class 9 maths chapter 3 case study questions with solutions

• Coordinate Geometry Class 9 Case Study Questions Maths Chapter 3

Last Updated on August 26, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 9 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 9 maths. In this article, you will find case study questions for CBSE Class 9 Maths Chapter 3 Coordinate Geometry. It is a part of Case Study Questions for CBSE Class 9 Maths Series.

Table of Contents

Case Study Questions on Coordinate Geometry

Four friends Aakansha, Prabhat, Puneet and Lalit are sitting in a park at points A, B, C and D respectively. This park has been divided into small squares by drawing equally distanced horizontal and vertical lines. Consider XOX’ and YOY’ as coordinate axes.

On the basis of the above information, solve the following questions:

Q. 1. Find the coordinates of B.

Q. 2. In which quadrant, point A is located?

Q. 3. Find the image of a point A with respect to Y-axis.

Q 4. Find the area of figure.

Ans 1. The perpendicular distance of B from y is 2 in positive direction and perpendicular distance of B from X-axis is 3 in negative direction of Y-axis. Hence, coordinates of B  are (2, -3).

Ans 2. Point A is located in III quadrant.

Ans 3. The coordinate of point A is (-3, 3). The image of a point A (-3, -3) with respect to Y-axis (3, -3).

Ans 4. Now, length of AB = |-3| + 2 = 3 + 2 = 5 Height = perpendicular distance of D from AB = 4 Therefore, Area of parallelogram = length x height = 5 x 4 = 20 sq. units.

Understanding Coordinate Geometry

• Cartesian System: The system used to describe the position of a point in a plane. In this system, two mutually perpendicular lines are required, one is horizontal XOX’ called X-axis and the other is vertical YOY’ called Y-axis.
• Cartesian Plane: The plane in cartesian system is called cartesian plane and the lines in it are called coordinate axes.
• Origin: It is the point of intersection of the axes and is denoted by O. Its coordinates are (0, 0).
• Quadrants: The coordinate-axes divide the plane into four parts called quadrants, numbered I, II, III and IV are in anti-clockwise from OX.

Positive and Negative Directions:

• The positive numbers lie in the directions OX and OY are said to be positive directions of X-axis and Y-axis respectively.
• The negative numbers lie in the directions OX’ and OY’ are said to be negative directions of X-axis and Y-axis respectively.
• Heron’s Formula Class 9 Case Study Questions Maths Chapter 10
• Circles Class 9 Case Study Questions Maths Chapter 9
• Quadrilaterals Class 9 Case Study Questions Maths Chapter 8
• Triangles Class 9 Case Study Questions Maths Chapter 7
• Lines and Angles Class 9 Case Study Questions Maths Chapter 6
• Introduction to Euclid’s Geometry Class 9 Case Study Questions Maths Chapter 5
• Linear Equations in Two Variables Class 9 Case Study Questions Maths Chapter 4

Polynomials Class 9 Case Study Questions Maths Chapter 2

Number systems class 9 case study questions maths chapter 1, topics from which case study questions may be asked.

• The Cartesian plane
• Coordinates of a point
• Names and terms associated with the coordinate plane

In stating the coordinates of a point in cartesian plane, the x-coordinate comes first and then the y-coordinate, We place the coordinates in brackets, i.e., (x, y)

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

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Frequently Asked Questions (FAQs) on Coordinate Geometry Case Study

Q1: what is coordinate geometry.

A1: Coordinate Geometry, also known as analytic geometry, is the study of geometry using a coordinate system. This branch of mathematics uses algebraic equations to represent geometric shapes and analyze their properties, positions, and relationships in a two-dimensional plane.

Q2: What are the main concepts covered in Class 9 Coordinate Geometry?

A2: Class 9 Coordinate Geometry covers topics like the Cartesian coordinate system, plotting points on the coordinate plane, finding the distance between two points, and understanding the section formula.

Q3: What common mistakes should be avoided in Coordinate Geometry?

A3: Common mistakes include mis-plotting points on the coordinate plane, confusing the order of coordinates, incorrect application of formulas, and errors in arithmetic operations. It’s important to double-check your work and understand the underlying concepts to avoid these errors.

Q4: What is the Cartesian coordinate system?

A4: The Cartesian coordinate system is a two-dimensional plane defined by two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). The point where they intersect is called the origin, and each point on the plane is represented by a pair of coordinates (x, y).

Q5: How do you plot a point on the coordinate plane?

A5: To plot a point, first move along the x-axis to the x-coordinate, then move parallel to the y-axis to the y-coordinate. Mark the intersection of these positions on the plane.

Q6: What is the significance of the origin in Coordinate Geometry?

A6: The origin (0, 0) is the central point where the x-axis and y-axis intersect. It serves as the reference point for locating all other points on the plane.

Q8: How do you determine the quadrant of a point?

A8: The coordinate plane is divided into four quadrants: Quadrant I: Both x and y are positive. Quadrant II: x is negative, y is positive. Quadrant III: Both x and y are negative. Quadrant IV: x is positive, y is negative.

Q8: Are there any online resources or tools available for practicing coordinate geometry case study questions?

A8: We provide case study questions for CBSE Class 9 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

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

By QB365 on 08 Sep, 2022

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

QB365 - Question Bank Software

Coordinate geometry case study questions with answer key.

9th Standard CBSE

Final Semester - June 2015

Mathematics

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

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

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

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

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

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

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

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

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

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

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

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

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

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

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

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

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

Coordinate geometry case study questions with answer key answer keys.

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

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

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

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

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

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

Cbse class 9 mathematics case study questions.

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

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

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

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Case studies in class 9 mathematics.

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

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

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

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

myCBSEguide

• Mathematics
• CBSE Class 9 Mathematics...

CBSE Class 9 Mathematics Case Study Questions

Table of Contents

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

Significance of Mathematics in Class 9

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

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

Case studies in Class 9 Mathematics

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

Example of Case study questions in Class 9 Mathematics

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

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

Class 9 Mathematics Case study question 1

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

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

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

Now answer the following questions:

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

Class 9 Mathematics Case study question 3

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

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

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

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

Class 9 Mathematics Curriculum at Glance

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

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

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

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

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

myCBSEguide: Blessing in disguise

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

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17 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

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I am Riddhi Shrivastava… These questions was very good.. That’s it.. ..

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

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

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

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

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

CBSE Case Study Questions for Class  9 Maths

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

Chapter Wise Case Based Questions for Class 9 Maths

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

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

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

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

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

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

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

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

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

Class 9 Maths Curriculum at Glance

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

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

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

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

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

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

What is case-based questions.

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

What are case-based questions in Maths?

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

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

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

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FAQs on CBSE Case Study Questions for Class 9 Maths - Pdf

CBSE Case Study Questions for Class 9 Maths - Pdf

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

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NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

• NCERT Solutions
• Chapter 3 Coordinate Geometry

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

NCERT Solutions for Class 9 Mathematics introduces you to a new realm of concepts, theorems, applications, and problem-solving procedures. Coordinate Geometry class 9 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 maths chapter 3 for this. This answer was produced by Vedantu's best Mathematics teachers. We've also supplied it in PDF format.

Glance on Class 9 Maths Chapter 3 - Coordinate Geometry

The coordinate plane is a flat surface where a horizontal line (x-axis) and a vertical line (y-axis) intersect at a right angle, forming a grid system known as the Cartesian Plane or Coordinate Plane.

The axes divide the plane into four sections called quadrants, which are numbered I, II, III, and IV in an anti-clockwise direction starting from the positive x-axis.

Coordinates identify each point on a plane using an ordered pair of numbers (x, y). The x-coordinate, or abscissa, indicates the horizontal distance from the y-axis, while the y-coordinate, or ordinate, shows the vertical distance from the x-axis.

To plot a point's coordinates (x, y) on a graph, start at the origin (where the axes intersect), move x units to the right if x is positive or to the left if x is negative, and then move y units up if y is positive or down if y is negative.

The signs of the coordinates tell you in which quadrant the point lies.

Both positive (x, y) - Quadrant I

Negative x, positive y - Quadrant II

Both negative (x, y) - Quadrant III

Positive x, negative y - Quadrant IV

This article contains chapter notes, important questions, exemplar solutions, exercises, and video links for Chapter 3 - Coordinate Geometry, which you can download as PDFs.

There are two exercises (4 fully solved questions) in class 9th maths chapter 3 Coordinate Geometry.

Access Exercise wise NCERT Solutions for Chapter 3 Maths Class 9

Exercises Under NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

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.

Access NCERT Solutions for Class 9 Maths 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 \[(-3,0)\].

Overview of Deleted Syllabus for CBSE Class 9 Maths Coordinate Geometry

Class 9 Maths Chapter 3: Exercises Breakdown

NCERT Solutions for Coordinate Geometry class 9  provides 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. In previous years exams, around 2-3 questions have been asked from this chapter. NCERT Solutions for Ch 3 maths class 9 delves into the concept of the distance formula, enabling Students to calculate the distance between two points on the coordinate plane. 

Other Study Material for CBSE Class 9 Maths Chapter 3

Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

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.

8. What is the Cartesian coordinate system in class 9 chapter 3 maths?

In class 9 chapter 3 maths the cartesian coordinate system uses two perpendicular lines, the x-axis and the y-axis, to define points on a plane. The intersection of these axes is called the origin. Each point is represented by an ordered pair (x, y), indicating its distance from the axes.

9. How do you find the distance between two points in coordinate geometry?

In class 9 maths chapter 3 solutions, to find the distance between two points, imagine a straight line connecting them. Measure the length of this line, considering their x and y coordinates. This process involves a specific calculation, often visualized as forming a right triangle.

10. What is the section formula in coordinate geometry in class 9th maths chapter 3?

In coordinate geometry class 9 the section formula helps to find the coordinates of a point that divides a line segment into a given ratio. It involves using the coordinates of the endpoints and the specified ratio. This is useful in locating a precise point along the segment.

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9.

CBSE Class 9 Maths 30 Most Important Case Study Questions with Answers

Cbse class 9 maths 30 most important case study questions with answers download here free in pdf format..

CBSE Class 9 Maths exam 2023 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 webpage 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. Candidates can easily download these questions in PDF format and refer to them for exam preparation 2023.

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• Punjab Board Class 12 Maths Practice Paper with Solution 2023 February 28, 2023

NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

Extra Questions for Class 9 Maths with Solutions Chapter Wise

August 18, 2019 by Veerendra

Extra Questions for Class 9 maths will help you with practice. We have selectively graded these extra questions for more practice. We request Students to solve these questions without going through solutions. If you face any difficulty in solving these Extra Questions, Please refer solutions.

Extra Questions for Class 9 Maths with Solutions

Here is the list of Extra Questions for Class 9 Maths with Answers based on latest NCERT syllabus prescribed by CBSE.

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

NCERT Solutions for Class 9 Maths

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Class 9 Maths Case Study Questions Chapter 4 Linear Equations in two variables

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Case study Questions in Class 9 Mathematics Chapter 4  are very important to solve for your exam. Class 9 Maths Chapter 4 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 4 Linear Equations in two variables

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.

Linear Equations in two variables Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 4 Linear Equations in two variables

Case Study/Passage-Based Questions

Case Study 1: Deepak bought 3 notebooks and 2 pens for Rs. 80. His friend Ram said that the price of each notebook could be Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs.5 and each pen could be Rs. 2.50. Another friend Ajay felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of each notebook would also be Rs.16

Lohith also bought the same types of notebooks and pens as Aditya. He paid 110 for 4 notebooks and 3 pens. Later, Deepak guesses the cost of one pen is Rs. 10 and Lohith guess the cost of one notebook is Rs. 30.

(i) Form the pair of linear equations in two variables from this situation by taking the cost of one notebook as Rs. x and the cost of one pen as Rs. y. (a) 3x + 2y = 80 and 4x + 3y = 110 (b) 2x + 3y = 80 and 3x + 4y = 110 (c) x + y = 80 and x + y = 110 (d) 3x + 2y = 110 and 4x + 3y = 80

Answer: (a) 3x + 2y = 80 and 4x + 3y = 110

(ii) Which is the solution satisfying both the equations formed in (i)? (a) x = 10, y = 20 (b) x = 20, y = 10 (c) x = 15, y = 15 (d) none of these

Answer: (b) x = 20, y = 10

(iii) Find the cost of one pen? (a) Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15

Answer: (b) Rs. 10

(iv) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens. (a) Rs. 400 (b) Rs. 350 (c) Rs. 450 (d) Rs. 420

Answer: (d) Rs. 420

(v) Find whose estimation is correct in the given statement. (a) Deepak (b) Lohith (c) Ram (d) Ajay

Answer: (a) Deepak

Case Study 2: In the below given layout, the design and measurements have been made such that area of two bedrooms and Kitchen together is 95 sq. m.

(i) The area of two bedrooms and kitchen are respectively equal to (a) 5x, 5y (b) 10x, 5y (c) 5x, 10y (c) x, y

(ii) Find the length of the outer boundary of the layout. (a) 27 m (b) 15 m (c) 50 m (d) 54 m

(iii) The pair of linear equations in two variables formed from the statements are (a) x + y = 13, x + y = 9 (b) 2x + y = 13, x + y = 9 (c) x + y = 13, 2x + y = 9 (d) None of the above

(iv) Which is the solution satisfying both the equations formed in (iii)? (a) x = 7, y = 6 (b) x = 8, y = 5 (c) x = 6, y = 7 (d) x = 5, y = 8

(v) Find the area of each bedroom. (a) 30 sq. m (b) 35 sq. m (c) 65 sq. m (d) 42 sq. m

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 4 Linear Equations in two variables with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Linear Equations in two variables Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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• NCERT Exemplar
• Maths Exemplar Class 9
• Coordinate Geometry

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

Ncert exemplar solutions class 9 maths chapter 3 – free pdf download.

NCERT Exemplar Solutions Class 9 Maths Chapter 3 Coordinate Geometry are provided here in PDF for the students to access easily and prepare well for exams. They can make use of these exemplar solutions as a reference tool while practising the NCERT textbook exercise questions, as well. The exemplar problems with solutions are designed by the subject experts at BYJU’S in accordance with the CBSE Syllabus for 9th Standard , which covers the following topics of the chapter Coordinate Geometry:

• Cartesian system and coordinates of the points
• Plotting a point in XY plane, if its coordinates are given
• Horizontal axis and the vertical axis
• The intersection point of the axes, etc.

Coordinate Geometry is one of the most important chapters of CBSE Class 9 Maths. In this chapter, students will learn about the Cartesian System and plotting a point in the plane if its coordinates are given. Solve NCERT Exemplar for Class 9 Maths Chapter 3 Coordinate Geometry to understand the fundamentals in a better way. To promote easy learning and help students understand the concepts of Coordinate Geometry, free NCERT Exemplars are provided below, which can be downloaded in the form of a PDF.

Download the PDF of NCERT Exemplar Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry

Access Answers to NCERT Exemplar Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

Exercise 3.1 Page No: 25

Write the correct answer in each of the following:

1. Point (–3, 5) lies in the

A. first quadrant

B. second quadrant

C. third quadrant D. fourth quadrant

B. Second Quadrant

Explanation:

(-3,5) is of form (-x,y).

In the point (-3, 5), the abscissa is negative, and the ordinate is positive. So, it lies in the second quadrant.

Hence, (B) is the correct option.

2. Signs of the abscissa and ordinate of a point in the second quadrant are, respectively

A. +, + B. –, – C. –, + D. +, –

Signs of the abscissa and ordinate of a point in the second quadrant is –, +.

Hence, (C) is the correct option.

3. Point (0, –7) lies

A. on the x-axis B. in the second quadrant C. on the y-axis D. in the fourth quadrant

C. on the y-axis

Since the abscissa is 0, Point (0, –7) lies on the y-axis.

4. Point (– 10, 0) lies

A. on the negative direction of the x-axis B. on the negative direction of the y-axis C. in the third quadrant D. in the fourth quadrant

A. on the negative direction of the x-axis

Point (– 10, 0) lies on the negative direction of the x-axis.

Hence, (A) is the correct option.

5. Abscissa of all the points on the x-axis is

A. 0 B. 1 C. 2 D. any number

D. any number

Abscissa of all the points on the x-axis can be any number.

Hence, (D) is the correct option.

6. Ordinate of all points on the x-axis is

A. 0 B. 1 C. – 1 D. any number

The ordinate of all the points on the x-axis is 0.

7. The point at which the two coordinate axes meet is called the

A. abscissa B. ordinate C. origin D. quadrant

Explanation :

The points at which the two coordinate axes meet is called the origin.

8. A point both of whose coordinates are negative will lie in

A. I quadrant B. II quadrant C. III quadrant D. IV quadrant

C. III quadrant

A point whose both of the coordinates are negative will lie in the III quadrant.

9. Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4)

A. lie in II quadrant B. lie in III quadrant C. lie in IV quadrant D. do not lie in the same quadrant

D. do not lie in the same quadrant

Points (1, – 1), (2, – 2), (4, – 5) lie in IV quadrant and (– 3, – 4) lie in III quadrant.

10. If y coordinate of a point is zero, then this point always lies

A. in I quadrant

B. in II quadrant

C. on x-axis

D. on y-axis

We know that if the y-coordinate of a point, i.e., the ordinate is zero, then this point always lies on

11. The points (–5, 2) and (2, – 5) lie in the

A. same quadrant B. II and III quadrants, respectively C. II and IV quadrants, respectively D. IV and II quadrants, respectively

(-5,2) is of the form (-x,y) so it lies in the II quadrant.

(2,-5) is of the form (x,-y) so it lies in IV quadrant.

(C) II and IV quadrants, respectively

12. If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies in the negative direction of the x-axis, then point P has

A. x – coordinate = – 5 B. y – coordinate = 5 only C. y – coordinate = – 5 only D. y – coordinate = 5 or –5

D. y – coordinate = 5 or –5

Perpendicular distance from x-axis = Ordinate = 5

The negative direction of the x-axis doesn’t decide the sign of the ordinate.

(D) y-coordinate = 5 or -5.

Exercise 3.2 Page No: 28

1. Write whether the following statements are True or False? Justify your answer.

(i) Point (3, 0) lies in the first quadrant.

(ii) Points (1, –1) and (–1, 1) lie in the same quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa is 1 are – ½, 1.

(iv) A point lies on the y -axis at a distance of 2 units from the x -axis. Its coordinates are (2, 0).

(v) (–1, 7) is a point in the II quadrant.

Justification:

The ordinate of the point (3, 0) is zero.

Hence, the point lies on the x-axis

(1, -1) lies in IV quadrant

(-1, 1) lies in II quadrant.

(iii) The coordinates of a point whose ordinate is – ½ and abscissa is 1 are – ½ , 1.

The coordinates of a point whose ordinate is – ½ and abscissa is 1 is (1, -1/2).

A point lies on the y -axis at a distance of 2 units from the x -axis. Its coordinates are (0, 2).

(–1, 7) is a point in the II quadrant.

Exercise 3.3 Page No: 29

1. Write the coordinates of each of the points P, Q, R, S, T and O from Fig. 3.5.

The coordinates of the points P, Q, R, S, T and O are as follows:

Q = (-3, 0)

R = (-2, -3)

T = (4, -2)

2. Plot the following points and write the name of the figure obtained by joining them in order: P(– 3, 2), Q (– 7, – 3), R (6, – 3), S (2, 2)

The figure obtained is a Trapezium.

3. Plot the points (x, y) given by the following table:

4. Plot the following points and check whether they are collinear or not:

(i) (1, 3), (– 1, – 1), (– 2, – 3)

(ii) (1, 1), (2, – 3), (– 1, – 2)

(iii) (0, 0), (2, 2), (5, 5)

The points (1, 3), (– 1, – 1), (– 2, – 3) lie in a straight line,

Hence, the points are collinear.

The points (1, 1), (2, – 3), (– 1, – 2) lie in a straight line,

Hence, the points are not collinear.

The points (0, 0), (2, 2), (5, 5) lie in a straight line,

5. Without plotting the points, indicate the quadrant in which they will lie, if

(i) ordinate is 5 and abscissa is – 3 (ii) abscissa is – 5 and ordinate is – 3 (iii) abscissa is – 5 and ordinate is 3 (iv) ordinate is 5 and abscissa is 3

(i) The point is (-3,5).

Hence, the point lies in the II quadrant.

(ii) The point is (-5,-3).

Hence, the point lies in the III quadrant.

(iii) The point is (-5,3).

(iv) The point is (3,5).

Hence, the point lies in the I quadrant.

6. In Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units.

(i) What are the coordinates of the points P, R and Q? (ii) What is the difference between the abscissa of points L and M?

(i) The coordinates are:

(ii) Since, all the points on the line have the same abscissa = 3.

The difference in abscissa of L and M = 0.

Exercise 3.4 Page No: 32

1. Points A (5, 3), B (–2, 3) and D (5, –4) are three vertices of a square ABCD. Plot these points on a graph paper and hence find the coordinates of the vertex C.

From the graph, we get that,

The coordinates of C = (-2, -4).

2. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units, respectively, with one vertex at the origin, the longer side lies on the x-axis, and one of the vertices lies in the third quadrant.

The coordinates of the points of the rectangle are (0, 0), (-5, 0), (-5, -3) and (0, -3).

BYJU’S also provides other learning resources, such as Exemplar books , NCERT solutions, notes and question papers, to make students of Class 9 prepare well for exams. Students are advised to solve sample papers and previous years’ question papers as well to get familiar with the type of questions asked from Maths Chapter 3 and the marks weightage for them.

Students of Class 9 can download BYJU’S – The Learning App to get personalised videos explaining different types of Maths topics, such as Coordinate Geometry and other chapter topics, as well as to experience a new way of learning to understand the concepts easily.

Frequently Asked Questions on NCERT Exemplar Solutions for Class 9 Maths Chapter 3

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• Study Material /

100+ Maths Questions for Class 9 with Answers for Competitive Exams: Download Free PDF

• Updated on  
• Sep 20, 2024

This blog post presents a collection of over 100 carefully curated math questions for Class 9 for competitive exams. These questions cover a wide range of topics, from basic arithmetic to more advanced concepts like algebra, geometry, and trigonometry. By practising these questions, you can enhance your problem-solving skills, improve your understanding of mathematical concepts, and gain confidence in your ability to tackle challenging problems. Also, you can download the Maths questions for Class 9 with answers PDF here. Keep reading!!

Table of Contents

• 1.1 Number Systems
• 1.2 Polynomials
• 1.3 Coordinate Geometry
• 1.4 Lines and Angles
• 1.5 Triangles
• 1.6 Quadratic Equations
• 1.7 Area of Parallelogram and Triangle
• 1.8 Mensuration
• 1.9 Statistics
• 1.10 Probability
• 2 Maths Questions for Class 9: PDF Link Available
• 3 Importance of Maths Questions for Class 9 Students
• 4 Tips for Preparing Maths Questions for Class 9

Sample Maths Questions for Class 9 with Answers

Solve Maths Questions for Class 9 of number systems, polynomial equations, coordinate geometry, lines and angles, triangles, quadratic equations, menstruation, statistics, and probability. 

Number Systems

1. Simplify: 3√27​×3√8​

Solution: 3×2=6

2. Rationalize the denominator: 1/(√5​−2)​

Solution: √5+2 / (√5​−2)(√5​+2) = √5−4/5​+2​ = √5​+2

Polynomials

3. Find the product: (x+3)(x−2)

Solution: x 2 −2x+3x−6 = x 2 +x−6

4. Factorize: x 2 −9

Solution: (x+3)(x−3)

5. Divide: (x 3 −3x 2 +2x+5)÷(x−2)

Solution: Using synthetic division, we get a quotient of x 2 −x+1 and a remainder of 7.

Coordinate Geometry

6. Find the distance between points A(2, 3) and B(5, 7).

Solution: d = √(5−2) 2 +(7−3) 2 ​ = √9+16 ​= 5

7. Find the midpoint of the line segment joining points A(3, 5) and B(7, 9).

Solution: M=((3+7)/2​,(5+9)/2​) = (5,7)

Lines and Angles

8. If two lines intersect, prove that the vertically opposite angles are equal.

Solution: This is a standard geometry proof that involves using the properties of linear pairs and adjacent angles.

9. If the angles in a triangle are in the ratio 2:3:7, find the angles.

Solution: Let the angles be 2x, 3x, and 7x. Since the sum of angles in a triangle is 180°, we get 12x = 180, so x = 15. Therefore, the angles are 30°, 45°, and 105°.

10. In a right-angled triangle, the hypotenuse is 13 cm and one of the legs is 5 cm. Find the length of the other leg.

Solution: Using the Pythagorean theorem, we get a 2 +5 2 =132, so a 2 =144 and a = 12 cm.

11. Prove that the angles opposite to equal sides of an isosceles triangle are equal.

Solution: This is another standard geometry proof that involves drawing a perpendicular bisector of the base.

Quadratic Equations

13. Solve the quadratic equation: x 2 −5x+6=0

Solution: Factoring, we get (x−2)(x−3)=0, so x = 2 or x = 3.

14. Find the discriminant of the quadratic equation: 2x 2 −3x+1=0

Solution: The discriminant is b 2 −4ac=(−3) 2 −4(2)(1)=1.

Area of Parallelogram and Triangle

15. Find the area of a parallelogram with base 12 cm and height 8 cm.

Solution: Area = base × height = 12 cm × 8 cm = 96 cm²

16. The area of a triangle is 24 cm². If the base is 8 cm, find the height.

Solution: Height = (2 × Area) / base = (2 × 24 cm²) / 8 cm = 6 cm

Mensuration

17. Find the volume of a cube with a side 5 cm.

Solution: Volume = side³ = 5³ cm³ = 125 cm³

18. Find the total surface area of a sphere with a radius 7 cm.

Solution: Total surface area = 4πr² = 4 × π × 7² cm² = 616π cm²

19. Find the mean, median, and mode of the data: 2, 4, 5, 3, 2, 5, 4, 6.

Solution: Mean = (2+4+5+3+2+5+4+6)/8 = 3.75, Median = 4, Mode = 4 and 5.

20. Draw a histogram for the following frequency distribution:

| Class Interval | Frequency | |—|—| | 0-10 | 5 | | 10-20 | 8 | | 20-30 | 12 | | 30-40 | 6 |

Solution: A histogram can be drawn using the given data, with the x-axis representing the class intervals and the y-axis representing the frequency.

Probability

21. A coin is tossed twice. Find the probability of getting two heads.

Solution: The total possible outcomes are HH, HT, TH, and TT. The probability of getting two heads is 1/4.

Maths Questions for Class 9: PDF Link Available

Looking for a fun way to master Maths questions for Class 9? This Maths Questions PDF is perfect for 9th graders! It includes a wide range of interesting and challenging questions on topics like algebra, geometry, trigonometry, and more. Download it today to sharpen your math skills and make learning both enjoyable and rewarding. Click the link to download and start your journey toward becoming a math expert!

Importance of Maths Questions for Class 9 Students

The importance of Maths questions for Class 9 students cannot be overstated! Here’s why they are essential:

• Builds Strong Foundation : Class 9 is an important year as it sets the base for higher-level math in Class 10 and beyond. Practicing maths questions helps strengthen this foundation.
• Improves Problem-Solving Skills : Maths questions encourage students to think critically and find solutions to complex problems. This improves their problem-solving skills, which is useful in both academics and daily life.
• Boosts Confidence for Exams : Regular practice with a variety of questions helps students feel more prepared and confident when facing their exams.
• Helps with Logical Thinking : Maths is all about logic and reasoning. By solving different types of questions, students sharpen their ability to think logically and make better decisions.
• Prepares for Competitive Exams : For students aiming for competitive exams like Olympiads or entrance tests, solving maths questions in Class 9 is an excellent practice.

Tips for Preparing Maths Questions for Class 9

Here are some quick tips for preparing Maths questions for Class 9 students:

• Know the Syllabus : Make sure the questions cover important topics like algebra, geometry, and statistics.
• Mix Topics : Include questions from different chapters to give students complete practice.
• Start Easy : Begin with simple questions, then gradually increase difficulty.
• Use Word Problems : Add real-life problems to help students apply what they’ve learned.
• Vary Question Types : Use multiple-choice, short answer, and long problems for variety.
• Practice Formulas : Include questions that help students remember and use important formulas.
• Provide Solutions : Give clear, step-by-step answers to help students understand.
• Focus on Mistakes : Include questions that correct common errors.
• Use Old Papers : Look at past exam papers to create similar questions.
• Add Tough Questions : Challenge students with a few harder problems for extra practice.

Class 9 maths can be challenging, but with consistent practice and a good understanding of the fundamentals, it can be manageable. Some topics like geometry and algebra can be particularly tricky, but with focused effort, you can overcome these hurdles.

The most important thing in Class 9 math is to build a strong foundation in fundamental concepts. This includes understanding number systems, polynomials, coordinate geometry, linear equations, and basic geometry. A solid grasp of these topics will be crucial for your future studies in mathematics.

Class 9 maths covers topics like number systems, algebra, geometry, coordinate geometry, mensuration, and statistics. These topics build on the foundation of basic arithmetic and introduce more complex concepts.

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This was all about the “ Maths Questions for Class 9 ”. For more such informative blogs, check out our Study Material Section , or you can learn more about us by visiting our  Indian exams page.

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Mohit Rajak, a soul entwined with the rhythm of words, finds solace in crafting verses that dance between the lines of poetry. With a pen as his wand, he weaves intricate tales and musings, breathing life into the blank canvas of pages. Through the art of blogging, Mohit embraces the world, sharing his thoughts, emotions, and unique perspective with those who venture into the realm of his written expressions. Each word, a brushstroke painting the canvas of his literary journey.

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CBSE Case Study Questions Class 9 Maths Chapter 2 Polynomials PDF Download

CBSE Case Study Questions Class 9 Maths Chapter 2 Polynomials PDF Download  are very important to solve for your exam. Class 9 Maths Chapter 2 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Case Study Questions Class 9 Maths Chapter 2 Polynomials

• Checkout: Class 9 Science Case Study Questions
• Checkout: Class 9 Maths Case Study Questions

Polynomials Case Study Questions With Answers

Case study questions class 9 maths chapter 2.

Case Study/Passage-Based Questions

Case Study 1. Ankur and Ranjan start a new business together. The amount invested by both partners together is given by the polynomial p(x) = 4x 2 + 12x + 5, which is the product of their individual shares.

Coefficient of x 2 in the given polynomial is (a) 2 (b) 3 (c) 4 (d) 12

Answer: (c) 4

Total amount invested by both, if x = 1000 is (a) 301506 (b)370561 (c) 4012005 (d)490621

Answer: (c) 4012005

The shares of Ankur and Ranjan invested individually are (a) (2x + 1),(2x + 5)(b) (2x + 3),(x + 1) (c) (x + 1),(x + 3) (d) None of these

Answer: (a) (2x + 1),(2x + 5)

Name the polynomial of amounts invested by each partner. (a) Cubic (b) Quadratic (c) Linear (d) None of these

Answer: (c) Linear

Find the value of x, if the total amount invested is equal to 0. (a) –1/2 (b) –5/2 (c) Both (a) and (b) (d) None of these

Answer: (c) Both (a) and (b)

Case Study 2. One day, the principal of a particular school visited the classroom. The class teacher was teaching the concept of a polynomial to students. He was very much impressed by her way of teaching. To check, whether the students also understand the concept taught by her or not, he asked various questions to students. Some of them are given below. Answer them

Which one of the following is not a polynomial? (a) 4x 2 + 2x – 1 (b) y+3/y (c) x 3 – 1 (d) y 2 + 5y + 1

Answer: (b) y+3/y

The polynomial of the type ax 2 + bx + c, a = 0 is called (a) Linear polynomial (b) Quadratic polynomial (c) Cubic polynomial (d) Biquadratic polynomial

Answer: (a) Linear polynomial

The value of k, if (x – 1) is a factor of 4x 3 + 3x 2 – 4x + k, is (a) 1 (b) –2 (c) –3 (d) 3

Answer: (c) –3

If x + 2 is the factor of x 3 – 2ax 2 + 16, then value of a is (a) –7 (b) 1 (c) –1 (d) 7

Answer: (b) 1

The number of zeroes of the polynomial x 2 + 4x + 2 is (a) 1 (b) 2 (c) 3 (d) 4

Answer: (b) 2

Case Study 3. Amit and Rahul are friends who love collecting stamps. They decide to start a stamp collection club and contribute funds to purchase new stamps. They both invest a certain amount of money in the club. Let’s represent Amit’s investment by the polynomial A(x) = 3x^2 + 2x + 1 and Rahul’s investment by the polynomial R(x) = 2x^2 – 5x + 3. The sum of their investments is represented by the polynomial S(x), which is the sum of A(x) and R(x).

Q1. What is the coefficient of x^2 in Amit’s investment polynomial A(x)? (a) 3 (b) 2 (c) 1 (d) 0

Answer: (a) 3

Q2. What is the constant term in Rahul’s investment polynomial R(x)? (a) 2 (b) -5 (c) 3 (d) 0

Answer: (c) 6

Q3. What is the degree of the polynomial S(x), representing the sum of their investments? (a) 4 (b) 3 (c) 2 (d) 1

Answer: (c) 2

Q4. What is the coefficient of x in the polynomial S(x)? (a) 7 (b) -3 (c) 0 (d) 5

Answer: (b) -3

Q5. What is the sum of their investments, represented by the polynomial S(x)? (a) 5x^2 + 7x + 4 (b) 5x^2 – 3x + 4 (c) 5x^2 – 3x + 5 (d) 5x^2 + 7x + 5

Answer: (b) 5x^2 – 3x + 4

Case Study 4. A school is organizing a fundraising event to support a local charity. The students are divided into three groups: Group A, Group B, and Group C. Each group is responsible for collecting donations from different areas of the town.

Group A consists of 30 students and each student is expected to collect ‘x’ amount of money. The polynomial representing the total amount collected by Group A is given as A(x) = 2x^2 + 5x + 10.

Group B consists of 20 students and each student is expected to collect ‘y’ amount of money. The polynomial representing the total amount collected by Group B is given as B(y) = 3y^2 – 4y + 7.

Group C consists of 40 students and each student is expected to collect ‘z’ amount of money. The polynomial representing the total amount collected by Group C is given as C(z) = 4z^2 + 3z – 2.

Q1. What is the coefficient of x in the polynomial A(x)? (a) 2 (b) 5 (c) 10 (d) 0

Answer: (b) 5

Q2. What is the degree of the polynomial B(y)? (a) 2 (b) 3 (c) 4 (d) 1

Answer: (b) 3

Q3. What is the constant term in the polynomial C(z)? (a) 4 (b) 3 (c) -2 (d) 0

Answer: (c) -2

Q4. What is the sum of the coefficients of the polynomial A(x)? (a) 2 (b) 5 (c) 10 (d) 17

Answer: (c) 10

Q5. What is the total number of students in all three groups combined? (a) 30 (b) 20 (c) 40 (d) 90

Answer: (c) 40

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 2 Polynomials with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Polynomials Case Study and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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