case study questions maths for class 9

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CBSE Class 9 Mathematics Case Study Questions

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Significance of Mathematics in Class 9

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

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

Case studies in Class 9 Mathematics

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

Example of Case study questions in Class 9 Mathematics

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

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

Class 9 Mathematics Case study question 1

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

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

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

Now answer the following questions:

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

Class 9 Mathematics Case study question 3

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

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

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

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

Class 9 Mathematics Curriculum at Glance

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

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

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

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

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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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16 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.

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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 Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF 10 February, 2023, 6:20 pm
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CBSE Case Study Questions for Class 9 Maths - Pdf PDF Download

CBSE Case Study Questions for Class  9 Maths

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

Chapter Wise Case Based Questions for Class 9 Maths

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

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

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

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

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

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

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

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

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

Class 9 Maths Curriculum at Glance

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

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

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

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

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

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

What is case-based questions.

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

What are case-based questions in Maths?

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

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

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

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

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

Cbse class 9 mathematics case study questions.

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

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

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

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Case studies in class 9 mathematics.

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

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

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

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

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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 Case Study Questions for Class 9 Maths Surface Areas and Volumes Free PDF

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

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

CBSE Case Study Questions for Class 9 Maths Surface Areas and Volumes PDF

Checkout our case study questions for other chapters.

• Chapter 11 Constructions Case Study Questions
• Chapter 12 Heron’s Formula Case Study Questions
• Chapter 14 Statistics Case Study Questions
• Chapter 15 Probability Case Study Questions

How should I study for my upcoming exams?

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

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

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

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

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

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

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

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NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

NCERT Solutions for Maths Chapter 10 Class 9 Heron’s Formula - FREE PDF Download

NCERT Solutions for heron's formula class 9 maths ch 10 Heron’s Formula curated by our subject experts to facilitate a practical and smooth understanding of the concepts related to Heron's Formula. These NCERT Solutions can be accessed anytime and anywhere, at your convenience, to understand the concepts in a better way.  These solutions to each exercise question in the PDF are explained using a clear step-by-step method. It acts as an essential tool for you to prepare the chapter quickly and efficiently during exams. You can download and practice these NCERT Solutions for herons formula Class 9 Maths Chapter 10 to thoroughly understand the concepts covered in the chapter.

Glance on Maths Chapter 10 Class 9 - Heron's Formula

This article deals with Heron's Formula, which is a method to calculate the area of a triangle when the lengths of all three sides are known.

The questions cover topics such as finding the area of a triangle when the sides are given, finding the missing side when the area and two sides are given, and finding the height of a triangle when the area and the base are given.

Chapter 10 Maths Class 9 recalls how to calculate the perimeter of various figures and shapes.

This article contains chapter notes, exercises, explanation videos, links, and important questions for Chapter 10 - Heron's Formula where you can download a FREE PDF.

There is one exercise (6 fully solved questions) in class 9th maths chapter 10 Heron's Formula.

Access Exercise Wise NCERT Solutions for Chapter 10 Maths Class 9

Exercises Under NCERT Solutions for Class 9 Maths Chapter 10 Heron's Formula

Exercise 10.1: This exercise consists of six questions that are based on the concept of Heron's Formula. The questions cover topics such as finding the area of a triangle when the sides are given, finding the missing side when the area and two sides are given, and finding the height of a triangle when the area and the base are given. The exercise also includes word problems that require the application of Heron's Formula to find the area of triangles.

Access NCERT Solutions Maths Chapter 10 - Heron’s formula

Exercise 10.1 .

1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side $'a'$. Find the area of the signal board, using Heron’s formula. If its perimeter is $180\ \text{cm}$, what will be the area of the signal board?

Length of the side of traffic signal board $=a$ 

Perimeter of traffic signal board which is an equilateral triangle $=3\times a$

We know that,

$2s=$ Perimeter of the triangle, 

So, $2s=3a$

$\Rightarrow s=\dfrac{3}{2}a$

 Area of triangle can be evaluated by Heron’s formula:

$A=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$

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

\[s=\dfrac{a+b+c}{2}\]

Substituting $s=\dfrac{3}{2}a$ in Heron’s formula, we get:

Area of given triangle:

 $A=\sqrt{\dfrac{3}{2}a\left( \dfrac{3}{2}a-a \right)\left( \dfrac{3}{2}a-a \right)\left( \dfrac{3}{2}a-a \right)}$ 

$A=\dfrac{\sqrt{3}}{2}{{a}^{2}}\ \ ......\text{(1)}$

Perimeter of traffic signal board:

$P=180\ \text{cm}$

Hence, side of traffic signal board

$a=\left( \dfrac{180}{3} \right)$

$a=60\ \ ......\text{(2)}$

Substituting Equation (2) in Equation (1), we get:

Area of traffic signal board is $A=\dfrac{\sqrt{3}}{2}{{\left( 60\,cm \right)}^{2}}$

$\Rightarrow A=\left( \dfrac{3600}{4}\sqrt{3} \right)\,c{{m}^{2}}$

$\Rightarrow A=900\sqrt{3}\,c{{m}^{2}}$

Hence, the area of the signal board is $900\sqrt{3}\text{ c}{{\text{m}}^{2}}$.

2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122m,\,22m,$ and $120m$. The advertisements yield on earning of Rs. $5000\,per\,{{m}^{2}}$ per year. A company hired one of its walls for $3$ months. How much rent did it pay?

Ans: The length of the sides of the triangle are (say $a$, $b$ and $c$)

$a=122\ \text{m}$

$b=22\ \text{m}$

$c=120\ \text{m}$

Perimeter of triangle = sum of the length of all sides

Perimeter of triangle is:

$P=122+22+120$

$P=264\ \text{m}$

$2s=264\ \text{m}$

$s=132\ \text{m}$

Area of triangle can be evaluated by Heron’s formula:

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

So, in this question,

$s=\dfrac{122+22+140}{2}$

Substituting values of $s$ $a$, $b$, $c$ in Heron’s formula, we get:

Area of given triangle $=\left[ \sqrt{132\left( 132-122 \right)\left( 132-22 \right)\left( 132-120 \right)} \right]{{m}^{2}}$

$=\left[ \sqrt{132\left( 10 \right)\left( 110 \right)\left( 12 \right)} \right]\,{{m}^{2}}=1320\,{{m}^{2}}$ 

It is given that:

Rent of $1{{m}^{2}}$ area per year is:

$R=Rs.\text{ 5000/}{{\text{m}}^{2}}$ 

Rent of $1{{m}^{2}}$ area per month will be:

$R=Rs.\ \dfrac{5000}{12}/{{m}^{2}}$

Rent of $1320{{m}^{2}}$ area for $3$ months:

$R=\left( \dfrac{5000}{12}\times 3\times 1320 \right)/{{m}^{2}}$

$\Rightarrow R=Rs.\ 1650000$

Therefore, the total cost rent that company must pay is Rs. $1650000$.

3. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

Ans: It is given that the sides of the wall are 15 m, 11 m and 6 m.

So, the semi perimeter of triangular wall (s) = (15+11+6)/2 m = 16 m

Using Heron’s formula,

$A=\sqrt{16(16 - 15)(16 - 11)(16 - 6)}$

$A=\sqrt800 m^2$

$A=20\sqrt2 m^2$

4. Find the area of a triangle two sides of which are $18\mathbf{cm}$ and $10\mathbf{cm}$ and the perimeter is $42cm$.

Ans: Let the length of the third side of the triangle be $x$. 

Perimeter of the given triangle:

Let the sides of the triangle be $a$, $b$ and $c$.

Perimeter of the triangle = sum of all sides

$18+10+x=42$

$\Rightarrow 28+x=42$

$\Rightarrow x=14$

$\Rightarrow s=\dfrac{18+10+14}{2}$

$\Rightarrow s=21cm$

Substituting values of  $s$ $a$, $b$, $c$ in Heron’s formula, we get:

$A=\left[ \sqrt{21\left( 21-18 \right)\left( 21-10 \right)\left( 21-14 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{21\left( 3 \right)\left( 11 \right)\left( 7 \right)} \right]$

$\Rightarrow A=21\sqrt{11}\text{ }c{{m}^{2}}$

Hence, the area of the given triangle is $21\sqrt{11}\text{ }c{{m}^{2}}$.

5. Sides of a triangle are in the ratio of $12:17:25$ and its perimeter is $540cm$. Find its area.

Ans: Let the common ratio between the sides of the given triangle be $x$. 

Therefore, the side of the triangle will be $12x$, $17x$, and $25x$.

It is given that,

Perimeter of this triangle $=540cm$

Perimeter = sum of the length of all sides

$12x+17x+25x=540$

$\Rightarrow 54x=540$

$\Rightarrow x=10$

Sides of the triangle will be:

\[12\times 10=120cm\]

$17\times 10=170cm$

$25\times 10=250cm$

$\Rightarrow s=\dfrac{120+170+250}{2}$

$\Rightarrow s=270cm$

$A=\left[ \sqrt{270\left( 270-120 \right)\left( 270-170 \right)\left( 270-250 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{270\left( 150 \right)\left( 100 \right)\left( 20 \right)} \right]$

$\Rightarrow A=9000c{{m}^{2}}$

Therefore, the area of this triangle is $9000\,c{{m}^{2}}.$

6. An isosceles triangle has perimeter $30cm$ and each of the equal sides is $12cm$. Find the area of the triangle.

Ans: Let the third side of this triangle be $x$.

Measure of equal sides is $12cm$ as the given triangle is an isosceles triangle.

Perimeter of triangle, $P=30cm$

Perimeter of triangle = Sum of the sides 

$12+12+x=30$

$\Rightarrow x=6cm$

$\Rightarrow s=\dfrac{12+12+6}{2}$

$\Rightarrow s=15cm$

Substituting values of $s$ $a$, $b$, $c$ in Heron’s formula we get:$A=\left[ \sqrt{15\left( 15-12 \right)\left( 15-12 \right)\left( 15-6 \right)} \right]$

$\Rightarrow A=\left[ \sqrt{15\left( 3 \right)\left( 3 \right)\left( 9 \right)} \right]$

$\Rightarrow A=9\sqrt{15}c{{m}^{2}}$

Hence, the area of the given isosceles triangle is $9\sqrt{15}c{{m}^{2}}$.

Overview of Deleted Syllabus for CBSE Class 9 Maths Heron's Formula

Class 9 Maths Chapter 10: Exercises Breakdown

NCERT Solutions for Class 9 Maths Chapter 10 - Heron's Formula provides a necessary resource for students diving into the world of geometry and trigonometry. In this chapter, students are equipped with Heron's Formula, a powerful method for easily calculating triangle areas. Mastering this chapter not only enhances their understanding of geometry but also improves their problem-solving abilities. Heron's Formula is a valuable addition to their mathematical toolkit, setting a solid foundation for future studies in mathematics and various real-life scenarios where the calculation of triangle areas is essential.

Other Study Material for CBSE Class 9 Maths Chapter 10

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 10 Heron's Formula

1. How to find altitude in Heron's Formula class 9?

In class 9 maths herons formula , Heron's formula itself doesn't directly calculate the altitude of a triangle. However, it can be used along with the concept of area to find the altitude in a scalene triangle (one with all sides unequal). Here's the process:

Heron's formula gives the area (A) of a triangle with sides a, b, and c as:

A = $\sqrt{s(s-a)(s-b)(s-c)}$

where s is the semi-perimeter (s = (a + b + c) / 2)

The area of a triangle can also be calculated as 1/2 * base * height (where base is the side along which the altitude is drawn, and the height is the altitude itself).

By equating these two expressions for area and solving for the height (h) with base (b) known, you can get the formula for altitude using Heron's formula:

h = 2 * $\sqrt{s(s-a)(s-b)(s-c)}$ / b

2. Is Heron's formula applicable for all triangles in chapter 10 class 9 maths solutions pdf?

Yes, In class 9 ch 10 , Heron's formula is applicable to all triangles, irrespective of their type (scalene, isosceles, or equilateral). As long as you know the lengths of all three sides, you can use the formula to find the area of the triangle.

3. What is the real-life application of Heron's formula?

Suppose you have to calculate the area of a triangular land. What is the probability that the area is of a regular shape? It is impossible that you will come across lands with regular spaces and sizes, and this is where Heron’s formula comes into use. To calculate the area of real-life objects, the best way to find the exact area of the land is to use Heron’s formula.

4. What is Heron's formula?

Triangle is a three-dimensional closed shape. Heron’s formula calculates the area of a triangle when the length of all three sides is given. Using Heron's formula, we can calculate the area of any triangle, be it a scalene, isosceles or equilateral triangle. For example, the sides of a triangle are given as a, b, and c. Using Heron’s formula, the area of the triangle can be calculated by Area = √S (S-a)(S-b)(S-c) where s is the semi-perimeter of the triangle.

5. How do you solve Heron's formula questions?

To solve questions based on Heron’s formula, you need to remember Heron’s formula, Area= Area= √S (S-a)(S-b)(S-c). Here, ‘s’ is the semi-perimeter of the triangle, and a, b, and c are the lengths of the sides of the triangle. The semi perimeter is denoted by S. It can be calculated by using the formula: S = a+b+c/2. By substituting the values given in these formulas, you can calculate the area of a triangle.

6. What is the meaning of s in Heron's formula?

In Heron’s formula, Area = √S (S-a)(S-b)(S-c), where ‘s’ stands for the semi-perimeter of the triangle whose area we need to calculate. Semi-perimeter can be calculated by the given formula: S = a+b+c/2. To learn more about the semi-perimeter and its usage in calculating the area of a triangle, you can download the Vedantu app or check out the official website of  Vedantu .

7. What is a Semi-Perimeter?

In Geometry, the Semi-perimeter of any polygon is half of its perimeter. In Class 9, Chapter 12, Heron’s Formula explains the semi-perimeter of a triangle. Semi-perimeter is denoted by ‘s’ in Heron’s formula, which is Area= √s  (s-a)(s-b)(s-c) ‘s’ stands for semi-perimeter, which can be calculated by the given formula: s = a+b+c/2, where a, b, and c are the sides of the triangle of which the area has to be calculated.

8. What is a Semi-Perimeter?

In Geometry, the Semi-perimeter of any polygon is half of its perimeter. In Class 9, Chapter 12, Heron’s Formula explains the semi-perimeter of a triangle. Semi-perimeter is denoted by ‘s’ in Heron’s formula, which is Area= √s  (s-a)(s-b)(s-c)

‘s’ stands for semi-perimeter, which can be calculated by the given formula:

s = a+b+c/2, where a, b and c are the sides of the triangle of which the area has to be calculated.

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9.

• Simple Equations Class 7 Case Study Questions Maths Chapter 4

Last Updated on August 18, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 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 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 4 Simple Equations. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Simple Equations

The teacher tells the class that the lowest marks obtained by a student in his class is half the highest marks plus 5. The lowest score is 45. What is the highest score ?

Q. 1. Find the marks which is 20 more than the lowest: (a) 25 (b) 65 (c) 70 (d) None of these

Difficulty Level: Easy

Ans. Option (b) is correct. Explanation: Given lowest marks is 45 and 20 more it is 45 + 20 = 65

Q. 2. Just to pass in the examination border line marks is just 12 less than the lowest marks obtained by the student in the class. Write the required passing marks. (a) 56 (b) 40 (c) 33 (d) 57

Difficulty Level: Medium

Ans. Option (c) is correct. Explanation: Given passing marks = lowest marks – 12 = 45 – 12 = 33

Q. 3. If one student Aavya of another class who scored 9 marks more than the doubled of lowest marks of this class, find the aavya’s marks: (a) 92 (b) 50 (c) 89 (d) 99

Ans. Option (d) is correct. Explanation: Aavya score = 2 × Lowest marks + 9 = 2(45) + 9 = 90 + 9 = 99

Q. 4. Find the highest marks.

Difficulty Level: Hard

Explanation: let the highest marks be $x$ according to the question, lowest marks

$$ \begin{aligned} & =\frac{1}{2} \text { (highest marks) }+5 \\ 45 & =\frac{1}{2}(x)+5 \\ 45-5 & =\frac{1}{2} x \text { [transposing } 5 \text { to LHS] } \\ 40 & =\frac{1}{2} x \\ 40 \times 2 & =x \text { [multiplying both sides by } 2] \\ 80 & =x \\ x & =80 \end{aligned} $$

• Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
• Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
• Lines and Angles Class 7 Case Study Questions Maths Chapter 5
• Data Handling Class 7 Case Study Questions Maths Chapter 3

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Linear equation
• Solution of a linear equation
• Transposition

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

• An equation is a statement of equality which involves one or more literal numbers.
• The value of the variable which satisfies an equation is called the solution or the root of an equation.
• A term in an equation can be transposed from one side of an the sign of equality to another side by changing its sign.
• A number that divides a literal or another number on one side of an equation, when transposed multiplies the other side and viceversa.

A linear equation remains the same when the expression in the left and right are interchanged.

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Frequently Asked Questions (FAQs) on Simple Equations Case Study

Q1: what are simple equations.

A1: Simple equations are mathematical statements that express equality between two expressions. They usually involve a variable (like x) and can be solved to find the value of the variable that makes the equation true.

Q2: How do you solve a simple equation?

A2: To solve a simple equation, you need to isolate the variable on one side of the equation. This can be done by performing the same mathematical operations on both sides of the equation, such as addition, subtraction, multiplication, or division.

Q3: Can simple equations have more than one solution?

A3: Simple equations usually have a single unique solution. However, certain types of equations, like identities, can have infinite solutions, but those are not typically covered under “simple equations” in Class 7.

Q4: Why is it important to learn simple equations?

A4: Learning simple equations is important because it forms the foundation for more advanced topics in algebra and mathematics. It helps in developing problem-solving skills and understanding how to work with variables and mathematical relationships.

Q5: What are some real-life applications of simple equations?

A5: Simple equations can be used in various real-life situations, such as calculating expenses, determining distances, solving for unknown quantities in recipes, and even in basic physics problems involving speed, distance, and time.

Q6: What common mistakes should students avoid when solving simple equations?

A6: Common mistakes include not performing the same operation on both sides of the equation, incorrectly combining like terms, and forgetting to change the sign when moving terms from one side of the equation to the other.

Q7: What are some tips for mastering simple equations?

A7: To master simple equations, students should focus on understanding the basic principles of balancing equations, practice regularly, and check their solutions by substituting the value back into the original equation to ensure it holds true.

Q8: How can students practice solving simple equations effectively?

A8: Students can practice effectively by solving a variety of problems, starting with simple ones and gradually moving to more complex equations. They can also use online resources, worksheets, and practice tests to reinforce their learning.

Q9: Are there any online resources or tools available for practicing comparing quantities case study questions?

A9: We provide case study questions for CBSE Class 8 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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Case Interview Math Guide: Everything You Need to Know

Master case interview math with our friendly guide! Learn essential tips, tricks, and strategies to ace every calculation and impress in your consulting interviews.

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Table of Contents

Are you ready to conquer case interview math? Whether you're aiming for a consulting career or preparing for a challenging case interview, mastering the art of case interview math is crucial to your success. This guide will enhance your ability to tackle complex math problems, crunch numbers efficiently, and impress your interviewers with your analytical skills. By refining these abilities, you'll be better prepared to meet the high standards of management consulting firms and stand out in the competitive interview process.

In this comprehensive case interview math guide , we'll explore the three main types of math problems you'll encounter, along with practical examples. You'll learn essential formulas to have at your fingertips and discover techniques to sharpen your consulting math skills. We'll also share tips to help you stand out, provide effective preparation strategies, and offer valuable practice drills and resources. By the end, you'll be well-equipped to handle any math challenge that comes your way in your case interviews.

3 Types of Math Problems with Examples

In case interviews , you'll encounter three main types of math problems: word problems, straight calculations, and estimation questions. Each type tests different aspects of your quantitative skills and problem-solving abilities.

Word Problems

Word problems in case interviews often require algebraic calculations. These questions are designed to assess your ability to translate real-world scenarios into mathematical equations. For example, you might need to calculate the breakeven point for a product launch or determine the impact of a cost-cutting initiative on a company's financials.

Word problems require you to analyze a business scenario and apply your case math skills to find a solution. For instance, you might be asked to determine the profitability of a new product line based on market math data like costs, revenues, and market share.

Key Strategy: Break down the problem into smaller steps. Start by identifying key variables (such as costs, revenues, or quantities), and then translate them into equations. Practice framing business scenarios into solvable math problems by focusing on what the interviewer is truly asking.

Tip: Stay organized by writing down your calculations step-by-step. This will allow you to clearly explain your thought process to the interviewer and minimize errors, while also demonstrating your structured thinking skills.

Straight Calculations

Straight calculations involve performing direct calculations, such as multiplying revenue figures or dividing costs by units produced. These problems assess your ability to quickly and accurately handle basic arithmetic operations, which are crucial in management consulting.

They are often presented as standalone questions or follow-up queries within a larger case study. These problems test your ability to perform quick mental math under pressure. For instance, you might need to divide 100,000 by 50 to determine employee productivity or calculate 13% of $160 million to find the cost of goods sold.

Key Strategy: Prioritize accuracy before speed. Focus on methodical, step-by-step calculations rather than rushing to an answer. If you're unsure about mental math, write out each step. It’s better to be slightly slower but accurate than to provide a wrong answer quickly.

Tip: Always verify your results by double-checking your work. While speed is important, accuracy is even more crucial. Mistakes in simple calculations can affect your overall analysis and the recommendation you give to the interviewer.

Estimation Questions

Also known as market sizing questions, estimation problems require you to arrive at a value with minimal initial data. These questions assess your structured problem-solving skills and business judgment. For example, you might need to estimate the number of pizzas sold in New York City annually or the market size for a new tech product.

Key Strategy: Focus on logical reasoning and simplification. Instead of breaking the problem into smaller pieces, start by setting up a logical framework. Use approximate numbers and relevant assumptions to guide your estimate, aiming for an answer that's reasonable within a broad range.

Tip: Use reasonable assumptions and round numbers to keep your calculations simple and easy to follow. Don’t hesitate to state your assumptions clearly to the interviewer; they care more about your approach and logic than the exact answer.

By mastering these types of math problems, you'll be better equipped to tackle the quantitative challenges that arise in case interviews for management consulting roles.

Essential Case Interview Math Formulas

While most case interviews only require basic algebra like addition, subtraction, multiplication, division, and fractions/percentages, it’s best to be prepared for the following math formulas just in case you have to use them in the case interview:

Revenue and Profit Margin Calculations

To excel in case interviews, you need to master key formulas.

Start with the basics : Revenue = Price x Volume. This formula helps you calculate a company's total sales.

Next, understand profit calculations. Gross Profit = Revenue - Cost of Goods Sold, while Net Profit = Gross Profit - All other cost items.

These formulas are crucial for assessing a company's financial health.

Read : Unlocking Marginal Profit: A Step-by-Step Guide to Finding It

Market Sizing Equations

Market sizing is a common challenge in case interviews.

Use this formula : Market Size = # of Target Customers x Expected Annual Purchases. For market share, calculate: Market Share = Company Revenue / Total Market Revenue.

These equations help you estimate market potential and a company's position within it.

Break-Even Analysis

Break-even analysis is vital for assessing whether a company should put down an initial investment on a product or service.

The key formula is : Break-even Point = Fixed Costs / Contribution Margin.

Remember, contribution margin is (Price - Variable Cost) per unit. This analysis helps determine how many units a company needs to sell to cover its costs before generating profit.

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Master Mental Math Techniques

To excel in case interviews, you need to sharpen your mental calculations. These techniques will help you perform calculations quickly and accurately without a calculator, giving you an edge in tackling case interview math problems. By practicing these methods, you'll become more confident in solving consulting math problems, allowing you to approach each case interview with precision and ease.

Rounding and Estimation

Simplify large numbers by removing zeros and using labels (m, k, b). For example, 200 million becomes 200m. This method helps you manage zeros efficiently and makes calculations more manageable.

Percentage Calculations

For percentage growth, use the Rule of 72. Divide 72 by the growth rate to estimate doubling time. For instance, at 12% growth, a value doubles in approximately 6 years (72 ÷ 12 = 6).

Quick Multiplication and Division

Break down complex calculations into simpler steps. For 14 x 6, calculate (10 x 6) + (4 x 6) = 84. Use the Halve and Double Method for tricky multiplications. For 160 x 350, halve 160 and double 350, then multiply: 80 x 700 = 56,000.

How to Stand Out in Case Interview Math

To excel in case interview math, you need to demonstrate efficiency and confidence. Here are key strategies to help you stand out:

Simplify your calculations

If the question doesn’t demand a specific answer, round numbers to make them more manageable. For example, instead of calculating 29 x 4, round 29 to 30 and multiply by 4. This shows you're focused on solving math problems efficiently, rather than getting bogged down in trivial details.

Master the common fractions

Memorize common fractions, their percentage values, and decimal conversions from 1/2 to 1/10. This knowledge can save you significant time during calculations. For instance, knowing that 1/8 equals 0.125 can help you quickly arrive at an exact answer during case math exercises.

Do not miscount the zeros

When working with large numbers, keep close track of zeros to prevent errors. Instead of writing out long numbers, use scientific notation, like expressing 60,000,000 as 6 x 10^7. This simplifies consulting math calculations and reduces the risk of mistakes.

How to Prepare for Case Interview Math

Understand the theory.

To excel in case interview math, you need to master key formulas and concepts. Focus on revenue and profit calculations, market sizing equations , and break-even analysis. While in-depth understanding isn't required, having a rough idea of business terms and their formulas can be handy. Remember, calculators aren't allowed in case interviews, so practice mental math.

Put the Theory into Practice

Once you've grasped the theory, it's time to practice. Use calculation drills to sharpen your skills. Focus on simplifying calculations, factoring and expanding expressions, and dealing with growth rates efficiently. Memorize common statistics, like local population figures, to save time. Practice within full case contexts for the most realistic experience.

Practice Drills and Resources

Online math tools.

Strengthen your consulting math skills by using online tools designed specifically for case interview preparation. These resources offer a range of exercises to help you master essential consulting math formulas, such as percentages, ratios, and basic arithmetic, ensuring you can tackle quantitative problems with confidence during your interviews.

Sample Problems

Practice with real-world scenarios. For instance, try estimating the market demand for cell phones over 30 years or calculating the profit-maximizing layout for a convenience store. These problems mirror the types of questions you might encounter in actual case interviews.

Timed Exercises

Engage in timed math drills to improve your speed and accuracy. Aim to solve problems within 5-10 seconds, gradually increasing difficulty as you progress. Focus on areas where you struggle, and practice consistently to maintain your skills. Remember to verbalize your thought process while solving problems to simulate interview conditions.

Land Your Dream Consulting Job With the Help of an Expert

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Mastering case interview math is a game-changer for aspiring consultants. This comprehensive guide has provided a comprehensive overview of the types of math problems you'll face, essential formulas to memorize, and techniques to sharpen your mental math skills. By applying these strategies and consistently practicing, you'll be well-prepared to tackle any case interview math challenge that comes your way.

Remember, success in case interview math isn't just about crunching numbers quickly. It's also about demonstrating your structured thinking, problem-solving approach, and business acumen, all of which are crucial in management consulting. By honing these skills and staying calm under pressure, you'll be able to stand out and make a lasting impression on your interviewers. Keep practicing, stay confident, and you'll be well on your way to acing the math portion of your case interviews, especially when faced with market math scenarios.

What exactly is 'case math'?

• Case Interview Math involves analyzing data to form a well-informed recommendation to address a business issue. It assumes a basic understanding of operations like multiplication, addition, subtraction, division, and percentages. More importantly, it requires an understanding of how to interpret these mathematical results within the context of the case problem.

What mathematical abilities are essential for case interviews?

• In case interviews, the essential math skills include basic arithmetic operations such as addition, subtraction, multiplication, and division. You will also need to work with percentages, decimals, or fractions, and be able to calculate percentage values, which involves division.

How important is mental math in consulting interviews?

• Mental math is essential in consulting interviews as it allows you to perform quick calculations without relying on a calculator. This ability is particularly useful when you're under time constraints or need to make rapid decisions during the case interview process.

Is the math involved in case interviews difficult?

• The math typically encountered in case interviews is not particularly challenging. It involves basic algebra, including operations like addition, subtraction, multiplication, division, and working with fractions and percentages. Additionally, you may need to extract and interpret data from tables.

Why do consulting firms emphasize math skills in case interviews?

• Consulting firms prioritize math skills because consultants frequently need to analyze data, create models, and make recommendations based on numerical insights. Strong case math abilities allow you to approach problems methodically and deliver precise, actionable advice.

How can I enhance my mathematical skills for case interviews?

• Improving your math skills for case interviews primarily involves extensive practice. Engaging in numerous practice problems will help you become quicker, familiarize you with various problem types, and improve your ability to apply fundamental mathematical skills in different scenarios. Participating in mock case interviews is an effective way to practice.

How much time should I dedicate to practicing case interview math?

• Dedicating regular time to practice is crucial. Aim for at least 30 minutes a day of focused math drills. This consistency will help you build speed and confidence, especially in performing calculations under pressure during a consulting interview.

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Class 9 Maths Case Study Questions of Chapter 8 Quadrilaterals PDF Download

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Class 9 Maths Case Study Questions Chapter 8  are very important to solve for your exam. Class 9 Maths Chapter 8 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based questions for Class 9 Maths Chapter 8 Quadrilaterals

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These case study questions challenge students to apply their knowledge of quadrilaterals in practical scenarios, enhancing their problem-solving abilities. This article provides the Class 9 Maths Case Study Questions of Chapter 8: Quadrilaterals, enabling students to practice and excel in their examinations.

Quadrilaterals Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 8 Quadrilaterals

Case Study/Passage-Based Questions

Case Study 1: Laveena’s class teacher gave students some colorful papers in the shape of quadrilaterals. She asked students to make a parallelogram from it using paper folding. Laveena made the following parallelogram.

How can a parallelogram be formed by using paper folding? (a) Joining the sides of a quadrilateral (b) Joining the mid-points of sides of a quadrilateral (c) Joining the various quadrilaterals (d) None of these

Answer: (b) Joining the mid-points of sides of quadrilateral

Which of the following is true? (a) PQ = BD (b) PQ = 1/2 BD (c) 3PQ = BD (d) PQ = 2BD

Answer: (b) PQ = 1/2 BD

Which of the following is correct combination? (a) 2RS = BD (b) RS = 1/3 BD (c) RS = BD (d) RS = 2BD

Answer: (a) 2RS = BD

Which of the following is correct? (a) SR = 2PQ (b) PQ = SR (c) SR = 3PQ (d) SR = 4PQ

Answer: (b) PQ = SR

Case Study/Passage Based Questions

Case Study 2: Anjali and Meena were trying to prove mid-point theorem. They draw a triangle ABC, where D and E are found to be the midpoints of AB and AC respectively. DE was joined and extended to F such that DE = EF and FC is also joined.

▲ADE and ▲CFE are congruent by which criterion? (a) SSS (b) SAS (c) RHS (d) ASA

Answer: (b) SAS

∠EFC is equal to which angle? (a) ∠DAE (b) ∠EDA (c) ∠AED (d) ∠DBC

Answer: (b)∠EDA

∠ECF is equal to which angle? (a) ∠EAD (b) ∠ADE (c) ∠AED (d) ∠B

Answer: (a) ∠EAD

CF is equal to (a) EC (b) BE (c) BC (d) AD

Answer: (d) AD

CF is parallel to (a) AE (b) CE (c) BD (d) AC

Answer: (c) BD

Case Study 3. A group of students is exploring different types of quadrilaterals. They encountered the following scenario:

Four friends, Aryan, Bhavana, Chetan, and Divya, participated in a geometry project. They constructed a figure with four sides and made the following observations:

• The opposite sides of the figure are parallel.
• The opposite angles of the figure are congruent.
• The figure has two pairs of congruent adjacent sides.
• The sum of the measures of the interior angles of the figure is 360 degrees.

Based on this information, the students were asked to analyze the properties of the quadrilateral they constructed. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The type of quadrilateral formed by their figure is: (a) Parallelogram (b) Rhombus (c) Rectangle (d) Square

Answer: (a) Parallelogram

Q2. The measure of each angle in the figure is: (a) 90 degrees (b) 120 degrees (c) 135 degrees (d) 180 degrees

Answer: (d) 180 degrees

Q3. The figure is an example of a quadrilateral that satisfies the: (a) Opposite sides are equal condition (b) Opposite angles are congruent condition (c) Diagonals bisect each other condition (d) None of the above

Answer: (b) Opposite angles are congruent condition

Q4. The sum of the measures of the exterior angles of the figure is: (a) 90 degrees (b) 180 degrees (c) 270 degrees (d) 360 degrees

Answer: (d) 360 degrees

Q5. The figure has rotational symmetry of: (a) Order 1 (b) Order 2 (c) Order 3 (d) Order 4

Answer: (a) Order 1

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 8 Quadrilaterals with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Quadrilaterals 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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CBSE Case Study Questions Class 9 Maths Chapter 14 Statistics PDF Download

Case Study Questions Class 9 Maths Chapter 14 Statistics  are very important to solve for your exam. Class 9 Maths Chapter 14 Case Study Questions have been prepared for the latest exam pattern . You can check your knowledge by solving  case study-based   questions for Class 9 Maths Chapter 14  Statistics

Case Study Questions Class 9 Maths Chapter 14 Statistics PDF

Case Study 1: A group of students is learning about statistics in their math class. They encountered the following scenario:

Riya and Aryan conducted a survey among their classmates to collect data on the number of hours they spent studying every day. They made the following observations:

• Riya collected data from 30 students and found that the mean number of hours they spent studying was 4 hours per day.
• Aryan collected data from 25 students and found that the median number of hours they spent studying was 3 hours per day.

Based on this information, the students were asked to analyze the data collected by Riya and Aryan. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The mean and median provide measures of: (a) Central tendency (b) Dispersion (c) Variation (d) Skewness

Answer: (a) Central tendency

Q2. The mean number of hours spent studying per day, as collected by Riya, is: (a) 3 hours (b) 4 hours (c) 5 hours (d) Cannot be determined

Answer: (b) 4 hours

Q3. The median number of hours spent studying per day, as collected by Aryan, is: (a) 2 hours (b) 3 hours (c) 4 hours (d) Cannot be determined

Answer: (b) 3 hours

Q4. Which measure of central tendency would be affected the most if there was an outlier in the data? (a) Mean (b) Median (c) Mode (d) All measures equally

Answer: (a) Mean

Q5. If there was a student who reported studying 8 hours per day, what effect would it have on the mean and median? (a) Mean would increase, the median would remain unchanged (b) Mean would decrease, the median would remain unchanged (c) Mean would remain unchanged, the median would increase (d) Mean would remain unchanged, the median would decrease

Answer: (a) Mean would increase, the median would remain unchanged

Case Study 2: A group of students is studying statistics in their math class. They encountered the following scenario:

Rahul and Sneha decided to conduct a survey among their classmates to gather data on their monthly allowances. They made the following observations:

• Rahul collected data from 50 students and found that the range of their monthly allowances was ₹2000.
• Sneha collected data from 40 students and found that the standard deviation of their monthly allowances was ₹1000.

Based on this information, the students were asked to analyze the data collected by Rahul and Sneha. Let’s see if you can answer the questions correctly:

Q1. The range provides a measure of: (a) Central tendency (b) Dispersion (c) Variation (d) Skewness

Answer: (b) Dispersion

Q2. The range of monthly allowances, as collected by Rahul, is: (a) ₹2000 (b) ₹1000 (c) ₹3000 (d) Cannot be determined

Answer: (a) ₹2000

Q3. The standard deviation of monthly allowances, as collected by Sneha, is: (a) ₹500 (b) ₹750 (c) ₹1000 (d) Cannot be determined

Answer: (c) ₹1000

Q4. The range is affected by: (a) Extreme values in the dataset (b) The mean value (c) The mode value (d) None of the above

Answer: (a) Extreme values in the dataset

Q5. Which measure of dispersion provides a more accurate representation of the spread of the data? (a) Range (b) Standard deviation (c) Mean (d) Median

Answer: (b) Standard deviation

Hope the information shed above regarding Case Study and Passage Based Questions for Case Study Questions Class 9 Maths Chapter 14 Statistics with Answers Pdf free download has been useful to an extent. If you have any other queries about Case Study Questions Class 9 Maths Chapter 14 Statistics and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible.

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