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9th Math Sc. Test Series – Chapter Wise, Half Book, Full Book Test Papers

9th Math Sc. Test Series – Chapter Wise, Half Book, Full Book Test Papers. Chapter Wise, Half Book, Full Book Test Series with Syllabus. 9th Math – Chapter Wise Solved Test Papers.

Chapter Wise / Unit-wise Tests by NOTESPK

9th class mathematics chapter wise / unit wise tests.

NOTESPK Unit Wise Tests, with Syllabus:

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Chapter wise test series (9th mathematics), 9th class mathematics brain test series.

Unit Wise / Chapter Wise Test Series / Test Papers with different versions of the syllabus for class 9 Mathematics . The syllabus of each test of 9th class Mathematics is mentioned on the test . Duel Medium Chapter Wise Test Series in different versions with chapter-wise solved tests . Urdu and English Medium Chapter Wise Test Papers for Class 9 Mathematics with Chapter Wise Tests Solution .

Chapter Wise Test Series ( 9th Mathematics ):

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Chapter Wise Solved Papers / Tests:

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9th Class Mathematics Versatile Test Series

Unit Wise, Quarter Wise / Pair Wise Tests, Half Book Tests, and Full Book Tests for Class 9 Mathematics . The syllabus is mentioned on each test. Separate Urdu Medium and English Medium Chapter Wise, Half Book, Full Book Test Series / Test Papers. The Solution of MCQs / Answer Key is also given with tests in PDF file. 9th Mathematics Test Series with the syllabus.

Mathematics Class 9 Test Series.

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Maths Chapter 1

Maths Chapter 2

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9th Class Math – 1st Half Book Tests

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9th Class Chapter-Wise MCQs (Solved/Unsolved)

9th Mathematics Chapter Wise Test Papers. Chapter Wise Solved Papers for 9th Mathematics. Urdu Medium Test Series – Mathematics Class 9. English Medium Test Series – Mathematics Class 9. Chapter Wise Tests, Half Book Tests, Full Book Tests – 9th Maths. 9th Mathematics Test Series by NOTESPK .

The 9th Class Test Series is for the following BsISE of Punjab: BISE Multan, BISE Sahiwal, BISE Sargodha, and BISE Lahore. BISE Faisalabad, BISE Gujranwala, BISE Dera Ghazi Khan, BISE Rawalpindi, and BISE Bahawalpur. (All Punjab Boards of Education, BsISE Punjab).

Boost Your Class 9 Math Skills with NOTESPK Practice Test Series for BsISE Punjab

Are you a Class 9 student studying under the Board of Intermediate and Secondary Education (BsISE) Punjab and looking for a reliable way to enhance your math skills? Look no further! Introducing the comprehensive and efficient Class 9 Math Practice Test Series by NOTESPK. Designed to help you excel in your math exams, this test series offers chapter-wise, half book, and full book test papers to ensure thorough preparation and improved confidence in tackling any math challenge.

Chapter-Wise Test Papers: A Stepping Stone to Success

The Class 9 Math Practice Test Series by NOTESPK offers chapter-wise test papers meticulously crafted to cover each topic in the syllabus. By following this structured approach, you can focus on one concept at a time, reinforcing your understanding and clarifying doubts along the way. This method ensures a solid foundation and helps build your math skills incrementally, making complex concepts more manageable and easy to grasp.

Half Book Test Papers: Mastering Midterm Preparations

As the academic year progresses, midterms come knocking at the door and being well-prepared is crucial. The NOTESPK Practice Test Series includes Half Book Test Papers tailored for your midterm exam preparations. These test papers cover essential topics and concepts from the first half of your Class 9 Math textbook. Solving these papers allows you to assess your progress and identify areas that need improvement, empowering you to fine-tune your study plan accordingly.

Full Book Test Papers: Ace Your Finals with Confidence

The culmination of your Class 9 Math journey lies in your final exams. To excel in these high-stakes assessments, practicing with Full Book Test Papers is imperative. NOTESPK offers a comprehensive set of test papers that encompass the entire syllabus, simulating the actual exam scenario. By solving these papers, you can gauge your readiness, manage time effectively, and build the confidence needed to tackle any question that comes your way.

Why Choose NOTESPK Practice Test Series for Class 9 Math?

Extensive Coverage: The test series covers all topics and concepts specified in the Class 9 Math syllabus for BsISE Punjab, leaving no stone unturned in your preparation.

Quality Content : Each test paper is meticulously curated by experienced educators, ensuring accuracy, relevance, and alignment with the latest examination patterns.

Progressive Difficulty: The test papers are designed to start from basic concepts and gradually progress to more challenging problems, allowing you to grow your skills organically.

Real Exam Simulation: By mimicking the format and difficulty level of actual exams, these test papers prepare you for the real deal, reducing test anxiety and enhancing your performance.

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With the NOTESPK Practice Test Series for Class 9 Math , you have a powerful tool at your disposal to conquer your exams with confidence. The chapter-wise, half-book, and full-book test papers ensure comprehensive coverage of the syllabus and steady progress in your learning journey. Sharpen your math skills, boost your grades, and pave the way for a successful academic future with NOTESPK. Start your practice today and embrace the path to excellence in mathematics!

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Test Papers for practice for BISE Lahore papers for class 9. Grade 9 BISE Faisal Abad Test Series. BISE Bahawalpur Test Series for class 9. Practice Test Papers for BISE Gujranwala for class 9. BISE Sahiwal Test Series for class 9. Grade 9 BISE Dera Ghazi Khan Test Series. Practice Test Paper for BISE Rawalpindi for class 9. Grade 9 BISE Sargodha Practice Test Papers.

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CBSE Class 9 Maths Sample Question Paper - 1 2024-25
Sample Papers

Maths Mock Paper-1 for CBSE Class 9 Exams Free PDF Download From Vedantu

The Class 9 CBSE Maths papers are curated by highly professional experts of Vedantu who have years of expertise in their respective fields, to help every student understand the core concepts of Class 9 Maths. Regularly practising problems and going through the solved exams is extremely crucial for excelling at your exams. In addition to this, finding suitable study material is a quintessential aspect of preparing well for exams. Vedantu offers detailed CBSE sample papers for Class 9 Maths to help students overcome the difficulty of solving fundamental maths problems. Vedantu provides free PDFs of NCERT solutions for the students. You can also download the NCERT Solutions for Class 9 Maths and Class 9 Science through our official webpage.

CBSE Sample Papers for Class 9 Maths

Many students often find it challenging to prepare well for their Maths examinations therefore, to release unnecessary anxiety, preparing ahead is essential. In the CBSE Class 9 Maths mock paper, students will learn meticulously about number systems, polynomials, coordinate geometry, triangles, quadrilaterals, surface area and volumes, probability, circles, Euclid's geometry, Constructions, and so on. All these concepts are well-structured by our skilled experts, who do extensive research before incorporating the questions into the Sample PDFs.

All these questions will help students build a robust foundation for their higher classes. Students can refer to these exemplar problems, worksheets, exercises, and much more to gain a thorough knowledge of every concept of Class 9 Maths.

Vedantu helps students prepare for Maths based on their ability and level of understanding. If you look for a high score in Class 9 Maths, practice these NCERT questions and sample papers regularly.

You can also visit Class 9 Maths Chapter wise notes to get additional knowledge about Maths concepts. Here we have provided all question papers with solutions so that students can take feedback and assess their performance.

Maths Sample Paper for Class 9 Detailed Introduction

CBSE sample question papers for Class 9 Maths are full of essential questions which are related to the syllabus of Mathematics for Class 9th. The sample papers will provide you with accurate information about the exam pattern and exam duration so that students can prepare accordingly, which will help them score better in the examination.

The sample question paper is designed in such a way that it covers all the chapters which are prescribed for Class 9th CBSE students. This will help you to get an idea about the weightage of different chapters and also what type of questions can be asked in the exam. Students must go through the question paper and try to solve as many questions as possible because it will help them in the exam. After attempting the mock test, students can also check their solutions with the help of given solutions to get an idea about their mistakes.

So instead of waiting, students of Class 9th should solidify their exam preparations with the assistance of the CBSE Class 9 Maths Sample Question Paper - 1 that is available on this page.

Benefits of Revising from CBSE Sample Papers for Class 9 Maths

Each Maths mock paper for Class 9th, designed at Vedantu undergoes deliberate research so that students are offered only the most reliable study material. Here are some benefits of learning with us and practising CBSE Sample Papers for Class 9 Maths:

You can get an idea about the examination pattern and types of questions that are generally asked in the exams.

The solved papers will help you understand the marking scheme followed by CBSE for different questions.

After solving these papers, you can analyse your mistakes and weaknesses.

The experience of solving these papers will help you practice systematically and improve your speed as well as accuracy.

It is important to keep revising the topics that you are not comfortable with so that they do not hamper your overall performance in the exams. You can revise all these questions easily at Vedantu because we provide direct links to each question.

Our practice tests will offer you an accurate idea of your exam preparation and help you identify the areas that require more thorough revision. You can also set a time frame for completing your work and completing the test in the given duration. At Vedantu, we encourage students to solve previous papers repeatedly to get better examination results.

Sample question paper for Class 9 Maths is incorporated with informative content that follows the syllabus and guidelines of the central board of secondary education.

Students can refer to a mix of questions, worksheets, exemplar solutions, and much more to choose for an exciting path to learning.

Vedantu sample PDFs are aimed at helping students clear their doubts in no time.

The easy-to-understand sample guides will help students learn how to solve problems easily and quickly.

Vedantu carries pride in offering some of the most distinguished and accurate PDFs that help students reach their fullest potential. All of the PDFs offered here are systematically designed to help improve every student's problem-solving and critical thinking skills. Now download the CBSE sample papers for Class 9 Maths to do well in your upcoming exams and get the scholarship and other opportunities, and students can also get scholarship opportunities for class 9 Maths.

FAQs on CBSE Class 9 Maths Sample Question Paper - 1 2024-25

1. What is the question paper pattern for CBSE Class 9 Maths?

The CBSE Class 9 Maths question paper will be divided into different sections. There will be a section on number systems, followed by another on polynomial and linear equations with rational expressions, another one on quadratic equations and inequalities, yet another one on permutations and combinations, followed by - dimensional geometry, two-dimensional geometry, trigonometry, Statistics & Probability which is followed by a section on miscellaneous topics students can expect to find on the sample question paper for class 9th mathematics 2024-25.

2. What are the topics covered under CBSE Class 9 Maths?

Students can expect to see some of the following concepts in the Class 9 Maths question paper:

Properties of Real numbers, arithmetic operations, simplification, factors, multiples, and their applications.

Linear equations in one and two variables, linear inequalities, the system of linear equations in three variables, functions.

Rate of growth comparison, laws of indices (positive integral exponent).

Systematic representation of conic sections.

Statistics (central tendency), data interpretation.

Quadratic equations.

Exponential functions, logarithmic functions.

Miscellaneous topics etc.

3. How can I download sample papers for Class 9 Maths?

Just visit the Vedantu home page or download the Vedantu app , and you will find links to every question paper, every practice test, and much more that we have on offer for Class 9 Maths at Vedantu. Now follow the instructions carefully and clear all your doubts with ease! The CBSE Class 9 Maths Sample Question Paper - 1 2024-25 is now available for download. This question paper follows the latest syllabus and guidelines of the Central Board of Secondary Education (CBSE). The paper consists of a total of 36 questions, which are distributed among different sections.

4. What kind of questions should I expect in the CBSE Class 9 Maths question paper?

There will be objective type, multiple-choice questions, mostly with 4 to 5 options for every question. The language used in the paper is simple and easy to understand, and students can come across questions from different topics in the syllabus. The CBSE Class 9 Maths Sample Question Paper - 1 2024-25 comprises a total of 36 questions, which are distributed among different sections. The number systems section has eight questions, polynomial and linear equations with rational expressions section have 10 questions, quadratic equations and inequalities section has 9 questions, permutations and combinations section has 6 questions, one-dimensional geometry section has 7 questions, two-dimensional geometry section has 10 questions, trigonometry section has 3 questions, Statistics & Probability section has 5 questions, and Miscellaneous, etc. section

5. What should I do if I am unable to solve a question in the CBSE Class 9 Maths sample paper?

If you are unable to solve a question in the CBSE Class 9 Maths question paper, then don't panic! Just skip the question and move on to the next one. You can try Vedantu's free online Maths classes to get the solutions to your doubts. Our team of experts is always here to help you with anything and everything related to school education, right from homework, assignments, projects, notes, etc., and CBSE Class 9 Maths Sample Question Paper - 1 2024-25 is now available for download. This question paper follows the latest syllabus and guidelines of the Central Board of Secondary Education (CBSE). The paper consists of a total of 36 questions, which are distributed among different sections.

9th Class Math’s Test Papers

Last updated on April 17, 2022

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We provided chapter-wise, 1 st half/2 nd half & full book Mathematics test papers according to board patterns in both English and Urdu medium.

9th Mathematics Chapter Wise Tests Urdu & English Medium

You can download class 9th test papers chapter wise in both medium English And Urdu in pdf. We divide each chapter in four types, type1, type2, type3 and type4, so that’s student prepares their exam in best way.

9th Mathematics Chapter Half & Full Tests Urdu & English Medium

Student can also download half test papers of class 9th math and full book test papers. We divide these tests according to the board patterns.

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Class 9 Maths MCQ Test (Online Available)

Free mcq test, table of content.

4. Social Science
6. Mental Ability
7. Elements of Business
8. General Knowledge

Introduction to Euclids Geometry Test - 16

Duration: 10 Mins

Maximum Marks: 10

Read the following instructions carefully.

1. The test contains 10 total questions.

2. Each question has 4 options out of which only one is correct .

3. You have to finish the test in 10 minutes.

4. You will be awarded 1 mark for each correct answer.

5. You can view your Score & Rank after submitting the test.

6. Check detailed Solution with explanation after submitting the test.

7. Rank is calculated on the basis of Marks Scored & Time

Introduction to Euclids Geometry Test - 15

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The Class 9 Maths MCQ is a form of objective questions in which the test takers need to select any one of the options. Students can select the accurate option by completing all chapters included in Class 9 Maths syllabus. After attempting the objective questions, students can analyse the given answers of Class 9 Maths as the question analysis is given on the website.

The Class 9 Maths MCQ are considered to be standardised tests which can be useful for both teachers and students. Teachers can use the study resource so that they can provide the ready made questions of Class 9 Maths to students for practising. Students can also use the study resource of objective questions to practise and to understand the concepts in a better way.

Maths MCQ Class 9 Online Test

Students can attempt the Maths MCQ Class 9 in an online mode so that they don’t face any difficulty in attempting questions. Regular solving questions from the Class 9 Maths, can help students to be more confident while attempting objective questions. It can also help students to score well in the Class 9 Maths final, accordingly they can be promoted to the next grade.

Where Can Students Find Class 9 Maths MCQ?

Students can find the Class 9 Maths MCQ from the Selfstudys website, steps to attempt the MCQ are clearly explained below:

Open the Selfstudys website.
Bring the arrow towards the CBSE which can be seen in the navigation bar.
A drop down menu will appear, select MCQ Test from the given list.

Class 9 Maths MCQ, Class 9 Maths MCQ Test, Class 9 Maths Online MCQ, MCQ Test for Class 9 Maths, Maths MCQ Test for Class 9, Maths MCQ Class 9 Online Test

A new page will appear, select Class 9th from the list of classes.
Click Maths from the list of subjects.
A drop down menu will appear, select Latest Test from the list.

Again a new page will appear, select any of the chapters to Start Test to practise.

Features of Class 9 Maths MCQ

The Class 9 Maths MCQ are those questions which are provided with 4 options, this is one of the important feature of the MCQ, other features are:

Question Analysis is Given: In the analysis, knowledge about the correct ; wrong and skipped questions are given so that students can improve accordingly.
Rank is Given: Rank refers to the position or order in reference to the performance; students can look through the rank after attempting Maths Class 9 MCQ.
Solutions are Given: It is very important for students to solve their doubts after attempting Maths Class 9 MCQ as it is provided in the website.
Redo Option is Given: Students are provided with the option of redo, so that they can attempt the Maths MCQ Class 9 once again without getting stuck.

All Chapters are Covered: In the latest MCQ of Class 9 Maths MCQ, students are provided with questions related to all the chapters.
For CBSE Board: The Maths MCQ Class 9 are basically for students following the CBSE syllabus as all the chapters are arranged and organised according to it.

Top 6 Benefits of Class 9 Maths MCQ

The Class 9 Maths MCQ offers ample of benefits, some of the benefits are discussed below:

Scoring: The Maths MCQ Class 9 is considered to be easy scoring as students just need to select the accurate option to score 1 mark and they don’t need to write a subjective answer.
Provides Quick Feedback: The Maths Class 9 MCQ provides quick feedback to the test takers so they can try to improve then and there.
Saves Time: The Maths MCQ of Class 9 can be analysed and completed quickly without wasting much time in looking for answers.
Highly Reliable: The content inside the Maths MCQ Class 9 is highly reliable as it is created with good research so that students can attempt all questions without confusions.
Mobile Friendly: Students can attempt the Maths Class 9 MCQ from their smartphones as it can be attempted from anywhere and wherever possible.
Helpful in Self Evaluation: The multiple choice questions of Class 9 Maths can be helpful while self evaluation: ability to examine, accordingly students can improvise.

How to Mark the Right Answer While Attempting Class 9 Maths MCQ?

It is must for students to mark the right answer while attempting Class 9 Maths MCQ, then only they can improvise their score, tips to mark the right answer are:

Read the Question Carefully: Students need to read the multiple choice questions of Class 9 Maths, then only they can get an idea about what is asked accordingly they can answer it.
Read the Options: Students are advised to read all the 4 options while attempting Class 9 Maths MCQ so that they can guess the accurate option.
Try to Eliminate Incorrect Options: Students are advised to eliminate obvious incorrect options from the Maths Class 9 MCQ, this can increase the chances of selecting the right option.
Look for Clues: Students are advised to look for clues which can be visible in the questions of Class 9 Maths, this can ease the process of selecting the right option.
Double Check the Answers: Students need to double check the answer given while attempting the Class 9 Maths MCQ so as to decrease the amount of silly mistakes.

How To Analyse the Answers After Solving Class 9 Maths MCQ?

After solving Class 9 Maths MCQ, it is very important for students to analyse, accordingly they will be able to know their strengths and weaknesses as well as gaps in the understanding of the chapter, tips to analyse the answers are discussed below:

Review Answers: Students need to analyse the answers of Maths MCQ Class 9 so that they can get an idea about wrong as well as right answers.
Review the Correct Answers: Students need to revise the correct answers of Maths MCQ so that they can get an idea about why the answers are right as well as strong topics.
Review the Incorrect Answers: Students are advised to review the incorrect answers of Maths MCQ so that they can identify misconception and errors in their thinking.
Identify the Pattern: Students are advised to identify patterns or concepts in those incorrect questions of Class 9 Maths MCQ so that they can study accordingly.
Note Down the Mistakes: Students need to note down the mistakes in a scrap paper or in a separate book, this can help them to rectify quickly.

When is the Right Time to Solve the Class 9 Maths MCQ?

The best time to solve the Class 9 Maths MCQ depends upon the student’s learning style and their preferences, right time to solve the questions are discussed below:

After Completing a Topic: The Maths MCQ Class 9 can be very useful after completing a particular topic as it helps to revise or review the topic.
As Part of the Study Schedule: Students can incorporate the Maths Class 9 MCQ into their study schedule, accordingly they can track their performance on a daily basis and improve their understanding of the subject.
Before an Exam or Assessment: The Class 9 Maths MCQ can be helpful during an exam or assessment as it helps students to test their knowledge and can identify the gaps.
During Revision: The Maths Class 9 MCQ can be a useful tool as it helps students to know the key concepts and can increase the level of understanding.
To Improve the Test Taking Skills: When students need to improve their test taking skills, they can take the help of Class 9 Maths MCQ as it helps to improve the time management skills as well as critical thinking.

How to Prepare Well for Class 9 Maths MCQ?

Preparing for the Class 9 Maths MCQ requires a combination of understanding the concepts and practising the objective questions, here are some tips to be followed so that students can prepare well and score good marks:

Study the Concepts: The first step in preparing the Maths MCQ Class 9 is to study the concepts thoroughly so that students can have a better understanding.
Focus on Important Topics: Identify those topics and concepts which are likely to be covered in the Maths Class 9 MCQ, this can help students to score better.
Practise Regularly: It is important for students to practise Maths Class 9 MCQ regularly so that they can get an idea about the test format and can easily improve their test taking skills.
Analyse the Mistakes: Students need to analyse the mistakes done while attempting Class 9 Maths MCQ so that they can know their weaknesses and study accordingly.
Form a Study Schedule: Students need to allocate a specific time to cover the concepts and to practise Class 9 MCQ of Maths so that they can analyse their progress.
Use Reference Books: Students can utilise the reference books so that they can practise vast amounts of Class 9 multiple choice questions.
Revise Regularly: Students are advised to revise all concepts on a regular basis then only they can be prepared well for Class 9 MCQ Maths.
Seek Help: If in case students are struggling with any of the topics or concepts, they can seek help from the teachers so that they can be well prepared for Class 9 Maths MCQ.

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CBSE Class 9 Mathematics Practice Papers Free PDF Download

Mathematics checks your creative and analytical skills. You will always find mathematics having a direct or indirect connection with other subjects like science and social science (i.e. in economics). Mathematics always plays a significant role in solving real-world problems. There are various government platforms that provide free practice papers for mathematics and other subjects, one such platform is DoE (Department of Education, Delhi)

Here at Educart, we provide the best and most reliable resources to our students without requiring them to login. In the below table, you can find the PDF downloadable links to various sets of mathematics practice papers.

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NCERT Class 9
NCERT 9 Maths

NCERT Solutions for Class 9 Maths

Ncert solutions for class 9 maths – free pdf updated for 2023-24 session.

NCERT Solutions for Class 9 Maths includes solutions to all the questions given in the NCERT textbook for Class 9. The students can download PDFs of chapter-wise solutions to these problems from the links provided below on this page. These NCERT Solutions for Class 9 cover all the topics included in the NCERT textbook, like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

With the help of these Solutions of NCERT Books for Class 9 Maths , students can practise all types of questions from the chapters. The CBSE Class 9 Maths Solutions have been designed by our experts in a well-structured format to provide several possible methods of answering the problems and ensure a proper understanding of concepts. The students are suggested to practise all these solutions thoroughly for their exams. It will also help them in building a foundation for higher-level classes.

NCERT Solutions Class 9 Maths Chapters

Chapter 1 Number System
Chapter 2 Polynomials
Chapter 3 Coordinate Geometry
Chapter 4 Linear Equations in Two Variables
Chapter 5 Introduction to Euclids Geometry
Chapter 6 Lines and Angles
Chapter 7 Triangles
Chapter 8 Quadrilaterals
Chapter 9 Circles
Chapter 10 Heron’s Formula
Chapter 11 Surface Areas and Volumes
Chapter 12 Statistics

The following chapters have been removed from the NCERT Class 9 Maths textbook 2023-24.

Areas of Parallelograms and Triangles
Constructions
Probability

Along with NCERT Solutions , students are also provided with other online learning materials available at BYJU’S, such as notes, books, question papers, exemplar problems, worksheets etc. These materials are designed with respect to the CBSE syllabus and NCERT curriculum. Students are also advised to practise CBSE Class 9 Sample Papers to get an idea of the question pattern in the final exam.

15 chapters are present in the NCERT Solutions for Class 9 Maths . These chapters given in the NCERT Class 9 Maths lay a foundation for the chapters present in Class 10. The PDFs given at BYJU’S are accessible to everyone and can be downloaded by the students for free.

NCERT Solutions of Class 9 Maths Book Chapter Brief:

Students having trouble solving tough Math problems can refer to these CBSE Maths Class 9 Solutions of NCERT for better guidance and for quick review. Solving these exercises in each chapter will ensure positive results.

NCERT Solutions Class 9 Maths Chapter 1 Number System

This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it. A total of 6 exercises are present in this chapter that contains the problems based on all the topics asked in the chapter. This chapter also teaches students the representation of terminating/non-terminating recurring decimals (and successive magnification method) as well as the presentation of square roots of 2, 3 and other non-rational numbers on the number line. The chapter also deals with the laws of integral powers and rational exponents with positive real bases in the Number System.

Topics Covered in Class 9 Maths Chapter 1 Number System

Review of representation of natural numbers, integers, and rational numbers on the number line. Representation of terminating/non-terminating recurring decimals on the number line through successive magnification. Rational numbers as recurring/terminating decimals.

Examples of nonrecurring/non-terminating decimals such as √2, √3, √5 etc. 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, every point on the number line represents a unique real number.

Existence of √x for a given positive real number x (visual proof to be emphasised). Definition of n th root of a real number.

Recall of laws of exponents with integral powers. Rational exponents with positive real bases (to be done by particular cases, allowing the learner to arrive at the general laws).

Rationalisation (with precise meaning) of real numbers of the type (and their combinations) \(\begin{array}{l}\frac{1}{a+b\sqrt{x}}\: and\: \frac{1}{\sqrt{x}+\sqrt{\sqrt{y}}}\end{array} \) where x and y are natural numbers, and a and b are integers.

Important Formulas –

Operations on Real Numbers

√(a/b) = √a/√b

√ab = √a √b

(√a + √b) (√a – √b) = a – b

(a + √b) (a – √b) = a 2 – b

(√a + √b) (√c + √d) = √ac + √ad + √bc + √bd

(√a + √b) 2 = a + 2√ab + b

Laws of Exponents for Real Numbers

a m . a n = a m + n

(a m ) n = a mn

a m /a n = a m – n , m > n

a m b m = (ab) m

Also, access the following resources for Class 9 Chapter 1 Number System, at BYJU’S:

NCERT Number System Class 9 Notes
Number System Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Number Systems
RD Sharma Solutions Number Systems Class 9

NCERT Solutions Class 9 Maths Chapter 2 Polynomials

This chapter discusses a particular type of algebraic expression called polynomial and the terminology related to it. Polynomial is an expression that consists of variables and coefficients involving the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. The chapter also deals with the Remainder Theorem and the Factor Theorem with the uses of these theorems in the factorisation of polynomials. Students will be taught several examples as well as the definition of different terms like polynomials, degrees, coefficients, zeros and terms of a polynomial. A total of 5 exercises are present in this chapter, which includes problems related to all the topics mentioned in the chapter.

Topics Covered in Class 9 Maths Chapter 2 Polynomials

Definition of a polynomial in one variable, its coefficients, with examples and counter examples, its terms, zero polynomial. Degree of a polynomial. Constant, linear, quadratic, cubic polynomials; monomials, binomials, trinomials. Factors and multiples. Zeros/roots of a polynomial/equation. State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of ax 2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.

Recall algebraic expressions and identities. Further identities of the type:

(x + y + z) 2 = x 2 + y 2 + z 2 + 2xy + 2yz + 2zx

(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)

and their use in the factorisation of polynomials. Simple expressions are reducible to these polynomials.

Important Formulas –

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

(x – y) 2 = x 2 – 2xy + y 2

x 2 – y 2 = (x + y) (x – y)

(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)

Dividend = (Divisor × Quotient) + Remainder

Remainder Theorem

Let p(x) be any polynomial of degree greater than or equal to one, and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

Factor Theorem

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), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).

Also, access the following resources for Class 9 Chapter 2 Polynomials, at BYJU’S:

NCERT Polynomials Class 9 Notes
Polynomials Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Polynomials
RD Sharma Solutions factorisation of Polynomials Class 9

NCERT Solutions Class 9 Maths Chapter 3 Coordinate Geometry

The chapter Coordinate Geometry includes the concepts of the cartesian plane, coordinates of a point in xy–plane, terms, and notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more. Students, in this chapter, will also be studying the concepts of abscissa and ordinates of a point as well as plotting and naming a point in xy–plane. There are 3 exercises in this chapter that contain questions revolving around the topics mentioned in the chapter, helping the students get thorough with the concepts.

Topics Covered in Class 9 Maths Chapter 3 Coordinate Geometry

The Cartesian plane, coordinates of a point, names and terms associated with the coordinate plane, notations, plotting points in the plane, graph of linear equations as examples; focus on linear equations of the type ax + by + c = 0 by writing it as y =mx + c and linking with the chapter on linear equations in two variables.

Important Points –

To locate the position of an object or a point in a plane, we require two perpendicular lines. One of them is horizontal, and the other is vertical.
The plane is called the Cartesian, or coordinate plane, and the lines are called the coordinate axes.
The horizontal line is called the x-axis, and the vertical line is called the y-axis.
The coordinate axes divide the plane into four parts called quadrants.
The point of intersection of the axes is called the origin.
The distance of a point from the y-axis is called its x-coordinate, or abscissa, and the distance of the point from the x-axis is called its y-coordinate, or ordinate.

Also, access the following resources for Class 9 Chapter 3 Coordinate Geometry, at BYJU’S:

NCERT Coordinate Geometry Class 9 Notes
Coordinate Geometry Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Coordinate Geometry
RD Sharma Solutions Coordinate Geometry Class 9

NCERT Solutions Class 9 Maths Chapter 4 Linear Equations in Two Variables

Along with recalling the knowledge of linear equations in one variable, this chapter will introduce the students to the linear equation in two variables, i.e. ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. There are 4 exercises in this chapter that consist of questions related to finding the solutions of a linear equation, plotting a linear equation on the graph and other topics discussed in the chapter.

Topics Covered in Class 9 Maths Chapter 4 Linear Equations in Two Variables:

Recall of linear equations in one variable. Introduction to the equation in two variables. Prove 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 seem to lie on a line. Examples, problems from real life, including problems on Ratio and Proportion and with algebraic and graphical solutions being done simultaneously.

Important Points –

An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
A linear equation in two variables has infinitely many solutions.
The graph of every linear equation in two variables is a straight line.
x = 0 is the equation of the y-axis, and y = 0 is the equation of the x-axis.
The graph of x = a is a straight line parallel to the y-axis.
The graph of y = a is a straight line parallel to the x-axis.
An equation of the type y = mx represents a line passing through the origin.

Also, access the following resources for Class 9 Chapter 4 Linear Equations in Two Variables, at BYJU’S:

NCERT Linear Equations in Two Variables Class 9 Notes
Linear Equations in Two Variables Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Linear Equations in Two Variables
RD Sharma Solutions Linear Equations in Two Variables Class 9

NCERT Solutions Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

This chapter discusses Euclid’s approach to geometry and tries to link it with present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms. Students will be taken deeper into the topic of axioms, postulates and theorems with the two exercises present in the chapter.

Topics Covered in Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry:

History – Euclid and geometry in India. Euclid’s method of formalising observed phenomenon into rigorous mathematics with definitions, common/obvious notions, axioms/postulates, and theorems. The five postulates of Euclid. Equivalent versions of the fifth postulate. Showing the relationship between axiom and theorem. 1. Given two distinct points, there exists one and only one line through them. 2. (Prove) Two distinct lines cannot have more than one point in common.

Important Axioms and Postulates –

Some of Euclid’s axioms are:

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part.

(6) Things which are double of the same things are equal to one another.

(7) Things which are halves of the same thing are equal to one another.

Euclid’s Five Postulates

Postulate 1 – A straight line may be drawn from any one point to any other point.

Postulate 2 – A terminated line can be produced indefinitely.

Postulate 3 – A circle can be drawn with any centre and any radius.

Postulate 4 – All right angles are equal to one another.

Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

Also, access the following resources for Class 9 Chapter 5 Introduction to Euclid’s Geometry, at BYJU’S:

NCERT Introduction to Euclid’s Geometry Class 9 Notes
Introduction to Euclid’s Geometry Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Introduction to Euclid’s Geometry
RD Sharma Solutions Introduction to Euclid’s Geometry Class 9

NCERT Solutions Class 9 Maths Chapter 6 Lines and Angles

This chapter revolves around the theorems present in the topics of Lines and Angles. Students might often be asked to prove the statements given in the questions. There are 3 exercises in the chapter, solving which students would be able to understand the concepts covered in the chapter thoroughly. There are four axioms and eight theorems covered in the chapter.

Topics Covered in Class 9 Maths Chapter 6 Lines and Angles:

1. (Motivate) If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and the converse. 2. (Prove) If two lines intersect, the vertically opposite angles are equal. 3. (Motivate) Results on corresponding angles, alternate angles, and interior angles when a transversal intersects two parallel lines. 4. (Motivate) Lines, which are parallel to a given line, are parallel. 5. (Prove) The sum of the angles of a triangle is 180°. 6. (Motivate) If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice versa. This property is called the Linear pair axiom.
If two lines intersect each other, then the vertically opposite angles are equal.
If a transversal intersects two parallel lines, then

(i) each pair of corresponding angles is equal,

(ii) each pair of alternate interior angles is equal,

(iii) each pair of interior angles on the same side of the transversal is supplementary.

If a transversal intersects two lines such that, either

(i) any one pair of corresponding angles is equal, or

(ii) any one pair of alternate interior angles is equal, or

(iii) any one pair of interior angles on the same side of the transversal is supplementary, then the lines are parallel.

Also, access the following resources for Class 9 Chapter 6 Lines and Angles, at BYJU’S:

NCERT Lines and Angles Class 9 Notes
Lines and Angles Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Lines and Angles
RD Sharma Solutions Lines and Angles Class 9

NCERT Solutions Class 9 Maths Chapter 7 Triangles

In this chapter, students will study in detail the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles. The chapter has a total of 5 exercises, in which the students are asked “to-prove” as well as application-level problems. With this chapter, students will also learn to prove the properties that they learnt in earlier classes. The chapter also teaches the students to apply the various congruence rules while solving the problems. There are about eight theorems covered in this chapter.

Topics Covered in Class 9 Maths Chapter 7 Triangles:

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 the 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. 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. 7. (Motivate) Triangle inequalities and the relation between ‘angle and facing side’; inequalities in a triangle.

Important Axioms and Theorems –

Axiom 7.1 (SAS congruence rule) – Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle.

Theorem 7.1 (ASA congruence rule) – Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

Theorem 7.2 – Angles opposite to equal sides of an isosceles triangle are equal.

Theorem 7.3 – The sides opposite to equal angles of a triangle are equal.

Theorem 7.4 (SSS congruence rule) – If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

Theorem 7.5 (RHS congruence rule) – If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

Theorem 7.6 – If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater).

Theorem 7.7 – In any triangle, the side opposite to the larger (greater) angle is longer.

Theorem 7.8 – The sum of any two sides of a triangle is greater than the third side.

Also, access the following resources for Class 9 Chapter 7 Triangles, at BYJU’S:

NCERT Triangles Class 9 Notes
Triangles Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Triangles
RD Sharma Solutions Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 8 Quadrilaterals

A figure obtained by joining four points in order is called a quadrilateral. This chapter takes the students to the depth of the topics of Quadrilaterals. The chapter contains 2 exercises that contain only one theorem to prove. However, there are a total of nine theorems that can be used to solve the application or conceptual-level questions asked. The angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem are explained in this chapter to help the students in learning the concepts thoroughly.

Topics Covered in Class 9 Maths Chapter 8 Quadrilaterals:

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 are parallel and equal. 5. (Motivate) In a parallelogram, the diagonals bisect each other conversely. 6. (Motivate) In a triangle, the line segment joining the midpoints of any two sides is parallel to the third side and (motivate) its converse.

Important Theorems –

A quadrilateral has four sides, four angles and four vertices.

Angle Sum Property of a Quadrilateral – The sum of the angles of a quadrilateral is 360 o .

Theorem 8.1 – A diagonal of a parallelogram divides it into two congruent triangles

Theorem 8.2 – In a parallelogram, opposite sides are equal.

Theorem 8.3 – If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Theorem 8.4 – In a parallelogram, opposite angles are equal.

Theorem 8.5 – If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

Theorem 8.6 – The diagonals of a parallelogram bisect each other.

Theorem 8.7 – If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Theorem 8.8 – A quadrilateral is a parallelogram if a pair of opposite sides are equal and parallel.

Theorem 8.9 – The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

Theorem 8.10 – The line drawn through the mid-point of one side of a triangle, parallel to another side, bisects the third side.

Also, access the following resources for Class 9 Chapter 8 Quadrilaterals, at BYJU’S:

NCERT Quadrilaterals Class 9 Notes
Quadrilaterals Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Quadrilaterals
RD Sharma Solutions Quadrilaterals Class 9

NCERT Solutions Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles

In this chapter, an attempt has been made to consolidate the knowledge about the formulae to find the areas of different figures by studying relationships between the areas of geometric figures, provided they lie on the same base and between the same parallels. This study will also be useful in understanding some results on the ‘similarity of triangles’. The chapter contains 4 exercises, of which most of the questions ask the students to prove the statements given.

Topics Covered in Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles:

Review the concept of area and recall the area of a rectangle. 1. (Prove) Parallelograms on the same base and between the same parallels have the same area. 2. (Motivate) Triangles on the same base and between the same parallels are equal in area and its converse.

Theorem 9.1 – Parallelograms on the same base and between the same parallels are equal in area.

Theorem 9.2 – Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Theorem 9.3 – Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.

Also, access the following resources for Class 9 Chapter 9 Areas of Parallelograms and Triangles, at BYJU’S:

NCERT Areas of Parallelograms and Triangles Class 9 Notes
Areas of Parallelograms and Triangles Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Areas of Parallelograms and Triangles
RD Sharma Solutions Areas of Parallelograms and Triangles Class 9

NCERT Solutions Class 9 Maths Chapter 10 Circles

A circle can be defined as a collection of all the points in a plane at a fixed distance from a fixed point in the plane. Topics like Angle Subtended by a Chord at a Point, Equal Chords and their respective distances from the Centre, the Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals and other terms related to circles are covered in this chapter. A total of twelve theorems are present in this chapter, learning which the students will get a clearer idea of the concepts taught. There are 6 exercises in this chapter which consist of questions from all the concepts present in the chapter.

Topics Covered in Class 9 Maths Chapter 10 Circles:

Through examples, arrive at definitions of circle-related concepts, radius, circumference, diameter, chord, arc, and subtended angle. 1. (Prove) Equal chords of a circle subtend equal angles at the centre and (motivate) its converse. 2. (Motivate) The perpendicular from the centre of a circle to a chord bisects the chord, and conversely, the line drawn through the centre of a circle to bisect a chord is perpendicular to the chord. 3. (Motivate) There is one and only one circle passing through three given non-collinear points. 4. (Motivate) Equal chords of a circle (or of congruent circles) are equidistant from the centre(s) and conversely. 5. (Prove) The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. 6. (Motivate) Angles in the same segment of a circle are equal. 7. (Motivate) If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the segment, the four points lie on a circle. 8. (Motivate) The sum of either pair of opposite angles of a cyclic quadrilateral is 180 0 and its converse.

Theorem 10.1 – Equal chords of a circle subtend equal angles at the centre.

Theorem 10.2 – If the angles subtended by the chords of a circle at the centre are equal, then the chords are equal.

Theorem 10.3 – The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem 10.4 – The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Theorem 10.5 – There is one and only one circle passing through three given non-collinear points.

Theorem 10.6 – Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres).

Theorem 10.7 – Chords equidistant from the centre of a circle are equal in length.

Theorem 10.8 – The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 10.9 – Angles in the same segment of a circle are equal.

Theorem 10.10 – If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle (i.e. they are concyclic).

Theorem 10.11 – The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Theorem 10.12 – If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

Also, access the following resources for Class 9 Chapter 10 Circles, at BYJU’S:

NCERT Circles Class 9 Notes
Circles Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Circles
RD Sharma Solutions Circles Class 9

NCERT Solutions Class 9 Maths Chapter 11 Constructions

In this chapter, students will learn some basic constructions. The method learnt will then be used to construct certain kinds of triangles. There are 2 exercises present in this chapter, of which the first exercise deals with the construction of a certain angle or the bisector of a given angle. On the other hand, the second exercise deals with the constructions of triangles when different parameters are given.

Topics Covered in Class 9 Maths Chapter 11 Constructions:

1. Construction of bisectors of a line segment and angle, 60°, 90°, 45° angles etc., equilateral triangles. 2. Construction of a triangle given its base, sum/difference of the other two sides and one base angle. 3. Construction of a triangle of given perimeter and base angles.

Construction 11.1 – To construct the bisector of a given angle.

Construction 11.2 – To construct the perpendicular bisector of a given line segment.

Construction 11.3 – To construct an angle of 600 at the initial point of a given ray.

Construction 11.4 – To construct a triangle, given its base, a base angle and the sum of the other two sides.

Construction 11.5 – To construct a triangle given its base, a base angle and the difference between the other two sides.

Construction 11.6 – To construct a triangle, given its perimeter and its two base angles.

Also, access the following resources for Class 9 Chapter 11 Constructions, at BYJU’S:

NCERT Constructions Class 9 Notes
Constructions Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Constructions
RD Sharma Solutions Constructions Class 9

NCERT Solutions Class 9 Maths Chapter 12 Heron’s Formula

The chapter discusses Heron’s formula, which can be used to calculate the area of a triangle when the length of all three sides is given. In this method, there is no need to calculate the angles or other distances in the triangle. This formula can be used not only to find the area of triangles but also to find the areas of quadrilaterals and other polygons by dividing them into triangles. There are 2 exercises in this chapter which help the student understand the method of solving the problems based on Heron’s formula.

Topics Covered in Class 9 Maths Chapter 12 Heron’s Formula:

Area of a triangle using Heron’s formula (without proof) and its application in finding the area of a quadrilateral.

Area of a triangle = 1/2 × base × height

Area of a triangle by Heron’s Formula = \(\begin{array}{l}\sqrt{s(s-a)(s-b)(s-c)}\end{array} \)

Where a, b and c are the sides of a triangle

s is the semi-perimeter, i.e. half of the perimeter of a triangle = (a + b + c)/2

Also, access the following resources for Class 9 Chapter 12 Heron’s Formula, at BYJU’S:

NCERT Heron’s Formula Class 9 Notes
Heron’s Formula Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Heron’s Formula
RD Sharma Solutions Heron’s Formula Class 9

NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes

In this chapter, students shall learn to find the surface areas and volumes of cuboids and cylinders in detail and broaden the study to some other solids, such as cones and spheres. This chapter is just an extended version of the chapter mensuration, in which the students learnt about the surface areas and volumes in earlier classes. There are 8 exercises in this chapter, and these exercises contain problems that are based on surface areas and volumes of different solids such as cubes, cuboids, spheres, cylinders, cones, and hemispheres.

Topics Covered in Class 9 Maths Chapter 13 Surface Areas and Volumes :

Surface areas and volumes of cubes, cuboids, spheres (including hemispheres) and right circular cylinders/cones.

Surface Area of a Cuboid = 2(lb + bh + hl)

where l, b and h are, respectively, the three edges of the cuboid

Surface Area of a Cube = 6a 2

where a is the edge of the cube.

Curved Surface Area of a Cylinder = 2πrh

where r is the radius of the base of the cylinder and h is the height of the cylinder

Total Surface Area of a Cylinder = 2πr(r + h)

where h is the height of the cylinder and r is its radius

Curved Surface Area of a Cone = 1/2 × l × 2πr = πrl

where r is its base radius, and l is its slant height

Total Surface Area of a Cone = πrl + πr 2 = πr(l + r)

Surface Area of a Sphere = 4 π r 2

where r is the radius of the sphere.

Curved Surface Area of a Hemisphere = 2πr 2

where r is the radius of the sphere of which the hemisphere is a part.

Total Surface Area of a Hemisphere = 3πr 2

Volume of a Cuboid = base area × height = length × breadth × height

Volume of a Cube = edge × edge × edge = a 3

Volume of a Cylinder = πr 2 h

where r is the base radius, and h is the height of the cylinder.

Volume of a Cone = 1/3 πr 2 h

where r is the base radius, and h is the height of the cone.

Volume of a Sphere = 4/3 πr 3

Volume of a Hemisphere = 2/3 πr 3

where r is the radius of the hemisphere.

Also, access the following resources for Class 9 Chapter 13 Surface Areas and Volumes, at BYJU’S:

NCERT Surface Areas and Volumes Class 9 Notes
Surface Areas and Volumes Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Surface Areas and Volumes
RD Sharma Solutions Surface Areas and Volumes Class 9

NCERT Solutions Class 9 Maths Chapter 14 Statistics

The branch of Mathematics in which the extraction of meaningful information is studied is known as Statistics. It can also be defined as the collection of data on different aspects of the life of people useful to the State. The chapter teaches about the different presentations of the data, including the frequency distribution as well. The chapter also helps the students learn the graphical representation of data using different graphs such as Bar graphs, Histograms, Frequency polygons, etc. The chapter also lets the students learn the measure of central tendency mean, median and mode of the raw data. A total of 4 exercises are present in the chapter that includes problems related to all these concepts.

Topics Covered in Class 9 Maths Chapter 14 Statistics:

Introduction to Statistics: Collection of data, presentation of data – tabular form, ungrouped/grouped, bar graphs, histograms (with varying base lengths), frequency polygons, qualitative analysis of data to choose the correct form of presentation for the collected data. Mean, median, and mode of ungrouped data.

Statistics deals with the collection, presentation, and analysis of data, as well as the drawing of meaningful conclusions from the data.

Mean – It is found by adding all the values of the observations and dividing it by the total number of observations. It is denoted by \(\begin{array}{l}\overline{x}\end{array} \) .

So, \(\begin{array}{l}\overline{x}=\frac{\sum_{i=1}^{n}x_{i}}{n}\end{array} \)

For an ungrouped frequency distribution, it is \(\begin{array}{l}\overline{x}=\frac{\sum_{i=1}^{n}f_{i}x_{i}}{\sum_{i=1}^{n}f_{i}}\end{array} \)

Median – It is the value of the middle-most observation (s).

If n is an odd number, the median = value of the [(n + 1)/2] th observation

If n is an even number, median = Mean of the values of the (n/2) th and [(n/2) + 1] th observations.

Mode – The mode is the most frequently occurring observation.

Also, access the following resources for Class 9 Chapter 14 Statistics, at BYJU’S:

NCERT Statistics Class 9 Notes
Statistics Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Statistics
RD Sharma Solutions Statistics Class 9

NCERT Solutions Class 9 Maths Chapter 15 Probability

The collection of some outcomes of an experiment is known as an event of an experiment. The chances of occurrence of an event are known as probability. In this chapter, students will learn to measure the chance of occurrence of a particular outcome in an experiment. This chapter contains only 1 exercise. The problems covered in this exercise are based on real-life incidents, enhancing the interest of the students in solving the questions.

Topics Covered in Class 9 Maths Chapter 15 Probability:

History, Repeated experiments and observed frequency approach to probability. Focus is on empirical probability. (A large amount of time to be devoted to group and to individual activities to motivate the concept; the experiments to be drawn from real-life situations and from examples used in the chapter on statistics).

The empirical probability P(E) of an event E happening is given by

P (E) = Number of trials in which the event happened/The total number of trials

Also, access the following resources for Class 9 Chapter 15 Probability, at BYJU’S:

NCERT Probability Class 9 Notes
Probability Class 9 Important Questions
NCERT Exemplar Solutions Class 9 Probability
RD Sharma Solutions Probability Class 9

Benefits of BYJU’S NCERT Maths Solutions for Class 9

The solutions are given in easy steps so that students can easily understand them.
Students can access these solutions for free and clear any doubts instantly.
Exercise-wise PDFs are also provided for all chapters of CBSE 9th Class Maths.
Detailed explanations also help students to develop problem-solving skills and help them to learn concepts more effectively.
The questions are solved using the easiest method.
Diagrams are also given to help students visualise the questions and solutions.

CBSE Class 9 Maths Unit-wise Weightage for 2023-24

Internal assessment class 9.

During the exam preparation, students should first complete the units carrying more weightage and then move on to the lower weightage. This helps students to first cover the important concepts and improves their confidence level to perform well in the annual exam.

The students are advised to analyse all the concepts covered in the Syllabus of Class 9 Maths and prepare a proper preparation strategy. It’s merely impossible to score well in Maths by simply reading and memorising the concepts. Students should always try to understand the concept and logic given in any particular topic. The students are suggested to practise these NCERT Solutions Class 9 materials on a regular basis to develop a strong understanding of basic mathematics concepts.

Along with the NCERT Solutions, we have also provided a brief summary of important formulas and different methods of solving similar problems to help students understand the concepts thoroughly. Keep visiting BYJU’S to get more updated learning materials, and download the BYJU’S app for a better and personalised learning experience with engaging video lessons.

Frequently Asked Questions on NCERT Solutions for Class 9 Maths

How can i learn the class 9 maths chapters in a fast and efficient way, can i get solved answers for the questions from the ncert class 9 maths chapters, should i daily solve the questions from the ncert solutions for class 9 maths , how can i download the ncert solutions for class 9 maths at byju’s, leave a comment cancel reply.

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chapter wise test of 9th class maths pdf

9th class mathematics chapterwise pdf tests.

Unit 1 test
Unit 2 test
Unit 3 test
Unit 4 tests
Unit 5 test
Unit 6 test
Unit 7 test
Unit 8 test
Unit 9 test
Unit 10 test
Unit 11 test PDF
Unit 12 test PDF
Complete tests in Single PDF file
9th class all subjects tests
10th class chapterwise tests all subjects
1st year all subjects tests
2nd year chapterwise tests PDF

9th class paper scheme maths 2022

9th class 2022 paper schemes pdf, 9th class guess papers 2022, no comments:.

9th class all subject SA 1 question paper 2023-24

Post author By scoringtarget
Post date 13/09/2023
Categories In 9th class

9 th class all subject SA 1 question paper 2023-24. Download 9 th class SA 1 question paper. You can also download pdf question paper for class 9.

In this post we are going to download summative assessment question paper for class 9. 9 th standard all subject SA 1 question paper download.

To get more video notes for class 9, visit our YouTube channel. This channel is very useful for 9 th class exam preparation.

9th class all subject SA 1 question paper 2023-24

Subject: All subject

Class: 9 th

Medium: Kannada and other subject

State: Karnataka

Sub-topic: SA 1 Question paper

File type: PDF

Share: Sharable link is given

Download: Given download link

Year: 2023-24

Board: Karnataka KSEEB

Print Enable: Yes

Editable Text: No

Copy Text: No

Scanned Copy: Yes

Password Encrypted: No

File Size Reduced: No

Quality: High

Download Link Available: Yes

File View Available: Yes

Here are the model summative assessment (SA-1) papers prepared to help the teachers of classes 9. These papers have been prepared in accordance with the Karnataka state government’s syllabus. Teachers can download the model Summative Assessment-1 (SA-1) papers from the links in the table below.

In Karnataka half year exam will be conducting Summative Assessment-1 midterm CCE examinations for students in class 9. From the links provided below, you can download previous and model question papers for all subjects for the next SA1 exam.

Class 9 th SA 1 Question paper 2022 PDF download. SA1 Exam Papers for Class 9. 9th SA1 Question paper 2024- Board has been conducted the exam Sa 1 exam paper and summative assessment 1 Question paper you can download the pdf.

Class 9 all subject SA 1 question paper download

9 th class SA 1 question papers:

4. Mathematics

6. Social Science

10th class all subject SA 1 question paper 2023-24

CBSE Sample Papers For Class 9 Maths

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About Sample papers for class 9 Maths

Sample papers for class 9 Maths is prepared by experts of Physics Wallah as per the recommendation of CBSE. Our academic team uploaded more than 20 sample papers for class 9 Maths with solution and few sample papers are without solutions. Solve these sample paper as within time mentioned in each sample paper. If you have any doubt while solving the sample paper post your doubts in ask your doubt section.CBSE Sample Papers class 9 Maths from 1 to 5 consist of all types of questions and than after all sample papers consist of advance questions based on class 9 Maths and all are MCQ based for complete revision. Do solve questions given in NCERT exercise with the help of Physics Wallah NCERT Solutions for class 9 Maths.

Find Below Sample papers for class 9 Maths for reference

List of sample papers for class 9 maths.

Sample papers-1 for class 9 Maths
Sample papers-2 for class 9 Maths
Sample papers-3 for class 9 Maths
Sample papers-4 for class 9 Maths
Sample papers-5 for class 9 Maths

List of Sample Papers for Class 9 Maths (MCQ Based)

Sample Papers-6 for class 9 Maths (Objective Type Questions)
Sample papers-7 for class 9 Maths (Objective Type Questions)
Sample papers-8 for class 9 Maths (Objective Type Questions)
Sample papers-9 for class 9 Maths (Objective Type Questions)
Sample papers-10 for class 9 Maths (Objective Type Questions)
Sample papers-11 for class 9 Maths (Objective Type Questions)
Sample papers-12 for class 9 Maths (Objective Type Questions)

Understand the pattern of class 9 Maths

Total Marks of Class 9 Maths Exam is = 100 marks
Out of which 80 marks are assigned to the theory paper and rest 20 marks are kept for internal assessment.
(i) Pen Paper Test and Multiple Assessment = 5+5 = 10 Marks
(ii) Portfolio = 05 Marks
(iii) Lab Practical (Lab activities) = 05 Marks

Understand the unit wise weightage of CBSE Class 9 Maths Sample papers

Sample papers for class 9 Maths design will be as per the following scheme

The class 9 Maths test paper will comprise of a total of total 40 questions divided into four sections, such as A, B, C and D sections.

Section A will consist of 20 questions of 1 mark each.
Section B will consist of 6 questions of 2 marks each.
Section C will consist of 8 questions of 3 marks each.
Section D will consist of 6 questions of 4 marks each.

Students can also get class 9 maths notes at Physics Wallah and they can also check their skills and understanding towards the subject by taking Maths Quiz class 9 .

FAQ FOR CBSE SAMPLE PAPERS CLASS 9 MATHS

Q1. How CBSE sample papers are useful for class 9 maths?

Ans. CBSE sample papers are the best resource for class 9 math as through it students can understand the pattern of exam question papers. By solving these CBSE sample papers, students have a good idea of what to expect during the exam. They also know the questionnaire model, the weight of the questions in each section, and the evaluation scheme. So to help prepare students, we have provided class 9 math CBSE sample papers.

Q2. What are CBSE class 9 maths sample papers?

Ans. CBSE Class 9 math is a school exam, so different schools organize different questionnaires. There is no common questionnaire for all class 9 student schools. Therefore, it is difficult to obtain last year's class 9 math questionnaires. However, students can easily find CBSE Class 9 math questionnaires online and offline for practice.

Q3 Which is the best site for class 9 maths sample papers?

Ans. Students can find class 9 math CBSE sample papers in PDF download format. At Physics Wallah we provide sample papers for class 9 mathematics with solutions by our academic expert teachers. Sample papers for summative assessment 1 and 2 were also provided by students for practice. Students can download math class 9 sample papers by our site.

Q4 How many sample papers should be practiced for the CBSE class 9 maths?

Ans. It depends on whether your preparation is good enough and you have completed the whole syllabus of class 9 maths and if you are confident enough in almost the topics, you don't have to solve many sample papers. But if some topics are good and you're not sure about other topics, you need to solve 7-9 papers so that you can build confidence for the exam.

Q5 What are the benefits of practicing CBSE Sample papers for class 9 math?

Ans. Each class 9 students will gain multiple benefits by practicing CBSE sample papers for class 9 maths. With the help of these paper sample sets, you can easily improve your exam preparation. In this way, you can also improve the topics in which you are weak, such as algebra, probability, trigonometry or geometry, etc. The best advantage you can get from this is that you can improve your time management skills.

Q6 Does Physics Wallah provide solutions for the CBSE sample papers for class 9 maths?

Ans. Yes, Physics Wallah offers solutions for CBSE sample papers for class 9 mathematics. You can access them through our website or mobile app. These are available in PDF format for easy download. Another advantage is that they are free. All of these solutions have been put together by our excellent subject matter experts, so you can refer to them without a doubt.

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9th Class Math Chapter Wise Tests PDF Free Download

Surely you are looking for 9th grade math Chapter Wise Tests PDF Free Download , which includes MCQs, short questions and long questions. Congratulations your search is over and on this page you can download class 9 math test pdf free download in urdu medium and class 9 math test pdf free download in english medium absolutely free with one click. For your convenience, we have created a syllabus for test session class 9th so that you can download the required test by looking at the syllabus. CEO and team Easy Notes is always striving to provide best study material for both students and teachers to maintain the quality of education.

9 Class Math Chapter Wise Tests PDF

Click below to download.

9th Class Math Test Papers - English and Urdu Medium

1. ready-made tests for all subjects..

9th class math test chapter wise helps students a lot when it comes to preparing for board exams. When students take the 9th grade math test several times before the final exams, it makes the final exam easier because the students are already familiar with it. Here on Easy Notes students and teachers can have free access to 9th chapter wise math test series that is the true replica of board exams. These chapter wise tests of 9th class math are made according to board paper pattern. There is a huge advantage to teachers for class 9 math test paper who spent lot of time to make tests. We provide ease to teachers who are so much busy in their routines in both school/college and academies. So they don’t have enough time to make a standardized test for students. Easy Notes provides 9th math chapter wise test papers which contains MCQs, short questions and long questions. Students and teachers can download 9th class math chapter wise test series free of cost and use them for nonprofit study purpose.

2. Self Study Plan.

Study plan is a structured schedule of study timing weekly or daily. A well organized and optimized study plan will help you to achieve your desired score easily. While random study ultimately makes things more complicated and chaotic. In this regard helpful self study tips are recommended by team Easy Notes. Set aside your mobile phone or if you are reading from it then put it on flight mode or don’t disturb mode. Choose your study point like a corner of the serene room of your home. Make schedule and fix the timing like 8 p.m. to 12 p.m. daily without gap. Identify the weak subject and give more time to that particular book. Read the extra information that is given in the form of boxes like “point to ponder” or “do you know that?”. Make your own notes or get well explained notes from Easy Notes .

3. Be An Active Student.

Passive students attend classes and get knowledge only which is brought to them. They are like an empty glass that is waiting to be fill by someone. But this way of learning is not enough if you want good score as well as to get admission in well reputed college or university . To be an active leaner helpful tips are recommended by team Easy Notes. Ask questions and participate in a discussion during lecture. Highlight the important points on Books as well as on your notes. Practice example questions that are given in every chapter of the book. Daily review the previous lecture material and mark the ambiguous points and clarify about them in the next coming class. Always ready to share your math Test Paper of 9th class with your classmates.

4. Reading Mode: Protect Your Eyes!

Even though, there are lot of advantages of reading online, some precautions are needed to save eyes for any kind of myopia. According to the recent research focusing a bright screen for a long time without blinking the eyes can cause eye dryness. Mover over ultraviolet and blue spectrum of light is also harmful for eyes so students must follow these advices. While reading reduce the brightness of screen to minimum level. Blink your eyes periodically so that your eyes get enough water to stay healthy. Always use blue ray screen protections glasses while using laptop or mobile. Put your phone or laptop on reading mode.

Here on Easy Notes one can get access to Free Download PDF Notes , Free Download PDF Text Books , Free Download Chapter Wise Tests , Free Date Sheets , Free Pairing Schemes and Free Results of any board on a single click.

9th Maths, Unit 1 Online Test, Important MCQ’s

Online Test Instructions

Test Name : 9th Math Unit 1 Online Test
Type : MCQ's
Total Questions : 10
Total Marks : 10
Time : 10 minutes
Questions will be shuffled each time you start the test.
Any question you have not answered will be marked incorrect .
Once you are finished, click the View Results button.

Start - Online Test

This Post Has 11 Comments

i have scored 90 in maths

I also scored 90% in maths

i have scored hundred in maths

How is this (1 0) b and c matrix??? ——————–(0 1) Isn’t it identity???

There’s an issue: Order of transpose of [ 2 1 ] [ 0 1 ] [ 3 2 ]

The answer should be, 3-by-2. Since the columns turn into rows and rows into columns.

No, mcqs and its answer is correct. matrix has 3 by 2 order. after transpose it will have 2 by 3.

I got 10 out of 10

Ans of question 4 is it correct

I got 10 out of 10 marks.

I am very happy to give this test thanks

AP Summative(SA2)/CBA3 Model Papers(PDF) 2024 6th,7th, 8th, 9th Classes

Download summative assessment(sa2)/cba3 model papers-2024 all subjects.

Summative Model Papers(SA2) 2024: As the month of April approaches, students begin search model papers to prepare for the Summative Assessment (SA2) examination. Formative Assessment tests and project works are already over. Pupils in Primary and Secondary School will study hard for the final Summative-2 Examination as per timetable in order to achieve good results. We have prepared model summative question papers to assist the students for all subjects Telugu, Hindi, English, Math, Physical Science, Bio.Science, Social Studies for all classes from 6th Class to 9th Class. Model Summative-2 question papers-2024 are provided here in preparation for the annual final exam, which will be held from 06/04/2024 to 19/04/2024 as per schedule by Commissioner of School Education, AP. Students from 6th Class, 7th Class, 8th Class, 9th Class can download summative model papers from www.apteacher.net for final their final exams.

Read Also : AP SA2/CBA3 Examination Time Table-2024

Overview of SA2/ CBA3 Timetable 2024

SA2/ CBA3 Model Papers are prepared based on blueprint and competences. These model papers are composed by subject experts. Students who are studying VI Class, VII Class, VIII Class, IX Class download the Summative-2 Model papers of all subjects Telugu, Hindi, English, Math, Physical Science, Social Studies from the following.

6th Class to 9th Class SA2/CBA3 Telugu Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 Telugu Model Papers 2024 and SA3 9th Class Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

6th Class to 9th Class SA2/CBA3 Hindi Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 Hindi Model Papers 2024 and SA3 9th Class Hindi Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

6th Class to 9th Class SA2/CBA3 English Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 English Model Papers 2024 and SA3 9th Class English Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

6th Class to 9th Class SA2/CBA3 Math Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 Math Model Papers 2024 and SA3 9th Class Math Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

6th Class to 9th Class SA2/CBA3 Science Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 Science Model Papers 2024 and SA3 9th Class Science Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

6th SA 2 General Science EM Question paper
6th SA 2 General Science TM Question paper
7th SA 2 General Science EM Question paper
7th SA 2 General Science TM Question paper
8th SA 2 Biological Science TM Question paper
9th SA 2 Biology EM Question paper
9th SA 2 Biological Science TM Question paper
8th SA 2 Physical Science TM Question paper
8th SA 2 Physical Science EM Question paper
9th SA 2 Physical Science TM Question Paper
9th SA 2 Physical Science EM Question Paper

6th Class to 9th Class SA2/CBA3 Social Studies Model Papers-2024

Here, we are providing 6th, 7th, 8th Class CBA3 Social Studies Model Papers 2024 and SA3 9th Class Social Studies Model Paper. Students & teachers of concerned class can download the model papers and make use of it while preparing final exams.

Table of Contents SA2 Model Papers-2022

6th Class SA2 Model Papers Tel, Eng, Hin, Math, Science, Social Studies
7th Class SA2 Model Papers Tel, Eng, Hin, Math, Science, Social Studies
8th Class SA2 Model Papers Tel, Eng, Hin, Math, Science, Social Studies
9th Class SA2 Model Papers Tel, Eng, Hin, Math, Science, Social Studies

Download Summative Assessment(SA) Model Papers-2022

Download SA Model Question Papers(PDF) from VI to IX Class

Here we are providing model papers for the classes from 6th to 9th as well as 10th class. Students are advised to download model question papers from www.apteacher.net and make use of it. These question papers are prepared by various teachers across AP State based on the academic standards as stated in AP SCERT .

Read Also : AP SA1 Model Question Papers & Principles of Evaluation

6th Class SA2 Model Question Papers, All Subjects

Download 6th Class Summative Assessment-2(SA2) Model Papers. These SA2 6th Class model papers are collected from various subject experts. 6th Class students, those who are appearing to SA2 Summative exams can download the Model Question Papers and make use of it.

SA 2 6th Class Telugu Hindi English

sa 2 6th class maths science em tm social em tm , 7th class sa2 model papers, all subjects.

All students, who are appearing to 7th Class final exams Summative-2(SA2) can download model papers from the links given below.

Maths Science EM TM Social EM TM

8th Class SA2 Model Papers, All Subjects

Students of 8th Class should download SA2 Model Papers of all subjects from the following links given below. These model papers are composed by subject experts across all over Andhdra Pradesh.

Telugu Hindi English
Maths paper 1 & Paper 2 Science PS NS (Bi0logy) Social paper 1 & Paper 2

9th Class SA2 Model Papers, All Subjects

Following 9th Class SA2 Model Papers are useful to those who are appearing final SA2 exams. Students and Teachers of 9th Class can download and make use of 9th Class SA2 Model Papers.

Telugu Hindi English Paper 1 & Paper 2

How to Download Summative-2 Model Question Papers

Login to the website www.apteacher.net
Search for the Summative Model Question Papers using search box.
In the search results, find your class and subject.
Click on the given link and download it.
After downloading the Summative Model Question Paper take printout for further use.

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