, 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
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There are many ways to ascertain whether a student has understood the important points and topics of a particular chapter and is he or she well prepared for exams and tests of that particular chapter. Apart from reference books and notes, Question Banks are very effective study materials for exam preparation. When a student tries to attempt and solve all the important questions of any particular subject , it becomes very easy to gauge how much well the topics have been understood and what kind of questions are asked in exams related to that chapter.. Some of the other advantaging factors of Question Banks are as follows
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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.
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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.
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CBSE Expert
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
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 are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 2 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.
Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.
Below we have listed the topics that have been discussed in this chapter. As this is one of the important topics in maths, It comes under the unit – Algebra which has a weightage of 20 marks in class 9 maths board exams.
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By QB365 on 21 May, 2021
QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get more marks in Exams
10th Standard CBSE
Final Semester - June 2015
Case Study Questions
(ii) The expression of the polynomial represented by the graph is
(iii) Find the value of the polynomial represented by the graph when x = 6.
(iv) The sum of zeroes of the polynomial x 2 + 2x - 3 is
(v) If the sum of zeroes of polynomial at 2 + 5t + 3a is equal to their product, then find the value of a.
(ii) Find the value of \(\alpha\) + \(\beta\) + \(\alpha\) \(\beta\) .
(iii) The value of p(2) is
(iv) If \(\alpha\) and \(\beta\) are zeroes of \(x^{2}+x-2, \text { then } \frac{1}{\alpha}+\frac{1}{\beta}=\)
(v) If sum of zeroes of \(q(x)=k x^{2}+2 x+3 k\) is equal to their product, then k =
(ii) The axis of symmetry of the given parabola is
(iii) The zeroes of the polynomial, represented in the given graph, are
(iv) Which of the following polynomial has -2 and -3 as its zeroes?
(v) For what value of 'x', the value of the polynomial \(f(x)=(x-3)^{2}+9 \text { is } 9 ?\)
(ii) What will be the expression of the polynomial given in diagram?
(iii) What is the value of the polynomial, represented by the graph, when x = 4?
(iv) If the tunnel is represented by x 2 + 3x - 2, then its zeroes are
(v) If one zero is 4 and sum of zeroes is -3, then representation of tunnel as a polynomial is
(ii) The sum of product of zeroes taken two at a time is
(iii) Product of zeroes of polynomial p(x) is
(iv) The value of the polynomial p(x), when x = 4 is
(v) If \(\alpha,\beta,\gamma\) are the zeroes of a polynomial g(x) such that \(\alpha+\beta+\gamma=3, \alpha \beta+\beta \gamma+\gamma \alpha=-16\) and \(\alpha \beta \gamma=-48\) then, g(x) =
Cbse 10th standard maths subject polynomials case study questions with solution 2021 answer keys.
(i) (b): Graph of a quadratic polynomial is a parabolic in shape. (ii) (c): Since the graph of the polynomial cuts the x-axis at (-6,0) and (6, 0). So, the zeroes of polynomial are -6 and 6. \(\therefore\) Required polynomial is p(x) = x 2 - (-6 + 6)x + (-6)(6) = x 2 - 36 (iii) (c) : We have, p(x) = x 2 - 36 Now, p( 6) = 62 - 36 = 36 - 36 = 0 (iv) (b): Letf (x) = x 2 + 2x - 3. Then, \(\text { Sum of zeroes }=-\frac{\text { coefficient of } x}{\text { coefficient of } x^{2}}=-\frac{(2)}{1}=-2\) (v) (d): The given polynomial is at 2 + 5t + 3a Given, sum of zeroes = product of zeroes. \(\Rightarrow \quad \frac{-5}{a}=\frac{3 a}{a} \Rightarrow a=\frac{-5}{3}\)
(i) (b): Given, a and \(\beta\) are the zeroes of \(p(x)=x^{2}-24 x+128\) \(\text { Putting } p(x)=0 \text { , we get }\) \( x^{2}-8 x-16 x+128=0 \) \(\Rightarrow x(x-8)-16(x-8)=0 \) \(\Rightarrow (x-8)(x-16)=0 \Rightarrow x=8 \text { or } x=16 \) \(\therefore \alpha=8, \beta=16\) (ii) (c) : \(\alpha+\beta+\alpha \beta =8+16+(8)(16) =24+128=152 \) (iii) (d) : \(p(2)=2^{2}-2 4(2)+128=4-48+128=84\) (iv) (a): Since a and \(\beta\) are zeroes of \(x^{2}+x-2\) \(\therefore \quad \alpha+\beta=-1 \text { and } \alpha \beta=-2 \) \(\text { Now, } \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\beta+\alpha}{\alpha \beta}=\frac{-1}{-2}=\frac{1}{2}\) (v) (c): Sum of zeroes \(=\frac{-2}{k}\) Product of zeroes \(=\frac{3 k}{k}=3\) According to question, we have \(\frac{-2}{k}=3\) \(\Rightarrow \quad k=\frac{-2}{3}\)
(i) (b): The shape of the path of the soccer ball is a parabola. (ii) (c): The axis of symmetry of the given curve is a line parallel to y-axis. (iii) (a): The zeroes of the polynomial, represented in the given graph, are -2 and 7, since the curve cuts the x-axis at these points. (iv) (d): A polynomial having zeroes -2 and -3 is \(p(x)=x^{2}-(-2-3) x+(-2)(-3)=x^{2}+5 x+6\) (v) (c): We have \(f(x)=(x-3)^{2}+9\) \(\text { Now, } 9=(x-3)^{2}+9 \) \(\Rightarrow(x-3)^{2}=0 \Rightarrow x-3=0 \Rightarrow x=3\)
(i) (a): Since, the graph intersects the x-axis at two points, namely x = 8, -2. So, 8, - 2 are the zeroes of the given polynomial. (ii) (b): The expression of the polynomial given in diagram is \(-x^{2}+6 x+16\) (iii) (c) : Let \(p(x)=-x^{2}+6 x+16\) \(\text { When } x=4, p(4)=-4^{2}+6 \times 4+16=24\) (iv) (d): Let \(f(x)=-x^{2}+3 x-2\) Now, consider \(f(x)=0 \Rightarrow-x^{2}+3 x-2=0\) \(\begin{aligned} &\Rightarrow x^{2}-3 x+2=0 \Rightarrow(x-2)(x-1)=0\\ &\Rightarrow x=1,2 \text { are its zeroes. } \end{aligned}\) (v) (b): Let a and \(\beta\) are the zeroes of the required polynomial. Given \(\alpha + \beta = - 3\) If \(\alpha\) = 4, then \(\beta\) = -7 \(\therefore \quad \text { Representation of tunnel is }-x^{2}-3 x+28 \text { . }\)
(i) (c): For finding \(\alpha,\beta,\) \(\gamma\) consider p(x) = 0 \(\Rightarrow \quad x^{3}-18 x^{2}+95 x-150=0 \) \(\Rightarrow \quad(x-3)\left(x^{2}-15 x+50\right)=0 \) \(\Rightarrow \quad(x-3)(x-5)(x-10)=0 \Rightarrow x=10 \text { or } x=5 \text { or } x=3 \) \(\text { Thus } \alpha=10, \beta=5 \text { and } \gamma=3\) (ii) (d): Here \(\alpha=10, \beta=5 \text { and } \gamma=3\) \(\therefore\) Sum of product of zeroes taken two at a time \(\begin{array}{l} =\alpha \beta+\beta \gamma+\gamma \alpha=(10)(5)+(5)(3)+(3)(10) \\ =50+15+30=95 \end{array}\) (iii) (a): Product of zeroes of polynomial p(x) = \(\alpha\beta\gamma\) = (10) (5) (3) = 150 (iv) (b): We have \(p(x)=x^{3}-18 x^{2}+95 x-150\) \(\begin{array}{l} \text { Now, } p(4)=4^{3}-18(4)^{2}+95(4)-150 \\ =64-288+380-150=6 \end{array}\) (v) (d): \(g(x)=x^{3}-(\alpha+\beta+\gamma) x^{2} +(\alpha \beta+\beta \gamma+\gamma \alpha) x-\alpha \beta \gamma \) \(\Rightarrow g(x)=x^{3}-3 x^{2}-16 x-(-48)=x^{3}-3 x^{2}-16 x+48\)
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10 questions mcq test - test: polynomials- case based type questions, beti bachao, beti padhao (bbbp) is a personal campaign of the government of india that aims to generate awareness and improve the efficiency of welfare services intended for girls. in a school, a group of (x + y) teachers, (x 2 + y 2 ) girls and (x 3 + y 3 ) boys organised a campaign on beti bachao, beti padhao. q. if in the group, there are 10 teachers and 58 girls, then what is the number of boys.
No. of teachers = x + y = 10
⇒ (x + y) 2 = (10) 2
⇒ x 2 + y 2 + 2xy = 100
[Since (a + b) 2 = a 2 + b 2 + 2ab]
No. of students = (x 2 + y 2 ) = 58
⇒ 58 + 2xy = 100
⇒ 2xy = 100 – 58
⇒ xy = 42/2
Now, since (x + y) 3 = [x 3 + y 3 + 3xy(x + y)]
⇒ (10) 3 = [x 3 + y 3 + 3 × 21(10)]
⇒ 1000 = (x 3 + y 3 + 630)
⇒ 1000 – 630 = (x 3 + y 3 )
⇒ (x 3 + y 3 ) = 370
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Beti Bachao, Beti Padhao (BBBP) is a personal campaign of the Government of India that aims to generate awareness and improve the efficiency of welfare services intended for girls.
In a school, a group of (x + y) teachers, (x 2 + y 2 ) girls and (x 3 + y 3 ) boys organised a campaign on Beti Bachao, Beti Padhao.
Q. (x – y) 3 =
(x 2 – y 2 – 3xy(x – y))
(x 3 – y 3 – 2xy(x – y)
(x 3 – y 3 – 3xy(x – y)
(x 3 – y 3 – 3xyx – y)
We know that (x - y) 3 can be written as
(x - y)(x - y)(x - y)
We know that (x - y)(x - y) can be multiplied and written as
= x 2 - xy - yx + y 2 (x - y)
= x 2 - 2xy + y 2 (x - y)
= x 3 - 2x 2 y + xy 2 - yx 2 + 2xy 2 - y 3
= x 3 – y 3 – 2xy(x – y)
Q. Using part (D), find (x 2 – y 2 ) if x – y = 23.
Also, x + y = 10
x 2 – y 2 = (x + y)(x – y)
National Association For The Blind (NAB) aimed to empower and well-inform visually challenged population of our country, thus enabling them to lead a life of dignity and productivity.
Q. Find the amount donated by Ravi.
Q. (x – y) 3 =
x 2 - xy - yx + y 2 (x - y)
= x 3 – y 3 – 3xy(x – y)
Q. (x + a)(x + b) = x 2 + ................ x + ab
Q. Which mathematical concept is involved in the above situation?
Polynomials- case based type questions mcqs with answers, online tests for polynomials- case based type questions, welcome back, create your account for free.
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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.
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.
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 ...
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.
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...
CBSE Class 9 Maths Polynomials Notes:-Download PDF Here. ... Polynomials Class 9 Important Questions. Find value of polynomial 2x 2 + 5x + 1 at x = 3. ... Visit BYJU'S for all Maths related queries and study materials. Your result is as below. 0 out of 0 arewrong. 0 out of 0. are correct
SAMPLE PAPER -2 CLASS 9 MATHS 2022-23 https://rzp.io/l/pxh4q1oSAMPLE PAPER -1 CLASS 9 MATHS 2022-23 https://rzp.io/l/NlyY0twVRcPlaylist of all case study bas...
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.
Subjective Case Based Questions -🔥Polynomials Class 9 Maths Chapter 2 | CBSE Board Exam 2022 Preparation | NCERT Solutions | #VedantuClass9and10 Are all wor...
List of Exercises in Class 9 Maths Chapter 2 Polynomials. Class 9 Maths Chapter 2 Polynomials contains 5 exercises. Based on the concept of polynomials, each exercise provides a number of questions. Click on the below links to access the exercise-wise NCERT solutions for Class 9 Maths Chapter 2 polynomials. Exercise 2.1 Solutions 5 Questions
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 ...
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 ...
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.
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.
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.
Here you will get complete NCERT Solutions for Class 9 Maths Chapter 2 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.
CBSE 10th Standard Maths Subject Polynomials Case Study Questions With Solution 2021 Answer Keys. Case Study Questions. (i) (b): Graph of a quadratic polynomial is a parabolic in shape. (ii) (c): Since the graph of the polynomial cuts the. x-axis at (-6,0) and (6, 0).
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 ...
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 ...
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.