case study based questions class 9 maths chapter 12

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

This method is not easy for me

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

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

Cbse case study questions for class  9 maths.

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

Chapter Wise Case Based Questions for Class 9 Maths

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

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

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

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

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

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

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

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

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

Class 9 Maths Curriculum at Glance

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

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

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

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

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

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

What is case-based questions.

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

What are case-based questions in Maths?

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

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

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

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

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

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

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

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

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

All Of You Can Also Read

Case studies in class 9 mathematics.

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

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

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

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

Class 9th Maths - Linear Equations in Two Variables Case Study Questions and Answers 2022 - 2023

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Linear Equations in Two Variables, 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

Linear equations in two variables case study questions with answer key.

9th Standard CBSE

Final Semester - June 2015

Mathematics

(ii) Find the length of the outer boundary of the layout.

(iii) The pair of linear equation 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)?

(v) Find the area of each bedroom.

(iii) Find the cost of one pen?

(iv) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.

(v) Find whose estimation is correct in the given statement.

(b) How to represent the above situation in linear equations in two variables ?

(c) If Sita contributed Rs. 76, then how much was contributed by Gita ?

(d) If both contributed equally, then how much is contributed by each?

(e) Which is the standard form of linear equations x = – 5 ?

(ii) Which is the solution of the equations formed in (i)?

(c) If the cost of one notebook is Rs. 15 and cost of one pen is 10, then find the total amount.

(d) If the cost of one notebook is twice the cost of one pen, then find the cost of one pen?

(e) Which is the standard form of linear equations y = 4 ?

(b) If the number of children is 15, then find the number of adults?

(c)  If the number of adults is 12, then find the number of children?

(d) Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.

(e) Which is the standard form of linear equations in two variables: y - x = 5?

(b) If the cost of chocolates A is 5, then find the cost of chocolates B?

(c) Which of the follwing point lies on the line x + y = 7?

(d) The point where the line x + y = 7 intersect y-axis is 

(e) For what value of k, x = 2 and y = -1 is a soluation of x + 3y -k = 0.

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

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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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CBSE Class 9 Maths Extra Questions: Chapter 12 - Heron's Formula (with Answers)

Cbse class 9 maths extra questions for chapter 12 - heron's formula are provided here for students to prepare for their class 9 maths exam 2020-2021. these questions are totally based on the ncert class 9 maths textbook..

CBSE Class 9 Maths extra questions for Chapter 12 - Heron's Formula are based on the important fundamental concepts mentioned in the chapter. Practicing with these questions will help you sharpen your basics and develop a better understanding of the concepts. This will also help you to formulate an idea about your string and weak areas. Therefore, students must try to solve all the questions given below to strengthen their preparations for the exams. You can also check here some other important resources to help you in preparations of your CBSE Class 9 Maths Exam 2020-2021.

CBSE Class 9 Maths Extra Questions for Chapter 12 - Heron's Formula :

Question. Area of a right angled triangle can be found using which formula?

Area of a right angled triangle = 1/2 × Base × Height

Question. When do we use Which Heron's formula to find the area of a triangle?

Heron's formula is useful to find the area of a triangle when it is not possible to find the height of the triangle easily.

Question. Two sides of a triangular field are 112m and 50m. Then find the height of the altitude on the side of 78 m length if perimeter of the triangle is 240m.

Height of the altitude = 43.07m

Question. Find the length of the hypotenuse of an isosceles right angle triangle if its area is 50m 2 .

Length of hypotenuse = 14.1m

Height = Base

And area of triangle = 1/2 × Base × Height

Also Check:

NCERT Book for Class 9 Maths

NCERT Solutions for Class 9 Maths

Question. Perpendicular distance between the parallel sides of a trapezium is 8cm. Find the area of the trapezium if the lengths of its parallel sides are 9cm and 11cm.

Area of trapezium = 80cm 2

Question. Sides of triangular field are in the ratio of 4:5:6. Then find the area of the field if its perimeter is 300m.

Area of the field = 1500 √7

Hint: Let the three sides of the field be 4x, 5x and 6x.

Question. A park is in the shape of a right angled triangle. Fencing of grass beds is to be spread along the longest side of the park. If one side of the park is 60 m and its area is 1350 m 2 then find the cost of spreading the grass bed at the rate of Rs 20 per meter length.

Cost of spreading the grass bed along the longest side of park = Rs 1500

Hint: Hypotenuse is the longest side of a right angled triangle.

So, find the length of hypotenuse here.

Extra Questions for CBSE Class 9 Maths - All Chapters

Students must go through the latest CBSE Syllabus for Class 9 Maths so that they can prepare according to the contents prescribed by the board.

Also check:

CBSE Class 9 Maths Important Questions and Answers

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Class 12 Maths: Case Study Based Questions PDF Download

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• Post published:
• Post category: 12 board / Class 12
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You must practice some good Case Study questions of Class 12 Maths to boost your preparation to score 95+% on Boards. In this post, you will get Case Study Questions of All Chapters which will come in CBSE Class 12 Maths Board Exams.

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

We have provided here Case Study questions for the Class 12 Maths exams. You can read these chapter-wise Case Study questions. Prepared by subject experts and experienced teachers. The answer key is also provided so that you can check the correct answer for each question. Practice these questions to score well in your Board Final exams.

We are providing Case Study questions for class 12 Biology based on the latest syllabi. There is a total of 13 chapters included in CBSE class 12 Maths exams. Students can practice these questions for concept clarity and score better marks in their exams.

Table of Contents

CBSE Class 12th – MATHS : Chapterwise Case Study Question & Solution

CBSE will ask two Case Study Questions in the CBSE class 12 maths questions paper. Question numbers 15 and 16 are case-based questions where 5 MCQs will be asked based on a paragraph. Each theme will have five questions and students will have a choice to attempt any four of them.

Case Study Based Questions for Class 12 Maths

Class 12 Physics Case Study Questions Class 12 Chemistry Case Study Questions Class 12 Biology Case Study Questions Class 12 Maths Case Study Questions

Books for Class 12 Maths

Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 12 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 12th.

Class 12 Maths Syllabus 2022-23

Unit-i: relations and functions.

1. Relations and Functions (15 Periods)

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions.

2. Inverse Trigonometric Functions (15 Periods)

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions.

Unit-II: Algebra

1. Matrices (25 Periods)

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Oncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2). Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

2. Determinants 25 Periods

Determinant of a square matrix (up to 3 x 3 matrices), minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

Unit-III: Calculus

1. Continuity and Differentiability (20 Periods)

Continuity and differentiability, chain rule, derivative of inverse trigonometric functions, 𝑙𝑖𝑘𝑒 sin −1  𝑥 , cos −1  𝑥 and tan −1  𝑥, derivative of implicit functions. Concept of exponential and logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives.

2. Applications of Derivatives (10 Periods)

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).

3. Integrals (20 Periods)

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals (15 Periods)

Applications in finding the area under simple curves, especially lines, circles/ parabolas/ellipses (in standard form only)

5. Differential Equations (15 Periods)

Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

Unit-IV: Vectors and Three-Dimensional Geometry

1. Vectors (15 Periods)

Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.

2. Three – dimensional Geometry (15 Periods)

Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.

Unit-V: Linear Programming

1. Linear Programming (20 Periods)

Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

Unit-VI: Probability

1. Probability 30 (Periods)

Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean of random variable.

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• Class 9 Maths MCQs
• Chapter 12 Herons Formula Mcq

Class 9 Maths Chapter 12 Heron’s Formula MCQs

Class 9 Maths Chapter 12 Heron’s Formula MCQs are available online here, with solved answers. The MCQs are prepared as per the latest exam pattern for Class 9. The objective questions are prepared chapter-wise, as per the CBSE syllabus (2022-2023) and NCERT curriculum. These questions are provided with detailed explanations. Get Chapter-wise Class 9 Maths MCQs at BYJU’S.

Download the below PDF to get more MCQs on Class 9 Maths Chapter 12 Heron’s Formula.

Class 9 Maths Chapter 12 Heron’s Formula MCQs – Download PDF

MCQs on Class 9 Maths Chapter 12 Heron’s Formula

Choose the correct answer and solve the MCQs on Heron’s formula.

1) Area of a triangle is equal to:

a. Base x Height

b. 2(Base x Height)

c. ½(Base x Height)

d. ½ (Base + Height)

2) If the perimeter of an equilateral triangle is 180 cm. Then its area will be:

a. 900 cm 2

b. 900√3 cm 2

c. 300√3 cm 2

d. 600√3 cm 2

Explanation: Given, Perimeter = 180 cm

3a = 180 (Equilateral triangle)

Semi-perimeter = 180/2 = 90 cm

Now as per Heron’s formula,

In the case of an equilateral triangle, a = b = c = 60 cm

Substituting these values in the Heron’s formula, we get the area of the triangle as:

= √(90× 30 × 30 × 30)

A = 900√3 cm 2

3) The sides of a triangle are 122 m, 22 m and 120 m respectively. The area of the triangle is:

a. 1320 sq.m

b. 1300 sq.m

c. 1400 sq.m

d. 1420 sq.m

Explanation: Given,

Semi-perimeter, s = (122 + 22 + 120)/2 = 132 m

Using heron’s formula:

= √(132 × 10 × 110 × 12)

= 1320 sq.m

4) The area of a triangle with given two sides 18 cm and 10 cm, respectively and a perimeter equal to 42 cm is:

a. 20√11 cm 2

b. 19√11 cm 2

c. 22√11 cm 2

d. 21√11 cm 2

Explanation: Perimeter = 42

a + b + c = 42

18 + 10 + c = 42

c = 42 – 28 = 14 cm

Semi perimeter, s = 42/2 = 21 cm

Using Heron’s formula:

= √(21 × 3 × 11 × 7)

= 21√11 cm 2

5) The sides of a triangle are in the ratio 12: 17: 25 and its perimeter is 540 cm. The area is:

a. 1000 sq.cm

b. 5000 sq.cm

c. 9000 sq.cm

d. 8000 sq.cm

Explanation: The ratio of the sides is 12: 17: 25

Perimeter = 540 cm

Let the sides of the triangle be 12x, 17x and 25x.

12x + 17x + 25x = 540 cm

54x = 540 cm

a = 12x = 12 × 10 = 120

b = 17x = 17 × 10 = 170

c = 25x = 25 × 10 = 250

Semi-perimeter, s = 540/2 = 270 cm

= √(270 × 150 × 100 × 20)

= 9000 sq.cm

6) The equal sides of the isosceles triangle are 12 cm, and the perimeter is 30 cm. The area of this triangle is:

a. 9√15 sq.cm

b. 6√15 sq.cm

c. 3√15 sq.cm

d. √15 sq.cm

Perimeter = 30 cm

Semiperimeter, s = 30/2 = 15 cm

a = b = 12 cm

a + b + c = 30

12 + 12 + c = 30

c = 30 – 24 = 6 cm

= √(15 × 3 × 3 × 9)

= 9√15 sq.cm

7) A quadrilateral whose sides are 3 cm, 4 cm, 4 cm, 5 cm and one of the diagonal is equal to 5 cm as per the below figure. The area of the quadrilateral is:

a. 19.17 sq.cm

b. 15.17 sq.cm

c. 20.17 sq.cm

d. 22.17 sq.cm.

Explanation: Using Pythagoras theorem, in ΔABC,

AC 2 = AB 2 + BC 2

⇒ 5 2 = 3 2 + 4 2

Hence, ABC is a right triangle.

Area of ΔABC = ½ x 3 x 4 = 6 sq.cm

Semiperimeter of ΔACD = s = (5+5+4)/2 = 14/2 = 7 cm

Area of ΔACD can be determined by using Heron’s formula.

= √(7 × 2 × 2 × 3)

= 9.17 sq.cm

Therefore, the area of quad.ABCD = Area of ΔABC + Area of ΔACD = (6 + 9.17) sq.cm = 15.17 sq.cm

8) The area of an equilateral triangle having side length equal to √3/4 cm (using Heron’s formula) is:

a. 2/27 sq.cm

b. 2/15 sq.cm

c. 3√3/64 sq.cm

d. 3/14 sq.cm

Explanation: Here, a = b = c = √3/4

Semiperimeter = (a + b + c)/2 = 3a/2 = 3√3/8 cm

Using Heron’s formula,

= 3√3/64 sq.cm

9) The sides of a parallelogram are 100 m each and the length of the longest diagonal is 160 m. The area of a parallelogram is:

a. 9600 sq.m

b. 9000 sq.m

c. 9200 sq.m

d. 8800 sq.m

Explanation: The diagonal divides the parallelogram into two equivalent triangles. Hence, its area will be equal to the sum of the area of the two triangles.

Thus, the sides of one triangle will be 100 m, 160 m, and 100 m.

So, a = 100 m, b = 160 m, c = 100 m

Semiperimeter (s) = (a + b + c)/2 = (100 + 160 + 100)/2 = 360/2 = 180 m

= √(180 × 80 × 20 × 80)

= 4800 sq.m

Thus, the area of the parallelogram = 2 × 4800 sq.m = 9600 sq.m

10) The sides of a triangle are in the ratio of 3: 5: 7 and its perimeter is 300 cm. Its area will be:

a. 1000√3 sq.cm

b. 1500√3 sq.cm

c. 1700√3 sq.cm

d. 1900√3 sq.cm

Explanation:

The ratio of the sides is 3: 5: 7

Perimeter = 300 cm

Let the sides of the triangle be 3x, 5x and 7x.

3x + 5x + 7x = 300 cm

15x = 300 cm

a = 3x = 3 × 20 = 60

b = 5x = 5 × 20 = 100

c = 7x = 7 × 20 = 140

Semi-perimeter, s = 300/2 = 150 cm

= √(150 × 90 × 50 × 10)

= 1500√3 sq.cm

11) The base of a right triangle is 8 cm and the hypotenuse is 10 cm. Its area will be

(a) 24 cm 2

(b) 40 cm 2

(c) 48 cm 2

(d) 80 cm 2

Given: Base = 8 cm and Hypotenuse = 10 cm

Hence, height = √[(10 2 – 8 2 ) = √36 = 6 cm

Therefore, area = (½)×b×h = (½)×8×6 = 24 cm 2 .

12) The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per cm 2 is

(a) Rs 2.00

(b) Rs 2.16

(c) Rs 2.48

(d) Rs 3.00

Given: a = 6 cm, b = 8 cm, c = 10 cm.

s = (6 + 8 + 10)/2 = 12 cm

Hence, by using Heron’s formula, we can write:

A = √[12(12 – 6)(12 – 8)(12 – 10)] = √[(12)(6)(4)(2)] = √576 = 24 cm 2

Therefore, the cost of painting at a rate of 9 paise per cm 2 = 24 × 9 paise = Rs. 2.16

13) An isosceles right triangle has an area of 8 cm 2 . The length of its hypotenuse is

Given that area of the isosceles triangle = 8 cm 2 .

As the given triangle is isosceles triangle, let base = height = h

(½)×h×h = 8

Since it is isosceles right triangle, Hypotenuse 2 = Base 2 +Height 2

Hypotenuse 2  = 4 2  + 4 2

Hypotenuse 2  = 32

Hypotenuse = √32 cm

14) The area of an isosceles triangle having a base 2 cm and the length of one of the equal sides 4 cm, is

(a) √15 cm 2

(b) √(15/2) cm 2

(c) 2√15 cm 2

(d) 4√15 cm 2

Given that a = 2 cm, b= c = 4 cm 

s = (2 + 4 + 4)/2 = 10/2 = 5 cm

By using Heron’s formula, we get:

A =√[5(5 – 2)(5 – 4)(5 – 4)] = √[(5)(3)(1)(1)] = √15 cm 2 .

15) The perimeter of an equilateral triangle is 60 m. The area is

(a) 10√3 m 2

(b) 15√3 m 2

(c) 20√3 m 2

(d) 100√3 m 2

Given: Perimeter of an equilateral triangle = 60 m

3a = 60 m (As the perimeter of an equilateral triangle is 3a units)

We know that area of equilateral triangle = (√3/4)a 2  square units

A = (√3/4)20 2

A = (√3/4)(400) = 100√3 m 2 .

16) The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude

(a) 16√5 cm

(b) 10√5 cm

(c)  24√5 cm

Given: a = 35 cm, b = 54cm, c = 61cm

s = (35 + 54 + 61)/2 = 150/2 = 75 cm.

Hence, by using Heron’s formula, A = √[75(75 – 35)(75 – 54)(75 – 61)] = √(882000) = 420√5 cm 2

The area of triangle with longest altitude “h” is given as”

(½)×a×h = 420√5 {a is less than b and c}

(½)×35×h = 420√5

h = (840√5)/35 = 24√5 cm.

17) The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is

(a) 1322 cm 2

(b) 1311 cm 2

(c) 1344 cm 2

(d) 1392 cm 2

Since, all the sides of a triangle are given, we can find the area of a triangle using Heron’s formula.

Let a = 56 cm, b= 60 cm, c = 52 cm

s = (56+60+52)/2 = 84 cm.

Area of triangle using Heron’s formula, A = √[s(s-a)(s-b)(s-c)] square units

A = √[84(84-56)(84-60)(84-52)] = √(1806336) =1344 cm 2 .

18) If the area of an equilateral triangle is 16√3 cm 2 , then the perimeter of the triangle is

Explanation: 

Given: Area of equilateral triangle = 16√3 cm 2

(√3/4)a 2  = 16√3

a 2  = [(16√3)(4)]/ √ 3

a = 8cm Therefore, perimeter = 3(8) = 24 cm.

19) The area of an equilateral triangle with sides 2√3 cm is

(a) 5.196 cm 2

(b) 0.866 cm 2

(c) 3.496 cm 2

(d) 1.732 cm 2

Given: Side = 2√3 cm

We know that, area of equilateral triangle = (√3/4)a 2  square units

A = (√3/4)(2√3) 2  = (√3/4)(12) = 3√3 = 3(1.732) = 5.196 cm 2  .

20) The length of each side of an equilateral triangle having an area of 9√3 cm 2 is

Given: Area of equilateral triangle = 9√3 cm 2

Hence, (√3/4)a 2  = 9√3

a 2  = [(9√3)(4)]/√3

Related Articles

• Heron’s Formula
• Maths Formulas for Class 9
• Important Questions for Class 9 Maths
• Heron’s Formula Class 9 Notes: Chapter 12
• Important Questions Class 9 Maths Chapter 12-Heron’s Formula
• CBSE Class 9 Maths Examination 2018: Important 3 marks questions

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Case Study Questions for Class 9 Science Chapter 1 Matter in Our Surroundings

• Last modified on: 1 week ago
• Reading Time: 6 Minutes

Here we are providing case study questions for class 9 science chapter 12 sound. Students are suggested to go through each and every case study questions for better understanding of the chapter.

Case Study/Passage Based Questions:

Question 1:

Read the following passage and answer the questions given below.

Every matter is made up of tiny particles. These particles are so tiny that they can’t be seen with naked eyes.

The three characteristics shown by particles of matter are as follows:

(i) There are small voids between particles in a matter. This characteristic is the concept behind the solubility of a substance in other substances.

(ii) Particles of matter show continuous random movements, that is they possess kinetic energy. The spreading of ink in a beaker of glass, smell of agarbattis, etc. are few illustrations that show the movement of particles of a substance.

(iii) The particles of matter attract each other with a force called interparticle force of attraction. Read the given passage carefully and give the answer of the following questions:

Q 1. Spreading of fragrance of a burning incense stick in a room shows that:

a. particles of matter have spaces between them.

b. particles of matter attract each other.

c. particles of matter are constantly moving.

d. None of the above

Q 2. What happens when we add sugar to water?

a. Volume of water doubles.

b. Volume of water decreases

c. Volume of water remains the same.

Q 3. A stream of water cannot be cut by fingers. Which property of matter does this observation show?

a. Particles of matter attract each other.

b. Particles of matter have spaces between them.

c. Particles of matter are continuously moving.

Q 4. When we put some crystals of potassium permanganate in a beaker containing water, we observe that after some time, the whole water turns pink. This intermixing of particles of two different types of matter on their own is called:

a. Brownian motion

c. sublimation

d. diffusion

Q 5. Why is the rate of diffusion of liquids higher than that of solids?

a. In the liquid state, particles are tightly packed as compared to solids.

b. In the liquid state, particles move freely as compared to solids.

c. In solid state, particles have least force of attraction between the particles.

d. In solid state, particles cannot be compressed easily.

• (c) particles of matter are constantly moving.
• (c) Volume of water remains the same.
• (a) Particles of matter attract each other.
• (d) diffusion
• (b) In the liquid state, particles move freely as compared to solids

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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

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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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Class 9 Maths Case Study Questions of Chapter 13 Surface Areas and Volumes

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

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

Surface Areas and Volumes Case Study Questions With Answers

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

Case Study/Passage-Based Questions

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

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

Answer: (a) 288 π cm3

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

Answer: (d) Volume

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

Answer: (d) 6 cm

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

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

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

Answer: (b) 660 cm2

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

Answer: (c) 7 cm

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

Answer: (a) 154 cm2

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

Answer: (d) 71 cm2

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

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

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

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 13 Surface Areas and Volumes with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Surface Areas and Volumes Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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