class 9 maths chapter 3 case study questions with solutions

Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

• Post author: studyrate
• Post published:
• Post category: class 9th
• Post comments: 0 Comments

Case study Questions in Class 9 Mathematics Chapter 3  are very important to solve for your exam. Class 9 Maths Chapter 3 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 3 Coordinate Geometry

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

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

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 3 Coordinate Geometry

Case Study/Passage-Based Questions

Answer: (d) 2 units

(ii) How far is the library from Shaguns house?

Answer: (b) 2 units

(iii) How far is the library from Alia’s house?

Answer: (d) None of these

(iv) Which of the following is true?

Answer: (b) ABC forms an isosceles triangle

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of house from grocery store to that from electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to the food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 3 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Coordinate Geometry 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

You Might Also Like

Class 9 mcq questions for chapter 2 is matter around us with answers, mcq questions of class 9 maths chapter 9 areas of parallelogram and triangles with answers, class 9 mcq questions for chapter 9 force and laws of motion with answers, leave a reply cancel reply.

Save my name, email, and website in this browser for the next time I comment.

• New QB365-SLMS
• NEET Materials
• JEE Materials
• Banking first yr Materials
• TNPSC Materials
• DIPLOMA COURSE Materials
• 5th Standard Materials
• 12th Standard Materials
• 11th Standard Materials
• 10th Standard Materials
• 9th Standard Materials
• 8th Standard Materials
• 7th Standard Materials
• 6th Standard Materials
• 12th Standard CBSE Materials
• 11th Standard CBSE Materials
• 10th Standard CBSE Materials
• 9th Standard CBSE Materials
• 8th Standard CBSE Materials
• 7th Standard CBSE Materials
• 6th Standard CBSE Materials
• Tamilnadu Stateboard
• Scholarship Exams
• Scholarships

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

Related 9th Standard CBSE Mathematics Materials

9th standard cbse syllabus & materials, class 10th social science - pastoralists case study questions and answers 2022 - 2023, class 9th social science - forest society and colonialism case study questions and answers 2022 - 2023, class 9th social science - nazism and the rise of hitler case study questions and answers 2022 - 2023, class 9th social science - socialism in europe and the russian revolution case study questions and answers 2022 - 2023, class 9th social science - the french revolution case study questions and answers 2022 - 2023, class 9th science - work and energy case study questions and answers 2022 - 2023, class 9th science - force and laws of motion case study questions and answers 2022 - 2023, class 9th science - motion case study questions and answers 2022 - 2023, class 9th science - the fundamental unit of life case study questions and answers 2022 - 2023, class 9th science - is matter around us pure case study questions and answers 2022 - 2023, class 9th science - matter in our surroundings case study questions and answers 2022 - 2023, xam idea 9th standard economics ncert solutions for food security in india, xam idea 9th standard economics ncert solutions for poverty as a challenge, xam idea 9th standard economics ncert solutions for people as resource, xam idea 9th standard economics ncert solutions for the story of village palampur.

Class VI to XII

Tn state board / cbse, 3000+ q&a's per subject, score high marks.

9th Standard CBSE Study Materials

9th Standard CBSE Subjects

CBSE Expert

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.

Table of Contents

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.

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

Download India's best Exam Preparation App Now.

Key Features

• Revision Notes
• Important Questions
• Previous Years Questions
• Case-Based Questions
• Assertion and Reason Questions

No thanks, I’m not interested!

• Andhra Pradesh
• Chhattisgarh
• West Bengal
• Madhya Pradesh
• Maharashtra
• Jammu & Kashmir
• NCERT Books 2022-23
• NCERT Solutions
• NCERT Notes
• NCERT Exemplar Books
• NCERT Exemplar Solution
• States UT Book
• School Kits & Lab Manual
• NCERT Books 2021-22
• NCERT Books 2020-21
• NCERT Book 2019-2020
• NCERT Book 2015-2016
• RD Sharma Solution
• TS Grewal Solution
• TR Jain Solution
• Selina Solution
• Frank Solution
• Lakhmir Singh and Manjit Kaur Solution
• I.E.Irodov solutions
• ICSE - Goyal Brothers Park
• ICSE - Dorothy M. Noronhe
• Sandeep Garg Textbook Solution
• Micheal Vaz Solution
• S.S. Krotov Solution
• Evergreen Science
• KC Sinha Solution
• ICSE - ISC Jayanti Sengupta, Oxford
• ICSE Focus on History
• ICSE GeoGraphy Voyage
• ICSE Hindi Solution
• ICSE Treasure Trove Solution
• Thomas & Finney Solution
• SL Loney Solution
• SB Mathur Solution
• P Bahadur Solution
• Narendra Awasthi Solution
• MS Chauhan Solution
• LA Sena Solution
• Integral Calculus Amit Agarwal Solution
• IA Maron Solution
• Hall & Knight Solution
• Errorless Solution
• Pradeep's KL Gogia Solution
• OP Tandon Solutions
• Sample Papers
• Previous Year Question Paper
• Value Based Questions
• CBSE Syllabus
• CBSE MCQs PDF
• Assertion & Reason
• New Revision Notes
• Revision Notes
• HOTS Question
• Marks Wise Question
• Toppers Answer Sheets
• Exam Paper Aalysis
• Concept Map
• CBSE Text Book
• Additional Practice Questions
• Vocational Book
• CBSE - Concept
• KVS NCERT CBSE Worksheets
• Formula Class Wise
• Formula Chapter Wise
• JEE Crash Course
• JEE Previous Year Paper
• Important Info
• JEE Mock Test
• JEE Sample Papers
• SRM-JEEE Mock Test
• VITEEE Mock Test
• BITSAT Mock Test
• Manipal Engineering Mock Test
• AP EAMCET Previous Year Paper
• COMEDK Previous Year Paper
• GUJCET Previous Year Paper
• KCET Previous Year Paper
• KEAM Previous Year Paper
• Manipal Previous Year Paper
• MHT CET Previous Year Paper
• WBJEE Previous Year Paper
• AMU Previous Year Paper
• TS EAMCET Previous Year Paper
• SRM-JEEE Previous Year Paper
• VITEEE Previous Year Paper
• BITSAT Previous Year Paper
• UPSEE Previous Year Paper
• CGPET Previous Year Paper
• CUSAT Previous Year Paper
• AEEE Previous Year Paper
• Crash Course
• Previous Year Paper
• NCERT Based Short Notes
• NCERT Based Tests
• NEET Sample Paper
• Previous Year Papers
• Quantitative Aptitude
• Numerical Aptitude Data Interpretation
• General Knowledge
• Mathematics
• Agriculture
• Accountancy
• Business Studies
• Political science
• Enviromental Studies
• Mass Media Communication
• Teaching Aptitude
• NAVODAYA VIDYALAYA
• SAINIK SCHOOL (AISSEE)
• Mechanical Engineering
• Electrical Engineering
• Electronics & Communication Engineering
• Civil Engineering
• Computer Science Engineering
• CBSE Board News
• Scholarship Olympiad
• School Admissions
• Entrance Exams
• All Board Updates
• Miscellaneous
• State Wise Books
• Engineering Exam

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

SHARING IS CARING If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

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
• Social Media Channels
• Login Customize Your Notification Preferences
• 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

• Second click on the toggle icon

Provide prime members with unlimited access to all study materials in PDF format.

Allow prime members to attempt MCQ tests multiple times to enhance their learning and understanding.

Provide prime users with access to exclusive PDF study materials that are not available to regular users.

myCBSEguide

• Mathematics
• CBSE Class 9 Mathematics...

CBSE Class 9 Mathematics Case Study Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

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.

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Related Posts

• Competency Based Learning in CBSE Schools
• Class 11 Physical Education Case Study Questions
• Class 11 Sociology Case Study Questions
• Class 12 Applied Mathematics Case Study Questions
• Class 11 Applied Mathematics Case Study Questions
• Class 11 Mathematics Case Study Questions
• Class 11 Biology Case Study Questions
• Class 12 Physical Education Case Study Questions

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

MATHS PAAGAL HAI

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

Where is search ? bar

maths is love

Can I have more questions without downloading the app.

I love math

Hello l am Devanshu chahal and l am an entorpinior. I am started my card bord business and remanded all the existing things this all possible by math now my business is 120 crore and my business profit is 25 crore in a month. l find the worker team because my business is going well Thanks

Leave a Comment

Save my name, email, and website in this browser for the next time I comment.

(Education-Your Door To The Future)

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.

All Of You Can Also Read

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 3 Coordinate Geometry

Class 9 Maths Chapter 3 for CBSE Board Class 9 Maths Exercise 3.1 in English Class 9 Maths Exercise 3.2 in English

Class 9 Maths Chapter 3 for State Boards Class 9 Maths Chapter 3 Exercise 3.1 Class 9 Maths Chapter 3 Exercise 3.2 Class 9 Maths Chapter 3 Exercise 3.3

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry in Hindi and English Medium modified and updated for new academic session 2024-25 based on latest Curriculum. All educational resources on Tiwari Academy are available for free. This is advantageous for students who not have access to paid educational materials or prefer to save on expenses. Question-answers and solutions are prepared according to new NCERT books for class 9 issued for 2024-25 exams.

Being an online platform, our materials are usually accessible 24/7, allowing students to study at their own pace and convenience. Our solutions can serve as a useful revision tool for students preparing for exams. They can quickly review key concepts and problem-solving techniques. Class 9 Maths Chapter 3 in Hindi Medium Class 9 Maths Exercise 3.1 in Hindi Class 9 Maths Exercise 3.2 in Hindi

Class 9 Maths Chapter 3 Study Material

• 9th Maths Study Material for 2024-25 – English Medium
• 9th Maths Study Material for 2024-25 – Hindi Medium
• Class 9 Mathematics Solutions Page
• Class 9 all Subjects Solutions

UP Board students can get the UP Board Solutions for Class 9 Maths Chapter 3 from here. They can download Exercise 3.1 and Exercise 3.2 in English Medium or Prashnavali 3.1 and Prashnavali 3.2 in Hindi Medium PDF format free. View all exercises in Video Format for the students of CBSE and UP Board following the new NCERT (https://ncert.nic.in/) Books 2024-25 for their final exams in 2024-25. All the questions are described using simple and easy steps so that students can understand all the sums of 9th Maths Chapter 3. If someone is facing any problem to use these solutions, please contact us for help. Download Class 9 Maths App for CBSE and UP Board for Offline use or Download Kaksha 9 Ganit App for offline use.

All the solutions are re-prepared removing the error are simplifying the steps of solving including the formula on each step for the simplification. NCERT Solutions 2024-25 are up to date according to the new CBSE curriculum for 2024-25.

Important Questions on 9th Maths Chapter 3

In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie.

(–2, 4): Second Quadrant (3, –1): Fourth Quadrant (–1, 0): x–axis (1, 2): First Quadrant (–3, –5): Third Quadrant

How can we locate the position of an object?

• To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.

What is the coordinates of origin?

• The coordinates of the origin are (0, 0).

What is the coordinates of a point on x-axis or on y-axis?

• The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on the y-axis are (0, y).

What are quadrants?

• The coordinate axes divide the plane into four parts called quadrants.

NCERT Solutions for Class 9 Maths Chapter 3 all exercises and Prashnavali are given to download free for new academic session 2024-25. You can view these solutions in Video Format also. Download Kaksha 9 Ganit App for offline use. These apps work well without internet also. Ask your doubts in Discussion Forum and share your knowledge with your friends and other users.

We are updating and revising our contents are per student’s suggestion, need or for the simplicity. For any inconvenience, you may call us, Whats App, Mail or Message us. Vedic Maths is helpful to make calculation easier and faster. NCERT Solutions 2024-25 for class 9 Science is also available to download as well as Online to study. We always response to all calls, if we are not picking your call, it means we are busy with another user, call us little bit later or after an hour. You may leave message us on Whats App. Follow us on Instagram for latest Updates.

I. In Cartesian system, there are two perpendicular straight lines XX’ (horizontal line) and YY’ (vertical line) which intersect at origin. II. The x and y-coordinates of a point is the perpendicular distance from the Y-axis and X-axis measured along the X and Y-axes respectively. III. The y-coordinate of any point X-axis is zero and x-coordinate of any point on Y-axis is zero. IV. The axes divides the plane into four quadrants . 1. In 1st quadrants x > 0, y > 0 i.e (+, +) 2. In 2nd quadrants x < 0, y > 0 i.e (-, +) 3. In 3rd quadrants x < 0, y < 0 i.e (-, -) 4. In 4th quadrants x > 0, y < 0 i.e (+, -)

What are the main points of Class 9 Maths Chapter 3 for exams?

The main points for the term exam preparation from chapter 3 class 9th Maths are:

• The plane is called the Cartesian, or coordinate plane and the lines are called the coordinate axes.
• The horizontal line is called the x -axis, and the vertical line is called the y – axis.
• The point of intersection of the axes is called the origin.
• The distance of a point from the y – axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.
• If the abscissa of a point is x and the ordinate is y, then (x, y) are called the coordinates of the point.
• The coordinates of a point are of the form (+ , +) in the first quadrant, (–, +) in the second quadrant, (–, –) in the third quadrant and (+, –) in the fourth quadrant, where + denotes a positive real number and – denotes a negative real number.
• If x ≠ y, then (x, y) ≠ (y, x), and (x, y) = (y, x), if x = y.

How many problems are there in chapter 3 of class 9th Maths for exams?

As per latest NCERT books for class 9 Maths, in chapter 3, there are two exercises. The first exercise (Ex 3.1) contains two questions, and the second exercise (Ex 3.2) contains two questions, and two examples (examples 1, 2). So, there are in all six problems (6 questions and four examples) in chapter 3 (Coordinate Geometry) of class 9th Maths.

Is it possible to solve chapter 3 Coordinate Geometry of class 9th Maths in one day?

No, it is not possible to solve chapter 3 (Coordinate Geometry) of class 9th Maths in one day. Students need a maximum of 3 days to solve chapter 3 (Coordinate Geometry) of class 9th Maths if they give at least 1-2 hours per day to this chapter. This time also depends on student’s speed, efficiency, capability, and many other factors.

Is chapter 3 of class 9th Maths complicated?

No, chapter 3 of class 9th Maths is not at all complicated. It is the easiest chapter of class 9th Maths. This chapter is the student’s favourite chapter. Students quickly solve all questions of this chapter without any difficulty because the questions of this chapter are nice and easy.

« Chapter 2. Polynomials

Chapter 4. linear equations in two variables ».

Copyright 2024 by Tiwari Academy | A step towards Free Education

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry 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 3 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 3 Coordinate Geometry 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 3 Exercise 3.1

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.3

NCERT Solutions for Class 9 Maths Chapter 3 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

• Cartesian System
• Plotting a Point in the Plane if its Coordinates are Given

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Talk to our experts

1800-120-456-456

NCERT Solutions for Class 9 Maths Chapter 3 - Coordinate Geometry

• NCERT Solutions
• Chapter 3 Coordinate Geometry

CBSE Class 9 NCERT Solutions for Maths Chapter 3 Coordinate Geometry - Free PDF Download

Class 9 Mathematics introduces you to a new realm of concepts, theorems, applications, and problem-solving procedures. Chapter 3 of Class 9 Mathematics concentrates on the basics of coordinate geometry. Here you will learn about coordinate axes and how to plot a point using Cartesian Coordinates. To understand more about the principles and their applications, you must first read the full chapter and then complete all of the activities. You would need NCERT Answers for Class 9 Mathematics Chapter 3 for this. This answer was produced by Vedantu's best Mathematics teachers. We've also supplied it in PDF format.

In NCERT Solutions for Class 9 free PDF , You will find quality answers to all the exercise questions of the chapter. Use these solutions to make your techniques of using the concepts and their applications to attempt any question successfully. Chapter 3 Maths Class 9 is the foundation chapter to study; you will have to proceed to the next level in the higher classes and learn advanced concepts. Study Class 9 Maths Chapter 3 and use the Coordinate Geometry Class 9 NCERT Solutions to resolve all your queries. Subjects like Science, Maths, and English will become easy to study if you have access to Class 9 Science NCERT Solutions , Maths solutions, and solutions of other subjects that are available on the main page of Vedantu.

Important Topics under NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

Chapter 3 of the Class 9 Maths syllabus is on Coordinate Geometry. It is a very important chapter covered in Class 9 that helps bridge the gap between geometry and algebra. The following is a list of important topics under NCERT Class 9 Maths Chapter 3 Coordinate Geometry. These topics should be prepared well on to perform well in exams where students will come across questions based on coordinate geometry. 

Circle 

Ellipse 

Parabola 

Hyperbole 

Straight Lines

List of Exercises under NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

Class 9 Maths Chapter 3, "Coordinate Geometry", includes three exercises that each focus on a specific set of questions. Here is a detailed explanation of each exercise:

Exercise 3.1: This exercise introduces the fundamental concepts of coordinate geometry and aims to familiarise students with terms like the Cartesian plane, coordinates of points, quadrants, distance formula, and section formula. Additionally, students learn how to find the midpoint of a line segment and the area of a triangle.

Exercise 3.2: This exercise explores different forms of equations of a straight line. Students are expected to find the equation of a straight line that passes through two given points. They will also learn how to find the slope and intercept of a line, and how to write the equation of a line in different forms such as slope-intercept form, point-slope form, and general form.

Exercise 3.3: This exercise delves into the geometrical representation of linear equations. Students are tasked with plotting the graph of a linear equation on the Cartesian plane and identifying the intercepts, slope, and other characteristics of the graph. They will also learn how to find the equation of a line given its graph and how to write the equation of parallel and perpendicular lines.

Access NCERT Solutions for Maths Class - 9 Chapter 3 - Coordinate Geometry

Exercise 3.1

1. How will you describe the position of a table lamp on your study table to another person?

Ans: Consider the figure of a study stable given below, on which a study lamp is placed.

Consider the table as the rectangular plane and the lamp as a point. This table has a short edge and a long edge.

We can see that the distance of the lamp from the shorter edge is $15\ \text{cm}$ and from the longer edge, its $25\ \text{cm}$.

Therefore, depending on the order of the axes, we can conclude that the position of the lamp on the table can be described as $\left( 15,25 \right)$ or $\left( 25,15 \right)$.

2. (Street Plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are \[200\text{ }m\] apart. There are $5$ streets in each direction. Using \[1\text{ }cm\text{ }=\text{ }200\text{ }m\] , draw a model of the city in your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross- street is made by two streets, one running in the North–South direction and another in the East–West direction. Each cross street is referred to in the following manner: If the \[2nd\]  street running in the North–South direction and 5th in the East–West direction meet at some crossing, then we will call this cross-street \[\left( 2,\text{ }5 \right)\]. Using this convention, find:

i) How many cross - streets can be referred to as \[\left( 4,\text{ }3 \right)\] .

Ans: Draw two perpendicular lines depicting the two main roads of the city that cross each other at the center.

Mark it as \[NS\] and \[EW\] .

Consider the scale as \[1\text{ }cm\text{ }=\text{ }200\text{ }m\] .

Get the Figure given below by drawing five streets that are parallel to both the main roads,

From the Figure, we can see that there is only one cross street, which can be referred as \[\left( 4,\text{ }3 \right)\].

ii) How many cross - streets can be referred to as \[\left( 3,\text{ }4 \right)\] .

Ans: From the Figure, we can see that there is only one cross street, which can be referred to as \[\left( 3,\text{ }4 \right)\] .

Exercise 3.2

1. Write the answer of each of the following questions:

i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans:  X-axis is referred to as the horizontal line that is drawn to determine the position of any point in the Cartesian plane. Y-axis is the vertical line that is drawn to determine the position of any point in the Cartesian plane.

ii) What is the name of each part of the plane formed by these two lines?

Ans: Quadrant is the name of each part of the plane that is formed by x-axis and y-axis.

iii) Write the name of the point where these two lines intersect.

Ans: Origin $O$ is the point of intersection of \[x\] - axis and the $y$ - axis .

2. See the Figure, and write the following:

i) The coordinates of \[B\].

Ans: Coordinates of point \[B\] is the distance of \[B\] from $x$ - axis and \[y\] - axis.

Therefore, the coordinates of point \[B\] are \[(-5,2)\].

ii) The coordinates of \[C\].

Ans: Coordinates of point \[C\] is the distance of point \[C\] from \[x\] - axis and \[y\] -axis.

Therefore, the coordinates of point \[C\] are \[(5,-5)\].

iii) The point identified by the coordinates \[(-3,-5)\].

Ans: The point that represents the coordinates \[(-3,-5)\]  is \[E\].

iv) The point identified by the coordinates \[(2,-4)\].

Ans: The point that represents the coordinates $(2,-4)$ is \[G\].

v) The abscissa of the point \[D\].

Ans: The abscissa of point \[D\] is the distance of point \[D\] from the $y$ - axis. Therefore, the abscissa of point \[D\] is $6$.

vi) The ordinate of the point \[H\].

Ans: The ordinate of point $H$ is the distance of point $H$ from the $x$ -axis. Therefore, the ordinate of point $H$ is $-3$.

vii) The coordinates of the point \[L\].

Ans: In the Figure, the coordinates of point \[L\] is the distance of point \[L\] from $x$ -axis and $y$ -axis. Therefore, the coordinates of point \[L\] are \[(0,5)\].

viii) The coordinates of the point \[M\].

Ans: In the Figure, the coordinates of point \[M\] is the distance of point \[M\] from $x$ -axis and $y$-axis. Therefore, the coordinates of point \[M\] are \[(-3,0)\].

Exercise 3.3

1. In which quadrant or on which axis do each of the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0)},\text{ (1,2)}\] and \[(-3,-5)\] lie? Verify your answer by locating them on the Cartesian plane.

Ans: We have to get the quadrant or axis of the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0)}\] , \[(1,2)\] and \[(-3,-5)\].

First, plot the plot the points \[(-2,4),\text{ (3,-1)},\text{ (-1,0),}\ (1,2)\] and \[(-3,-5)\] on the graph, to get,

From the Figure given above, we can say that the points

\[(-2,4)\]  lie in \[IInd\] quadrant.

\[(3,-1)\]  lie in \[IVth\] quadrant.

\[(-1,0)\]  lie on the negative $x$ - axis.

\[(1,2)\]  lie in \[Ist\] quadrant.

\[(-3,-5)\]  lie in \[IIIrd\] quadrant

2. Plot the points \[\left( x,\text{ }y \right)\] given in the following table on the plane, choosing suitable units of distance on the axes.

Ans: Given,

First of all, draw \[X'OX\]  and \[Y'OY\]  as the coordinate axes and mark their point of intersection $O$ as the Origin \[\left( 0,\text{ }0 \right)\].

Then stay at origin.

To plot the points given in the above table,

Point \[A(-2,8)\] 

Move \[2\] units on \[OX'\] and then \[8\] units parallel to \[OY\]

Point \[B(-1,7)\]

Move -1 unit on \[OX'\] and then \[7\] units parallel to \[OY\]

Point \[C(0,-1.25)\],

Move \[1.25\] units below x-axis on \[OY'\] on the y-axis

Point \[D(1,3)\] 

Move \[1\] unit on \[OX\] and then \[3\] units parallel to \[OY\]

Point \[E(3,-1)\],

Move \[3\] units on \[OX\] and then move \[1\]  unit parallel to \[OY'\].

Chapter-wise Class 9 Maths NCERT Solutions Free PDF

Apart from NCERT Solutions for Class 9 Maths Chapter 3, you can also download the free PDFs of NCERT Solutions for the following chapters covered in NCERT Class 9 Maths textbook.

Chapter 1 - Number System

Chapter 2 - Polynomials  

Chapter 3 - Coordinate Geometry

Chapter 4 - Linear Equations in Two Variables

Chapter 5 - Introductions to Euclid Geometry

Chapter 6 - Lines and Angles

Chapter 7 - Triangles

Chapter 8 - Quadrilaterals

Chapter 9 - Areas of Parallelogram and Triangles

Chapter 10 - Circles

Chapter 11 - Constructions

Chapter 12 - Heron's formula

Chapter 13 - Surface area and Volumes

Chapter 14 - Statistics

Chapter 15 - Probability

NCERT Class 9 Chapter 3 Coordinate Geometry Solutions: Summary

Class 9 Chapter 3 Maths will introduce you to Cartesian coordinates. Here you will find a 2D world with two axes, ‘X’ and ‘Y’. Any point can be plotted on this plane using the coordinates and hints. As the chapter proceeds, the exercises provide a platform where you can judge your level of understanding of the concepts. You will have to solve all the questions prescribed in every exercise to develop your concepts well. This is where you will need the NCERT Solutions for Class 9 Maths Chapter 3 to clear your doubts and build a strong foundation that will help you learn higher concepts later.

Class 9 Maths Chapter 3 Solutions have been composed by expert teachers so that you will find your confusion cleared in a moment. The teachers know students' common problems while solving problems in the exercises of Chapter 3 Maths Class 9. Once you finish the classes, you can proceed to the exercise part and start solving the questions. You will discover how efficiently NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry has addressed the problems you faced while solving the exercises.

Follow the techniques used by the teachers and learn how to approach a coordinate geometry problem efficiently. Download the NCERT Solutions for Class 9 Maths Coordinate Geometry and get the best support from the top maths teachers.

Why Should I Follow CBSE Class 9 Maths Chapter 3 Solutions?

Students often find school sessions not enough to support and clarify their doubts. It is also almost impossible for school teachers to pay attention to the problems of all students at once. Using the NCERT Solutions for Class 9th Maths Chapter 3 Coordinate Geometry, you can add the following benefits to your study schedule.

Enjoy the Highest Convenience

How can the Class 9 Maths Chapter 3 Solution make a difference? When you are studying Class 9th Chapter 3 Maths, you will need a convenient way to find Chapter 3 Class 9 Maths NCERT Solutions. The best way to get it is by downloading Class 9 Maths Chapter 3 introduction and solution from here. It can be accessed offline anytime and can be used as a reference during studying. It means you will enjoy the highest convenience from this solution when you are studying Class 9 Maths NCERT Chapter 3.

Easy Class 9 Maths Chapter 3 Solutions to Prepare

The teachers are aware of the easiest ways to teach students the easiest approaches to solve questions related to Ch 3 Class 9 Maths. These Chapter 3 Maths Class 9 NCERT Solutions are composed using the simplest methods and language to make it easier for students to complete the chapter.

Learning New Techniques for NCERT Class 9 Maths Chapter 3

The new techniques taught by the teachers in the NCERT Solutions for Class 9 Maths Chapter 3 will help students score more in the exams. Referring to the solutions while solving the Maths Class 9 Chapter 3 exercises will help you gain confidence.

Extra Questions for Practice

1. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively. Note:  One of the vertices of the rectangle is at the origin, the longer side lies on the x-axis, and one of the vertices lies in the third quadrant.

2. Locate the following points in the Cartesian plane.

(5, 0), (0, 5), (2, 5), (5, 2), (–3, 5), (–3, –5), (5, –3) and (6, 1).

3. Solve the following equations:

(i) 3x + 3 = 15

(ii) 2y + 7 =19

Get NCERT Class 9 Maths Chapter 3 Solutions and make sure your knowledge base of coordinate geometry becomes stronger. Refer to the intelligent yet simple answers to the exercise questions of Class 9th Maths Chapter 3 and understand the concepts well.

Conclusion 

NCERT Solutions for Class 9 Maths Chapter 3 - Coordinate Geometry provide a comprehensive and detailed understanding of the fundamental concepts of coordinate geometry. This chapter introduces students to the Cartesian coordinate system and its applications in representing points and geometric shapes in a two-dimensional plane. The solutions begin by explaining the basics of coordinates, plotting points, and understanding the four quadrants of the coordinate plane. Students learn how to identify the coordinates of a point and how to plot points based on given coordinates. Moreover, NCERT Solutions for Class 9 Maths Chapter 3 delve into the concept of the distance formula, enabling students to calculate the distance between two points on the coordinate plane. They also explore the concept of the section formula, which helps in dividing a line segment into a given ratio.

FAQs on NCERT Solutions for Class 9 Maths Chapter 3 - Coordinate Geometry

1. Why should you prefer Vedantu for Maths NCERT Solutions Class 9 Chapter 3?

Vedantu is one of the most trusted education portals for the students of Class 9. The solutions of Class 9 Maths Chapter 3 developed by the expert teachers follow CBSE norms and deliver the best path for understanding the concepts of coordinate geometry well.

2. How can you prepare and complete Coordinate Geometry?

Pay attention to all the classes. Listen to the explanation given by the class teacher. Understand the concepts and solve the exercises. Refer to the NCERT Solutions Class 9 Maths Chapter 3 to clear your doubts.

3. How can you define the position of an object on a floor?

If you use the Chapter 3 Maths Class 9 NCERT Solutions, you can will learn to define the position of an object on the floor by considering two adjacent walls as two coordinate axes.

4. Which is the best solution for NCERT Class 9 Maths?

The best solutions that are available for Class 9 Maths are the NCERT Solutions Class 9 Maths available on Vedantu. These solutions are special because they have in-depth explanations of all concepts from the full solutions of exercises to miscellaneous questions. If you practise all the chapters from these NCERT Solutions PDFs, you will get a clearer idea of what can be asked from each section. These solutions are prepared by subject matter experts, so they are 100% reliable and to the point. They are based on the latest CBSE guidelines and exam patterns.

5. What are the signs of the coordinates in the four quadrants of a cartesian plane?

The signs of the coordinates in the four quadrants of a cartesian plane are - (+,+) in the first quadrant of a cartesian plane, (-, +) in the second quadrant of a cartesian plane, (-, -) in the third quadrant of a cartesian plane, and (+, -) in the fourth quadrant of a cartesian plane. + stands for positive coordinate point while - stands for a negative coordinate point. All the coordinate points in the different quadrants make up a coordinate plane

6. Are (5,0) and (0,5) ordered pairs in Class 9 Maths Chapter 3?

On plotting the above coordinates along the x-axis and the y-axis, we find that the positions of both pairs differ. (5,0) is differently placed on the Cartesian plane than (0,5). We know that when the values of both the pairs are the same but interchanged them, the position on the graph varies; we call these pairs ordered pairs. And clearly, (0,5) and (5,0) are ordered pairs because by interchanging them, their positions vary.

7. Is Class 9 Maths Chapter 3 easy?

Sure, Class 9 Mathematics Chapter 3 is simple if you put out the necessary effort and create a study plan for yourself. Vedantu is the ideal partner for you to conquer your phobia of Class 9 Mathematics Chapter 3 Coordinate Geometry. You may obtain entire solutions to the exercises by downloading the NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry. Vedantu even provides study programmes to assist you in organising your studies. These solutions are freely available on Vedantu's website (vedantu.com) and mobile app.

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9.

• NCERT Solutions
• NCERT Class 9
• NCERT 9 Maths

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9 maths – free pdf updated for 2023-24 session.

NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDFs of chapter-wise solutions to these problems from the links provided below on this page. These NCERT Solutions for Class 9   cover all the topics included in the NCERT textbook, like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

With the help of these Solutions of NCERT Books for Class 9 Maths , students can practise all types of questions from the chapters. The  CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

NCERT Solutions Class 9 Maths Chapters

• Chapter 1 Number System
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclids Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Circles
• Chapter 10 Heron’s Formula
• Chapter 11 Surface Areas and Volumes
• Chapter 12 Statistics

The following chapters have been removed from the NCERT Class 9 Maths textbook 2023-24. 

• Areas of Parallelograms and Triangles
• Constructions
• Probability

Along with NCERT Solutions , students are also provided with other online learning materials available at BYJU’S, such as notes, books, question papers, exemplar problems, worksheets etc. These materials are designed with respect to the CBSE syllabus and NCERT curriculum. Students are also advised to practise CBSE Class 9 Sample Papers to get an idea of the question pattern in the final exam.

15 chapters are present in the NCERT Solutions for Class 9 Maths . These chapters given in the NCERT Class 9 Maths lay a foundation for the chapters present in Class 10. The PDFs given at BYJU’S are accessible to everyone and can be downloaded by the students for free.

NCERT Solutions of Class 9 Maths Book Chapter Brief:

Students having trouble solving tough Math problems can refer to these CBSE Maths Class 9 Solutions of NCERT for better guidance and for quick review. Solving these exercises in each chapter will ensure positive results.

NCERT Solutions Class 9 Maths Chapter 1 Number System

This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it. A total of 6 exercises are present in this chapter that contains the problems based on all the topics asked in the chapter. This chapter also teaches students the representation of terminating/non-terminating recurring decimals (and successive magnification method) as well as the presentation of square roots of 2, 3 and other non-rational numbers on the number line. The chapter also deals with the laws of integral powers and rational exponents with positive real bases in the Number System.

Topics Covered in Class 9 Maths Chapter 1 Number System

Review of representation of natural numbers, integers, and rational numbers on the number line. Representation of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.

Examples of nonrecurring/non-terminating decimals such as √2, √3, √5 etc. 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, every point on the number line represents a unique real number.

Existence of √x for a given positive real number x (visual proof to be emphasised). Definition of n th root of a real number.

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

Rationalisation (with precise meaning) of real numbers of the type (and their combinations) \(\begin{array}{l}\frac{1}{a+b\sqrt{x}}\: and\: \frac{1}{\sqrt{x}+\sqrt{\sqrt{y}}}\end{array} \) where x and y are natural numbers, and a and b are integers.

Important Formulas – 

Operations on Real Numbers

√(a/b) = √a/√b

√ab = √a √b

(√a + √b) (√a – √b) = a – b

(a + √b) (a – √b) = a 2 – b

(√a + √b) (√c + √d) = √ac + √ad + √bc + √bd

(√a + √b) 2 = a + 2√ab + b

Laws of Exponents for Real Numbers

a m . a n = a m + n

(a m ) n = a mn

a m /a n = a m – n , m > n

a m b m = (ab) m

Also, access the following resources for Class 9 Chapter 1 Number System, at BYJU’S:

• NCERT Number System Class 9 Notes
• Number System Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Number Systems
• RD Sharma Solutions Number Systems Class 9

NCERT Solutions Class 9 Maths Chapter 2 Polynomials

This chapter discusses a particular type of algebraic expression called polynomial and the terminology related to it. Polynomial is an expression that consists of variables and coefficients involving the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The chapter also deals with the Remainder Theorem and the Factor Theorem with the uses of these theorems in the factorisation of polynomials. Students will be taught several examples as well as the definition of different terms like polynomials, degrees, coefficients, zeros and terms of a polynomial. A total of 5 exercises are present in this chapter, which includes problems related to all the topics mentioned in the chapter.

Topics Covered in Class 9 Maths Chapter 2 Polynomials

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of ax 2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall algebraic expressions and identities. Further identities of the type:

(x + y + z) 2 = x 2 + y 2 + z 2  + 2xy + 2yz + 2zx

(x ± y) 3  = x 3  ± y 3 ± 3xy (x ± y)

x 3  + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)

and their use in the factorisation of polynomials. Simple expressions are reducible to these polynomials.

Important Formulas –

(x + y) 2 = x 2 + 2xy + y 2

(x – y) 2 = x 2 – 2xy + y 2

x 2 – y 2 = (x + y) (x – y)

(x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx

(x + y) 3 = x 3 + y 3 + 3xy(x + y)

(x – y) 3 = x 3 – y 3 – 3xy(x – y)

x 3 + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)

Dividend = (Divisor × Quotient) + Remainder

Remainder Theorem

Let p(x) be any polynomial of degree greater than or equal to one, and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

Factor Theorem

If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).

Also, access the following resources for Class 9 Chapter 2 Polynomials, at BYJU’S:

• NCERT Polynomials Class 9 Notes 
• Polynomials Class 9 Important Questions 
• NCERT Exemplar Solutions Class 9 Polynomials
• RD Sharma Solutions factorisation of Polynomials Class 9

NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry

The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy–plane, terms, and notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of abscissa and ordinates of a point as well as plotting and naming a point in xy–plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.

Topics Covered in Class 9 Maths Chapter 3 Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y =mx + c and linking with the chapter on linear equations in two variables.

Important Points – 

• To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.
• The plane is called the Cartesian, or coordinate plane, and the lines are called the coordinate axes.
• The horizontal line is called the x-axis, and the vertical line is called the y-axis.
• The coordinate axes divide the plane into four parts called quadrants.
• The point of intersection of the axes is called the origin.
• The distance of a point from the y-axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.

Also, access the following resources for Class 9 Chapter 3 Coordinate Geometry, at BYJU’S:

• NCERT Coordinate Geometry Class 9 Notes
• Coordinate Geometry Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Coordinate Geometry
• RD Sharma Solutions Coordinate Geometry Class 9

NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables

Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e. ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consist of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.

Topics Covered in Class 9 Maths Chapter 4 Linear Equations in Two Variables:

Recall of linear equations in one variable. Introduction to the equation in two variables. Prove 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 seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

Important Points –

• An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
• A linear equation in two variables has infinitely many solutions.
• The graph of every linear equation in two variables is a straight line.
• x = 0 is the equation of the y-axis, and y = 0 is the equation of the x-axis.
• The graph of x = a is a straight line parallel to the y-axis.
• The graph of y = a is a straight line parallel to the x-axis.
• An equation of the type y = mx represents a line passing through the origin.

Also, access the following resources for Class 9 Chapter 4 Linear Equations in Two Variables, at BYJU’S:

• NCERT Linear Equations in Two Variables Class 9 Notes
• Linear Equations in Two Variables Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Linear Equations in Two Variables
• RD Sharma Solutions Linear Equations in Two Variables Class 9

NCERT Solutions Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

This chapter discusses Euclid’s approach to geometry and tries to link it with present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.

Topics Covered in Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry:

History – Euclid and geometry in India. Euclid’s method of formalising observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem. 1. Given two distinct points, there exists one and only one line through them. 2. (Prove) Two distinct lines cannot have more than one point in common.

Important Axioms and Postulates – 

Some of Euclid’s axioms are:

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part.

(6) Things which are double of the same things are equal to one another.

(7) Things which are halves of the same thing are equal to one another.

Euclid’s Five Postulates

Postulate 1 – A straight line may be drawn from any one point to any other point.

Postulate 2 – A terminated line can be produced indefinitely.

Postulate 3 – A circle can be drawn with any centre and any radius.

Postulate 4 – All right angles are equal to one another.

Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Also, access the following resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry, at BYJU’S:

• NCERT Introduction to Euclid’s Geometry Class 9 Notes
• Introduction to Euclid’s Geometry Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Introduction to Euclid’s Geometry
• RD Sharma Solutions Introduction to Euclid’s Geometry Class 9

NCERT Solutions Class 9 Maths Chapter 6 Lines and Angles

This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter, solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.

Topics Covered in Class 9 Maths Chapter 6 Lines and Angles:

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. 2. (Prove) If two lines intersect, the vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, and interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines, which are parallel to a given line, are parallel. 5. (Prove) The sum of the angles of a triangle is 180°. 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

• If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice versa. This property is called the Linear pair axiom.
• If two lines intersect each other, then the vertically opposite angles are equal.
• If a transversal intersects two parallel lines, then

(i) each pair of corresponding angles is equal,

(ii) each pair of alternate interior angles is equal,

(iii) each pair of interior angles on the same side of the transversal is supplementary.

• If a transversal intersects two lines such that, either

(i) any one pair of corresponding angles is equal, or

(ii) any one pair of alternate interior angles is equal, or

(iii) any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.

Also, access the following resources for Class 9 Chapter 6 Lines and Angles, at BYJU’S:

• NCERT Lines and Angles Class 9 Notes
• Lines and Angles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Lines and Angles
• RD Sharma Solutions Lines and Angles Class 9

NCERT Solutions Class 9 Maths Chapter 7 Triangles

In this chapter, students will study in detail the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.

Topics Covered in Class 9 Maths Chapter 7 Triangles:

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 the 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. 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. 7. (Motivate) Triangle inequalities and the relation between ‘angle and facing side’; inequalities in a triangle.

Important Axioms and Theorems –

Axiom 7.1 (SAS congruence rule) – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

Theorem 7.1 (ASA congruence rule) – Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

Theorem 7.2 – Angles opposite to equal sides of an isosceles triangle are equal.

Theorem 7.3 – The sides opposite to equal angles of a triangle are equal.

Theorem 7.4 (SSS congruence rule) – If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Theorem 7.5 (RHS congruence rule) – If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

Theorem 7.6 – If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).

Theorem 7.7 – In any triangle, the side opposite to the larger (greater) angle is longer.

Theorem 7.8 – The sum of any two sides of a triangle is greater than the third side.

Also, access the following resources for Class 9 Chapter 7 Triangles, at BYJU’S:

• NCERT Triangles Class 9 Notes
• Triangles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Triangles
• RD Sharma Solutions Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals

A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual-level questions asked. The angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are explained in this chapter to help the students in learning the concepts thoroughly.

Topics Covered in Class 9 Maths Chapter 8 Quadrilaterals:

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 are parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other conversely. 6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and (motivate) its converse.

Important Theorems –

A quadrilateral has four sides, four angles and four vertices.

Angle Sum Property of a Quadrilateral – The sum of the angles of a quadrilateral is 360 o .

Theorem 8.1 – A diagonal of a parallelogram divides it into two congruent triangles

Theorem 8.2 – In a parallelogram, opposite sides are equal.

Theorem 8.3 – If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Theorem 8.4 – In a parallelogram, opposite angles are equal.

Theorem 8.5 – If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

Theorem 8.6 – The diagonals of a parallelogram bisect each other.

Theorem 8.7 – If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Theorem 8.8 – A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.

Theorem 8.9 – The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

Theorem 8.10 – The line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.

Also, access the following resources for Class 9 Chapter 8 Quadrilaterals, at BYJU’S:

• NCERT Quadrilaterals Class 9 Notes
• Quadrilaterals Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Quadrilaterals
• RD Sharma Solutions Quadrilaterals Class 9

NCERT Solutions Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles

In this chapter, an attempt has been made to consolidate the knowledge about the formulae to find the areas of different figures by studying relationships between the areas of geometric figures, provided they lie on the same base and between the same parallels. This study will also be useful in understanding some results on the ‘similarity of triangles’. The chapter contains 4 exercises, of which most of the questions ask the students to prove the statements given.

Topics Covered in Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles:

Review the concept of area and recall the area of a rectangle. 1. (Prove) Parallelograms on the same base and between the same parallels have the same area. 2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.

Theorem 9.1 – Parallelograms on the same base and between the same parallels are equal in area.

Theorem 9.2 – Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Theorem 9.3 – Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

Also, access the following resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles, at BYJU’S:

• NCERT Areas of Parallelograms and Triangles Class 9 Notes
• Areas of Parallelograms and Triangles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Areas of Parallelograms and Triangles
• RD Sharma Solutions Areas of Parallelograms and Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 10 Circles

A circle can be defined as a collection of all the points in a plane at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.

Topics Covered in Class 9 Maths Chapter 10 Circles:

Through examples, arrive at definitions of circle-related concepts, radius, circumference, diameter, chord, arc, and subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. 2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre(s) and conversely. 5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 6. (Motivate) Angles in the same segment of a circle are equal. 7. (Motivate) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 8. (Motivate) The sum of either pair of opposite angles of a cyclic quadrilateral is 180 0 and its converse.

Theorem 10.1 – Equal chords of a circle subtend equal angles at the centre.

Theorem 10.2 – If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Theorem 10.3 – The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem 10.4 – The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Theorem 10.5 – There is one and only one circle passing through three given non-collinear points.

Theorem 10.6 – Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

Theorem 10.7 – Chords equidistant from the centre of a circle are equal in length.

Theorem 10.8 – The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 10.9 – Angles in the same segment of a circle are equal.

Theorem 10.10 – If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic).

Theorem 10.11 – The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Theorem 10.12 – If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

Also, access the following resources for Class 9 Chapter 10 Circles, at BYJU’S:

• NCERT Circles Class 9 Notes
• Circles Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Circles
• RD Sharma Solutions Circles Class 9

NCERT Solutions Class 9 Maths Chapter 11 Constructions

In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles when different parameters are given.

Topics Covered in Class 9 Maths Chapter 11 Constructions:

1. Construction of bisectors of a line segment and angle, 60°, 90°, 45° angles etc., equilateral triangles. 2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle. 3. Construction of a triangle of given perimeter and base angles.

Construction 11.1 – To construct the bisector of a given angle.

Construction 11.2 – To construct the perpendicular bisector of a given line segment.

Construction 11.3 – To construct an angle of 600 at the initial point of a given ray.

Construction 11.4 – To construct a triangle, given its base, a base angle and the sum of the other two sides.

Construction 11.5 – To construct a triangle given its base, a base angle and the difference between the other two sides.

Construction 11.6 – To construct a triangle, given its perimeter and its two base angles.

Also, access the following resources for Class 9 Chapter 11 Constructions, at BYJU’S:

• NCERT Constructions Class 9 Notes
• Constructions Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Constructions
• RD Sharma Solutions Constructions Class 9

NCERT Solutions Class 9 Maths Chapter 12 Heron’s Formula

The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student understand the method of solving the problems based on Heron’s formula.

Topics Covered in Class 9 Maths Chapter 12 Heron’s Formula:

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.

Area of a triangle = 1/2 × base × height

Area of a triangle by Heron’s Formula = \(\begin{array}{l}\sqrt{s(s-a)(s-b)(s-c)}\end{array} \)

Where a, b and c are the sides of a triangle

s is the semi-perimeter, i.e. half of the perimeter of a triangle = (a + b + c)/2

Also, access the following resources for Class 9 Chapter 12 Heron’s Formula, at BYJU’S:

• NCERT Heron’s Formula Class 9 Notes
• Heron’s Formula Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Heron’s Formula
• RD Sharma Solutions Heron’s Formula Class 9

NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes

In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in detail and broaden the study to some other solids, such as cones and spheres. This chapter is just an extended version of the chapter mensuration, in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.

Topics Covered in Class 9 Maths Chapter 13 Surface Areas and Volumes :

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

Surface Area of a Cuboid = 2(lb + bh + hl)

where l, b and h are, respectively, the three edges of the cuboid

Surface Area of a Cube = 6a 2

where a is the edge of the cube.

Curved Surface Area of a Cylinder = 2πrh

where r is the radius of the base of the cylinder and h is the height of the cylinder

Total Surface Area of a Cylinder = 2πr(r + h)

where h is the height of the cylinder and r is its radius

Curved Surface Area of a Cone = 1/2 × l × 2πr = πrl

where r is its base radius, and l is its slant height

Total Surface Area of a Cone = πrl + πr 2 = πr(l + r)

Surface Area of a Sphere = 4 π r 2

where r is the radius of the sphere.

Curved Surface Area of a Hemisphere = 2πr 2

where r is the radius of the sphere of which the hemisphere is a part.

Total Surface Area of a Hemisphere = 3πr 2

Volume of a Cuboid = base area × height = length × breadth × height

Volume of a Cube = edge × edge × edge = a 3

Volume of a Cylinder = πr 2 h

where r is the base radius, and h is the height of the cylinder.

Volume of a Cone = 1/3 πr 2 h

where r is the base radius, and h is the height of the cone.

Volume of a Sphere = 4/3 πr 3

Volume of a Hemisphere = 2/3 πr 3

where r is the radius of the hemisphere.

Also, access the following resources for Class 9 Chapter 13 Surface Areas and Volumes, at BYJU’S:

• NCERT Surface Areas and Volumes Class 9 Notes
• Surface Areas and Volumes Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Surface Areas and Volumes
• RD Sharma Solutions Surface Areas and Volumes Class 9

NCERT Solutions Class 9 Maths Chapter 14 Statistics

The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people useful to the State. The chapter teaches about the different presentations of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data using different graphs such as Bar graphs, Histograms, Frequency polygons, etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.

Topics Covered in Class 9 Maths Chapter 14 Statistics:

Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped/grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, and mode of ungrouped data.

Statistics deals with the collection, presentation, and analysis of data, as well as the drawing of meaningful conclusions from the data.

Mean – It is found by adding all the values of the observations and dividing it by the total number of observations. It is denoted by \(\begin{array}{l}\overline{x}\end{array} \) .

So, \(\begin{array}{l}\overline{x}=\frac{\sum_{i=1}^{n}x_{i}}{n}\end{array} \)

For an ungrouped frequency distribution, it is \(\begin{array}{l}\overline{x}=\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\end{array} \)

Median – It is the value of the middle-most observation (s).

If n is an odd number, the median = value of the [(n + 1)/2] th observation

If n is an even number, median = Mean of the values of the (n/2) th and [(n/2) + 1] th observations.

Mode – The mode is the most frequently occurring observation.

Also, access the following resources for Class 9 Chapter 14 Statistics, at BYJU’S:

• NCERT Statistics Class 9 Notes
• Statistics Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Statistics
• RD Sharma Solutions Statistics Class 9

NCERT Solutions Class 9 Maths Chapter 15 Probability

The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions.

Topics Covered in Class 9 Maths Chapter 15 Probability:

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations and from examples used in the chapter on statistics).

The empirical probability P(E) of an event E happening is given by

P (E) = Number of trials in which the event happened/The total number of trials

Also, access the following resources for Class 9 Chapter 15 Probability, at BYJU’S:

• NCERT Probability Class 9 Notes
• Probability Class 9 Important Questions
• NCERT Exemplar Solutions Class 9 Probability
• RD Sharma Solutions Probability Class 9

Benefits of BYJU’S NCERT Maths Solutions for Class 9

• The solutions are given in easy steps so that students can easily understand them.
• Students can access these solutions for free and clear any doubts instantly.
• Exercise-wise PDFs are also provided for all chapters of CBSE 9th Class Maths.
• Detailed explanations also help students to develop problem-solving skills and help them to learn concepts more effectively.
• The questions are solved using the easiest method.
• Diagrams are also given to help students visualise the questions and solutions.

CBSE Class 9 Maths Unit-wise Weightage for 2023-24

Internal assessment class 9.

During the exam preparation, students should first complete the units carrying more weightage and then move on to the lower weightage. This helps students to first cover the important concepts and improves their confidence level to perform well in the annual exam.

The students are advised to analyse all the concepts covered in the Syllabus of Class 9 Maths and prepare a proper preparation strategy. It’s merely impossible to score well in Maths by simply reading and memorising the concepts. Students should always try to understand the concept and logic given in any particular topic. The students are suggested to practise these NCERT Solutions Class 9 materials on a regular basis to develop a strong understanding of basic mathematics concepts.

Along with the NCERT Solutions, we have also provided a brief summary of important formulas and different methods of solving similar problems to help students understand the concepts thoroughly. Keep visiting BYJU’S to get more updated learning materials, and download the BYJU’S app for a better and personalised learning experience with engaging video lessons.

Frequently Asked Questions on NCERT Solutions for Class 9 Maths

How can i learn the class 9 maths chapters in a fast and efficient way, can i get solved answers for the questions from the ncert class 9 maths chapters, should i daily solve the questions from the ncert solutions for class 9 maths , how can i download the ncert solutions for class 9 maths at byju’s, leave a comment cancel reply.

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Gurukul of Excellence

Classes for Physics, Chemistry and Mathematics by IITians

Category: Case Study Questions for Class 9 Maths

Join our Telegram Channel for Free PDF Download

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.

Join our Online Test Series for CBSE, ICSE, JEE, NEET and Other Exams

Editable Study Materials for Your Institute - CBSE, ICSE, State Boards (Maharashtra & Karnataka), JEE, NEET, FOUNDATION, OLYMPIADS, PPTs