case study questions for class 9 maths chapter 2

Case Study Questions for Class 9 Maths

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Are you preparing for your Class 9 Maths board exams and looking for an effective study resource? Well, you’re in luck! In this article, we will provide you with a collection of Case Study Questions for Class 9 Maths specifically designed to help you excel in your exams. These questions are carefully curated to cover various mathematical concepts and problem-solving techniques. So, let’s dive in and explore these valuable resources that will enhance your preparation and boost your confidence.

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

CBSE Class 9 Maths Board Exam will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 9  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

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CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution

Case study questions are a form of examination where students are presented with real-life scenarios that require the application of mathematical concepts to arrive at a solution. These questions are designed to assess students’ problem-solving abilities, critical thinking skills, and understanding of mathematical concepts in practical contexts.

Chapterwise Case Study Questions for Class 9 Maths

Case study questions play a crucial role in the field of mathematics education. They provide students with an opportunity to apply theoretical knowledge to real-world situations, thereby enhancing their comprehension of mathematical concepts. By engaging with case study questions, students develop the ability to analyze complex problems, make connections between different mathematical concepts, and formulate effective problem-solving strategies.

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

The above  Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.

• Class 9 Science Case Study Questions
• Class 9 Social Science Case Study Questions

How to Approach Case Study Questions

When tackling case study questions, it is essential to adopt a systematic approach. Here are some steps to help you approach and solve these types of questions effectively:

• Read the case study carefully: Understand the given scenario and identify the key information.
• Identify the mathematical concepts involved: Determine the relevant mathematical concepts and formulas applicable to the problem.
• Formulate a plan: Devise a plan or strategy to solve the problem based on the given information and mathematical concepts.
• Solve the problem step by step: Apply the chosen approach and perform calculations or manipulations to arrive at the solution.
• Verify and interpret the results: Ensure the solution aligns with the initial problem and interpret the findings in the context of the case study.

Tips for Solving Case Study Questions

Here are some valuable tips to help you effectively solve case study questions:

• Read the question thoroughly and underline or highlight important information.
• Break down the problem into smaller, manageable parts.
• Visualize the problem using diagrams or charts if applicable.
• Use appropriate mathematical formulas and concepts to solve the problem.
• Show all the steps of your calculations to ensure clarity.
• Check your final answer and review the solution for accuracy and relevance to the case study.

Benefits of Practicing Case Study Questions

Practicing case study questions offers several benefits that can significantly contribute to your mathematical proficiency:

• Enhances critical thinking skills
• Improves problem-solving abilities
• Deepens understanding of mathematical concepts
• Develops analytical reasoning
• Prepares you for real-life applications of mathematics
• Boosts confidence in approaching complex mathematical problems

Case study questions offer a unique opportunity to apply mathematical knowledge in practical scenarios. By practicing these questions, you can enhance your problem-solving abilities, develop a deeper understanding of mathematical concepts, and boost your confidence for the Class 9 Maths board exams. Remember to approach each question systematically, apply the relevant concepts, and review your solutions for accuracy. Access the PDF resource provided to access a wealth of case study questions and further elevate your preparation.

Q1: Can case study questions help me score better in my Class 9 Maths exams?

Yes, practicing case study questions can significantly improve your problem-solving skills and boost your performance in exams. These questions offer a practical approach to understanding mathematical concepts and their real-life applications.

Q2: Are the case study questions in the PDF resource relevant to the Class 9 Maths syllabus?

Absolutely! The PDF resource contains case study questions that align with the Class 9 Maths syllabus. They cover various topics and concepts included in the curriculum, ensuring comprehensive preparation.

Q3: Are the solutions provided for the case study questions in the PDF resource?

Yes, the PDF resource includes solutions for each case study question. You can refer to these solutions to validate your answers and gain a better understanding of the problem-solving process.

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CBSE Class 9 Mathematics Case Study Questions

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

Significance of Mathematics in Class 9

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

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

Case studies in Class 9 Mathematics

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

Example of Case study questions in Class 9 Mathematics

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

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

Class 9 Mathematics Case study question 1

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

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

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

Now answer the following questions:

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

Class 9 Mathematics Case study question 3

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

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

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

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

Class 9 Mathematics Curriculum at Glance

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

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

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

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

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

myCBSEguide: Blessing in disguise

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

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

This method is not easy for me

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

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CBSE 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.

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Important Questions Class 9 Maths Chapter 2

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Important Questions Class 9 Mathematics Chapter 2- Polynomials.

Mathematics Chapter 2 of Class 9  is about Polynomials. Polynomial consists of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is explained as an expression which is composed of variables, constants and exponents that are combined using mathematical operations like addition, subtraction, multiplication and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.

Quick Links

Extramarks is one of the leading online learning platforms trusted by lakhs of students and educators across the country.  Students can register on the Extramarks website to access our study materials, including NCERT solutions, CBSE sample papers, revision notes, etc. Our in-house mathematics faculty experts have developed these study materials s by referring to the CBSE curriculum.

Our Mathematics experts believe that students must practice questions regularly to perform  better in exams. For this purpose, they have prepared the Important Questions Class 9 Mathematics Chapter 2 to help students get access to questions from all the topics of the Polynomials. The questions are followed by their step-by-step answers, which will further help students to revise the chapter. The questions are curated from various sources such as the NCERT textbook and exemplar book, CBSE past years’ question papers, and other reference materials. 

Extramarks believes in incorporating joyful learning experiences through its own repository.

To get access to our comprehensive study solutions, students can register on Extramarks platform. Along with the Important Questions Class 9 Mathematics Chapter 2, students will be able to access other study resources such as NCERT solutions, chapter-wise notes, CBSE revision notes, CBSE mock tests, etc.

Important Questions Class 9 Mathematics Chapter 2 – With Solutions

Our in-house Mathematics faculty experts  have collated a complete list of Important Questions Class 9 Mathematics Chapter 2 by referring to various sources. The subject experts have meticulously prepared  illustration for individual questions that will enable students to comprehend the notions used in each question. Furthermore, the questions are selected in a way that would cover all the topics. So by practising from our question bank, students will be able to revise the chapter and understand their strong and weak topics. And enhance their preparation by further concentrating on weaker sections of the chapter.

Given below are a few of the questions and answers from our question bank of Important Questions Class 9 Mathematics Chapter 2:

Question 1: Calculate the value of 9x² + 4y² if xy = 6 and 3x + 2y = 12.

Answer 1: Consider the equation 3x + 2y = 12

Now, square both sides:

(3x + 2y)² = 12²

=> 9x² + 12xy + 4y² = 144

=>9x² + 4y² = 144 – 12xy

From the questions, xy = 6

9x² + 4y² = 144 – 72

Thus, the value of 9x² + 4y² = 72

Question 2:Evaluate the following using suitable identity

Answer 2: We can write 102 as 100+2

Using identity,(x+y) ³ = x ³ +y ³ +3xy(x+y)

(100+2) ³ =(100) ³ +2 ³ +(3×100×2)(100+2)

= 1000000 + 8 + 600(100 + 2)

= 1000000 + 8 + 60000 + 1200

Question 3:Without any actual division, prove that the following 2x⁴

 – 5x³ + 2x² – x + 2 is divisible by x² – 3x + 2.

[Hint: Factorise x² – 3x + 2]

Answer 3: x²-3x+2

x(x-2)-1(x-2)

Therefore,(x-2)(x-1)are the factors.

Considering (x-2),

Then, p(x) becomes,

p(x)=2x⁴-5x³+2x²-x+2

p(2)=2(2)⁴-5(2)³+2(2)²-2+2

Therefore, (x-2) is a factor.

Considering (x-1),

p(1)=2(1)⁴-5(1)³+2(1)²-1+2

Therefore, (x-1) is a factor.

Question 4: Using the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case

(i) p(x) = 2x³+x²–2x–1, g(x) = x+1

Answer 4 :p(x) = 2x³+x²–2x–1, g(x) = x+1

∴Zero of g(x) is -1.

p(−1) = 2(−1)³+(−1)²–2(−1)–1

∴By the given factor theorem, g(x) is a factor of p(x).

Question 5: Obtain an example of a monomial and a binomial having degrees of 82 and 99, respectively.

Answer 5: An example of a monomial having a degree of 82 = x⁸²

An example of a binomial having a required degree of 99 = x⁹⁹ + 7

Question 6: If the two  x – 2 and x – ½ are the given factors of px ²

 + 5 x + r , show that p = r .

Answer 6: Given, f(x) = px²+5x+r and factors are x-2, x – ½

Substituting x = 2 in place of the equation, we get

f(x) = px²+5x+r

f(2) = p(2)²+5(2)+r=0

= 4p + 10 + r = 0 … eq.(i)

Substituting x = ½ in place of the equation, we get,

f( ½ ) = p( ½ )² + 5( ½ ) + r =0

= p/4 + 5/2 + r = 0

= p + 10 + 4r = 0 … eq(ii)

On solving eq(i) and eq(ii),

4p + r = – 10 and p + 4r = – 10

 the RHS of both equations are the same,

4p + r = p + 4r

Hence Proved.

Question 7: Identify constant, linear, quadratic, cubic and quartic polynomials from the following.

(i) – 7 + x

(iii) – ? ³

(iv) 1 – y – ? ³

(v) x – ? ³ + ?⁴

(vi) 1 + x + ?²

Answer 7: (i) – 7 + x

The degree of – 7 + x is 1.

Hence, it is a linear polynomial.

The degree of 6y is 1.

Therefore, it is a linear polynomial.

We know that the degree of – ? ³ is 3.

Therefore, it is a cubic polynomial.

We know that the degree of 1 – y – ? ³ is 3.

We know that the degree of x – ? ³ + ?⁴ is 4.

Therefore, it is a quartic polynomial.

We know that the degree of 1 + x + ?² is 2.

Therefore, it is a quadratic polynomial.

We know that the degree of -6?² is 2.

We know that -13 is a constant.

Therefore, it is a constant polynomial.

We know that the degree of –p is 1.

Question 8: Observe the value of the polynomial 5x – 4x² + 3 at x = 2 and x = –1.

Answer 8 : Let the polynomial be f(x) = 5x – 4x² + 3

Now, for x = 2,

f(2) = 5(2) – 4(2)² + 3

=> f(2) = 10 – 16 + 3 = –3

Or, the value of the polynomial 5x – 4x² + 3 at x = 2 is -3.

Similarly, for x = –1,

f(–1) = 5(–1) – 4(–1)² + 3

=> f(–1) = –5 –4 + 3 = -6

The value of the polynomial 5x – 4x² + 3 at x = -1 is -6.

Question 9:Expanding each of the following, using all the suitable identities:

(i) (x+2y+4z)²

(ii) (2x−y+z)²

(iii) (−2x+3y+2z)²

(iv) (3a –7b–c)²

(v) (–2x+5y–3z)²

Answer 9: (i) (x+2y+4z)²

Using identity, (x+y+z)² = x²+²+z²+2xy+2yz+2zx

Here, x = x

(x+2y+4z)² = x²+(2y)²+(4z)²+(2×x×2y)+(2×2y×4z)+(2×4z×x)

= x²+4y²+16z²+4xy+16yz+8xz

Using identity, (x+y+z)² = x²+y²+z²+2xy+2yz+2zx

Here, x = 2x

(2x−y+z)² = (2x)²+(−y)²+z²+(2×2x×−y)+(2×−y×z)+(2×z×2x)

= 4x²+y²+z²–4xy–2yz+4xz

Here, x = −2x

(−2x+3y+2z)² = (−2x)²+(3y)²+(2z)²+(2×−2x×3y)+(2×3y×2z)+(2×2z×−2x)

= 4x²+9y²+4z²–12xy+12yz–8xz

Using identity (x+y+z)²= x²+y²+z²+2xy+2yz+2zx

Here, x = 3a

(3a –7b– c)² = (3a)²+(– 7b)²+(– c)²+(2×3a ×– 7b)+(2×– 7b ×– c)+(2×– c ×3a)

= 9a² + 49b² + c²– 42ab+14bc–6ca

Here, x = –2x

(–2x+5y–3z)² = (–2x)² + (5y)² + (–3z)² + (2 × –2x × 5y) + (2 × 5y× – 3z)+(2×–3z ×–2x)

= 4x²+25y² +9z²– 20xy–30yz+12zx

Question 10: If the polynomials az³ + 4z² + 3z – 4 and z³ – 4z + leave the same remainder when divided by z – 3, find the value of a.

Answer 10: Zero of the polynomial,

Hence, zero of g(z) = – 2a

Let p(z) = az³+4z²+3z-4

Now, substituting the given value of z = 3 in p(z), we get,

p(3) = a (3)³ + 4 (3)² + 3 (3) – 4

⇒p(3) = 27a+36+9-4

⇒p(3) = 27a+41

Let h(z) = z³-4z+a

Now, by substituting the value of z = 3 in h(z), we get,

h(3) = (3)³-4(3)+a

⇒h(3) = 27-12+a

⇒h(3) = 15+a

As per the question,

The two polynomials, p(z) and h(z), leave the same remainder when divided by z-3

So, h(3)=p(3)

⇒15+a = 27a+41

⇒15-41 = 27a – a

Question 11: Compute the perimeter of a rectangle whose area is 25x² – 35x + 12. 

Answer 11: A rea of rectangle = 25x² – 35x + 12

We know the area of a rectangle = length × breadth

So, by factoring 25x² – 35x + 12, the length and breadth can be obtained.

25x² – 35x + 12 = 25x² – 15x – 20x + 12

=> 25x² – 35x + 12 = 5x(5x – 3) – 4(5x – 3)

=> 25x² – 35x + 12 = (5x – 3)(5x – 4)

Thus, the length and breadth of a rectangle are (5x – 3)(5x – 4).

So, the perimeter = 2(length + breadth)

Therefore, the perimeter of the given rectangle = 2[(5x – 3)+(5x – 4)]

                                                                                 = 2(5x – 3 + 5x – 4)

                                                                                = 2(10x – 7) 

                                                                                = 20x – 14

Hence, the perimeter of the rectangle = 20x – 14

Question 12: 2x²+y²+²–2√2xy+4√2yz–8xz

Answer 12: Using identity, (x +y+z)² = x²+y²+z²+2xy+2yz+2zx

We can say that, x²+²+²+2xy+2yz+2zx = (x+y+z)²

2x²+y²+8z²–2√2xy+4√2yz–8xz

= (-√2x)²+(y)²+(2√2z)²+(2×-√2x×y)+(2×y×2√2z)+(2×2√2×−√2x)

= (−√2x+y+2√2z)²

= (−√2x+y+2√2z)(−√2x+y+2√2z)

Question 13: If ? + 2? is a factor of ? ⁵ – 4?²?³ + 2? + 2? + 3, find a.

Answer 13: According to the question,

Let p(x) = x ⁵ – 4a²x³ + 2x + 2a + 3 and g(x) = x + 2a

⟹ x + 2a = 0

Hence, zero of g(x) = – 2a

As per the factor theorem,

If g(x) is a factor of p(x), then p( – 2a) = 0

So, substituting the value of x in p(x), we get,

p ( – 2a) = ( – 2a) ⁵ – 4a²( – 2a)³ + 2( – 2a) + 2a + 3 = 0

⟹ – 32a ⁵ + 32a ⁵ – 2a + 3 = 0

⟹ – 2a = – 3

Question 14: Find the value of x³+ y ³ + z ³ – 3xyz if x² + y² + z² = 83 and x + y + z = 1

Answer 14: Consider the equation x + y + z = 15

From algebraic identities, we know that (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)

From the question, x² + y² + z²= 83 and x + y + z = 15

152 = 83 + 2(xy + yz + xz)

=> 225 – 83 = 2(xy + yz + xz)

Or, xy + yz + xz = 142/2 = 71

Using algebraic identity a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca),

x ³ + y ³ + z ³ – 3xyz = (x + y + z)(x² + y² + z² – (xy + yz + xz))

x + y + z = 15, x² + y² + z² = 83 and xy + yz + xz = 71

So, x ³ + y ³ + z ³ – 3xyz = 15(83 – 71)

=> x ³ + y ³ + z ³ – 3xyz = 15 × 12

Or, x ³ + y ³ + z ³ – 3xyz = 180

Question 15:Verify that:

(i) x³+y³ = (x+y)(x²–xy+y²)

(ii) x³–y³ = (x–y)(x²+xy+y²)

Answer 15: (i) x³+y³ = (x+y)(x²–xy+y²)

                     We know that (x+y)³= x³+y³+3xy(x+y)

                      ⇒ x³+y³ = (x+y)³–3xy(x+y)

                      ⇒ x³+y³ = (x+y)[(x+y)²–3xy]

                     Taking (x+y) common ⇒ x³+y³ = (x+y)[(x²+y²+2xy)–3xy]

                     ⇒ x³+y³ = (x+y)(x²+y²–xy)

                   (ii) x³–y³ = (x–y)(x²+xy+y²) 

                   We know that (x–y)³ = x³–y³–3xy(x–y)

                    ⇒ x³−y³ = (x–y)³+3xy(x–y)

                    ⇒ x³−y³ = (x–y)[(x–y)²+3xy]

                  Taking (x+y) common ⇒ x³−y³ = (x–y)[(x²+y²–2xy)+3xy]

                    ⇒ x³+y³ = (x–y)(x²+y²+xy)

Question 16: For what value of m is ?³ – 2??² + 16 divisible by x + 2?

Answer 16: According to the question,

Let p(x) = x³ – 2mx² + 16, and g(x) = x + 2

⟹ x + 2 = 0

Hence, zero of g(x) = – 2

if p(x) is divisible by g(x), then the remainder of p(−2) should be zero.

Thus, substituting the value of x in p(x), we obtain,

p( – 2) = 0

⟹ ( – 2)³ – 2m( – 2)² + 16 = 0

⟹ 0 – 8 – 8m + 16 = 0

Question 17:If a + b + c = 15 and a² + b² + c² = 83, find the value of a³ + b³ + c³ – 3abc.

Answer 17: We know that,

a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca) ….(i)

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca ….(ii)

Given, a + b + c = 15 and a² + b² + c² = 83

From (ii), we have

152 = 83 + 2(ab + bc + ca)

⇒ 225 – 83 = 2(ab + bc + ca)

⇒ 142/2 = ab + bc + ca

⇒ ab + bc + ca = 71

Now, (i) can be written as

a³ + b³ + c³ – 3abc = (a + b + c)[(a² + b² + c² ) – (ab + bc + ca)]

a³ + b³+ c³ – 3abc = 15 × [83 – 71] = 15 × 12 = 180.

Question 18: Factorise: 27x³+y³+z³–9xyz

Answer 18: The expression27x³+y³+z³–9xyz can be written as (3x)³+y³+z³–3(3x)(y)(z)

27x³+y³+z³–9xyz = (3x)³+y³+z³–3(3x)(y)(z)

We know that x³+y³+³–3xyz = (x+y+z)(x²+y²+z²–xy –yz–zx)

= (3x+y+z)[(3x)²+y²+z²–3xy–yz–3xz]

= (3x+y+z)(9x²+y²+²–3xy–yz–3xz)

Question 19: If (x – 1/x) = 4, then evaluate (x² + 1/x²) and (x⁴ + 1/x⁴).

Answer 19: Given, (x – 1/x) = 4

Squaring both sides, we get,

(x – 1/x)² = 16

⇒ x² – 2.x.1/x + 1/x² = 16

⇒ x² – 2 + 1/x² = 16

⇒ x² + 1/x² = 16 + 2 = 18

∴ (x² + 1/x²) = 18 ….(i)

Again, squaring both sides of (i), we get

(x² + 1/x²)² = 324

⇒ x⁴ + 2.x².1/x² + 1/x⁴= 324

⇒ x⁴ + 2 + 1/x⁴ = 324

⇒ x⁴ + 1/x⁴ = 324 – 2 = 322

∴ (x⁴ + 1/x⁴) = 322.

Question 20: Factorise

Answer 20: The expression 64m³–343n³ can be written as (4m)³–(7n)³

64m³–343n³ =(4m)³–(7n)³

We know that x³–y³ = (x–y)(x²+xy+y²)

64m³–343n³ = (4m)³–(7n)³

= (4m-7n)[(4m)²+(4m)(7n)+(7n)²]

= (4m-7n)(16m²+28mn+49n² )

Question 21: Find out the values of a and b so that (2x³ + ax² + x + b) has (x + 2) and (2x – 1) as factors.

Answer 21: Let p(x) = 2x³ + ax² + x + b. Then, p( –2) = and p(½) = 0.

p(2) = 2(2)³ + a(2)² + 2 + b = 0

⇒ –16 + 4a – 2 + b = 0 ⇒ 4a + b = 18 ….(i)

p(½) = 2(½)³ + a(½)² + (½) + b = 0

⇒ a + 4b = –3 ….(ii)

On solving (i) and (ii), we get a = 5 and b = –2.

Hence, a = 5 and b = –2.

Question 22: Explain that p – 1 is a factor of p¹⁰ – 1 and p¹¹ – 1.

Answer 22: According to the question,

Let h(p) = ?¹⁰ − 1,and g(p) = ? – 1

zero of g(p) ⇒ g(p) = 0

Therefore, zero of g(x) = 1

We know that,

According to the factor theorem, if g(p) is a factor of h(p), then h(1) should be zero

h(1) = (1) ¹⁰ − 1 = 1 − 1 = 0

⟹ g (p) is a factor of h(p).

Here, we have h(p) = ?¹¹ − 1, g (p) = ? – 1

Putting g (p) = 0 ⟹ ? − 1 = 0 ⟹ ? = 1

As per the factor theorem, if g (p) is a factor of h(p),

Then h(1) = 0

⟹ (1) ¹¹ – 1 = 0

Hence, g(p) = ? – 1 is the factor of h(p) = ? ¹⁰ – 1

Question 23: Examine whether (7 + 3x) is a factor of (3×3 + 7x).

Answer 23: Let p(x) = 3×3 + 7x and g(x) = 7 + 3x. Now g(x) = 0 ⇒ x = –7/3.

By the remainder theorem, p(x) is divided by g(x), and then the remainder is p(–7/3).

Now, p(–7/3) = 3(–7/3)3 + 7(–7/3) = –490/9 ≠ 0.

∴ g(x) is not a factor of p(x).

Question 24:Prove that:

x³+y³+z³–3xyz = (1/2) (x+y+z)[(x–y)²+(y–z)²+(z–x)²]

Answer 24: We know that,

x³+y³+z³−3xyz = (x+y+z)(x²+y²+z²–xy–yz–xz)

⇒ x³+y³+z³–3xyz = (1/2)(x+y+z)[2(x²+y²+z²–xy–yz–xz)]

= (1/2)(x+y+z)(2×2+2y²+²–2xy–2yz–2xz)

= (1/2)(x+y+z)[(x²+y²−2xy)+(y²+z²–2yz)+(x²+z²–2xz)]

= (1/2)(x+y+z)[(x–y)²+(y–z)²+(z–x)²]

Question 25: Find out which of the following polynomials has x – 2 a factor:

(i) 3?² + 6?−24.

(ii) 4?² + ?−2.

Answer 25: (i) According to the question,

Let p(x) =3?² + 6?−24 and g(x) = x – 2

g(x) = x – 2

zero of g(x) ⇒ g(x) = 0

Hence, zero of g(x) = 2

Thus, substituting the value of x in p(x), we get,

p(2) = 3(2)² + 6 (2) – 24

= 12 + 12 – 24

 the remainder = zero,

We can derive that,

g(x) = x – 2 is factor of p(x) = 3?² + 6?−24

(ii) According to the question,

Let p(x) = 4?² + ?−2 and g(x) = x – 2

p(2) = 4(2)² + 2−2

Since the remainder ≠ zero,

We can say that,

g(x) = x – 2 is not a factor of p(x) = 4?² + ?−2

Question 26: Factorise x² + 1/x² + 2 – 2x – 2/x.

Answer 26 : x² + 1/x² + 2 – 2x – 2/x = (x² + 1/x² + 2) – 2(x + 1/x)

= (x + 1/x)² – 2(x + 1/x)

= (x + 1/x)(x + 1/x – 2).

Question 27: Factorise

8a³+b³+12a²b+6ab²

Answer 27: The expression, 8a³+b³+12a²b+6ab² can be written as (2a)³+b³+3(2a)²b+3(2a)(b)²

8a³+b³+12a²b+6ab² = (2a)³+b³+3(2a)²b+3(2a)(b)²

= (2a+b)(2a+b)(2a+b)

Here, the identity, (x +y)³ = x³+y³+3xy(x+y) is used.

Question 28: By Remainder Theorem, find out the remainder when p(x) is divided by g(x), where

(i) p(?) = ?³ – 2?² – 4? – 1, g(?) = ? + 1

(ii) p(?) = ?³ – 3?² + 4? + 50, g(?) = ? – 3

(iii) p(?) = 4?³ – 12?² + 14? – 3, g(?) = 2? – 1

(iv) p(?) = ?³ – 6?² + 2? – 4, g(?) = 1 – 3/2 ?

Answer 28: (i) Given p(x) = ?³ – 2?² – 4? – 1 and g(x) = x + 1

Here zero of g(x) = – 1

By applying the remainder theorem

P(x) divided by g(x) = p( – 1)

P ( – 1) = ( – 1)³ – 2 ( – 1)² – 4 ( – 1) – 1 = 0

Therefore, the remainder = 0

(ii) given p(?) = ?³ – 3?² + 4? + 50, g(?) = ? – 3

Here zero of g(x) = 3

By applying the remainder theorem p(x) divided by g(x) = p(3)

p(3) = 3³ – 3 × (3)² + 4 × 3 + 50 = 62

Therefore, the remainder = 62

(iii) p(x) = 4x³ – 12x² + 14x – 3, g(x) = 2x – 1

Here zero of g(x) = ½

By applying the remainder theorem p(x) divided by g(x) = p (½)

P( ½ ) = 4( ½ )³ – 12( ½ )² + 14 ( ½ ) – 3

           = 4/8 – 12/4 + 14/2 – 3

           = ½ + 1

           = 3/2

Hence, the remainder = 3/2

so, zero of g(x) = 2/3

By applying the remainder theorem p(x) divided by g(x) = p(2/3)

p(2/3) = (2/3)³ – 6(2/3)² + 2(2/3) – 4

Therefore, the remainder = – 136/27

Question 29:Factorise x² – 1 – 2a – a².

Answer 29: x² – 1 – 2a – a² = x² – (1 + 2a + a²)

= x² – (1 + a)²

= [x – (1 – a)][x + 1 + a]

= (x – 1 – a)(x + 1 + a)

∴ x² – 1 – 2a – a² = (x – 1 – a)(x + 1 + a).

Question 30:Evaluate the following using suitable identity

Answer 30: We can write 99 as 1000–2

Using identity,(x–y)³ = x³ –y³ –3xy(x–y)

(998)³ =(1000–2)³ 

=(1000)³ –2³ –(3×1000×2)(1000–2)

= 1000000000–8–6000(1000– 2)

= 1000000000–8- 6000000+12000

= 994011992

Question 31: Find the zeroes of the polynomial:

p(?)= (? –2)² −(? + 2)² 

Answer 31: p(x) = (? –2)² −(? + 2)² 

Zero of the polynomial p(x) = 0

Hence, we get,

⇒ (x–2)² −(x + 2)² = 0

Expanding using the identity, a² – b² = (a – b) (a + b)

⇒ (x – 2 + x + 2) (x – 2 –x – 2) = 0

⇒ 2x ( – 4) = 0

Therefore, the zero of the polynomial = 0

Benefits Of Solving Important Questions Class 9 Mathematics Chapter 2

Consistently solving questions is a vital element of mastering   Mathematics. By solving Mathematics Class 9 Chapter 2 important questions, students can get a further understanding of the polynomials chapter. 

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• Class 9 Mathematics Chapter 2 important questions provide details about the types of questions that may be expected in the exams, which increases their confidence in achieving a high grade. . 
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Q.1 By actual division, find the quotient and the remainder when x 5 + 1 is divided by x 1

Marks: 3 Ans

x 4 + x 3 + x 2 + x + 1 x 1 x 5 + 1 x 5 x 4 + x 4 + 1 x 4 x 3 + x 3 + 1 x 3 x 2 + ¯ x 2 + 1 x 2 x + x + 1 x 1 + 2 ¯ ¯ ¯ ¯ Quotient : x 4 + x 3 + x 2 + x + 1 Remainder : 2

Q.2 Find the value of k if x 5 is a factor of kx 2 + 3x + 7.

Marks: 2 Ans

Zero of x 5 is 5 as x 5 = 0 gives x = 5 . p(x) = kx 2 + 3 x + 7 p ( 5 ) = 0 25 k + 15 + 7 = 0 25 k + 22 = 0 k = 22 25

Q.3 If x + y + z = 6 and xy + yz + zx = 11, then find the value of x 2 + y 2 + z 2 .

Given : x + y + z = 6 and xy + yz + zx = 11 Squaring both sides , we get x + y + z 2 = 6 2 x 2 + y 2 + z 2 + 2 xy + 2 yz + 2 zx = 36 x 2 + y 2 + z 2 + 2 xy + yz + zx = 36 x 2 + y 2 + z 2 + 2 11 = 36 Since xy + yz + zx = 11 x 2 + y 2 + z 2 + 22 = 36 x 2 + y 2 + z 2 = 36 22 = 14

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Faqs (frequently asked questions), 1. what are the four types of polynomials.

The 4 types of polynomials are zero polynomial, linear polynomial, quadratic polynomial, and cubic polynomial.

2. Where can I get important questions for Class 9 Mathematics Chapter 2 online?

On the Extramarks website, you can find all of the important questions for Class 9 Mathematics Chapter 2, along with their answers. On the website, you can also find important questions and NCERT solutions for all classes from 1 to 12.

3. What are the important chapters in Class 9 Mathematics?

The NCERT Mathematics book has 15 chapters. Each chapter is equally important when it comes to learning the fundamentals and taking the test. Additionally, because CBSE does not specify the distribution of marks for each chapter, students are advised to fully study all chapters. Each and every chapter must be completely understood to acquire a good grade in exams.

 All the fifteen chapters of CBSE Class 9 Mathematics syllabus are given below:

• Chapter – Number Systems
• Chapter – Polynomials
• Chapter – Coordinate Geometry
• Chapter – Linear Equations In Two Variables
• Chapter – Introduction To Euclid’s Geometry
• Chapter – Lines And Angles
• Chapter – Triangles
• Chapter – Quadrilaterals
• Chapter – Areas Of Parallelograms And Triangles
• Chapter – Circles
• Chapter – Constructions
• Chapter – Heron’s Formula
• Chapter – Surface Areas And Volumes
• Chapter – Statistics
• Chapter – Probability

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

CBSE Case Study Questions for Class  9 Maths

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

Chapter Wise Case Based Questions for Class 9 Maths

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

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

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

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

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

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

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

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

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

Class 9 Maths Curriculum at Glance

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

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

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

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

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

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

What is case-based questions.

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

What are case-based questions in Maths?

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

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

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

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

CBSE Case Study Questions for Class 9 Maths - Pdf

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

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RS Aggarwal Solutions Class 9 Chapter 2 Polynomials

RS Aggarwal Solutions for Class 9 Maths Book Chapter 2 Polynomials are available here. Study path has prepared solutions of all the exercises of the chapter by our expert math teachers to help you to get good marks in exams. This lesson has a ton of questions that are very important from the examination point of view.

We at Study Path solved each questions step by step with detailed explanations. Students must practice from practice these problems to score high marks in Maths. Below we have listed the Class 9 RS Aggarwal Solutions Chapter 2 Polynomials Exercise 2A, Ex 2B, Ex 2C, Ex 2D and Multiple Choice Questions (MCQs).

Class 9 RS Aggarwal Solutions Chapter 2 Polynomials

Class 9 rs aggarwal solutions chapter 2 ex 2a.

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2B

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2C

Class 9 RS Aggarwal Solutions Chapter 2 Ex 2D

Class 9 RS Aggarwal Solutions Chapter 2 MCQs

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NCERT Solutions Class 9 Maths Chapter 2 Polynomials

NCERT solutions for class 9 maths Chapter 2 Polynomials are all about the basics of polynomials like the different types of polynomials, finding roots, or solutions to a polynomial equation. Polynomials are algebraic expressions having one variable or more. These NCERT solutions class 9 maths Chapter 2 also explain the remainder theorem and factor theory of polynomials in detail, the algebraic identities, and polynomials of various degrees.

Class 9 Maths NCERT Solutions Chapter 2 polynomials illustrate the difference between linear, quadratic, and cubic polynomials. Important theorems mentioned are the Remainder theorem and the Factor theorem, which help identify the factors of a polynomial. Students can access the solutions from the pdf links given below and also find some of these in the exercises given below.

• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.1
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.2
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.3
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.4
• NCERT Solutions Class 9 Maths Chapter 2 Ex 2.5

NCERT Solutions for Class 9 Maths Chapter 2 PDF

The exercises related to identifying the type of polynomial, finding the roots or solution of a polynomial equation, and finding factors of the polynomial are available for free pdf download using the four links provided below:

☛ Download Class 9 Maths NCERT Solutions Chapter 2 Polynomials

NCERT Class 9 Maths Chapter 2   Download PDF

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

These fundamental properties and theorems of polynomials form the building blocks for higher mathematics. Thus, it is very important to master the fundamentals by solving many different example exercises using the links provided above. These NCERT Solution exercises will help understand the properties of polynomials better, as well as how to utilize them. Chapter-wise detailed analysis of NCERT Solutions Class 9 Maths Chapter 2 Polynomials is given below.

• Class 9 Maths Chapter 2 Ex 2.1 - 21 Questions
• Class 9 Maths Chapter 2 Ex 2.2 - 22 Questions
• Class 9 Maths Chapter 2 Ex 2.3 - 7 Questions
• Class 9 Maths Chapter 2 Ex 2.4 - 7 Questions
• Class 9 Maths Chapter 2 Ex 2.5 - 41 Questions

☛ Download Class 9 Maths Chapter 2 NCERT Book

Topics Covered: The topics that are covered under the chapter on polynomials include an explanation of polynomials as a special set of algebraic equations, different types of polynomials, solutions of polynomial equations, factor theorem, and remainder theorem. Also, these class 9 maths NCERT solutions Chapter 2 define the algebraic identities , which help in factorizing the algebraic equations.

Total Questions: Class 9 Maths Chapter 2 Polynomials consists of a total of 45 questions, of which 31 are easy, 9 are moderate, and 5 are long answer type questions.

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

List of Formulas in NCERT Solutions Class 9 Maths Chapter 2

NCERT solutions class 9 maths Chapter 2 covers lots of important concepts crucial for understanding higher grade maths. By learning to factorize a polynomial expression, one can find the roots of the polynomial equation. This is a relatively simple process that can greatly improve an individual's understanding of polynomial equations. Some important algebraic identities or formulas which help in factorization and are covered in NCERT solutions for class 9 maths chapter 2 are given below.

• ( x + y ) 2 = x 2 + 2xy + y 2
• ( x + y ) 3 = x 3 + y 3 + 3xy (x+y)

Important Questions for Class 9 Maths NCERT Solutions Chapter 2

Video Solutions for Class 9 Maths NCERT Chapter 2

FAQs on NCERT Solutions Class 9 Maths Chapter 2

How cbse students can utilize ncert solutions class 9 maths chapter 2 effectively.

Algebra forms the basis of higher mathematical studies. Hence, students should focus on the important terms defined in this chapter, like the degree of a polynomial, the difference between constant and variable, to get a clear understanding of the polynomials. This will help them to make their base strong to appear for their board exams and face any kind of difficult questions.

Why are Class 9 Maths NCERT Solutions Chapter 2 Important?

The NCERT Solutions Class 9 Maths Chapter 2 includes a detailed explanation of the remainder and the factor theorem, which hold an important place in algebra. Also, the crucial algebraic identities are discussed in an elaborate manner with plenty of questions to solve for the students. A list of all key equations and concepts is available at the end of the chapter. This is a significant benefit because students can use this list whenever required instead of figuring it out from between the lengthy chapter text. Overall, these solutions cover all of the major concepts, approaches, and formulas, making them of utmost importance for class 9 math students.

How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 2 Polynomials?

Overall the NCERT Solutions Class 9 Maths Chapter 2 has 98 questions that can be categorized as easy, medium, and difficult ones. Roughly 70 questions are straightforward and easy to solve, 20 questions are of medium difficulty level while 8 would require some thinking as they are long-form questions.

What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 2?

The important topics that are covered under the NCERT Solutions Class 9 Maths Chapter 2 include the basic understanding of polynomials, the components of algebraic expressions, and their definitions. The chapter focuses on the types of polynomials and how to solve them, with special emphasis on factor and remainder theorem and the algebraic entities.

What are the Important Formulas in NCERT Solutions Class 9 Maths Chapter 2?

Since the NCERT Solutions Class 9 Maths Chapter 2 covers the polynomials from their basic structure, several definitions of important terms have been explained with their formulas, like the factor and the remainder theorem. But the most important formula would be the algebraic identities as they help in factorization itself. For example, (a + b) 2 = a 2 + 2ab + b 2

Do I Need to Practice all Questions Provided in NCERT Solutions Class 9 Maths Polynomials?

NCERT Solutions Class 9 Maths Polynomials encompass a variety of questions that explore all the algebraic concepts related to polynomials. Hence, it would be good if the students make use of this resource and start practicing by solving the examples first, which will help them in getting an idea of what steps are to be followed when questions related to polynomials are solved.

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

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

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

Polynomials Case Study Questions With Answers

Case study questions class 9 maths chapter 2.

Case Study/Passage-Based Questions

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

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

Answer: (c) 4

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

Answer: (c) 4012005

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

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

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

Answer: (c) Linear

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

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

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

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

Answer: (b) y+3/y

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

Answer: (a) Linear polynomial

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

Answer: (c) –3

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

Answer: (b) 1

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

Answer: (b) 2

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

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

Answer: (a) 3

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

Answer: (c) 6

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

Answer: (c) 2

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

Answer: (b) -3

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

Answer: (b) 5x^2 – 3x + 4

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

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

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

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

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

Answer: (b) 5

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

Answer: (b) 3

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

Answer: (c) -2

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

Answer: (c) 10

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

Answer: (c) 40

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

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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Ncert solutions for class 9 maths chapter 2 polynomials| pdf download.

• Exercise 2.1 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.2 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.3 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.4 Chapter 2 Class 9 Maths NCERT Solutions
• Exercise 2.5 Chapter 2 Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapters:

How can I download Chapter 2 Polynomials Class 9 NCERT Solutions PDF 

What do you mean by algebraic expressions, what is the coefficient of a zero polynomial, what is biquadratic polynomial, contact form.

• Class 9 Maths MCQs
• Chapter 2 Polynomials Mcq

Class 9 Maths Chapter 2 Polynomials MCQs

Class 9 Maths Chapter 2 Polynomials MCQs are provided here online with answers. All the objective questions are given here, as per the latest CBSE syllabus and NCERT curriculum. Solving these chapter-wise MCQs will help students to score good marks in the final exam. Also, check Important Questions for Class 9 Maths .

Download the below PDF to get more MCQs on Class 9 Maths Chapter 2 Polynomials.

Class 9 Maths Chapter 2 Polynomials MCQs – Practice Questions

MCQs on Class 9 Maths Chapter 2 Polynomials

Check the multiple-choice questions for 9th Class Maths Polynomial chapter. Each MCQ will have four options here, out of which only one is correct. Students have to pick the correct option and check the answer provided here.

1) x 2 -2x+1 is a polynomial in:

a. One Variable

b. Two Variables

c. Three variable

d. None of the above

Explanation: x 2 -2x+1 can be written as x 2 -2x 1 +1x 0 . Hence, we can see that x is the only variable having powers as whole numbers: 2,1 and 0.

2) The coefficient of x 2 in 3x 3 +2x 2 -x+1 is:

Explanation: The coefficient of x 2 in equation 3x 3 +2x 2 -x+1 is the multiple of x 2 .

3) A binomial of degree 20 in the following is:

b. x/20 + 1

Explanation: A polynomial having two terms and the highest degree 20 is called a binomial of degree 20.

4) The degree of 4x 3 -12x 2 +3x+9 is

Explanation: The degree is the highest power of a variable in an equation.

5) x 2 – x is ________ polynomial.

b. Quadratic

Explanation: A polynomial of degree two is known as a quadratic polynomial.

6) x – x 3 is a ________ polynomial.

Explanation: A polynomial of degree three is known as a cubic polynomial.

7) 1+3x is a _________ polynomial.

Explanation: A polynomial of degree one is known as a linear polynomial.

8) The value of f(x) = 5x−4x 2 +3 when x = -1, is:

Explanation: When x= -1

f(x)=5x−4x 2 +3

f(−1)=5(−1) −4(−1) 2 +3

9) The value of p(t) = 2+t+2t 2 −t 3 when t=0 is

Explanation: p(0)=2+0+2(0) 2 –(0) 3 =2

10) The zero of the polynomial f(x) = 2x+7 is

Explanation: f(x)=2x+7

∴x = −7/2 is a zero polynomial of the polynomial f(x).

11) What is the degree of the polynomial √3?

Explanation: The polynomial √3 can also be written as √3(x 0 ) .

Hence, the degree of the polynomial √3 is 0.

12) The degree of the constant polynomial is

Explanation: The degree of the constant polynomial is 0. For example, 3 is a constant polynomial that is equal to 3x 0 , and its degree is 0.

13) One of the linear factors of 3x 2 +8x+5 is

Explanation: 3x 2 +8x+5 = 3x 2 + 3x+5x+5 

3x 2 +8x+5 = 3x(x+1)+5(x+1)

3x 2 +8x+5 = (3x+5)(x+1)

Therefore, (x+1) is one of the factors of 3x 2 +8x+5.

14) The coefficient of x in 7x 2 +6x-2 is 

Explanation: The coefficient of x in 7x 2 +6x-2 is 6. Because the number multiplied by x is 6.

15) Which of the following is an example of the quadratic polynomial?

b. 2x 2 +x-1

c. x+3x 3 -9

Explanation: 2x 2 +x-1 is a quadratic polynomial because the highest degree of the polynomial is 2.

16) Find the value of 7 2 -5 2 .

Explanation: 7 2 -5 2 = 49 – 25 = 24.

17) If x 2 +kx+6 = (x+2)(x+3) for all k, find the value of k.

Explanation: x 2 +kx+6 = (x+2)(x+3) 

x 2 +kx+6 = x 2 +3x+2x+6

x 2 +kx+6 = x 2 +5x+6

Hence, the value of k is 5.

18) What is the zero of the polynomial p(x)=cx+d?

Explanation: The zero of the polynomial p(x)= cx+d is -d/c. 

19) The zero of the polynomial p(x) = -5x+5 is

Explanation: p(x) = -5x+5

x = -5/-5 =1

20) which of the following is a constant polynomial?

Explanation: 3 is a constant polynomial, as 3 = 3x 0 . Whereas 4x+1 and 6x+3 are linear polynomial and 2x 2 is a quadratic polynomial.

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NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.2

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Topics and Subtopics:

• Polynomials
• Introduction
• Polynomials In One Variable
• Zeroes Of A Polynomial
• Remainder Theorem
• Factorisation Of Polynomials
• Algebraic Identities

Formulae Handbook for Class 9 Maths and Science  Educational Loans in India

• Chapter 2 Polynomials NCERT Solutions Ex 2.1
• Chapter 2 Polynomials NCERT Solutions Ex 2.3
• Chapter 2 Polynomials NCERT Solutions Ex 2.4
• Chapter 2 Polynomials NCERT Solutions Ex 2.5
• Extra Questions for Polynomials

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• NCERT Solutions Class 9 Maths
• NCERT Solutions Class 9 Science
• NCERT Solutions Class 9 Social Science
• NCERT Solutions Class 9 English
• NCERT Solutions Class 9 Hindi
• NCERT Solutions Class 9 Sanskrit
• NCERT Solutions Class 9 IT
• RD Sharma Class 9 Solutions

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (बहुपद) (Hindi Medium) Ex 2.2

NCERT Solutions for Class 9 Maths

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