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CBSE Class 9 Mathematics Case Study Questions
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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!
Significance of Mathematics in Class 9
Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.
CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .
Case studies in Class 9 Mathematics
A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.
Example of Case study questions in Class 9 Mathematics
The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.
The following are some examples of case study questions from Class 9 Mathematics:
Class 9 Mathematics Case study question 1
There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.
Answer the following questions:
Answer Key:
Class 9 Mathematics Case study question 2
- Now he told Raju to draw another line CD as in the figure
- The teacher told Ajay to mark ∠ AOD as 2z
- Suraj was told to mark ∠ AOC as 4y
- Clive Made and angle ∠ COE = 60°
- Peter marked ∠ BOE and ∠ BOD as y and x respectively
Now answer the following questions:
- 2y + z = 90°
- 2y + z = 180°
- 4y + 2z = 120°
- (a) 2y + z = 90°
Class 9 Mathematics Case study question 3
- (a) 31.6 m²
- (c) 513.3 m³
- (b) 422.4 m²
Class 9 Mathematics Case study question 4
How to Answer Class 9 Mathematics Case study questions
To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.
Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.
Class 9 Mathematics Curriculum at Glance
At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.
The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.
CBSE Class 9 Mathematics (Code No. 041)
Class 9 Mathematics question paper design
The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.
QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)
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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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Unit: Polynomials
Polynomials in one variable.
- Polynomials intro (Opens a modal)
- Polynomials intro Get 3 of 4 questions to level up!
- Finding terms and coefficients of a polynomial Get 3 of 4 questions to level up!
- Classify polynomials based on degree Get 3 of 4 questions to level up!
- Classify polynomials based on terms Get 3 of 4 questions to level up!
Zeroes of a polynomial
- Evaluating polynomials (Opens a modal)
- Polynomial factors and graphs — Basic example (Opens a modal)
- Finding value of a polynomial Get 3 of 4 questions to level up!
- Zeros of polynomial (intermediate) Get 3 of 4 questions to level up!
Remainder theorem
- Intro to the Polynomial Remainder Theorem (Opens a modal)
- Remainder theorem: checking factors (Opens a modal)
- Remainder theorem Get 3 of 4 questions to level up!
Factorisation of polynomials
- Which monomial factorization is correct? (Opens a modal)
- Perfect square factorization intro (Opens a modal)
- Factors of a polynomial (basic) Get 3 of 4 questions to level up!
- Factors of a polynomial (advanced) Get 3 of 4 questions to level up!
Multiplying polynomials
- Multiplying monomials by polynomials (Opens a modal)
- Multiplying binomials by polynomials (Opens a modal)
- Multiply binomials Get 3 of 4 questions to level up!
- Multiply binomials by polynomials Get 3 of 4 questions to level up!
Standard identities
- Special products of the form (ax+b)(ax-b) (Opens a modal)
- Squaring binomials of the form (ax+b)² (Opens a modal)
- Special products of binomials: two variables (Opens a modal)
- Polynomial special products: perfect square Get 3 of 4 questions to level up!
Algebraic identities
- No videos or articles available in this lesson
- Identities (basic) Get 3 of 4 questions to level up!
- Factorising using identities Get 3 of 4 questions to level up!
- Multiplying numbers using identities Get 3 of 4 questions to level up!
CBSE Expert
CBSE Class 9 Maths Case Study Questions PDF Download
Download Case Study Questions for Class 9 Mathematics to prepare for the upcoming CBSE Class 9 Exams 2022-23. 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.
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 9th MATHS: Chapterwise Case Study Questions
Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Maths subjects, there would be 5 case-based sub-parts questions, wherein a student has to attempt 4 sub-part questions.
Chapterwise Case Study Questions of Class 9 Maths
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.
- Case Study Questions for Chapter 1 Number System
- Case Study Questions for Chapter 2 Polynomials
- Case Study Questions for Chapter 3 Coordinate Geometry
- Case Study Questions for Chapter 4 Linear Equations in Two Variables
- Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
- Case Study Questions for Chapter 6 Lines and Angles
- Case Study Questions for Chapter 7 Triangles
- Case Study Questions for Chapter 8 Quadrilaterals
- Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
- Case Study Questions for Chapter 10 Circles
- Case Study Questions for Chapter 11 Constructions
- Case Study Questions for Chapter 12 Heron’s Formula
- Case Study Questions for Chapter 13 Surface Area and Volumes
- Case Study Questions for Chapter 14 Statistics
- Case Study Questions for Chapter 15 Probability
Checkout: Class 9 Science Case Study Questions
And for mathematical calculations, tap Math Calculators which are freely proposed to make use of by calculator-online.net
The above Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of cbseexpert.com for benefit of Class 10 students.
Class 9 Science Case Study Questions
Class 9 Maths Syllabus 2022-23
UNIT I: NUMBER SYSTEMS
1. REAL NUMBERS (18 Periods)
1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers of the type
(and their combinations) where x and y are natural number and a and b are integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)
UNIT II: ALGEBRA
1. POLYNOMIALS (26 Periods)
Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:
RELATED STORIES
and their use in factorization of polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)
Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.
UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.
UNIT IV: GEOMETRY
1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)
History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)
1. Given two distinct points, there exists one and only one line through them. (Theorem)
2. (Prove) Two distinct lines cannot have more than one point in common.
2. LINES AND ANGLES (15 Periods)
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Lines which are parallel to a given line are parallel.
3. TRIANGLES (22 Periods)
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
4. QUADRILATERALS (13 Periods)
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.
5. CIRCLES (17 Periods)
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
5. (Motivate) Angles in the same segment of a circle are equal.
6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
UNIT V: MENSURATION 1.
1. AREAS (5 Periods)
Area of a triangle using Heron’s formula (without proof)
2. SURFACE AREAS AND VOLUMES (17 Periods)
Surface areas and volumes of spheres (including hemispheres) and right circular cones.
UNIT VI: STATISTICS & PROBABILITY
STATISTICS (15 Periods)
Bar graphs, histograms (with varying base lengths), and frequency polygons.
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.
QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)
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MATHS CLASS IX CASE STUDY BASED QUESTIONS
FOR ANNUAL EXAM 2020-21
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Class 9 Maths: Case Study Questions for Board Exams PDF Download
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Download Case Study Questions for Class 9 Mathematics to prepare for the upcoming CBSE Class 9 Exam 2022-23. These Case Study and Passage Based questions are published by the experts of Study Rate for the students of CBSE Class 9 so that they can score 100% in Exams.
CBSE Class 9 Maths Board Exam 2022-23 will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.
If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out. CBSE Case Study Questions for Class 9 will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your NCERT Text Books !
Table of Contents
CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution
Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked. For Maths subjects, there would be 5 case-based sub-parts questions, wherein a student has to attempt 4 sub-part questions.
Chapterwise Case Study Questions for Class 9 Maths
- Case Study Questions for Chapter 1 Number System
- Case Study Questions for Chapter 2 Polynomials
- Case Study Questions for Chapter 3 Coordinate Geometry
- Case Study Questions for Chapter 4 Linear Equations in Two Variables
- Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
- Case Study Questions for Chapter 6 Lines and Angles
- Case Study Questions for Chapter 7 Triangles
- Case Study Questions for Chapter 8 Quadilaterals
- Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
- Case Study Questions for Chapter 10 Circles
- Case Study Questions for Chapter 11 Constructions
- Case Study Questions for Chapter 12 Heron’s Formula
- Case Study Questions for Chapter 13 Surface Area and Volumes
- Case Study Questions for Chapter 14 Statistics
- Case Study Questions for Chapter 15 Probability
The above Case Study ‘ s for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study’s have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.
- Class 9 Science Case Study Questions
- Class 9 Social Science Case Study Questions
Class 9 Maths Syllabus 2022-23
UNIT I: NUMBER SYSTEMS
1. REAL NUMBERS (18 Periods)
1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers.
2. Examples of non-recurring/non-terminating decimals. Existence of non-rational numbers (irrational numbers) such as √2, √3 and their representation on the number line. Explaining that every real number is represented by a unique point on the number line and conversely, viz. every point on the number line represents a unique real number.
3. Definition of nth root of a real number.
4. Rationalization (with precise meaning) of real numbers of the type
(and their combinations) where x and y are natural number and a and b are integers.
5. Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing learner to arrive at the general laws.)
UNIT II: ALGEBRA
1. POLYNOMIALS (26 Periods)
Definition of a polynomial in one variable, with examples and counter examples. Coefficients of a polynomial, terms of a polynomial and zero polynomial. Degree of a polynomial. Constant, linear, quadratic and cubic polynomials. Monomials, binomials, trinomials. Factors and multiples. Zeros of a polynomial. Motivate and State the Remainder Theorem with examples. Statement and proof of the Factor Theorem. Factorization of ax2 + bx + c, a ≠ 0 where a, b and c are real numbers, and of cubic polynomials using the Factor Theorem. Recall of algebraic expressions and identities. Verification of identities:
RELATED STORIES
and their use in factorization of polynomials.
2. LINEAR EQUATIONS IN TWO VARIABLES (16 Periods)
Recall of linear equations in one variable. Introduction to the equation in two variables. Focus on linear equations of the type ax + by + c=0.Explain that a linear equation in two variables has infinitely many solutions and justify their being written as ordered pairs of real numbers, plotting them and showing that they lie on a line.
UNIT III: COORDINATE GEOMETRY COORDINATE GEOMETRY (7 Periods)
The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations.
UNIT IV: GEOMETRY
1. INTRODUCTION TO EUCLID’S GEOMETRY (7 Periods)
History – Geometry in India and Euclid’s geometry. Euclid’s method of formalizing observed phenomenon into rigorous Mathematics with definitions, common/obvious notions, axioms/postulates and theorems. The five postulates of Euclid. Showing the relationship between axiom and theorem, for example: (Axiom)
1. Given two distinct points, there exists one and only one line through them. (Theorem)
2. (Prove) Two distinct lines cannot have more than one point in common.
2. LINES AND ANGLES (15 Periods)
1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180O and the converse.
2. (Prove) If two lines intersect, vertically opposite angles are equal.
3. (Motivate) Lines which are parallel to a given line are parallel.
3. TRIANGLES (22 Periods)
1. (Motivate) Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence).
2. (Prove) Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence).
3. (Motivate) Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).
4. (Motivate) Two right triangles are congruent if the hypotenuse and a side of one triangle are equal (respectively) to the hypotenuse and a side of the other triangle. (RHS Congruence)
5. (Prove) The angles opposite to equal sides of a triangle are equal.
6. (Motivate) The sides opposite to equal angles of a triangle are equal.
4. QUADRILATERALS (13 Periods)
1. (Prove) The diagonal divides a parallelogram into two congruent triangles.
2. (Motivate) In a parallelogram opposite sides are equal, and conversely.
3. (Motivate) In a parallelogram opposite angles are equal, and conversely.
4. (Motivate) A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal.
5. (Motivate) In a parallelogram, the diagonals bisect each other and conversely.
6. (Motivate) In a triangle, the line segment joining the mid points of any two sides is parallel to the third side and in half of it and (motivate) its converse.
5. CIRCLES (17 Periods)
1. (Prove) Equal chords of a circle subtend equal angles at the center and (motivate) its converse.
2. (Motivate) The perpendicular from the center of a circle to a chord bisects the chord and conversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord.
3. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the center (or their respective centers) and conversely.
4. (Prove) The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
5. (Motivate) Angles in the same segment of a circle are equal.
6. (Motivate) If a line segment joining two points subtends equal angle at two other points lying on the same side of the line containing the segment, the four points lie on a circle.
7. (Motivate) The sum of either of the pair of the opposite angles of a cyclic quadrilateral is 180° and its converse.
UNIT V: MENSURATION 1.
1. AREAS (5 Periods)
Area of a triangle using Heron’s formula (without proof)
2. SURFACE AREAS AND VOLUMES (17 Periods)
Surface areas and volumes of spheres (including hemispheres) and right circular cones.
UNIT VI: STATISTICS & PROBABILITY
STATISTICS (15 Periods)
Bar graphs, histograms (with varying base lengths), and frequency polygons.
Books for Class 9 Maths Exams
Strictly as per the new term-wise syllabus for Board Examinations to be held in the academic session 2022-23 for class 9 Multiple Choice Questions based on new typologies introduced by the board- Stand-Alone MCQs, MCQs based on Assertion-Reason Case-based MCQs. Include Questions from CBSE official Question Bank released in April 2022 Answer key with Explanations What are the updates in the book: Strictly as per the Term wise syllabus for Board Examinations to be held in the academic session 2022-23. Chapter-wise -Topic-wise Multiple choice questions based on the special scheme of assessment for Board Examination for Class 9th.
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Key Features
- Revision Notes
- Important Questions
- Previous Years Questions
- Case-Based Questions
- Assertion and Reason Questions
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- CBSE- Polynomials
- Sample Questions
Polynomials-Sample Questions
- STUDY MATERIAL FOR CBSE CLASS 9 MATH
- Chapter 1 - Area of Parallelograms and Triangles
- Chapter 2 - Circles
- Chapter 3 - Constructions
- Chapter 4 - Coordinate Geometry
- Chapter 5 - Herons Formula
- Chapter 6 - Introduction to Euclids Geometry
- Chapter 7 - Linear Equations in two variables
- Chapter 8 - Lines and Angles
- Chapter 9 - Number Systems
- Chapter 10 - Polynomials
- Chapter 11 - Probability
- Chapter 12 - Quadrilaterals
- Chapter 13 - Statistics
- Chapter 14 - Surface Areas and Volumes
- Chapter 15 - Triangles
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Important Questions with Solutions for CBSE Class 9 Maths Chapter 2 - Polynomials
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CBSE Class 9 Maths Chapter-2 Important Questions - Free PDF Download
Mathematics is one of the dominant subjects in the modern academic curriculum. Maths deals with statically and numerically operating a specific task. It is a subject full of crunching topics, formulas, and theories. So, the students must stress on the subject to climb the ladder of academic growth. The students must initiate a strong core knowledge from the lower class, which helps them deal with mathematics complexities in the higher classes as students require a lot of practice and toil to grip the subject.
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.
Download CBSE Class 9 Maths Important Questions 2022-23 PDF
Also, check CBSE Class 9 Maths Important Questions for other chapters:
Download PDF of Important Questions with Solutions for CBSE Class 9 Maths Chapter 2 - Polynomials
Important questions for class 9 maths polynomials.
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.
Class 9 Maths Chapter 2 Important Questions
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
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.
Types of Polynomials
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.
Polynomial Theorems
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
Important Questions of Polynomials for Class 9
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.
Benefits of Class 9 Maths Ch 2 Important Questions
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 gateway to logic and reasoning. Therefore, the students must work with weak core knowledge about Maths practice the important questions of polynomials for class 9 to understand the topic’s various concepts. To kick start the career in science and technology, the students must have a thorough understanding of the important questions for class 9 maths chapter 2.
Important Related Links for CBSE Class 9
Faqs on important questions with solutions for cbse class 9 maths chapter 2 - polynomials.
1. Where can I find some important questions for Class 9 Maths Chapter 2?
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 forChapter 2 of Class 9 Maths are sure to give you an edge over your peers. Curated by the experts in the field at Vedantu, the NCERT Solutions are carefully designed to provide students with effective solutions for problems while clearing their concepts so that they are never stuck with the same thing in future. This will ensure that you score the best marks and perfectly understand complex concepts. Thus, you must choose NCERT Solutions for Chapter 2 of Class 9 Maths without any doubt.
CBSE Class 9 Maths Important Questions
Cbse study materials.
- Math Article
- Polynomials Class 9
Polynomial Class 9 Notes - Chapter 2
Cbse class 9 maths polynomials notes:- download pdf here.
Polynomial derived from the words “poly” which means “many” and the word “nomial” which means “term”. In maths, a polynomial expression consists of variables which are also known as indeterminates and coefficients. The coefficients involve the operations of subtraction, addition, non-negative integer exponents of variables and multiplication.In Mathematics, both algebraic expressions and polynomials are made up of variables and constants, including arithmetic operations.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. These notes are of great help when they have to revise chapter 2 polynomials before the exam. The note here provides a brief of the chapter so that students find it easy to have a glance at once. The key points covered in the chapter have been noted. Go through the points and solve problems based on them. The topics and subtopics covered in class 9 polynomials chapter 2 include:
- Introduction
Polynomials in One Variable
- Zeros of Polynomials
Remainder Theorem
Factorisation of polynomials, algebraic identities, polynomial definition.
Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. An algebraic expression p(x) = a 0 x n + a 1 x n-1 + a 2 x n-2 + … a n is a polynomial where a 0 , a 1 , ………. a n are real numbers and n is non-negative integer. Examples of polynomials are:
- w + x + y + z
- x 2 + x + 1
To know more about polynomials, click here .
In the polynomial, each expression in it is called a term . Suppose x 2 + 5x + 2 is polynomial, then the expressions x 2 , 5x, and 2 are the terms of the polynomial.
Coefficient
Each term of the polynomial has a coefficient . For example, if 2x + 1 is the polynomial, then the coefficient of x is 2.
Types of Polynomial
A polynomial of 1 term is called a monomial. Example: 2x. A polynomial of 2 terms is called binomial. Example: 5x + 2. A polynomial of 3 terms is called a trinomial. Example: 2x + 5y – 4.
Constant Polynomial
The real numbers can also be expressed as polynomials. Like 3, 6, 7, are also polynomials without any variables. These are called constant polynomials . The constant polynomial 0 is called zero polynomial . The exponent of the polynomial should be a whole number. For example, x -2 + 5x + 2, cannot be considered as a polynomial, since the exponent of x is -2, which is not a whole number.
Degree of a Polynomial
The highest power of the polynomial is called the degree of the polynomial . For example, in x 3 + y 3 + 3xy(x + y), the degree of the polynomial is 3. For a non zero constant polynomial, the degree is zero. Apart from these, there are other types of polynomials such as:
- Linear polynomial – of degree one
- Quadratic Polynomial- of degree two
- Cubic Polynomial – of degree three
This topic has been widely discussed in class 9 and class 10.
Polynomials in one variable are the expressions which consist of only one type of variable in the entire expression. Example of polynomials in one variable:
- 2x 2 + 5x + 15
To know more about polynomials in one variable, click here .
Zeroes of Polynomial
The zeroes of polynomials are the points, where the polynomial equal to 0 as a whole.
To know more about the zeroes of polynomials, click here .
If p(x) is any polynomial having degree greater than or equal to 1 and if it is divided by the linear polynomial x – a, then the remainder is p(a).
To know more about the Remainder Theorem, click here .
Factor Theorem
x – c is a factor of the polynomial p(x), if p(c) = 0. Also, if x – c is a factor of p(x), then p(c) = 0.
To know more about the Factor Theorem Theorem, click here .
Factorisation of polynomials is the process of expressing the polynomials as the product of two or more polynomails. For example, the polynomial x 2 -x-6 can be factorised as (x-3)(x+2)
Also read: Factorisation of Polynomials
The algebraic identities are the algebraic equations, which is valid for all values. The important algebraic identities used in class 9 Maths chapter 2 polynomials are listed below:
- (x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx
- (x + y) 3 = x 3 + y 3 + 3xy(x + y)
- (x – y) 3 = x 3 – y 3 – 3xy(x – y)
- x 3 + y 3 + z 3 – 3xyz = (x + y + z) (x 2 + y 2 + z 2 – xy – yz – zx)
To learn more about Algebraic Identities for class 9, Click here .
Explore More:
For more information on quadratic polynomial, watch the below video..
Polynomials Class 9 Examples
Write the coefficients of x in each of the following:
- 23x 2 – 5x + 1
In 3x + 1, the coefficient of x is 3.
In 23x 2 – 5x + 1, the coefficient of x is -5.
What are the degrees of following polynomials?
- 3a 2 + a – 1
- 32x 3 + x – 1
- 3a 2 + a – 1 : The degree is 2
- 32x 3 + x – 1 : The degree is 3
Polynomials Class 9 Important Questions
- Find value of polynomial 2x 2 + 5x + 1 at x = 3.
- Check whether x = -1/6 is zero of the polynomial p(a) = 6a + 1.
- Divide 3a 2 + x – 1 by a + 1.
- Find value of k, if (a – 1) is factor of p(a) = ka 2 – 3a + k.
- 4x 2 + 9y 2 + 16z 2 + 12xy – 24yx – 16xz
- 2x 2 + y 2 + 8z 2 – 2√2xy + 4√2yz – 8xz
Stay tuned with BYJU’S – The Learning App and get detailed notes of all concepts of Class 9 Mathematics.
Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!
Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz
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Assertion and Reason Questions for Class 9 Maths Chapter 2 Polynomials
Directions: Choose the correct answer out of the following choices : (a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion. (b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion. (c) Assertion is correct statement but Reason is wrong statement. (d) Assertion is wrong statement but Reason is correct statement.
Q.1. Assertion : 3x 2 + x – 1 = (x + 1) (3x – 2) + 1. Reason : To factorise ax 2 + bx + c, write b as sumof two numbers whose product is ac.
Q.2. Assertion : The value of 593 × 607 is 359951. Reason : (a + b) (a – b) = a 2 – b 2
Q.3. Assertion : The degree of the polynomial(x 2 – 2)(x – 3)(x + 4) is 3. Reason : A polynomial of degree 3 is called a cubic polynomial.
Q.4. Assertion : The expression 3x 4 – 4x 3/2 + x 2 = 2is not a polynomial because the term – 4x 3/2 contains a rational power of x. Reason : The highest exponent in various terms of an algebraic expression in one variable is called its degree.
Q.5.. Assertion : If 2x 2 – 32 is the volume of a cuboid, then length of cuboid can be x – 8. Reason : Volume of a cuboid = l × b × h.
Q.6. Assertion : –7 is a constant polynomial. Reason : Degree of a constant polynomial is zero.
Questions for practice:
Directions: (a) Both assertion and reason are true and reason is the correct explanation of assertion. (b) Both assertion and reason are true but reason is not the correct explanation of assertion. (c) Assertion is true but reason is false. (d) Assertion is false but reason is true
1. Assertion : If f(x) = 3x 7 – 4x 6 + x + 9 is a polynomial, then its degree is 7. Reason : Degree of a polynomial is the highest power of the variable in it.
2. Assertion : (x + 2) and (x – 1) are factors of the polynomial x 4 + x 3 + 2x 2 + 4x – 8. Reason : For a polynomial p(x) of degree ≥ 1, x – a is a factor of the polynomial p(x) if and only if p(a) ≥1 .
3. Assertion : 3x 2 + x – 1 = (x + 1)(3x – 2x) + 1. Reason : If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x) , where r(x) = 0 of degree of r(x) <degree of g(x).
4. Assertion : (x + 2) is a factor of x 3 + 3x 2 + 5x + 6 . and of 2x + 4 Reason : If p(x)be a polynomial of degree greater than or equal to one, then (x – a) is a factor of p(x), if p(a) = 0
5. Assertion : The remainder when p(x) = x 3 – 6x 2 + 2x – 4 is divided by (3x – 1) is – 107/27. Reason : If a polynomial p(x) is divided by ax –b , the remainder is the value of p(x) at x = b/a.
6. Assertion : If (x + 1) is a factor of f(x) = x 2 + ax + 2 then a = – 3 . Reason : If (x – a ) is a factor of p(x), if p(a) = 0.
7. Assertion : If f(x) = x 4 + x 3 – 2x 2 + x + 1 is divided by (x – 1) , then its remainder is 2. Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x – a , then the remainder is p(- a ) .
8. Assertion : The degree of the polynomial (x – 2 )(x – 3 )(x + 4) is 4. Reason : The number of zeroes of a polynomial is the degree of that polynomial.
9. Assertion : If p(x) = ax + b , a≠ 0 is a linear polynomial, then x = – b/a is the only zero of p(x). Reason : A linear polynomial has one and only one zero.
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NCERT Solutions Class 9 Maths Chapter 2 Polynomials
NCERT solutions for class 9 maths Chapter 2 Polynomials are all about the basics of polynomials like the different types of polynomials, finding roots, or solutions to a polynomial equation. Polynomials are algebraic expressions having one variable or more. These NCERT solutions class 9 maths Chapter 2 also explain the remainder theorem and factor theory of polynomials in detail, the algebraic identities, and polynomials of various degrees.
Class 9 Maths NCERT Solutions Chapter 2 polynomials illustrate the difference between linear, quadratic, and cubic polynomials. Important theorems mentioned are the Remainder theorem and the Factor theorem, which help identify the factors of a polynomial. Students can access the solutions from the pdf links given below and also find some of these in the exercises given below.
- NCERT Solutions Class 9 Maths Chapter 2 Ex 2.1
- NCERT Solutions Class 9 Maths Chapter 2 Ex 2.2
- NCERT Solutions Class 9 Maths Chapter 2 Ex 2.3
- NCERT Solutions Class 9 Maths Chapter 2 Ex 2.4
- NCERT Solutions Class 9 Maths Chapter 2 Ex 2.5
NCERT Solutions for Class 9 Maths Chapter 2 PDF
The exercises related to identifying the type of polynomial, finding the roots or solution of a polynomial equation, and finding factors of the polynomial are available for free pdf download using the four links provided below:
☛ Download Class 9 Maths NCERT Solutions Chapter 2 Polynomials
NCERT Class 9 Maths Chapter 2 Download PDF
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials
These fundamental properties and theorems of polynomials form the building blocks for higher mathematics. Thus, it is very important to master the fundamentals by solving many different example exercises using the links provided above. These NCERT Solution exercises will help understand the properties of polynomials better, as well as how to utilize them. Chapter-wise detailed analysis of NCERT Solutions Class 9 Maths Chapter 2 Polynomials is given below.
- Class 9 Maths Chapter 2 Ex 2.1 - 21 Questions
- Class 9 Maths Chapter 2 Ex 2.2 - 22 Questions
- Class 9 Maths Chapter 2 Ex 2.3 - 7 Questions
- Class 9 Maths Chapter 2 Ex 2.4 - 7 Questions
- Class 9 Maths Chapter 2 Ex 2.5 - 41 Questions
☛ Download Class 9 Maths Chapter 2 NCERT Book
Topics Covered: The topics that are covered under the chapter on polynomials include an explanation of polynomials as a special set of algebraic equations, different types of polynomials, solutions of polynomial equations, factor theorem, and remainder theorem. Also, these class 9 maths NCERT solutions Chapter 2 define the algebraic identities , which help in factorizing the algebraic equations.
Total Questions: Class 9 Maths Chapter 2 Polynomials consists of a total of 45 questions, of which 31 are easy, 9 are moderate, and 5 are long answer type questions.
List of Formulas in NCERT Solutions Class 9 Maths Chapter 2
NCERT solutions class 9 maths Chapter 2 covers lots of important concepts crucial for understanding higher grade maths. By learning to factorize a polynomial expression, one can find the roots of the polynomial equation. This is a relatively simple process that can greatly improve an individual's understanding of polynomial equations. Some important algebraic identities or formulas which help in factorization and are covered in NCERT solutions for class 9 maths chapter 2 are given below.
- ( x + y ) 2 = x 2 + 2xy + y 2
- ( x + y ) 3 = x 3 + y 3 + 3xy (x+y)
Important Questions for Class 9 Maths NCERT Solutions Chapter 2
Video solutions for class 9 maths ncert chapter 2, faqs on ncert solutions class 9 maths chapter 2, how cbse students can utilize ncert solutions class 9 maths chapter 2 effectively.
Algebra forms the basis of higher mathematical studies. Hence, students should focus on the important terms defined in this chapter, like the degree of a polynomial, the difference between constant and variable, to get a clear understanding of the polynomials. This will help them to make their base strong to appear for their board exams and face any kind of difficult questions.
Why are Class 9 Maths NCERT Solutions Chapter 2 Important?
The NCERT Solutions Class 9 Maths Chapter 2 includes a detailed explanation of the remainder and the factor theorem, which hold an important place in algebra. Also, the crucial algebraic identities are discussed in an elaborate manner with plenty of questions to solve for the students. A list of all key equations and concepts is available at the end of the chapter. This is a significant benefit because students can use this list whenever required instead of figuring it out from between the lengthy chapter text. Overall, these solutions cover all of the major concepts, approaches, and formulas, making them of utmost importance for class 9 math students.
How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 2 Polynomials?
Overall the NCERT Solutions Class 9 Maths Chapter 2 has 98 questions that can be categorized as easy, medium, and difficult ones. Roughly 70 questions are straightforward and easy to solve, 20 questions are of medium difficulty level while 8 would require some thinking as they are long-form questions.
What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 2?
The important topics that are covered under the NCERT Solutions Class 9 Maths Chapter 2 include the basic understanding of polynomials, the components of algebraic expressions, and their definitions. The chapter focuses on the types of polynomials and how to solve them, with special emphasis on factor and remainder theorem and the algebraic entities.
What are the Important Formulas in NCERT Solutions Class 9 Maths Chapter 2?
Since the NCERT Solutions Class 9 Maths Chapter 2 covers the polynomials from their basic structure, several definitions of important terms have been explained with their formulas, like the factor and the remainder theorem. But the most important formula would be the algebraic identities as they help in factorization itself. For example, (a + b) 2 = a 2 + 2ab + b 2
Do I Need to Practice all Questions Provided in NCERT Solutions Class 9 Maths Polynomials?
NCERT Solutions Class 9 Maths Polynomials encompass a variety of questions that explore all the algebraic concepts related to polynomials. Hence, it would be good if the students make use of this resource and start practicing by solving the examples first, which will help them in getting an idea of what steps are to be followed when questions related to polynomials are solved.
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CBSE Class 9 Maths: Extra Questions - Chapter 2 - Polynomials (with Answers)
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
CBSE Class 9 Maths Important MCQ (Chapter-wise)
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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.
questions to students. Some of them are given below. Answer them. (i) 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 (ii) The polynomial of the type ax2 + bx + c, a = 0 is called (a) Linear polynomial (b) Quadratic polynomial (c) Cubic polynomial (d) Biquadratic polynomial
Class 9 Mathematics Case study question 1 Read the Source/Text given below and answer any four questions: 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.
(a) Linear polynomial (b) Quadratic polynomial (c) Cubic polynomial (d) Biquadratic polynomial Show Answer The value of k, if (x - 1) is a factor of 4x3 + 3x2 - 4x + k, is (a) 1 (b) -2 (c) -3 (d) 3 Show Answer If x + 2 is the factor of x3 - 2ax2 + 16, then value of a is (a) -7 (b) 1 (c) -1 (d) 7 The number of zeroes of the polynomial x2 + 4x + 2 is
Zeroes of a polynomial. Quiz 1: 6 questions Practice what you've learned, and level up on the above skills. Remainder theorem. Factorisation of polynomials. Multiplying polynomials. Standard identities. Algebraic identities. Quiz 2: 8 questions Practice what you've learned, and level up on the above skills. Unit test Test your knowledge of ...
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
Class 9 Science Case Study Questions Class 9 Maths Syllabus 2022-23 UNIT I: NUMBER SYSTEMS 1. REAL NUMBERS (18 Periods) 1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 2.
MATHS CLASS IX CASE STUDY BASED QUESTIONS FOR ANNUAL EXAM 2020-21 S. No.QuestionChapterYouTube Link1Maths Case Study Question 01Linear Equations in two variables Case Study Question 02Linear Equati…
Class 9 Maths Syllabus 2022-23 UNIT I: NUMBER SYSTEMS 1. REAL NUMBERS (18 Periods) 1. Review of representation of natural numbers, integers, and rational numbers on the number line. Rational numbers as recurring/ terminating decimals. Operations on real numbers. 2. Examples of non-recurring/non-terminating decimals.
Class IX Math Sample Paper for Polynomials 1. If x + y = 12 and xy = 32, Find the value of x 2 + y 2. 2. If 3x + 2y = 12 and xy = 6, find the value of 9x 2 + 4y 2. 3. Write the following cubes in the expanded form: (i) (3a + 4b) 3 (ii) (5p - 3q) 3 4. If find the values of each of the following: (i) (ii) 5. If then evaluate 6.
Important Questions of Polynomials for Class 9 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?
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
Q.4. Assertion : The expression 3x 4 - 4x 3/2 + x 2 = 2is not a polynomial because the term - 4x 3/2 contains a rational power of x. Reason : The highest exponent in various terms of an algebraic expression in one variable is called its degree. Answer Answer: (b)
8. 1+3x is a _________ polynomial. 9. The value of k for which x - 1 is a factor of the polynomial 4x 3 + 3x 2 - 4x + k is :-. 10. The value of p (t) = 2+t+2t 2 −t 3 when t=0 is. 11. If 3 + 5 - 8 = 0, then the value of (3) 3 + (5) 3 - (8) 3 is. 12. If x + 2 is a factor of x 3 - 2ax 2 + 16, then value of a is.
@Maths Cluster Case study based questions for class 9Case study based on Polynomials for class 9Case study based on factorisation of polynomialsClass IX CBSE...
This is a relatively simple process that can greatly improve an individual's understanding of polynomial equations. Some important algebraic identities or formulas which help in factorization and are covered in NCERT solutions for class 9 maths chapter 2 are given below. ( x + y )2 = x2 + 2xy + y2. ( x + y )3 = x3 + y3 + 3xy (x+y)
a) All are Polynomials. b) All are rational numbers. c) 'a' is a non zero real number and b and c are any Polynomials. d) All are integers. Answers: c) 'a' is a non zero real number and b and c...
@Maths Cluster Case study based questions of chapter PolynomialsCase study based questions for class 9 maths CBSE board syllabusCase study on PolynomialsAlg...
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 ...