, cbse class 9 maths chapter wise important questions - free pdf download.
CBSE Important Questions for Class 9 Maths are available in Printable format for Free Download.Here you may find NCERT Important Questions and Extra Questions for Class 9 Mathematics chapter wise with answers also. These questions will act as chapter wise test papers for Class 9 Mathematics. These Important Questions for Class 9 Mathematics are as per latest NCERT and CBSE Pattern syllabus and assure great success in achieving high score in Board Examinations
Maths Topics to be covered for Class 9
Structure of CBSE Maths Sample Paper for Class 9 is
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CBSE Class 9 Maths Sample Papers
CBSE Class 9 Maths Worksheets
CBSE Class 9 Maths Question Papers
CBSE Class 9 Maths Test Papers
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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!
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 .
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.
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:
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:
Now answer the following questions:
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.
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)
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.
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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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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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.
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:
NCERT Class 9 Maths Chapter 2 Download PDF
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.
☛ 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.
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.
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.
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.
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.
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.
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
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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Mathematics is one of the most important disciplines in today's academic curriculum. Maths is concerned with the operation of a certain job statically and quantitatively. It is a complex subject with several themes, formulae, and theories. As a result, students must focus on the topic in order to progress academically. Students must begin with a strong core understanding in order to deal with the difficulties of mathematics in upper grades.
Class 9 is a vital part of a student's academic career as the first board examinations knock at the door in the upcoming year. Therefore they must have a good understanding of crucial subjects like Maths to secure well in the examinations. Here, Vedantu steps in as an efficient guide to the students to provide a push to score well in their examinations through important questions for class 9 Maths Chapter 2 and solutions framed by professionals. You can also Download NCERT Maths Class 9 to help you to revise the complete Syllabus and score more marks in your examinations. Students can also avail of NCERT Solutions for Class 9 Science from our website. Besides, find NCERT Solutions to get more understanding of various subjects. The solutions are up-to-date and are sure to help in your academic journey.
Also, check CBSE Class 9 Maths Important Questions for other chapters:
It is the most extensively used subject in science and computer, standing based on logic and reasoning. Therefore, every student must have an in-depth learning of the subject to frame a successful career. Students with a weak core of knowledge in Mathematics may face difficulties to deal with the complex formulas and concepts of Maths, which in return serves as a hurdle to score well in the examination. In class 9, algebra is one of the crucial domains of Maths where maximum students fumble.
An efficient learning algebra and its concepts enable the students to dismantle diplomatic Mathematics problems into more straightforward and convenient processes. Therefordents must practice important questions for class 9 maths chapter 2 to master the topic perfectly. Students who find the topic challenging or get stuck with any concept or problems of algebra many refer to the detailed solutions available on the Internet. Quality study material like important questions for class 9 maths polynomials are also availed for the students to access freely in text and PDF formats.
Students are presented with an extensive view of the algebraic concepts and theories in class 9 Maths Ch 2 important questions. To explore different concepts of the chapter and practice a variety of problems, students must have their hands on important polynomials for class 9. Now, let's discuss some of the details about the chapter:
Polynomials can be quoted as an algebraic expression formed using indeterminates or variables and constants or coefficients. This algebraic expression allows such to perform addition, subtraction, multiplication, positive integer exponentiation of variables. The word polynomial is framed from 'poly' meaning 'many' and 'nominal' meaning 'term,' depicting many terms, which means a polynomial contains many terms but not infinite terms.
A polynomial expression comprises variables like x, y,z, coefficients like 1,2, and exponents like 2 in x². The polynomial function is generally depicted by P(x), where x is the variable. For instance,
P(x) = x² + 7x + 15, here x is the variable and 15 is the constant.
Polynomials are categorised into three groups depending upon the number of terms it comprises of. Here are the types of polynomials.
A monomial is a type of polynomial in algebra consisting of a single non-zero term. A polynomial expression consists of one or more terms. Therefore, every term of a polynomial expression is a monomial. Every numeric value such as 6, 12, 151 is a monomial by itself, whereas the variables can x, y, a can also be included in the list of monomials in algebra. Example of a monomial expression – 7x².
Rules for monomial algebraic expressions:
If a monomial is multiplied by a constant, the output will also be a monomial.
If a monomial is multiplied by a monomial, the result will also be a monomial. For instance, if a monomial three is multiplied by 3, the result 8 is also a monomial.
A binomial is a type of polynomial expression comprising of two non-zero terms. Let's see some examples to make it clear,
7x² + 8y is a binomial expression with two variables.
10x⁴ + 9y is also a binomial expression with two variables.
A trinomial is a type of polynomial expression comprising of three non-zero terms. Let's see some examples to make it clear,
5x²+8x+9 is a trinomial expression with one variables x.
a + b+ c is a trinomial expression with three variables.
7x – 6y + 9z is a trinomial expression with three variables.
Students can explore different questions polynomial types through the class 9 Maths chapter 2 important questions.
Some of the vital theorems of polynomials are as follows:
Remainder Theorem
The polynomial remainder theorem, also quoted as the little Bezout's theorem, implies that if a polynomial P(x) is divided by any linear polynomial depicted by (x – a), the remainder of the operation will be a constant given by P(a), i.e., r = P(a).
Factor Theorem
The factor theorem implies that if P(x) is a polynomial of degree n > 1, and 'a' is a real number, this portrays that:
If P(x) = 0, then (x – a) is the factor of P(x),
If (x – a) is the factor of P(x), P(x) = 0.
Bezout's Theorem
Bezout's Theorem states that if P(x) = 0, then P(x) gets divided by (x – a), with 'r' as the remainder.
Intermediate Value Theorem
The intermediate value theorem states that when a polynomial function transforms from a negative to a positive value, it must cross the x-axis. In other words, the theorem highlights the properties of continuity of a function.
Fundamental Theorem of Algebra
The fundamental theorem of algebra states that each non-constant single variable that consists of a complex coefficient possess a minimum of one complex root.
Polynomial Equations
A polynomial equation is an algebraic equation comprising of variables with positive integer exponents and constants. A polynomial expression may contain many exponents, and the highest exponent value is termed as the degree of the equation. Let's take an example to make it clear,
ax⁴ + bx² + x + c, is a polynomial expression with degree = 4.
Algebraic identities of polynomials
Identity 1 : (x + z )2 = x² + 2xz + z²
Identity 2 : (y – z) 2 = y² – 2yz + z²
Identity 3 : y² – z² = (y + z) (y – z)
Identity 4 : (x + y) (x + z) = x² + (y + z)x + yz
To present the students an insight into the algebraic world, we have highlighted here some of the important questions class 9 Maths chapter 2 , after a proper analysis of sample question papers:
What is a polynomial? Explain with example.
What are the types of polynomial expressions?
Explain the Remainder Theorem with an example.
Prove the Factor theorem of polynomials.
Illustrate Bezout's Theorem, and mention it's importance.
What do you mean by the degree of the polynomial? Explain with examples.
How can we add or subtract polynomials?
Explain the standard form of polynomials.
What do you mean by roots of equations? And how to find them.
Find the roots of polynomial equation, f(x) = x⁴ + 5x² + 7x + 19.
The students preparing for the boards in the upcoming year must prepare a strong core foundation for developing an in-depth logic and understanding of algebra. Therefore they can blend the benefits by practising the class 9th Maths chapter 2 important questions . Here we have listed some of the fruitfulness of class 9 polynomials important questions:
Students can develop deep learning of the topics by exploring different types of questions presented in the important polynomials for class 9.
Vedantu, with an efficient team of top-notch educators, has carefully designed the questions after proper research and analysis of the past year's question papers and sample test papers.
The important questions of ch 2 Maths class 9 are carefully designed under the CBSE board's rules ’ strict guidance.
To perform well in mathematics, academic success is practice; the students must efficiently practice the polynomials class 9 important questions.
To prevent any issues or mistakes in the important questions for class 9 maths polynomials , expert teachers have reviewed and analysed the papers.
Mathematics is the foundation for logic and reasoning. As a result, in order to grasp the topic's various subjects, students must work with insufficient fundamental Mathematics comprehension and study important polynomial questions for class 9. Students must have a good comprehension of the crucial questions for class 9 mathematics chapter 2 in order to begin a career in science and technology.
Important Related Links for CBSE Class 9
1. Where can I find some important questions for Class 9 Maths Chapter 2?
Ans: Crucial Class 9 Maths Chapter 2 questions titled Polynomials assist students in preparing for the Class 9 Mathematics Test. This will give you a general sense of the types of questions you could encounter in the test and from which chapter. Understanding what to study in a subject makes learning easier and faster since it requires less time. Hence, while preparing for Class 9 Maths Chapter 2 named Polynomials in CBSE Class 9 Mathematics, students in Class 9th are encouraged to answer these key questions.
2. Does Vedantu provide solutions to Class 9 Maths Chapter 2 of NCERT textbook?
Ans: Free PDF download of Important Questions with solutions for CBSE Class 9 Maths Chapter 2 named Polynomials are prepared by Vedantu’s in-house expert Mathematics teachers from the latest edition of NCERT textbooks. You can register online for Maths tuition on Vedantu if you are eager to score more marks in the final examination. You can also Download NCERT Maths Class 9 Solutions in order to help yourself revise the complete syllabus and score more marks in your examinations. All the Class 9th students can also avail of NCERT Solutions for Science from Vedantu website and mobile application very easily which help them to prepare for the exam along with the important questions.
3. Can I download the solutions to Important Questions with solutions for CBSE Class 9 Maths Chapter 2 offered by Vedantu?
Ans: Yes, you can download the solutions to Important Questions with solutions for CBSE Class 9 Maths Chapter 2 offered by Vedantu. These are available on Vedantu’s official website and mobile app at free of cost in PDF format. In that case, you can download the Vedantu app from the Google play store to avail these Important Questions with solutions for CBSE Class 9 Maths Chapter 2 offered by Vedantu.
4. What is taught in Class 9 Maths Chapter 2 of CBSE curriculum?
Ans: Polynomials is the second chapter of Class 9 Maths. Polynomials are introduced and discussed in detail here. The chapter discusses the Polynomials and their applications. The introduction of the chapter includes whole numbers, integers, and rational numbers.
The chapter begins with the introduction of Polynomials in section 2.1 followed by two other very important topics explained in section 2.2 and 2.3.
Section 2.1 - Polynomials in one Variable – This topic discusses the Linear, Quadratic and Cubic Polynomial.
Section 2.2 - Zeros of a Polynomial – This chapter explains that a zero of a polynomial need not be zero and can have more than one zero.
Section 2.3 - Real Numbers and Their Decimal Expansions – Here you will study the decimal expansions of real numbers and understand if it can help in distinguishing between rationals and irrationals.
5. Can I print the MCQ Questions for Chapter 2 of Class 9 Maths with answers?
Ans: Yes, the MCQ Questions and Answers for Chapter 2 of Class 9 Maths are in a downloadable PDF format and can be printed easily. These are available on Vedantu's website and app and you can download them according to your comfort and timing and can print the MCQs for future reference. Studying these important questions will ensure you get a good score in the final exam for Class 9 Maths.
6. Are these free or is there any charge for the MCQ Questions for Chapter 2 of Class 9 Maths with answers?
Ans: Yes, the MCQ Questions and Answers for Chapter 2 of Class 9 Maths are absolutely free and do not carry any hidden charge or cost. You can also download these from the Vedantu app. You can download these anytime according to your comfort so that you can study as and when required. These important questions have been carefully selected by the experts at Vedantu and are guaranteed to help you to score the best.
7. How Many questions are there in NCERT Solutions of Chapter 2 of Class 9 Maths?
Ans: The question break-up of the exercises covered in NCERT Solutions of Chapter 2 of Class 9 Maths are as follows:
Exercise 2.1 includes five questions
Exercise 2.2 includes four questions
Exercise 2.3 includes three questions
8. What are the Important Topics covered in NCERT Solutions of Chapter 2 of Class 9 Maths?
Ans: The major topics covered in NCERT Solutions for Chapter 2 of Class 9 Maths are as follows:
Polynomials in One Variable
Zeros of a Polynomial
Factorisation of Polynomials
Algebraic Identities
9. Why should I opt for NCERT Solutions of Chapter 2 of Class 9 Maths?
Ans: NCERT Solutions for Class 9 Mathematics Chapter 2 will certainly give you an advantage. The NCERT Solutions are created by experts in the field at Vedantu to provide students with effective solutions to problems while explaining their concepts so that they are never stuck with the same issue again in the future. This will ensure that you get the greatest grades and fully comprehend complicated ideas. As a result, you must without a doubt select NCERT Solutions for Chapter 2 of Class 9 Mathematics.
Cbse study materials.
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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.
Case studies in class 9 mathematics.
The Central Board of Secondary Education (CBSE) has included case study based questions in the Class 9 Mathematics paper in current session. According to new pattern CBSE Class 9 Mathematics students will have to solve case based questions. This is a departure from the usual theoretical conceptual questions that are asked in Class 9 Maths exam in this year.
Each question provided in this post has five sub-questions, each followed by four options and one correct answer. All CBSE Class 9th Maths Students can easily download these questions in PDF form with the help of given download Links and refer for exam preparation.
There is many more free study materials are available at Maths And Physics With Pandey Sir website. For many more books and free study material all of you can visit at this website.
Given Below Are CBSE Class 9th Maths Case Based Questions With Their Respective Download Links.
Ncert solutions for class 9 maths chapter 2 polynomials| pdf download.
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.
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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
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
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15 questions mcq test - case based questions test: polynomials - 1, direction: read the following text and answer the following questions on the basis of the same: the below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. a parabolic arch is an arch in the shape of a parabola. in structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. if the sum of the roots is –p and product of the roots is then the quadratic polynomial is.
x2 - (Sum of roots)x + Product of roots
Putting values
We can multiply any constant to this polynomial
So, required quadratic polynomial is
Direction: read the following text and answer the following questions on the basis of the same: the below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. a parabolic arch is an arch in the shape of a parabola. in structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms. the graph of x 2 + 1 = 0.
y = x 2 + 1
Direction: Read the following text and answer the following questions on the basis of the same: The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
In the standard form of quadratic polynomial, ax 2 + bx, c, a, b and c are
All are real numbers.
All are rational numbers.
‘a’ is a non zero real number and b and c are any real numbers.
All are integers.
It can be written in the standard form ax2 + bx + c , where x is a variable, a, b, c are constants (numbers) and a = 0. The constants a, b, c are called the coefficients of the polynomial. A quadratic polynomial ax 2 + bx + c is called sometimes a quadratic trinomial.
Direction: Read the following text and answer the following questions on the basis of the same:
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If α are 1/α the zeroes of the quadratic polynomial 2x 2 – x + 8k, then k is
Product of zeroes = c/a = 8k/2
So, 8k/2 = 1
Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
What will be the expression of the polynomial?
Hence, the expression is (x + 3)(x + 1)(x – 2)
= [x 2 + x + 3x + 3](x – 2)
= x 3 + 4x 2 + 3x – 2x 2 – 8x – 6
= x 3 + 2x 2 – 5x – 6
The graph of parabola opens upwards, if _______
The three zeroes in the above shown graph are
2, 3, –1
–2, 3, 1
–3, –1, 2
–2, –3, –1
Zeroes are the values of x where graph intersects the x-axis
∴ Zeroes are -3, -1 and 2
The shape of the path traced shown is
Direction: Read the following text and answer the following questions on the basis of the same: Basketball and soccer are played with a spherical ball. Even though an athlete dribbles the ball in both sports, a basketball player uses his hands and a soccer player uses his feet. Usually, soccer is played outdoors on a large field and basketball is played indoor on a court made out of wood. The projectile (path traced) of soccer ball and basketball are in the form of parabola representing quadratic polynomial.
In the above graph, how many zeroes are there for the polynomial?
The number of zeroes of polynomial is the number of times the curve intersects the x-axis, i.e. attains the value 0. Here, the polynomial meets the x-axis at 3 points. So, number of zeroes = 3.
If the product of the zeroes of the quadratic polynomial p(x) = ax 2 – 6x – 6 is 4, then the value of a is:
p(x) = ax 2 – 6x – 6
Let α and β be the zeroes of the given polynomial, then
i.e., 4 = -6/a
Since the graph does not intersect the X-axis, therefore it has no zero.
If a and b are the zeroes of the quadratic polynomial p(x) = 4x 2 + 5x + 1, then the product of zeroes is:
∴ αβ = c/a = 1/4.
If a linear polynomial is 2x + 3, then the zero of 2x + 3 is:
Let p(x) = 2x + 3
For a zero of p(x), 2x + 3 = 0
If α and β are the zeroes of the quadratic polynomial x 2 – 5x + k such that α – β = 1, then the value of k is:
and αβ = k/1 = k
Also given, α – β = 1
⇒ 25 – 4k = 1(Squaring both sides)
⇒ – 4k = 1 – 25 = – 24
Case based questions test: polynomials - 1 mcqs with answers, online tests for case based questions test: polynomials - 1, welcome back, create your account for free.
Cbse board result 2024.
Check here the ncert based extra question for cbse class 9 maths chapter 2 polynomials. all these questions are important for the annual cbse exam..
CBSE Class 9 Maths extra questions (with answers) for Chapter 2 - Polynomials can be accessed from here. These extra questions are entirely based on the NCERT textbook. Most of the questions are simple and appropriate to test your conceptual understanding. So, you should solve all these questions for self-assessment and score well in your Maths Exam 2020-2021.
CBSE Class 9 Maths Extra Questions for Chapter 2 - Polynomials :
1. Degree of a zero polynomial is
(iii) Not defined
Not defined
2. What is the degree of a constant polynomial?
3. Number of zeroe(s) all the linear polynomial have is/are:
(iii) Three
4. Which of the following expressions is not a polynomial?
(i) 5x 3 +x 2 –2
(ii) x 1/2 +3x+1
(iii) 3x -1 +1
(iv) (9x +1) ÷ (x)
(i) 5x 3 +x 2 -2
5. Find the product of (x – 3y) (x + 3y) (x 2 + 9y 2 ).
(x 4 – 81y 4 )
Also Check:
NCERT Book for Class 9 Maths
NCERT Solutions for Class 9 Maths
6. Find the value of x – 1/x, If x 2 + 1/x 2 = 18.
x – 1/x = ±4
7. Find the value of 105 × 106 without actual multiplication?
Answer:
105 × 106 = 11,130
8. Which of the following statements (s) is/are correct?
(i) Every linear polynomial in one variable has a unique zero.
(ii) Every non-zero constant polynomial has no zero.
(iii) Every real number is a zero of the zero polynomial.
(iv) All of the above statements are correct
9. Factorise: (a – b) 3 + (b – c) 3 + (c – a) 3
3(a 2 (c−b) + b 2 (a−c) + c 2 (b−a))
10. If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x),
(i) If p(a) > 0
(ii) If p(a) < 0
(iii) If p(a) = 0
(iv) For any value of P(a)
If p(a) = 0
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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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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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
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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Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 2 Polynomials. Case Study/Passage Based Questions. 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.
Case Study Questions Question 1: On one day, principal of a particular school visited the classroom. Class teacher was teaching the concept of 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 variousquestions to students. … Continue reading Case Study Questions for Class 9 ...
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. Case Study Questions.
Download Class 9 Maths Case Study Questions to prepare for the upcoming CBSE Class 9 Exams 2023-24. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 9 so that they can score 100% in Exams. Case study questions play a pivotal role in enhancing students' problem-solving skills.
The only difference between them is that algebraic expressions contain irrational numbers in the powers. A detailed polynomials Class 9 notes are provided here along with some important questions so that students can understand the concept easily. Polynomials Class 9 Notes. To prepare for Class 9 exams, students will require notes to study.
Polynomials Case Study Questions (CSQ's) Practice Tests. Timed Tests. Select the number of questions for the test: Select the number of questions for the test: TopperLearning provides a complete collection of case studies for CBSE Class 9 Maths Polynomials chapter. Improve your understanding of biological concepts and develop problem-solving ...
Welcome to our Class 9 Maths exam preparation series for the academic year 2023-24! In this video, we dive deep into Case Study Questions from Chapter 2: Pol...
The powers of the variable x are: 3, 2, 1. The degree of 5x 3 +4x 2 +7x is 3, as 3 is the highest power of x in the equation. (ii) 4-y2. Solution: The highest power of the variable in a polynomial is the degree of the polynomial. Here, in 4-y 2, The power of the variable y is 2.
These questions will act as chapter wise test papers for Class 9 Mathematics. These Important Questions for Class 9 Mathematics are as per latest NCERT and CBSE Pattern syllabus and assure great success in achieving high score in Board Examinations. Class 9 Polynomials Case Study Questions - Podar International Atoms and Molecules HOTS ...
Class 9 Mathematics Case study question 2. Read the Source/Text given below and answer any four questions: Maths teacher draws a straight line AB shown on the blackboard as per the following figure. Now he told Raju to draw another line CD as in the figure. The teacher told Ajay to mark ∠ AOD as 2z.
These questions will help the 9th class students to get acquainted with a wide variety of questions and develop the confidence to solve polynomial questions more efficiently. 1. Give an example of a monomial and a binomial having degrees of 82 and 99, respectively. Solution: An example of a monomial having a degree of 82 = x 82.
Test: Polynomials- Case Based Type Questions for Class 9 2024 is part of Class 9 preparation. The Test: Polynomials- Case Based Type Questions questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Polynomials- Case Based Type Questions MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and ...
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 ...
Ans: Crucial Class 9 Maths Chapter 2 questions titled Polynomials assist students in preparing for the Class 9 Mathematics Test. This will give you a general sense of the types of questions you could encounter in the test and from which chapter. Understanding what to study in a subject makes learning easier and faster since it requires less time.
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 ...
So, it is a cubic polynomial. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (बहुपद) (Hindi Medium) Ex 2.1. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.2. Question 1. Find the value of the polynomial 5x - 4x 2 + 3 at (i) x = 0 (ii) x = - 1 (iii) x = 2 Solution: 1et p(x) = 5x - 4x 2 + 3
Chapter 2 Polynomials Class 9 Maths NCERT Solutions PDF download is very useful in understanding the basic concepts embedded in the chapter. It is very essential to solve every question before moving further to any other supplementary books.
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 x2 in the given polynomial is.
Detailed Solution for Case Based Questions Test: Polynomials - 1 - Question 4. It can be written in the standard form ax2 + bx + c , where x is a variable, a, b, c are constants (numbers) and a = 0. The constants a, b, c are called the coefficients of the polynomial. A quadratic polynomial ax 2 + bx + c is called sometimes a quadratic trinomial.
Get CBSE Class 9 Maths Extra Questions and Answers for Chapter 2 Polynomials. All the extra questions are based on the NCERT Book. Practice with theses important questions to score good marks in ...
3 months ago February 2, 2024 Physics Gurukul Leave a Comment on Case Study Questions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles. ... Case Study Questions for Class 9 Maths Chapter 2 Polynomials. Join our Telegram Channel for Free PDF Download. Join Now! NCERT Books & Solutions. NCERT Books 2022-23. NCERT Solutions ...
POLYNOMIALS CLASS 9 WITH TRICKS | MOST IMPORTANT QUESTIONSyour queries :maths class 9 polynomials,mathematics class 9 polynomials,math class 9 polynomials,ma...
Answer: c. Explanation: A polynomial having two terms and the highest degree 20 is called a binomial of degree 20. 4) The degree of 4x3-12x2+3x+9 is. a. 0. b. 1. c. 2. d. 3. Answer: d. Explanation: The degree is the highest power of a variable in an equation.