NCERT Books Class 9 Maths
NCERT Class 9 Maths Book
NCERT Books for Class 9 are prepared and published by the National Council of Educational Research and Training (NCERT). It is an independent organisation that offers advice and supports higher-quality educational developments in schools. In terms of educational policies, it also aids the national and state governments. NCERT Solutions for Class 9 are used in the CBSE school curriculum and by the state board. We hope that these NCERT Solutions will assist you in your test preparation and help you learn in an interesting and enjoyable manner.
Extramarks offers Class 9 Maths PDF free chapter-by-chapter ebook PDF downloads. The solutions are offered by the experienced faculty while strictly adhering to the NCERT books and the latest CBSE guidelines and examination pattern. To speed up their learning and improve their academic performance, students must download the syllabus and Maths PDF now, to begin their preparation without any further delay.
CBSE Class 9 NCERT Maths Books
Do you fear Mathematics?? Then perhaps our free download of the CBSE NCERT Maths Book for Class 9 PDF will be very useful. The NCERT Maths Book Class 9 PDF is a must-have for students who are taking their Class 9 final exams or for anyone who needs a quick review of high school mathematical concepts covered in 9th class. It sequentially introduces chapters and concepts of the latest CBSE syllabus. For all of the NCERT solutions to the most recent CBSE textbooks, Extramarks offers students a Free PDF download option. If you have access to the NCERT Class 9 Science, Math, and other subject solutions on Extramarks, studying topics like Science, Math, and English would be a lot easier. .
You might as well download NCERT Solutions for Class 9 Maths if you are going to download NCERT Books. Visit Extramarks.com to obtain a free PDF download of the NCERT Books for Class 9 Mathematics.
NCERT Books: How to read?
NCERTs serve as the backbone for the entire CBSE preparation because they provide the fundamental content and are covered in a very simple and easy-to-understand language. tyle. Additionally, they are lucid and modest. These books cover the majority of the learners’ needs. . Second, they are a crucial component of JEE Main preparation. To approach NCERTs effectively, underline key passages as you read them. Read the highlighted text again and make necessary edits if required. Make notes on the NCERTs in your most recent reading, then put the books away and just refer to your notes and move ahead. .
Class 9th Mathematics Question Paper Format and Annual Exam Blue Print:
The most recent pattern indicates that 25% of the questions on the test will be objective questions. In addition, there are now 40 rather than 30 questions on the test. Questions of the objective kind include short responses, multiple choice, and fill in the gaps. To prepare for all of these questions, students should read the fundamental concepts in the Class 9 Maths NCERT Book. The format of the CBSE Class 9 Maths question paper will be as follows: The mathematics question paper will include a total of 40 questions and be divided into parts A, B, C, and D, respectively.
- Section A will consist of 20 one-mark questions.
- Section B will include six questions worth two points each.
- Section C will have eight three-point questions.
- Section D will have six four-point questions.
Class 9 Unit-wise weightage:
The Class 9 Maths question paper for the annual exams will be written based on the unit-by-unit chapter-wise distribution provided by CBSE in the Class 9 Mathematics Syllabus for the current session. The units with the heaviest weight should be prepared first, followed by the units w They will review the most important information first, which will increase their confidence in their potential to do well in the exam. The list of units and their weightage for the annual test is given below:
|Unit No.||Unit Name||Weightage|
|6||Statistics and Probability||10|
NCERT Books for Class 9
- NCERT Books Class 9 Science
- NCERT Books Class 9 English
- NCERT Books Class 9 English Beehive
- NCERT Books Class 9 English Moments
- NCERT Books Class 9 Hindi
- NCERT Books Class 9 Hindi Kritika
- NCERT Books Class 9 Hindi Kshitij
- NCERT Books Class 9 Hindi Sanchayan
- NCERT Books Class 9 Hindi Sparsh
- NCERT Books Class 9 Social Science
- NCERT Books Class 9 Social Science Democratic Politics
- NCERT Books Class 9 Social Science Contemporary India
- NCERT Books Class 9 Social Science Economics
- NCERT Books Class 9 Social Science India and The Contemporary World 1
NCERT Solutions for Class 9
NCERT Solutions for Class 9 Mathematics
NCERT Solutions for Class 9 English
NCERT Solutions for Class 9 English Beehive
NCERT Solutions for Class 9 English Moments
NCERT Solutions for Class 9 Hindi
NCERT Solutions for Class 9 Hindi Kritika
NCERT Solutions for Class 9 Hindi Kshitij
NCERT Solutions for Class 9 Hindi Sanchayan
NCERT Solutions for Class 9 Hindi Sparsh
NCERT Solutions for Class 9 Social Science
NCERT Solutions for Class 9 Social Science Democratic Politics
NCERT Solutions for Class 9 Social Science Contemporary India
NCERT Solutions for Class 9 Social Science Economics
NCERT Solutions for Class 9 Social Science India and The Contemporary World
NCERT Books for Class 9 Maths Free Download
You need math if you want to succeed in science. You may have heard of this saying, yet this statement is true even today. Math has influenced the domains of other key Sciences like Physics and Chemistry and has brought about discoveries. It is the language of logic, and by studying it in depth, you can improve your analytical skills and become an expert at problem-solving skills quickly and easily. .
By offering you a quick refresher and review of the important ideas covered in the syllabus, our NCERT Maths PDFs will not only increase your confidence but also get you ready for any upcoming competitive tests.
Studying NCERT textbooks is crucial for students who are serious about passing engineering or college admission exams, as the IIT and JEE, two of the most popular national competitive assessments, even base their question paper patterns on these books. The chapter-by-chapter information for the Class 9 Math NCERT Books is provided here.
Chapter 1: Number System
Students will study the idea of an irrational number, real numbers, and their decimal expansions in this chapter. They will also study how to use real numbers on the number line, various real number operations, and the laws of exponents for real numbers. There are seven exercises in all; solve each of these exercises, then, if you have any questions, consult our book. Mathematics experts have outlined each question in detail to help you become an expert in the number system.
Chapter 2: Polynomial
One of the algebraic expressions is the polynomial. You mastered factoring algebraic expressions in earlier classes; now, use them to solve polynomials and pick up some new ideas. The idea of polynomials in one variable, a polynomial, the remainder theorem, the factorization of polynomials, and algebraic identities will all be introduced to the students in this section. This chapter contains 7 exercises. If you can’t figure out any of the questions, solve them, and then take help from our book if necessary.
Chapter 3: Coordinate geometry
You previously learned about the positions of points on a specific line. And now, in this chapter, you’ll discover how to find a point that isn’t on that line but rather somewhere else. The concept of the Cartesian system, which plots a point in the plane if its coordinates are known, will be explained to students in this chapter. Recognize the X and Y axes and use a graph to plot a point. In this chapter, there are a total of 5 exercises excluding the summary.
Chapter 4: Linear Equations and Two Variables
You learned about linear equations in one variable in earlier classes, and now it’s time to add another variable. Students will learn about linear equations in this chapter, as well as how to solve them, visualise them graphically, and use them to solve equations that have lines parallel to the x- and y-axes. There are a total of 5 activities, including the summary, the same as the preceding chapters. Try your hand at every question to determine your level of proficiency. If you require any assistance, refer to our book for any assistance.
Chapter 5: Introduction To Euclid’s Geometry
Students will study the definition, axioms, and postulates of Euclid, which are analogous to his fifth postulate. This chapter contains a theorem that asserts two separate lines cannot have more than one common point. Complete the exercises and educate yourself on Euclid’s postulates to clearly understand the chapter. And sure, our book, which contains answers to all the exercises, is a good resource for any difficulties.
Chapter 6: Lines and Angles
In Chapter 5, students learned some axioms and realised that a line must pass through at least two points to be drawn. In this chapter, words and definitions for lines and angles are introduced to the students. The pairs of angles, transversal and parallel lines, lines parallel to the same line, intersecting and non-intersecting lines, transversal and parallel lines, and lastly the angle sum property of a triangle will be covered in this chapter. Additionally, just like the preceding chapters, this chapter concludes with exercises.
Chapter 7: Triangles
You studied triangles in your earlier classes and gained an understanding of some of their characteristics in Chapter 6. In this chapter, students will study the congruence of triangles, requirements for congruence of triangles, characteristics of a triangle, and inequalities of the triangle. Congruent triangles are those whose sizes are equal or that are exact replicas of one another. Understanding congruent triangles are improved by completing the tasks at the end.
Chapter 8: Quadrilaterals
Students learned about triangles with three angles in previous chapters. Add another angle to the figure now and observe the results. Four angles make a quadrilateral. Students will discover the quadrilaterals’ angle sum property, several quadrilateral varieties, the characteristics of a parallelogram, and the prerequisites for a quadrilateral parallelogram in this lesson. Finally, the mid-point theorem will be explained to the class. Learn new ideas, and if you run into trouble, check out at Extramarks website.
Chapter 9: Areas of a parallelogram and triangle
Students will discover parallelograms on the same base and between the same parallels, triangles on the same base and between the same parallels, and figures having the same base and between the same parallels in this chapter. Discover the trapezium as well. This chapter contains 4 exercises. Solve each of them. At first, you might find them challenging, but try to tackle them on your own and take the necessary help from our book if necessary.
Chapter 10: Circles
Students will learn the definition of a circle and concepts linked to it, as well as the angle subtended by the arc of a circle, perpendicular to a chord from the centre, circles through three points, equal chords and their distance from the centre, and cyclic quadrilaterals. This chapter contains 2 chord-related theorems. Learn how to prove these theorems by going through them. Refer to our book of solved problems in case you run into any problems.
Chapter 11: Construction
You learnt about triangles in previous chapters. However, those triangles weren’t cut out precisely. As those were merely provided for your comprehension. Students will now study the fundamentals of construction in this chapter and practice some triangle construction. Understand how to draw a perpendicular line, measure angles with a protector, and use a compass. If you have the proper construction expertise, you might find this chapter to be intriguing. Finish the exercises by solving the in-text and chapter-end exercises to be thoroughly prepared and confident.
Chapter 12: Heron’s formula
You are familiar with squares, triangles, rectangles, and quadrilaterals from previous chapters. You are proficient at area and perimeter calculations. Now compute the area using a different formula in this chapter. Students will discover how to apply Heron’s formula to determine the area of a triangle and a quadrilateral in this lesson. Complete the activity to learn the new formula and solve the problem.
Chapter 13: Surface Area and Volumes
You learned about the area and perimeter of figures in earlier chapters. In this chapter, you will discover new sizes and shapes as well as how to determine their volume and surface area. The surface area of a cuboid, a cube, a right circular cylinder, a right circular cone, the surface area of a sphere, the volume of a cuboid, and the volume of a cylinder will all be taught to the students here. Additionally, students will learn about the volume of a sphere and the right circular cone.
Chapter 14: Statistics
You might come across numerous data in newspapers or periodicals during your daily life. Results of polls are another example you might use. When stored in a meaningful way, all of this information is referred to as statistics. Students will learn about data collecting, data presentation, graphic data representation, and central tendency measurement in this chapter. Work through tasks to gain knowledge of mean, median, and mode calculation. Since these three are significant in terms of statistics.
Chapter 15: Probability
Students will learn about the idea of probability and its experimental approach in this chapter. Probability is nothing more than the unpredictability of every situation. Probability calculations are also conceivable in Mathematics. The chapter includes tasks that you must complete on your own. Along with the exercises, it also includes examples. To master probability, comprehend examples and solve problems.
Chapter-wise important theorems, proofs and axioms:
Introduction to Euclid’s Geometry:-
- (Axiom) Two different points are connected by a single line.
- (Theorem) Two distinct lines cannot have more than one point in common.
Angles and lines:
- (Prove) The sum of the two consecutive angles created when a ray is parallel to a line is 180° and vice versa.
- (Theorem) When two lines intersect, vertically opposite angles are equal.
- (Theorem) When two lines intersect, vertically opposing angles are equal.
- (Prove)A transversal provides comparable angles, alternate angles, and inner angles when it joins two parallel lines.
- (Show) Parallel lines run beside a certain line.
- (Theorem) The sum of angles in a triangle is equal to 180°.
- (Prove) The exterior angle of a triangle’s side is equal to the product of its two opposite interior angles.
- (Show) If any two of the sides and included angles of two triangles are equal to each other, then the triangles are congruent (SAS Congruence).
- (Theorem) Two triangles are congruent if any two of their included sides and two of their respective angles are equal (ASA Congruence).
- If the three sides of one triangle match the three sides of the other, then the two triangles are congruent (SSS Congruence).
- If the hypotenuse and one of the sides of two right triangles are equal, then the hypotenuse and one of the sides must also be equal.
- (Theorem) A triangle has equal angles on each side.
- The sides of a triangle that face equal angles are equal.
- Establish triangle inequality and face side inequalities in triangles.
- (Theorem) The diagonal divides a parallelogram into two congruent triangles.
- A parallelogram’s opposite sides are equal, and vice versa.
- In a parallelogram, the opposing angles are equal, and vice versa.
- (Prove) When two opposing sides of a quadrilateral are parallel and equal, a parallelogram is created.
- (Show) A parallelogram’s diagonals are divided into half and vice versa.
- (Show that) Any line segment connecting the midpoints of two triangle sides is parallel to the third side, and the opposite is also true.
- (Theorem) Parallelograms with identical bases and parallels have the same area.
- Establish that triangles with the same base and parallels have the same area.
- (Show that) Any line segment connecting the midpoints of two triangle sides is parallel to the third side, and the opposite is also true.
- (Prove)Equal circles have equal angles at their centres, and vice versa.
- (Prove) A line traced through the centre of a circle to bisect a chord is perpendicular to the chord, whereas a perpendicular is drawn through the centre of a circle to bisect a chord.
- (Show) That there is a single circle that crosses three non-collinear points.
- (Prove) Equally spaced chords of a circle (or congruent circles) are equally spaced from the centre (or the centres of those circles, respectively), and vice versa.
- (Theorem) An arc’s centre angle is twice as large as its angle at any other location on the circle.
- Angles in a circle segment are identical to one another.
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FAQs (Frequently Asked Questions)
1. How many chapters are there in the Class 9 NCERT textbook?
There are a total of 15 chapters in the Class 9 NCERT textbook. Here is the list of chapters given below:
Chapter 1 – Number Systems
Chapter 2 – Polynomials
Chapter 3 – Coordinate Geometry
Chapter 4 – Linear Equations in Two Variables
Chapter 5 – Introduction to Euclid’s Geometry
Chapter 6 – Lines and Angles
Chapter 7 – Triangles
Chapter 8 – Quadrilaterals
Chapter 9 – Areas of Parallelograms and Triangles
Chapter 10 – Circles
Chapter 11 – Constructions
Chapter 12 – Heron’s Formula
Chapter 13 – Surface Areas and Volumes
Chapter 14 – Statistics
Chapter 15 – Probability
2. Why is the Class 9 Maths NCERT Book important?
The Class 9 Maths NCERT Book is renowned for presenting all the ideas most straightforwardly so that the students may grasp them quickly and easily. Because of this, the NCERT book is regarded as the ideal resource for students who want to achieve in their academics. The following is a list of reasons why the Class 9 Maths NCERT Book is important:
- The NCERT book for Class 9 Maths is made to provide comprehensive knowledge of all the subjects in an approachable and straightforward manner.
- Because this textbook precisely follows the most recent CBSE curriculum and norms, it is thought to be adequate for developing solid foundational knowledge for the final exams.
- Class 9 Maths NCERT Book features several exercises with many problems in various forms that are ideal for testing students’ comprehension and analytical skills.
- This book plays a significant role in helping students build a clear notion because it offers comprehensive knowledge of the subject.
3. What all is covered in triangles, Chapter 7 of Class 9 Maths NCERT Book?
Triangles, Chapter 7 of the Class 9 Maths NCERT Book, covers the properties of triangles. This chapter will teach Class 9 Maths students about triangle congruence, triangle congruence criteria, triangle characteristics, and triangle inequalities. This chapter on triangles covers congruence in-depth, as well as criteria for congruence such as SAS (Side Angle Side), SSS (Side Side Side), ASA (Angle Side Angle), AAS (Angle Angle Side), and RHS (Right Angle Hypotenuse Side). On the official website, you can have a quick look at the quick notes provided for Chapter 7 of Class 9.
4. How can I download the PDF file of the Class 9 Maths NCERT Book?
Yes, by using the aforementioned link on this page, all Class 9 students can obtain the CBSE board Class 9 Maths NCERT Solutions. Any student can effortlessly and completely download the Class 9 Maths NCERT book in PDF format free of cost.
This book aids in strengthening the concepts. Students benefit from the NCERT Book for Class 9 Math by receiving in-depth knowledge of the most crucial ideas and topics covered in the class’s math curriculum.NCERT offers deep learning that clarifies topics, which is helpful while attempting to respond to the most challenging questions.
5. Where can I get the NCERT solutions for the NCERT books for Class 9?
The article’s “NCERT solutions for Class 9” section includes NCERT book solutions. These solutions are presented in the same sequence as the NCERT books to avoid confusion. Solutions for each chapter are offered, along with thorough justifications. They can be downloaded for free in PDF format, making them available to students at their convenience. . NCERT books are also accessible for download and are available free of cost.. If you have any questions or issues, you can get in touch with us, and we’ll do our best to respond to you as quickly as possible. . On Extramarks website and mobile app, these solutions are offered free of cost.
6. How to read NCERT books more effectively?
The important techniques that must be followed to read NCERT books effectively are listed below –
- Carefully read each topic, taking the time to comprehend the relevance of each sentence that is part of it.
- Ask your teacher for clarification on any topics you find complicated or difficult to understand.
- Make a note of the critical information to review before the exam.
- Respond to all the practice questions that are provided at the end of each chapter. These inquiries are crucial for higher conceptual understanding as well as for examination preparation.
7. Are NCERT books enough to score more than 80% marks in Class 10 exams?
Any student’s grade is solely determined by how well they did on the test and during their preparation. By reading NCERT books, you would surely become a fundamentally sound person, giving you the ability to respond appropriately to different types of questions. To understand the information provided in the NCERTs, students are recommended to pay close attention to every detail and remain focused.
8. What are the advantages of employing the NCERT's critical questions?
Students can benefit from finding answers to these crucial issues. The following are some advantages to practising these questions:
- While answering these questions, students gain an insight into time management.
- The students will have a better understanding of the course framework by practising these questions, which include frequently asked questions from exam papers.
- By resolving these various problems from each chapter, students will be able to properly review the material.
Browse and discover the crucial inquiries for each Class 10 course. The table above contains the answers to these queries.
We hope that our information about CBSE Important Questions for Class 10 is helpful for students with their academic work. Students enrolled in CBSE Class 10 can also get sample papers, solutions, test advice, projects, etc