 (c) 240 π cm 3 (d) 216 π cm 3

Answer: (a) 288 π cm3

When clay changes into one shape to other, which of the following remains same? (a) Area (b) C.S.A (c) Radius (d) Volume

Answer: (d) Volume

The radius of the sphere is (a) 2 cm (b) 4 cm (c) 5 cm (d) 6 cm

Answer: (d) 6 cm

Find the volume of sphere, the teacher made. (a) 288 π cm 3 (b) 184 π cm 3 (c) 240 π cm 3 (d) 216 π cm 3

Case Study 2: Ankita realised the need of food for birds on her terrace and decided to make a bird feeder. She got a flexible plastic rectangular sheet of size 44 cm × 15 cm. She rolled it along its length and joined the two opposite ends using a tape for circular base of cylinder. She found a square sheet of size 15 cm × 15 cm by cutting it into required circular shape she prepared the bird feeder as shown in figure.

The curved surface area of the cylinder formed is (a) 550 cm 2 (b) 660 cm 2 (c) 430 cm 2 (d) 840 cm 2

Answer: (b) 660 cm2

The radius of the base of the cylinder is (a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm

Answer: (c) 7 cm

The area of the circular base required for the cylinder is (a) 154 cm 2 (b) 164 cm 2 (c) 240 cm 2 (d) 184 cm 2

Answer: (a) 154 cm2

How much will be the area of square sheet left unused after removing the circular base of the cylinder from it? (a) 78 cm 2 (b) 62 cm 2 (c) 75 cm 2 (d) 71 cm 2

Answer: (d) 71 cm2

Topics Covered in the Case Studies of Chapter 13: Surface Areas and Volumes

The case studies in the Class 9 Maths Case Study Questions of Chapter 13: Surface Areas and Volumes cover the following topics:

• Surface Areas of Solids (Cuboid, Cylinder, Cone, and Sphere)
• Volumes of Solids (Cuboid, Cylinder, Cone, and Sphere)
• Conversion of Units
• Application of Surface Areas and Volumes in Real-Life Scenarios

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 13 Surface Areas and Volumes with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Surface Areas and Volumes 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.

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NCERT Solutions for Class 9 Mathematics Chapter 1- Number Systems

Home » NCERT Solutions » NCERT Solutions for Class 9 Mathematics Chapter 1- Number Systems

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Mathematics is a subject which requires a lot of practice. . The more you practice the better you become. . Therefore, you must practice to perfection. There are plenty of  examples to practice with in Extramarks NCERT Solutions for Class 9 Mathematics Chapter 1.

The Chapter -Number Systems of Class 9 Mathematics covers all the fundamentals of Mathematics and will help students understand the core concepts covered in higher classes. . As Mathematics is totally based on  numbers, this  chapter tells about all the different types of numbers and various applications of numbers in Mathematics. If you are looking for a thorough knowledge of the concepts of the Chapter, Extramarks is the right platform to get the right amount of practice and to develop your mathematical abilities and be confident at an early age. 

You can avail of NCERT Solutions for Class 9 Mathematics Chapter 1 on the Extramarks website and turn your child into a smart learner. Number systems- Chapter 1 of Class 9 Mathematics comprises all the  fundamental concepts.. Based on the CBSE NCERT latest 2021-2022 syllabus, we have provided points to ponder as well as detailed solutions for the better understanding of the subject. It also encourages students to be curious and look for answers themselves.  Students are recommended  to use the NCERT solutions Class 9 Mathematics to realise their  true potential and to enjoy the entire process of learning and stay ahead of the competition.    

Visit the Extramarks website to keep yourself updated about the CBSE syllabus, NCERT Solutions and exam patterns. You may  also search for NCERT Solutions Class 10 to step up  your preparation and stay ahead of others.

Key Topics Covered In NCERT Solution for Class 9 Mathematics Chapter 1

Number system is entirely the study of numeracy, and hence the students must understand the concepts and enjoy the learning experience.   It will directly connect to  chapters like Quadratic equations, Sets etc in higher classes. As a result, students aiming for good grades should be able to identify different types of numbers, know their representation and identities and should know how to rationalise them efficiently.

In Extramarks NCERT Solutions for Class 9 Mathematics Chapter 1, students can expect all topics to be covered and explained in detail. The  chapter includes sections like real numbers and their decimal expansion, representing real numbers on the number line, operation on real numbers etc. For complete study material for NCERT Solutions Class 9, NCERT Solutions Class 10, NCERT Solutions Class 11, and NCERT Solutions Class 12, visit the Extramarks website and app which is trusted by students across India and  their  numbers have been growing by leaps and bounds because of the unshakable trust and faith these schools have in us. 

The key topics covered in NCERT Solutions of Class 9 Mathematics Chapter 1:

NCERT Solutions for Class 9 Mathematics Chapter 1 requires students to apply and correlate whatever they have learnt in their previous classes. . Students can also access NCERT Solutions for Mathematics Class 8 and Class 7  to review the  concepts studied last year or earlier.

1.1 Introduction

This Chapter on Number Systems begins with the basic introduction of numbers and their applications in our daily lives. Further, it categorises  numbers as Natural numbers, Whole numbers, Integers, Rational numbers and Irrational numbers. The various examples provided in the chapter help recognise different numbers, which can help easily recall the concepts in prior  Classes.

1.2 Irrational numbers

This section deals entirely with what makes a number irrational and how one can distinguish between rational and irrational numbers. Students have to keep in mind specific points while deciding it is an irrational number which they will find in our NCERT Solutions for Class 9 Mathematics Chapter 1. Students will also read about the set of numbers called real numbers.

At the end of this section, students will get a proper understanding of irrational as well as real numbers. Also, they will be available to locate certain square roots of numbers on the number line. 

1.3 Real numbers and their decimal expansion

In this section, first, you will learn about  decimal expansions of real numbers. Then you would evaluate whether you can distinguish between rational and irrational numbers based on the decimal expansion. You come across different cases and will illustrate them on the basis of examples.

1.4 Representing Real numbers on the number line

As learnt in the previous t section about the decimal expansion of real numbers, we will use it for application on the number line. The decimal expansion helps represent real numbers and get good practice with examples.  

After going through this section, you would be able to locate points of the number line with ease, learn to visualize points on the number line in a systematic way, learn to round off to the nearest decimal and know that a unique point represents every real number.

1.5 Operation on Real numbers

In the earlier Classes, we have learnt that rational numbers follow commutative, associative and distributive properties for mathematical operations, i.e. when you add, subtract, multiply or divide a rational number, you get a rational number. Likewise, this holds true for irrational numbers also. . 

The set of rational and irrational numbers is called real numbers. Hence, this applies to real numbers too. 

After completing this section, you will be able to carry out operations on non-terminating and non-recurring decimal expansions with the help of illustrative examples. Refer to our NCERT Solutions for Class 9 Mathematics Chapter 1 to get access to more solved questions based on Operations on Real Numbers. 

1.6 Law of exponents for real numbers

You are already acquainted with exponents and laws of exponents from your earlier Classes. In this section, we will specifically learn about the laws of exponents on real numbers. The application of laws of exponents remains the same in the case of real numbers. You have to learn to convert the square root or the cube root of the number into exponential form.

NCERT Solutions for Class 9 Mathematics Chapter 1 Exercise &  Solutions

Find NCERT Solutions for Class 9 Mathematics Chapter 1  on the Extramarks website. From a detailed analysis of the Chapter to short notes, you can find everything to level up your preparation and gear up your performance in the exams. You will get access to  all the questions on Number Systems once you access the NCERT Solutions for Class 9 Mathematics on our website.

Click on the below links to view exercise specific questions and solutions for NCERT Solutions for Class 9 Mathematics Chapter 1:

•  Chapter 9: Exercise 1.1 Question and answers    
•  Chapter 9: Exercise 1.2 Question and answers
• Chapter 9: Exercise 1.3 Question and answers
• Chapter 9: Exercise 1.4 Question and answers
• Chapter 9: Exercise 1.5 Question and answers

Along with Class 9 Mathematics Solutions, students can explore NCERT Solutions on our Extramarks website for all primary and secondary  classes.

• NCERT Solutions Class 5 
• NCERT solutions Class 10
• NCERT solutions Class 11
• NCERT solutions Class 12

NCERT Exemplar for Class 9 Mathematics 

NCERT Exemplar Class 9 Mathematics is an excellent resource  for students preparing for their 9th standard exams. The book consists of a variety of questions of different levels  of difficulty. It  encourages students to develop more interest in  Mathematics and get more significant insights into the  chapter to become proficient in facing challenging questions in the exams.

 NCERT Exemplar helps students to develop confidence during their preparation as they have questions of basic level  as well as advanced level. It has proved to be quite  beneficial for students, especially for  those preparing for various competitive exams. It covers  the entire chapters in detail  , which makes it fruitful for all curriculum students.

After referring to the NCERT Solutions and NCERT Exemplar, the students are confident   to solve all the complicated and tricky questions. As a result, students can easily switch  to more advanced and higher-level conceptual questions. By studying from the Exemplar, you can prepare well for entrance exams like Olympiad, NTSE and KVPY.

Key Features of NCERT Solutions for Class 9 Mathematics Chapter 1

In order to obtain a good score in exams, revision of previous concepts is a must. Hence, NCERT Solutions for Class 9 Mathematics Chapter 1 offers a complete solution for all problems. The key features of NCERT solutions are:  : 

• Mathematics experienced faculty and subject experts have designed Extramarks NCERT Solutions for Class 9 Mathematics Chapter 1. It is a thoroughly researched material made in sync with CBSE examination guidelines.
• Students have a very clear understanding of the concepts and overcome  all their doubts with the help of Extramarks NCERT solutions.
• After completing the NCERT Solutions for Class 9 Mathematics Chapter 1 students will be able to solve all the basic and advanced level problems with better  accuracy.The systemic and well-laid out balanced study plan boosts their performance naturally and effortlessly. 
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Yes, 0 is a rational number. It can be represented as (0/1), (0/2), (0/3) etc.

Find six rational numbers between 3 and 4.

There are infinite rational numbers between 3 and 4. 3 and 4 can be represented as 24/8 and 32/8 respectively. The rational numbers between 3 and 4 are 25/8, 26/8, 27/8, 28/8, 29/8, 30/8.

Q.3 Find five rational numbers between 3 5 and 4 5 .

Q.4 State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.

(i) True; since the collection of whole numbers contains all natural numbers. (ii) False; since integers may be negative but whole numbers are positive. For example: – 5 is an integer it is not a whole number. (iii) False; as rational number may be a fraction but whole number may not be a fraction. For example: 4/5 is a rational number and it is not a whole number.

State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the number line is of the form

where m is a natural number. (iii) Every real number is an irrational number.

(i) True; because real number is a collection of rational and irrational number. (ii) False; as negative numbers cannot be represented as the square root of any other number. (iii) False; as real numbers include both rational and irrational numbers i.e., irrational number is a part of real number. Therefore, every real number cannot be an irrational number.

Q.6 Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

No, the square roots of all positive integers are not irrational. For example: The square roots of 4 and 9 are 2 and 3 respectively.

how 5 can be represented on the number line .

Write the following in decimal form and say what kind of

decimal expansion each has: i   36 100    ii   1 11    iii  4 1 8    iv   3 13    v   2 11    vi   329 400

You know that

1 7  = 0 .142857 ¯ . Can you predict what the decimal expansions of  2 7  , 3 7  , 4 7 ,  5 7 ,  6 7  are, without actually doing the long division? If so, how?

Express the following in the form

p q , where p and q are integers and q¹0. i  0   ii  0.4 7 ¯    iii  0. 001 ¯

Express 0.99999, in the form

p q . Are you surprised by your answer? With your teacher and classmates discussway the answer makes sense.

can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1 17 ? Perform the division to check your answer .

at several examples of rational numbers in the form p q q ≠ 0 , where p and q are integers with no common factors other than 1 and having terminating decimal representations ( expansions ) . Can you guess what property q must satisfy ?

Write three numbers whose decimal expansions are non-terminating non-recurring.

Three numbers whose decimal expansions are non- terminating non-recurring are as follows:

0.030030012003000050004123000…

0.01200012500003500050010008879000102003…

1.5200050040060080010030010040038001…

three different irrational numbers between the rational numbers 5 7 and 9 11 .

Classify the following numbers as rational or irrational:

i   23    ii   225   iii  0.3796  iv  7.478478 . ..    v  1.101001000100001 . ..

Visualise 3.765 on the number line, using successive magnification.

3.765 can be visualised as in the following steps.

4 . 26 ¯ on the number line , upto 4 decimal places .

Classify the following numbers as rational or irrational:

i  2 − 5    ii   3+ 23 − 23    iii   2 7 7 7 iv   1 2   v  2π

each of the following expressions : ( i ) ( 3 + 3 ) ( 2 + 2 ) ( ii ) ( 3 + 3 ) ( 3 − 3 ) ( iii ) ( 5 + 2 ) 2 ( iv ) ( 5 − 2 ) ( 5 + 2 )

, π is defined as the ratio of the circumference ( say c ) of a circle to its diameter say d . That is , π = c d . This seems to contradict the fact that π is irrational . How will you resolve this contradiction ?

There is no contradiction. Remember that when you measure a length with a scale or any other device, you only get an approximate rational value. So, you may not realise that either c or d is irrational.

9 . 3 on the number line .

Mark a line segment AB = 9.3 on number line. Further, take BC of 1 unit. Draw a semi-circle on AC as diameter. Draw a perpendicular to line AC passing through point B. Let it intersect the semi circle at D. Taking B as centre and BD as radius, draw an arc intersecting number line at E. BE =

Rationalise

the denominators of the following : ( i ) 1 7 ( i i ) 1 7 − 6 ( i i i ) 1 5 + 2 ( i v ) 1 7 − 2

:   i 64 1 2       ii 32 1 5       iii 125 1 3

i 9 3 2    ii 32 2 5    iii 16 3 4     iv 125 − 1 3

:      ( i )   2 2 3 . 2 1 5       ( ii )   ( 1 3 3 ) 7       ( iii )   11 1 2 11 1 4         ( iv ) 7 1 2 . 8 1 2

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Faqs (frequently asked questions), 1. where should i search for the ncert solutions for class 9 mathematics chapter 1 online.

There are plenty of  online platforms that provide  study materials for Class 9 Mathematics. However students should rely on only those study solutions that are prepared by subject   experts and strictly follow the latest CBSE curriculum. 

Students can refer to Extramarks, one of the leading  e-learning platforms which  has made it possible for students to access NCERT Solutions for Class 9 Mathematics Chapter 1 as they are prepared by Mathematics subject matter experts with decades of experience. Along with Class 9th Solutions, one can find NCERT Solutions right from Class 1 to Class 12 on our website.  Extramarks has built its credibility and is trusted by students as well as private and government schools across India.

2. How to prepare for NCERT Class 9 Mathematics Chapter 1?

Students should start studying Class 9 Mathematics from NCERT textbook first. They should be attentive in their class lectures. Along with the NCERT textbook, students should solve questions from NCERT Exemplars to build a strong foundation. 

We highly recommend students  also register on reliable online learning platforms such as Extramarks which strictly follows NCERT books and provides solved exercises and practice questions to step up their learning experience and eliminate “mathematics phobia” among students. The additional support of online learning and classes  will  allow  students to clear  their doubts and strengthen their base. To get good grades in exams students  must refer to multiple study resources, practise a lot of questions  and  stick to a study schedule and follow it rigorously to come out with flying colours. 

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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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.

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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NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.1 Number Systems in Hindi Medium and English Medium modified for academic session 2024-25. The 9th Maths solutions are revised according to new curriculum. All the questions and solutions are updated as per new NCERT textbook issued for 2024-25.

Class 9 Maths Exercise 1.1 Solutions

• Class 9 Maths Exercise 1.1 in English
• Class 9 Maths Exercise 1.1 in Hindi
• 9th Maths Chapter 1 in PDF
• Class 9 Maths Chapter 1 Solutions
• Class 9 Maths NCERT Solutions
• Class 9 all Subjects Solutions

Download (Exercise 1.1) in PDF format otherwise you can use it online. These solutions are related to CBSE as well as Gujrat, MP and UP Board (High School) books. Visit to Discussion Forum to ask your doubts and answer the questions asked by other users.

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.1 of Number Systems is given below to use online or download in PDF for session 2024-25. Download options are given at the top of the page. Go back to Class 9 Maths Chapter 1 main page to see other exercises.

Here we are providing NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.1 to view online without downloading for academic session 2024-25. The option of download are also available on this page. In this way students have choice to download or view it online only. NCERT Books of class 9 are also given in PDF.

1. Are 3, -4 and -3.6 rational numbers? If yes, then express them in the form of p/q, where p is Number Systems and q is natural number. 2. Find six rational numbers between – 2 and 2. 3. Find three rational numbers between 2/7 and 3/7. 4. Are the following statements true or false? Give the reason. Every whole number is an integer. Every rational number is a whole number. Every integer is a rational number. Chose the correct answer in each of the following: 5. Between two rational numbers (A) there is no rational number (B) there is exactly one rational number (C) there are infinitely many rational numbers (D) there are only rational numbers and no irrational numbers 6. The product of any two irrational numbers is (A) always an irrational number (B) always a rational number (C) always an integer (D) sometimes rational, sometimes irrational

Download NCERT Books and Offline apps based on new CBSE Syllabus. Ask your doubts and share your knowledge with your friends and other users through Discussion Forum.

Which questions are important for class test from exercise 1.1 class 9 Maths?

In exercise 1.1 of class 9 Maths, there are four questions and two examples (examples 1, 2). All questions and examples of this exercise are equally important from the exam point of view. Example 1 and question 4 are of the same type. Example 2 and questions 2, 3 are of the same type. From this exercise, one mark and two marks questions can come in the exam.

Which question is the best question for exams in exercise 1.1 of class 9 Maths?

Question 1 (Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?) is the best question of exercise 1.1 of class 9 Maths. This question is very interesting, logical and good.

Is exercise 1.1 of class 9th Maths easy to understand?

Yes, exercise 1.1 of class 9th Maths is very easy to understand. Question 1 of this exercise is a yes or no type question. In Questions 2, 3 and example 2, students have to find rational numbers between any two given rational numbers. Question 4 and example 1 are true or false type questions.

How much time, students need to complete exercise 1.1 of class IX Maths?

Students need a maximum of one day to complete exercise 1.1 (chapter 1) of class 9th Maths. This time also depends on student’s speed, efficiency, capability, and many other factors.

Class 9 Maths Chapter 1 Exercise 1.2 »

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• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths
• Chapter 1: Number Systems
• Exercise 1.1

NCERT Solutions for class 9 Maths Chapter 1 - Number Systems Exercise 1.1

NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.1 are provided here. Our subject experts have prepared the NCERT Maths solutions for Class 9 chapter-wise so that it helps students to solve problems easily while using it as a reference. They also focus on creating solutions for these exercises in such a way that it is easy to understand for the students.

The first exercise in Number Systems Exercise 1.1 is the introduction. They provide a detailed and stepwise explanation of each answer to the questions given in the exercises in the NCERT textbook for Class 9. The NCERT Solutions are always prepared by following NCERT guidelines so that it covers the whole syllabus accordingly. These are very helpful in scoring well in CBSE examinations.

NCERT Solutions for Class 9 Maths Chapter 1- Number Systems Exercise 1.1

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Exercise 1.2 Solutions 4 Questions (3 long and 1 short)

Exercise 1.3 Solutions 9 Questions (9 long)

Exercise 1.4 Solutions 2 Questions (2 long)

Exercise 1.5 Solutions 5 Questions (4 long and 1 short)

Exercise 1.6 Solutions 3 Questions (3 long)

Access Answers to Maths NCERT Class 9 Chapter 1 – Number Systems Exercise 1.1

1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?

We know that a number is said to be rational if it can be written in the form p/q , where p and q are integers and q ≠ 0.

Taking the case of ‘0’,

Zero can be written in the form 0/1, 0/2, 0/3 … as well as , 0/1, 0/2, 0/3 ..

Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.

Hence, 0 is a rational number.

2. Find six rational numbers between 3 and 4.

There are infinite rational numbers between 3 and 4.

As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)

i.e., 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7. The numbers between 21/7 and 28/7 will be rational and will fall between 3 and 4.

Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

3. Find five rational numbers between 3/5 and 4/5.

There are infinite rational numbers between 3/5 and 4/5.

To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5

with 5+1=6 (or any number greater than 5)

i.e., (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

The numbers between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.

Hence, 19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5

4. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)

i.e., Natural numbers= 1,2,3,4…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)

i.e., Whole numbers= 0,1,2,3…

Or, we can say that whole numbers have all the elements of natural numbers and zero.

Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.

i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}

i.e., Whole numbers= 0,1,2,3….

Hence, we can say that integers include whole numbers as well as negative numbers.

Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.

i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

All whole numbers are rational; however, all rational numbers are not whole numbers.

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Exercise 1.1 is the first exercise of Chapter 1 of Class 9 Maths. This exercise explains how to find rational numbers between two given numbers.

Key Features of NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.1

• These NCERT Solutions help you solve and revise all questions of Exercise 1.1.
• After going through the stepwise solutions given by our subject expert teachers, you will be able to score more marks.
• It follows NCERT guidelines which help in preparing the students accordingly.
• It contains all the important questions from the examination point of view.

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• Important Questions for CBSE Class 9 Maths (2024-25)

CBSE Class 9 Maths Chapter wise Important Questions - Free PDF Download

Students studying in 9th standard need quality preparation for their upcoming examinations. Mathematics is such a subject that needs practice from the very beginning. Mostly, students are terrified of this particular subject and have no clear concept of mathematical chapters. Ultimately they end up scoring poor marks which drops their aggregate during finals. Students can follow Important Questions for Class 9 Maths by Vedantu to improve their mathematical knowledge and also to get good marks in exams. The PDF provided here highlights the Important Questions of Class 9 Maths . The downloadable PDF is designed according to the CBSE syllabus of 9th grade . It will help students to improve their mathematical skills and helps them to move a step forward to understand the subject. By practising Class 9 Maths Important Questions , students will build their confidence and clear their exams with flying colours.

You can also Download NCERT Solutions for Class 9 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Vedantu provides students with a Free PDF download option for all the NCERT Solution of updated CBSE textbooks . Subjects like Science, Maths, Engish will become easy to study if you have access to NCERT Class 9 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

Chapter wise Important Questions for CBSE Class 9 Maths

CBSE Class 9 Maths Chapter wise Important Questions (2024-25)

Importance of cbse class 9 maths book.

Books of CBSE board ensure that students don’t miss out on any topic and have complete coverage of the syllabus. The solutions provided in this book can be taken as a reference to understand how answers are written in an exam. These books contain formatted answers as suggested by CBSE board and allow students to study the answers and recreate it in the exam in similar language and get good marks.

CBSE Class 9 Maths Important Questions

If the students are looking for specific and detailed solutions of 9 th Class Maths Important Questions, then they are in the right place. Maths solutions include all the questions offered as per new revised syllabus of 9 th grade. The Chapters Of Class 9th Maths include-

Students can get different types of questions related to the chapters. As the chapters proceed, Important Questions For Class 9 Maths get tougher. Students can find questions from various chapters like-

Question from Linear Equations:

Q) The cost of a notebook is twice the cost of a pen. Illustrate linear equations in two variables to signify the statement. Consider two variables as “x” and “y”.

Question from Surface area and Volumes :

Q) If the base radius and height of a cone is 3.5cm and 12cm, then how much ice-cream can be put into the cone?

There are many more questions related to other vital chapters. From the above-mentioned questions, students can get a precise idea about Important Questions for Class 9 Maths .

Questions of Maths for Class 9 with Answers

As the above segment includes the detailed idea of probable Important Questions for Class 9 Maths chapter-wise, now students can follow Maths Questions for Class 9 With Answers .

Given Below is a Question and Solution from the Chapter of Statistics:

Q) The mean of 20 observations is 17. If observation 40 is changed to 12, what will be the value of the new mean?

Ans. Since 17 is the mean of 20 observations

        Sum of 20 observations= 17×20= 340

        New sum of 20 observations= 340-40+12

        New mean= 312/20= 15.6

Interested students can follow images related to important questions for class 9 maths with solutions:

Students can download the PDF, follow Vedantu’s official website or can download the app to get access to online classes arranged by expert subject teachers. To solve important questions of Maths Class 9 , students can go for RD Sharma and RS Agarwal or books from Arihant Publications referred by NCERT which are available on the app and the official website of Vedantu as well.

Class 9 Maths Study Materials

Other cbse class 9 important related links.

Important Questions for CBSE Class 9 Science

FAQs on Important Questions for CBSE Class 9 Maths (2024-25)

Q1. How Many Chapters are Covered in Class 9th Maths Important Questions?

Ans:  Overall, 15 chapters are covered in Important Questions for Class 9 Maths. They imply a thorough study of how the chapters agree with the overall subject matter as prescribed in the course.

Q2. Which is the Most Challenging Chapter in Class 9 Maths?

Ans:  The difficulty of a chapter varies from student to student and their overall understanding of a chapter. Some students find Geometry difficult, whereas some find Surface Area and Volume, Constructions and Statistics difficult. Generally, students find Geometry as the most difficult topic. Also, under the Geometry section, students consider Triangles as the most difficult part of 9 th grade Maths.

Q3. How Do Students Need to Practise Maths in Class 9?

Ans:  If the subject is Maths, then practice is the key for scoring superb marks in the exam. If students practice different types of mathematical problems, solve CBSE sample papers in one sitting within a set time limit, then it would be highly useful for the students to get through different competitive exams. Students must also give importance to high weightage chapters.

Q4. Which chapter is the most difficult for students in Class 9 Maths?

Ans: Class 9 Maths includes 11 chapters. Students find Geometry as a difficult chapter in Class 9 Maths. Students have to practice important questions and NCERT questions for all chapters to score high marks in Class 9 Maths. As one proceeds to different chapters, one will start getting difficult questions. Students can refer to the NCERT solutions for Class 9 Maths on Vedantu for free that can help students to understand all concepts easily. These solutions are available at free of cost on Vedantu(vedantu.com) and mobile app.

Q5. Is Class 9 Maths tough?

Ans: Class 9 Maths is not difficult if students practise it regularly. Students should understand the basic concepts given in so that they can also understand the concepts of Class 10 maths later. Students need to work hard to get good marks in Class 9 maths. They can also download the NCERT Solutions for all chapters to understand the basic concepts of math and for scoring full marks.

Q6. Which is the most important chapter in Maths Class 9 NCERT?

Ans: All chapters of Class 9 Maths NCERT are important because students of Class 9 will get similar chapters in Class 10th. They have to also understand all concepts of Class 9 maths for higher classes such as 11th and 12th. Important questions for Class 9 Maths are available online on Vedantu that can help students to understand all concepts and practise questions based on all chapters easily and quickly.

Q7. How can I practise Math in Class 9?

Ans: Students of Class 9 can practise maths from the NCERT Solutions and important questions available on Vedantu. Students should practise all questions given at the back of each exercise in the NCERT book. Students can also practise extra questions given on Vedantu that can help students to understand the concepts and score high marks in Class 9 Maths. All questions are solved and concepts are explained properly by expert Maths teachers.

Q8. How could I learn Class 9 Maths in an efficient and fast way?

Ans: Students can learn Class 9 Maths by practising all questions given in the NCERT book of class 9. They should revise and practice all questions regularly to understand the concepts. Students can also learn class 9 maths by doing extra and important questions available online. Students can download important questions for Class 9 Maths from Vedantu. They can solve important questions to practise Class 9 Maths and get high marks in exams.

Important Questions for CBSE Class 9

Cbse class 9 study materials, home tuitions in india.