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CBSE Class 9 Maths Case Study Questions PDF Download

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. By presenting real-life scenarios, these questions encourage students to think beyond textbook formulas and apply mathematical concepts to practical situations. This approach not only strengthens their understanding of mathematical concepts but also develops their analytical thinking abilities.

Table of Contents

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 Class 9 Maths Case Study Questions, there would be 5 case-based sub-part questions, wherein a student has to attempt 4 sub-part questions.

Chapterwise Case Study Questions of 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 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  Class 9 Maths Case Study Question s will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Study Questions have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

Class 9 Maths Syllabus 2023-24

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.

Benefits of Practicing CBSE Class 9 Maths Case Study Questions

Regular practice of CBSE Class 9 Maths case study questions offers several benefits to students. Some of the key advantages include:

• Deeper Understanding : Case study questions foster a deeper understanding of mathematical concepts by connecting them to real-world scenarios. This improves retention and comprehension.
• Practical Application : Students learn to apply mathematical concepts to practical situations, preparing them for real-life problem-solving beyond the classroom.
• Critical Thinking : Case study questions require students to think critically, analyze data, and devise appropriate solutions. This nurtures their critical thinking abilities, which are valuable in various academic and professional domains.
• Exam Readiness : By practicing case study questions, students become familiar with the question format and gain confidence in their problem-solving abilities. This enhances their readiness for CBSE Class 9 Maths exams.
• Holistic Development: Solving case study questions cultivates not only mathematical skills but also essential life skills like analytical thinking, decision-making, and effective communication.

Tips to Solve CBSE Class 9 Maths Case Study Questions Effectively

Solving case study questions can be challenging, but with the right approach, you can excel. Here are some tips to enhance your problem-solving skills:

• Read the case study thoroughly and understand the problem statement before attempting to solve it.
• Identify the relevant data and extract the necessary information for your solution.
• Break down complex problems into smaller, manageable parts to simplify the solution process.
• Apply the appropriate mathematical concepts and formulas, ensuring a solid understanding of their principles.
• Clearly communicate your solution approach, including the steps followed, calculations made, and reasoning behind your choices.
• Practice regularly to familiarize yourself with different types of case study questions and enhance your problem-solving speed.Class 9 Maths Case Study Questions

Remember, solving case study questions is not just about finding the correct answer but also about demonstrating a logical and systematic approach. Now, let’s explore some resources that can aid your preparation for CBSE Class 9 Maths case study questions.

Q1. Are case study questions included in the Class 9 Maths Case Study Questions syllabus?

Yes, case study questions are an integral part of the CBSE Class 9 Maths syllabus. They are designed to enhance problem-solving skills and encourage the application of mathematical concepts to real-life scenarios.

Q2. How can solving case study questions benefit students ?

Solving case study questions enhances students’ problem-solving skills, analytical thinking, and decision-making abilities. It also bridges the gap between theoretical knowledge and practical application, making mathematics more relevant and engaging.

Q3. How do case study questions help in exam preparation?

Case study questions help in exam preparation by familiarizing students with the question format, improving analytical thinking skills, and developing a systematic approach to problem-solving. Regular practice of case study questions enhances exam readiness and boosts confidence in solving such questions.

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

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

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

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

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• CBSE Class 9th Maths 2023 : 30 Most Important Case Study Questions with Answers; Download PDF 10 February, 2023, 6:20 pm
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• CBSE Class 9th Exam 2023 : Social Science Most Important Short Notes; Download PDF 16 January, 2023, 4:29 pm
• CBSE Class 9th Mathematics 2023 : Most Important Short Notes with Solutions 27 December, 2022, 6:05 pm
• CBSE Class 9th English 2023 : Chapter-wise Competency-Based Test Items with Answer; Download PDF 21 December, 2022, 5:16 pm
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CBSE Class 9 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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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

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

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Where is search ? bar

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Can I have more questions without downloading the app.

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

Cbse case study questions for class  9 maths.

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

Chapter Wise Case Based Questions for Class 9 Maths

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

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

Chapter 1: Number System

• Case Based Questions: Number System

Chapter 2: Polynomial

• Case Based Questions: Polynomial

Chapter 3: Coordinate Geometry

• Case Based Questions: Coordinate Geometry

Chapter 4: Linear Equations

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

Chapter 5: Introduction to Euclid’s Geometry

• Case Based Questions: Lines and Angles

Chapter 7: Triangles

• Case Based Questions: Triangles

Chapter 8: Quadrilaterals

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

Chapter 9: Areas of Parallelograms

• Case Based Questions: Circles

Chapter 11: Constructions

• Case Based Questions: Constructions

Chapter 12: Heron’s Formula

• Case Based Questions: Heron’s Formula

Chapter 13: Surface Areas and Volumes

• Case Based Questions: Surface Areas and Volumes

Chapter 14: Statistics

• Case Based Questions: Statistics

Chapter 15: Probability

• Case Based Questions: Probability

Weightage of Case Based Questions in Class 9 Maths

Why are Case Study Questions important in Maths Class  9?

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

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

Class 9 Maths Curriculum at Glance

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

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

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

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

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

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

What is case-based questions.

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

What are case-based questions in Maths?

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

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

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

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

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CBSE Class 9 Maths Most Important Case Study Based Questions With Solution

Cbse class 9 mathematics case study questions.

In this post I have provided CBSE Class 9 Maths Case Study Based Questions With Solution. These questions are very important for those students who are preparing for their final class 9 maths exam.

All these questions provided in this article are with solution which will help students for solving the problems. Dear students need to practice all these questions carefully with the help of given solutions.

As you know CBSE Class 9 Maths exam will have a set of cased study based questions in the form of MCQs. CBSE Class 9 Maths Question Bank given in this article can be very helpful in understanding the new format of questions for new session.

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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.

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

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Case Study Questions for Class 9 Maths Chapter 1 Real Numbers

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

Himanshu has made a project on real numbers, where he finely explained the applicability of exponential laws and divisibility conditions on real numbers. He also included some assessment questions at the end of his project as listed below. Answer them.

(i) For what value of n, 4 n  ends in 0?

(a) 10 (b) when n is even (c) when n is odd (d) no value of n

(ii) If a is a positive rational number and n is a positive integer greater than 1, then for what value of n, a is a rational number?

(a) when n is any even integer (b) when n is any odd integer (c) for all n > 1 (d) only when n=0

(iii) If x and y are two odd positive integers, then which of the following is true?

(a) x 2 +y 2  is even (b) x 2 +y 2  is not divisible by 4 (c) x 2 +y 2  is odd (d) both (a) and (b)

(iv) The statement ‘One of every three consecutive positive integers is divisible by 3’ is

(a) always true (b) always false (c) sometimes true (d) None of these

(v) If n is any odd integer, then n 2  – 1 is divisible by

(a) 22 (b) 55 (c) 88 (d) 8

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FREE CBSE Online Coaching for Class 9 Maths. No Conditions

Extra questions for class 9 maths chapter 1, number systems | real numbers | rational & irrational numbers.

NCERT Class 9 Math / Number System Extra Questions

C hapter 1 of CBSE NCERT Class 9 Math covers number systems. Concepts covered in chapter 1 include rational numbers, irrational numbers, rationalizing irrational numbers by multiplying with their conjugates, decimal expansion of real numbers, operations on real numbers and laws of exponents or rules of indices. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT.

Here is a quick recap of the key concepts that are covered in this chapter in the CBSE NCERT Class 9 Math text book.

What are rational numbers?

A number that can be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is a rational number.

Possibility 1 : If the decimal expansion of the number is terminating it is a rational number. Note: Integers are terminating decimals and are therefore, rational numbers.

Possibility 2 : If the decimal expansion of the number is non-terminating but is recurring , it is rational. Example \\frac{1}{3}\\) = 0.333.. is a non-terminating recurring decimal and is a rational number.

What are irrational numbers?

A number that CANNOT be written in the form \\frac{p}{q}\\) where p and q are integers and p ≠ 0 is an irrational number.

If the decimal expansion of the number is non-terminating AND non-recurring it is an irrational number. Example: \\sqrt{2}\\), π

How to Rationalize Irrational Numbers?

For an irrational number of the form a + √b, a - √b is its conjugate. And for an irrational number of the from a - √b, a + √b is its conjugate.

Important Laws of Exponents (Rules of Indices)

If a > 0 is a real number and m and n are rational numbers, the following laws of exponents hold good.

• a m × a n = a m + n Example .: 10 3 × 10 2 = 10 3 + 2 = 10 5
• (a m ) n = a mn Example : (10 3 ) 2 = 10 (3 \\times\\) 2) = 10 6
• \\frac{a^m}{a^n}\\) = a (m - n) Example : \\frac{10^3}{10^2}\\) = 10 (3 - 2) = 10
• a m b m = (ab) m Example : 2 2 × 5 2 = (2 × 5) 2 = 10 2

Extra Questions for Class 9 Maths - Number Systems

Prime Factorise & Rationalise Denominator: \\frac{14}{{\sqrt {108}} - {\sqrt {96}} + {\sqrt {192}} - {\sqrt {54}}}\\)

Rational numbers - Fractions: Find 5 rational numbers between \\frac{3}{4}) and \\frac{4}{5}).

Express as Fractions Express 1.363636... in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Express in the form \\frac{p}{q}) Express 0.4323232… in the form \\frac{p}{q}), where p and q are integers and q ≠ 0.

Simplify the following (a) \({8 + \sqrt{5})}) \({8 - \sqrt{5})}) (b) \({10 + \sqrt{3})}) \({6 + \sqrt{2})}) (c) \{(\sqrt {3} + \sqrt {11})}^2) + \{(\sqrt {3} - \sqrt {11})}^2)

Rationalize the denominator: (a) \\frac{2}{\sqrt{3} - 1}) (b) \\frac{7}{\sqrt{12} - \sqrt{5}}) (c) \\frac{1}{8 + 3\sqrt{5}}) (d) \\frac{1}{4 + \sqrt{2} + \sqrt{5}})

Simplify and find the value of (a) \{(729)}^{\frac{1}{6}}) (b) \{(64)}^{\frac{2}{3}}) (c) \{(243)}^{\frac{6}{5}}) (d) \{(21)}^{\frac{3}{2}} \times {(21)}^{\frac{5}{2}}) (e) \\frac{{(81)}^{\frac{1}{3}}}{{(81)}^{\frac{1}{12}}})

Operation on real numbers & Algebraic identities If x = \\frac{3 - {\sqrt{13}}}{2}\\), what is the value of \x^2 + \frac{1}{x^2}\\)?

Rationalise & find value of cubic expression If x = \\frac{1}{8-\sqrt{60}}\\), what is the value of (x 3 - 5x 2 + 8x - 4) ?

Question 10

Rationalise the denominator \\frac{1}{9 + {\sqrt{5} + \sqrt{6}}}\\)

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NCERT Solutions Class 9 Maths Chapter 1 Number Systems

NCERT solutions for class 9 maths chapter 1 number systems consists of an introduction about the number system and the different kinds of numbers in it. The number system has been classified into different types of numbers like natural numbers, whole numbers , integers, rational numbers, irrational numbers , etc. The NCERT solutions class 9 maths chapter 1 covers all the basics of the number system which will be helpful in forming the basic foundation of mathematics.

Class 9 maths chapter 1 number systems will help the students in differentiating between rational and irrational numbers, wherein irrational numbers cannot be expressed in the form of a ratio, and also about real numbers. Class 9 maths NCERT solutions chapter 1 number systems sample exercises can be downloaded from the links below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.1
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.2
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.3
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.4
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.5
• NCERT Solutions Class 9 Maths Chapter 1 Ex 1.6

NCERT Solutions for Class 9 Maths Chapter 1 PDF

These NCERT solutions for class 9 maths involving the important concepts of real numbers , rational and irrational numbers, are available for free pdf download. The questions involving real numbers and their decimal form, the law of exponents are given below:

☛ Download Class 9 Maths NCERT Solutions Chapter 1 Number Systems

NCERT Class 9 Maths Chapter 1   Download PDF

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

It is advisable for the students to practice the questions in the above links as this will give them better clarity on the kind of numbers and their properties. An exercise-wise detailed analysis of NCERT Solutions Class 9 Maths Chapter 1 number systems is given below for reference.

• Class 9 Maths Chapter 1 Ex 1.1 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.2 - 4 Questions
• Class 9 Maths Chapter 1 Ex 1.3 - 9 Questions
• Class 9 Maths Chapter 1 Ex 1.4 - 2 Questions
• Class 9 Maths Chapter 1 Ex 1.5 - 5 Questions
• Class 9 Maths Chapter 1 Ex 1.6 - 11 Questions

☛ Download Class 9 Maths Chapter 1 NCERT Book

Topics Covered: The important topics focussed upon are irrational numbers, real numbers, and real numbers when expanded in the decimal form. The class 9 maths NCERT solutions chapter 1 covers the representation of real numbers on a number line, methods to perform operations on real numbers, and laws of exponents when dealing with real numbers.

Total Questions: Class 9 maths chapter 1 Number Systems consists of total 35 questions of which 30 are easy, 2 are moderate and 3 are long answer-type questions.

List of Formulas in NCERT Solutions Class 9 Maths Chapter 1

NCERT solutions class 9 maths chapter 1 covers important facts about the number systems which will help strengthen the math foundation. Like if a number ‘a’ is rational, and ‘b’ represents an irrational number, then ‘a+b’, and ‘a-b’ are irrational numbers, and ‘ab’ and ‘a/b’ are supposed to be irrational numbers, and ‘b’ is not equal to zero. For ‘a’ and ‘b’ positive real numbers the following formula or entities will be true:

• √ab = √a √b
• √(a/b) = √a / √b

Important Questions for Class 9 Maths NCERT Solutions Chapter 1

Video solutions for class 9 maths ncert chapter 1, faqs on ncert solutions class 9 maths chapter 1, do i need to practice all questions provided in ncert solutions class 9 maths number systems.

Practicing the NCERT solutions class 9 maths number systems and exercises on real numbers, rational numbers will help in exploring the number systems in a better way. The NCERT Solutions Class 9 Maths Number Systems will also provide a good insight into the solving of problems.

Why are Class 9 Maths NCERT Solutions Chapter 1 Important?

Since the number systems chapter deals with rational and irrational numbers, real numbers, and their expansion, their decimal form, also covering the law of exponents. Hence, this makes the NCERT solutions class 9 maths important for examinations.

What are the Important Formulas in NCERT Solutions Class 9 Maths Chapter 1?

There are several formulas or entities for positive real numbers which will be helpful in learning mathematics even for higher grades. Like if one wants to rationalize the denominator of 1/ ( √a + b ), then we can multiply and divide by its algebraic conjugate which is √a - b

How Many Questions are there in NCERT Solutions Class 9 Maths Chapter 1 Real Numbers?

The questions in the NCERT Solutions Class 9 Maths Chapter 1 are a great way for learning real numbers. There are around 35 questions dealing with number systems with 25 of them being simple and have straightforward logic, 6 of them are with medium complexity and 4 are elaborative questions.

What are the Important Topics Covered in NCERT Solutions Class 9 Maths Chapter 1?

The NCERT Solutions Class 9 Maths Chapter 1 deal with integers, real numbers, rational and irrational numbers. Apart from these the important topics covered are the real numbers, and what happens when they are expanded in decimal form, the law of exponents in the case of real numbers, how to differentiate between rational and irrational numbers etc.

How CBSE Students can utilize NCERT Solutions Class 9 Maths Chapter 1 effectively?

The students should first practice all the examples to understand the logic and problem solving technique and should try to solve all the exercise questions. The CBSE itself recommends the NCERT Solutions Class 9 Maths for the board exam studies.

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CBSE Class 9 Maths: Extra Questions - Chapter 1 - Number System (with Answers)

Check cbse class 9 maths extra questions for chapter 1 - number system (with answers). these questions are based on 9th maths ncert textbook & important for the preparation of upcoming cbse 9th maths exam 2020-21..

CBSE Class 9 Maths  extra Questions for Chapter 1 - Number System (with Answers). These questions are NCERT based important for the preparation of the upcoming CBSE 9th Maths Exam 2020-21. Most of the questions given here are very simple and can be solved in less than 5 minutes. If someone is facing problems in solving these questions then more clarity of basic concepts is required. These extra questions from Class 9 Maths Chapter 1 - Number System are also expected to be asked in CBSE Class 9 Maths test.

CBSE Class 9 Maths Extra Questions from Chapter 1 - Number System (with Answers):

1: Simplify: [{(8 2  + 9 2 ) 2 } 0 ] 2  = ____

Answer:  1.

2: 2 (2/3)  x 2 (1/3)  

Answer:  2.

3: [2 + (3) 1/2 ] [2 - (3) 1/2 ] = ______

Answer:  1.

CBSE Class 9 Maths Syllabus 2020-2021 (Reduced) - Download in PDF

4: Let  a  > 0 be a real number and p and q be rational numbers. Then which of the following statement(s) is/are correct?

(i) a p  . a q  = a p + q

(ii) a p   b p   = (ab) p

(iii) (a p ) q  = a pq  

(iv) All of these

Answer:  (iv) All of these.

5: Find the value of 1/(4) 3  ÷ 1/(4) 3  + 1/(1) 3

Answer:  2.

6: Divide 10 √15 by 5 √3 .

Answer:  2√5.

7.  Which of the following given statement(s) is/are correct?

(i) The sum or difference of a rational number and an irrational number is irrational.

(ii) The product or quotient of a non-zero rational number with an irrational number is

irrational.

(iii)  If we add, subtract, multiply or divide two irrationals, the result may be rational or

(iv) All of these statements are correct

Answer: 

(iv) All of these statements are correct.

8. [1/(2 + √5)] can also be written as

(a) (2 - √5)

(b) (√5 - 2)

(c) [1/(2 ÷ √5)]

(d) [1 + (2 + √5)]

[1/(2 + √5)] can be rationalised and can be written as (√5 - 2).

9. π (Pi) is a rational number or irrational number?

π (Pi) is an irrational number.

10. The value of π = 22/7. 22/7 is a rational number then how come π is an irrational number?

It is true that 22/7 is a rational number but π is irrational. Please note that 22/7 is an approximate value of π. 

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Chapter 1 Number Systems Class 9 Math Most Important Questions in PDF Download

Mathematics Class 9 Chapter 1 is very important for the students as many Number System Important Questions are framed in class 9 final examinations. In this chapter, you are going to study about various topics like the definition of the Number System and types of numbers like Natural Numbers, Whole Numbers, Integers, Rational Numbers and Irrational Numbers.

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In the table given below, we have provided the links to Class 9 Maths Number System extra Questions with Solutions . You can download them without having to share any login info.

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

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Case study Questions in Class 9 Mathematics Chapter 2  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  Class 9 Maths Case Study Questions  Chapter 2 Polynomials

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These case study questions challenge students to apply their knowledge of polynomials in real-life scenarios, enhancing their problem-solving abilities. This article provides for the Class 9 Maths Case Study Questions of Chapter 2: Polynomials , enabling students to practice and excel in their examinations.

Polynomials Case Study Questions With Answers

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.

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)

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/Passage-Based Questions

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

The Class 9 Maths Case Study Questions of Chapter 2: Polynomials serve as a valuable resource for students seeking to enhance their understanding of polynomial concepts and problem-solving skills. By practicing these case studies, students can strengthen their grasp of polynomials and their applications in real-life scenarios. Embrace the opportunity to engage with practical problems and excel in your mathematical journey.

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The number of zeroes of the polynomial x2 + 4x + 2 is The answer is too easy, i.e. 2

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• CBSE Notes For Class 9
• Class 9 Math Notes
• Chapter 1: Number System

Number System Class 9 Notes - Chapter 1

Cbse class 9 maths number system notes, introduction to number systems.

The number system is the process of representing numbers on the number line using certain rules and symbols. A number line is a depiction of numbers on a straight line with a specified interval between them. The number system is used to do mathematical computations ranging from complex scientific calculations to counting the number of chocolates left in the box. In this article, we are going to discuss the Class 9 Maths Chapter 1 Number System. To know more about Number System, visit here .

What Are Numbers?

Number: An arithmetical value representing a particular quantity. The various types of numbers are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, etc.

To know more about Numbers, visit here .

Natural Numbers

Natural numbers (N) are positive numbers i.e. 1, 2, 3 and so on. Natural numbers are positive integers.

To know more about Natural Numbers, visit here .

Whole Numbers

Whole numbers (W) are 0, 1, 2 and so on. Whole numbers are all natural numbers, including ‘0’. Whole numbers do not include any fractions, negative numbers or decimals. To know more about Whole Numbers, visit here .

Integers are numbers that include whole numbers along with negative numbers. An integer is a number from a set of negative and positive numbers, including zero, which has no decimal or fractional value. -3, 2, 0, 15, 900, etc., are examples of integers. Z is the symbol for a set of integers.

To know more about Integers, visit here .

Rational Numbers

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0. Some examples of rational numbers include 3/5, 7/2, 11/13, and so on.

To know more about Rational Numbers, visit here .

Irrational Numbers

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π To know more about Irrational Numbers, visit here . Properties of Irrational Numbers The following are the four properties of irrational numbers: (i) Negative of an irrational number is an irrational number. (ii) Sum and difference of a rational and an irrational number is always an irrational number. (iii) Sum, product and difference of two irrational numbers is either a rational or irrational number. (iv) Product of a rational number with an irrational number is either rational or irrational.

Real Numbers

Any number which can be represented on the number line is a real number (R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number. Examples of real numbers include -15, 3.14, 25, 22/7 and so on. To know more about Real Numbers, visit here .

Also, read:

• Prime Numbers
• Composite Numbers
• Co Prime Numbers
• Even and Odd Numbers

For more information on Number Systems, watch the below video

Representation of Irrational Numbers on the Number Line

Let √x be an irrational number. To represent it on the number line we will follow the following steps:

• Take any point A. Draw a line AB = x units.
• Extend AB to point C such that BC = 1 unit.
• Find out the mid-point of AC and name it ‘O’. With ‘O’ as the centre draw a semi-circle with radius OC.
• Draw a straight line from B which is perpendicular to AC, such that it intersects the semi-circle at point D.

Length of BD=√x.

• With BD as the radius and origin as the centre, cut the positive side of the number line to get √x.

Identities for Irrational Numbers

Arithmetic operations between:

• Rational and irrational will give an irrational number. Example: 2 × √3 = 2√3 i.e. irrational.
• Irrational and irrational will give a rational or irrational number. Example: √3 × √3 = 3 which is rational

If a and b are real numbers,

• √(ab) = √a√b
• (√a+√b) (√a-√b) = a – b
• (a+√b)(a−√b) = a²−b
• (√a+√b)(√c+√d) = √ac+√ad+√bc+√bd
• (√a+√b)(√c−√d) = √ac−√ad+√bc−√bd
• (√a+√b) 2 = a+2√(ab)+b

Rationalisation

Rationalisation is the process of converting an irrational number into a rational number. For example, the rationalisation of 1/√2 is: 1/√2 × √2/√2 = √2/2 We know that √2 = 1.414. Hence, we can write it as = 1.414/2, which can be easily represented on the number line.

Laws of Exponents for Real Numbers

If a, b, m and n are real numbers then:

• a m  × a n = a m+n
• (a m ) n  = a mn
• a m /a n  = a m−n , where (m > n)
• a m b m =(ab) m

Here, a and b are the bases and m and n are exponents.

Decimal Representation of Rational Numbers

The decimal representation of a rational number is the process of converting a rational number into a decimal number. The converted decimal number should be equal to the given rational number. This process can be done with the help of the long division method. Once the rational numbers are converted into decimal values, we can easily represent them on the number line.

Decimal Expansion of Rational and Irrational Numbers

The decimal expansion of a rational number is either terminating or non-terminating and recurring.

Example: 1/2 = 0.5 , 1/3 = 3.33……. The decimal expansion of an irrational number is non terminating and non-recurring. Examples: √2 = 1.41421356.. To know more about decimal expansion of rational numbers, visit here .

Expressing Decimals as Rational Numbers

Case 1 – terminating decimals.

Example: 0.625

Let x = 0.625

Step 1: If the number of digits after the decimal point is y, then multiply and divide the number by 10 y .

So, x = 0.625 × (1000/1000) = 625/1000.

Step 2: Reduce the obtained fraction to its simplest form.

Hence, x = 5/8

Case 2: Recurring Decimals

If the number is non-terminating and recurring, then we will follow the following steps to convert it into a rational number:

Step 1: Let x be the given recurring decimal

Step 2: Multiply the first equation with 10 y , where y is the number of digits that are recurring.

Multiply both sides of (1) by 100.

Step 3. Subtract equation (1) from equation (2).

On subtracting equation (1) from (2), we get

⇒ 99x = 103.2

⇒ x = 103.2/99 = 1032/990

Which is the required rational number.

Step 4: Reduce the obtained rational number to its simplest form.

Thus, x = 172/165.

Frequently Asked Questions on CBSE Class 9 Maths Notes Chapter 1 Number System

What is the number system.

A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.

What is rationalisation?

Rationalization is the process of removing a radical or surd from the denominator and shifting it to the numerator.

What is a recurring decimal?

A recurring decimal exists when decimal numbers repeat forever.

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Important Questions for CBSE Class 9 Maths (2024-25)

• Class 9 Important Question

CBSE Class 9 Maths Chapter wise Important Questions - Free PDF Download

Students studying in 9th standard need quality preparation for their upcoming examinations. Mathematics is such a subject that needs practice from the very beginning. Mostly, students are terrified of this particular subject and have no clear concept of mathematical chapters. Ultimately they end up scoring poor marks which drops their aggregate during finals. Students can follow Important Questions for Class 9 Maths by Vedantu to improve their mathematical knowledge and also to get good marks in exams. The PDF provided here highlights the Important Questions of Class 9 Maths . The downloadable PDF is designed according to the CBSE syllabus of 9th grade . It will help students to improve their mathematical skills and helps them to move a step forward to understand the subject. By practising Class 9 Maths Important Questions , students will build their confidence and clear their exams with flying colours.

You can also Download NCERT Solutions for Class 9 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Vedantu provides students with a Free PDF download option for all the NCERT Solution of updated CBSE textbooks . Subjects like Science, Maths, Engish will become easy to study if you have access to NCERT Class 9 Science , Maths solutions, and solutions of other subjects that are available on Vedantu only.

Chapter wise Important Questions for CBSE Class 9 Maths

CBSE Class 9 Maths Chapter wise Important Questions (2024-25)

Importance of cbse class 9 maths book.

Books of CBSE board ensure that students don’t miss out on any topic and have complete coverage of the syllabus. The solutions provided in this book can be taken as a reference to understand how answers are written in an exam. These books contain formatted answers as suggested by CBSE board and allow students to study the answers and recreate it in the exam in similar language and get good marks.

CBSE Class 9 Maths Important Questions

If the students are looking for specific and detailed solutions of 9 th Class Maths Important Questions, then they are in the right place. Maths solutions include all the questions offered as per new revised syllabus of 9 th grade. The Chapters Of Class 9th Maths include-

Students can get different types of questions related to the chapters. As the chapters proceed, Important Questions For Class 9 Maths get tougher. Students can find questions from various chapters like-

Question from Linear Equations:

Q) The cost of a notebook is twice the cost of a pen. Illustrate linear equations in two variables to signify the statement. Consider two variables as “x” and “y”.

Question from Surface area and Volumes :

Q) If the base radius and height of a cone is 3.5cm and 12cm, then how much ice-cream can be put into the cone?

There are many more questions related to other vital chapters. From the above-mentioned questions, students can get a precise idea about Important Questions for Class 9 Maths .

Questions of Maths for Class 9 with Answers

As the above segment includes the detailed idea of probable Important Questions for Class 9 Maths chapter-wise, now students can follow Maths Questions for Class 9 With Answers .

Given Below is a Question and Solution from the Chapter of Statistics:

Q) The mean of 20 observations is 17. If observation 40 is changed to 12, what will be the value of the new mean?

Ans. Since 17 is the mean of 20 observations

        Sum of 20 observations= 17×20= 340

        New sum of 20 observations= 340-40+12

        New mean= 312/20= 15.6

Interested students can follow images related to important questions for class 9 maths with solutions:

Students can download the PDF, follow Vedantu’s official website or can download the app to get access to online classes arranged by expert subject teachers. To solve important questions of Maths Class 9 , students can go for RD Sharma and RS Agarwal or books from Arihant Publications referred by NCERT which are available on the app and the official website of Vedantu as well.

Class 9 Maths Study Materials

Other cbse class 9 important related links.

Important Questions for CBSE Class 9 Science

FAQs on Important Questions for CBSE Class 9 Maths (2024-25)

Q1. How Many Chapters are Covered in Class 9th Maths Important Questions?

Ans:  Overall, 15 chapters are covered in Important Questions for Class 9 Maths. They imply a thorough study of how the chapters agree with the overall subject matter as prescribed in the course.

Q2. Which is the Most Challenging Chapter in Class 9 Maths?

Ans:  The difficulty of a chapter varies from student to student and their overall understanding of a chapter. Some students find Geometry difficult, whereas some find Surface Area and Volume, Constructions and Statistics difficult. Generally, students find Geometry as the most difficult topic. Also, under the Geometry section, students consider Triangles as the most difficult part of 9 th grade Maths.

Q3. How Do Students Need to Practise Maths in Class 9?

Ans:  If the subject is Maths, then practice is the key for scoring superb marks in the exam. If students practice different types of mathematical problems, solve CBSE sample papers in one sitting within a set time limit, then it would be highly useful for the students to get through different competitive exams. Students must also give importance to high weightage chapters.

Q4. Which chapter is the most difficult for students in Class 9 Maths?

Ans: Class 9 Maths includes 11 chapters. Students find Geometry as a difficult chapter in Class 9 Maths. Students have to practice important questions and NCERT questions for all chapters to score high marks in Class 9 Maths. As one proceeds to different chapters, one will start getting difficult questions. Students can refer to the NCERT solutions for Class 9 Maths on Vedantu for free that can help students to understand all concepts easily. These solutions are available at free of cost on Vedantu(vedantu.com) and mobile app.

Q5. Is Class 9 Maths tough?

Ans: Class 9 Maths is not difficult if students practise it regularly. Students should understand the basic concepts given in so that they can also understand the concepts of Class 10 maths later. Students need to work hard to get good marks in Class 9 maths. They can also download the NCERT Solutions for all chapters to understand the basic concepts of math and for scoring full marks.

Q6. Which is the most important chapter in Maths Class 9 NCERT?

Ans: All chapters of Class 9 Maths NCERT are important because students of Class 9 will get similar chapters in Class 10th. They have to also understand all concepts of Class 9 maths for higher classes such as 11th and 12th. Important questions for Class 9 Maths are available online on Vedantu that can help students to understand all concepts and practise questions based on all chapters easily and quickly.

Q7. How can I practise Math in Class 9?

Ans: Students of Class 9 can practise maths from the NCERT Solutions and important questions available on Vedantu. Students should practise all questions given at the back of each exercise in the NCERT book. Students can also practise extra questions given on Vedantu that can help students to understand the concepts and score high marks in Class 9 Maths. All questions are solved and concepts are explained properly by expert Maths teachers.

Q8. How could I learn Class 9 Maths in an efficient and fast way?

Ans: Students can learn Class 9 Maths by practising all questions given in the NCERT book of class 9. They should revise and practice all questions regularly to understand the concepts. Students can also learn class 9 maths by doing extra and important questions available online. Students can download important questions for Class 9 Maths from Vedantu. They can solve important questions to practise Class 9 Maths and get high marks in exams.

Important Questions for CBSE Class 9

Cbse class 9 study materials, home tuitions in india.

CBSE MCQ for Class 9 Maths Chapter 1 Number System Free PDF

Guys, we are working very hard to provide you with TOPIC-WISE MCQs (as listed below). Till then, attached below is the Master PDF having all the topics. Hope you understand. Enjoy your preparation! All the Best! 

CBSE MCQ for Class 9 Maths Chapter 1 Number System PDF

The CBSE MCQ for Class 9 Maths Chapter 1 Number System are provided above, in detailed and free to download PDF format. The solutions are latest , comprehensive , confidence inspiring , with easy to understand explanation . To download NCERT Class 9 Solutions PDF for Free, just click ‘ Download pdf ’.

Other MCQ Questions for Maths Class 9th CBSE

• CBSE MCQ for Class 9 Maths Chapter 2 Polynomials
• CBSE MCQ for Class 9 Maths: Chapter 3 Coordinate Geometry
• CBSE MCQ for Class 9 Maths: Chapter 4 Linear Equations in Two Variables
• CBSE MCQ for Class 9 Maths Chapter 5 Euclid’s Geometry

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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KEAM 2024 Practice Test link is now active at cee.kerala.gov.in: Check revised exam pattern, important topics and more

Important topics from KEAM 2024 Math, Physics, Chemistry syllabus

Visual stories.

Rajasthan Board 8th Class Result 2024 Out, Check Online by Roll Number

Students can check their RBSE 8th Result 2024 at rajeduboard.rajasthan.gov.in. The direct 8th class result rajasthan board roll number link is shared below.

Table of Contents

Rajasthan Board of Secondary Education Board (RBSEB) has conducted the class 8 final examinations from March 28th to April 4th. 12,52,127 students registered for Class 8 final exams and their parents were keenly waiting for the Rajasthan Board Class 8th results 2024. Now the wait is over, the Board Secretary Shri Krisha Kunal announced the RBSE 8th Class Result 2024 on May 30, at 03:00 P.M. in Jaipur.

Rajasthan Board 8th Result 2024

The students and parents can check the online marksheet at rajeduboard.rajasthan.gov.in . Students only need their board exam roll number and date of birth to verify their results. Scroll down to get the direct link to download the Rajasthan Board 8th Result 2024 Scorecard.

Latest Update-  The RBSE class 8th result 2024 was scheduled to declare at 3 pm online but there was heavy traffic on the official RBSE result page and also technical issues. All the working official result links are given below. Parents and students were waiting to check the results from the official website, but later the result announced offilne.

8th Class Result Check Online by Roll No

Rajasthan Board is scheduled to release the RBSE class 8th results 2024 on 30 May 2024. The Board held a press conference at 03:00 P.M. to announce the results and statistics.  This year, a total of 12,64,913 students enrolled in class 8 last year.

The 2023-24 session final exam was conducted offline in pen-paper mode. The final exam was held for English, Math, Science, Social Study, and a third language subject. Students have the option to choose one-third language subjects from Sanskrit, Sindhi Urdu, Punjabi, and Gujarati. Check 8th class results online by roll no wise details here.

8th Class Result Rajasthan Board Roll Number wise Link

The 8th class result check online by roll no link is supplied in the box below. The download link is activated at around 3 pm. They can click on the link below and access the official page. In the login window mention all required information.

Sample RBSE 8th Result Image

Rajasthan Board 8th Result 2024 Statistics

Rbse 8th result 2024: around 11.9 lakh students passed the exam.

How many students appeared and passed the final exam, are tabulated below.

RBSE Class 8th Pass Percentage Grade Wise

Half of the students of the Rajasthan Board class 8 students passed with grade B. 21.05% of students passed in grade A. Check other grades with the pass rate below.

RBSE Class 8th Pass Percentage of Boys and Girls

Girls performed better than the boys in the class 8th final exam.

RBSE 8th Result 2024 Pass Percentage: Government School vs Private Schools

Also Check|   RBSE 5th Class Result 2024 Link

How to Check RBSE 8th Result 2024 by Roll Number?

Students or parents should follow the below steps to download the online Rajasthan Board 12th result.

• Step 1: Visit the official page of BSER at https://rajeduboard.rajasthan.gov.in/.
• Step 2: On the homepage click on the “RBSE class 8 final exam Result 2024 Link”.
• Step 3: Click on the link and submit the roll no, DOB, class, district.
• Step 4: After successful submission the result with subject-wise marks will be shown on the screen.
• Step 5: Download the PDF of the result and check all information carefully.

RBSE 8th Result 2024 Pass Percentage

Last year the overall RBSE class 8th Result pass percentage was 94.50%. Around 13 lakh students were registered for class 8 final exams. The total Number of Students who Appeared was 13,05,355. The total Number of Students who Passed in the previous year was 12,33,702.

What after downloading the RBSE 8th Marksheet?

Students have to check all the details mentioned on the mark sheet very carefully. In case of any wrong information immediately contact the school authority to change the information. Otherwise, if the students keep the wrong info, he or she will face trouble in the next class admission.

What is the grading system for the RBSE Class 12 exam?

Students who score between 91 to 100 will get an A+. 76+ marks kids can get an A grade. Minimum 40 to pass and will get a grade D. 61 to 75 marks holder will be awarded 61 to 75 marks.

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When will RBSE 8th result 2024 release?

The Rajasthan Board class 8 results will be announced on 1st week of May 2024.

How to check RBSE 8th results 2024?

Students can check their Rajasthan Board 8th result using roll no , district or roll no , DOB.

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