# CBSE Maths Class 9

**CBSE CLASS 9: AN OVERVIEW**

Have you at any point felt that an assessment makes you apprehensive and restless? This feeling can make one cause errors in even the answers to the questions they otherwise know. Thus, an NCERT Class 9 Solutions Book ensures that students’ concentrate only on important topics.

With the change in policies in the post-pandemic world, sticking to important topics becomes essential.

The Indian Education system experienced a ground-breaking change with the implementation of the New Education Policy. According to the policy, CBSE introduces a new assessment and evaluation method and is incorporating Competency-based questions. There will be questions based on real-life applications testing the conceptual knowledge of a student. These will be a part of CBSE Class 10 and CBSE Class 12 board exams, and CBSE Class 9 and CBSE Class 11 final examination. These competency-based questions will carry a 30% weightage for classes 9-10 and 20% for classes 11-12.

Everything you need to know about competency-based questions:

- These are case-based questions, multiple-choice questions or course-based integrated questions.
- Competency-based questions can be both objective and subjective.
- These questions are based on practical and real-life applications
- CBSE board has released questions banks to practise these kinds of questions. Students and teachers can be acquainted with the pattern of questions.
- The questions are released for every chapter from CBSE 9-12 Curriculum.
- This can be a very scoring section for the students.
- This approach will focus more on the practical and conceptual understanding of the topics.
- Considering the modification, CBSE Class 9 and 10 standard question paper will comprise:

Objective Questions: 20%

Competency-based Questions: 30%

Short and Long Questions: 50%

The CBSE Board will also be releasing sample papers based on the updated paper pattern soon. Students can prepare for the academic session 2020-21 in the following ways:

- Plan your studies focusing on every concept in detail. Give special attention to the real-life applications of the topic.
- Practise as much as possible to ace every section of the question paper. Refer to the most important questions, sample papers for 2020-21 and NCERT solutions.
- Get immediate assistance from subject experts and understand all the topics efficiently.
- Familiarize yourself with the new pattern paper and boost your scores. It is advisable to take help from teachers to go through new types of questions.
- Check out every type of competency-based question released by the CBSE board. Practise them well and check study material for more insight.
- Assess your knowledge with tests and sample papers once you are completely thorough with the topic.

# Syllabus For Class 9 Maths

The CBSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn in a playful way. It makes the process of conveying knowledge to the students efficient and healthy.

**Chapter-1 Number Systems**

The topics like the definition of rational numbers, problems on p/q form, finding the missing rational number between the range, representation of a particular rational number or decimal number on a number line, dividing small by big number (1/11, 3/13, 2/11,…etc), rational and irrational numbers, their difference and problems based on that, are discussed here. Every topic has an ample number of exercises for good practice.

**Chapter-2 Polynomials**

Here beginning with a basic introduction to polynomials, topics like polynomials in one variable, zeros of a polynomial, remainder theorem, factorization of polynomials, algebraic identities, etc are discussed here followed with solved examples and exercises for a better understanding and practice.

**Chapter-3 Coordinate Geometry**

In this chapter topics like a cartesian plane, notations, plotting points are well explained with detailed examples and exercises. As this chapter can be a little tough for beginners, regular practice and deep understanding make the preparation process for examinations easy.

**Chapter-4 Linear Equations in Two Variables**

Here, the problems where values of a,b,c, finding, comparing two different equations, finding the nature and missing values of a given equation, plotting solutions on graphs with the help of x, y, z-axis, etc are some of the important topics covered in this chapter.

**Chapter-5 Introduction to Euclid Geometry**

Beginning with the general introduction to Euclid geometry, definitions of Parallel lines, Perpendicular lines, Line segment, Radius of a circle, Square with examples and solved problems, problems on Euclid’s fifth postulate, simple formula derivations are also discussed here. There is an ample number of problems for a better understanding and practice.

**Chapter-6 Lines and Angles**

Here the problems on the combination of lines and angles are explained with solved examples, problems where statements are given to prove with a good explanation, formulas and axioms are used, problems based on given diagrams, various types of angles their derivations, etc are thoroughly discussed with a set of exercises for good practice purposes.

**Chapter-7 Triangles**

Here problems are solved with a given diagram and statement, problems based on bisectors, the definition of types of triangles with their principles and rules, that need to be followed while problem-solving, SAS, ASA congruences are also discussed here. Apart from that, the basic problems on the statement and proving the given statement with a reasonable explanation are also discussed here in this chapter. As there are many models covered, there is an equal number of exercises provided for practice purposes.

**Chapter-8 Quadrilaterals**

Beginning with a brief introduction on quadrilaterals, finding angles when ratios are given, finding the diagonals in a given diagram, construction of quadrilaterals following the given set of instructions, proving of quadrilaterals using axioms, principles, etc are a few types of problems discussed here in detail and are important in term of examination point of view.

**Chapter-9 Areas of Parallelograms and Triangles**

Problems like common base and two parallel lines, with given parallelogram finding the missing values using given statements, proving the given statements with the point of median or midpoint of the median, comparing two figures and proving their areas are equal, etc are few topics and problems covered in this chapter also provided with a set of exercises for better understanding.

**Chapter-10 Circles**

Terms like interior, exterior, diameter, semicircle, the chord, etc are explained with examples, problems based on chords, their equality, max number of common points, chords and angles combination, point of intersection, etc are a few types of problems discussed here with detailed information.

**Chapter-11 Constructions**

Using protractor and compass, constructions are done following the given instructions, starting from measuring an angle, drawing a line segment, to finding X by solving equations are discussed here by explaining with a set of example problems and exercises.

**Chapter-12 Heron’s Formula**

This chapter is exclusively based on the heron formula and its derivation and its application in problems. Heron formula is nothing but the area of the triangle i.e.,

Area = Square root of√s(s – a)(s – b)(s – c) where s=semi-perimeter, a,b,c, is the length of sides a,b,c respectively. This is a very important and easy chapter to secure good marks as there are many solved examples and exercises provided for practice purposes.

**Chapter-13 Surface Areas and Volumes**

Here the surface areas and volumes of cone, cube, sphere, etc are explained with examples and exercises for practice purposes.

**Chapter-14 Statistics**

Here this chapter discusses the problems which have more reasoning and analytical than just formula-based models followed with examples for practice and thorough understanding purposes.

**Chapter-15 Probability**

This is another important and reasoning and analytical chapter that has problems like, drawing n balls from set x, simple formulas, tricks, and tips to solve the problems easily and fast. There are ample sets of examples provided for practice purposes after every topic.

# NCERT Solutions For Maths Class 9

The CBSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn in a playful way. It makes the process of conveying knowledge to the students efficient and healthy.

## NCERT Class 9 Book Pdfs

## NCERT Solutions

## Chapter 1- Real Numbers

## 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 – Area of Parallelogram and Triangles

## Chapter 10 – Circles

## Chapter 11 – Constructions

## Chapter 12 – Heron’s Formula

## Chapter 13 – Surface Area and Volume

## Chapter 14 – Statistics

## Chapter 15 – Probability

# Important Questions For Class 9 Mathematics

The CBSE course structure is designed in a manner to ensure that students do not go through a lot of pressure, moreover, books are made interactive and interesting for students to enjoy their studies. A lot of fun activities are included in between the chapters to help students learn in a playful way. It makes the process of conveying knowledge to the students efficient and healthy.

*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 – Area of Parallelogram and Triangles**Chapter 10 – Circles**Chapter 11 – Constructions**Chapter 12 – Heron’s Formula**Chapter 13 – Surface Area and Volume**Chapter 14 – Statistics**Chapter 15 – Probability*

# Important Questions For Class 9 Mathematics

*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 – Area of Parallelogram and Triangles**Chapter 10 – Circles**Chapter 11 – Constructions**Chapter 12 – Heron’s Formula**Chapter 13 – Surface Area and Volume**Chapter 14 – Statistics**Chapter 15 – Probability*

## CBSE Class 9 Maths Videos

The formula for the lateral surface area of a right cone is L.S.A=πrl , where l is the slant height of the cone and l=√((r^2+h^2 ) ) . The volume of a cone =(1/3)πr^2 h cubic units Where, ‘ r’ is the base radius of the cone ‘ h ‘ is the height of the cone. Students are advised to watch the entire video to get in-depth understanding of the topic.

If a ray stands on a line, then the sum of two adjacent angles so formed is 180°. when the sum of two adjacent angles is 180°, then they are called a linear pair of angles. in this video, we will find out the value of x. Students are advised to watch the entire video to get in-depth understanding of the topic.

In this video, we are given the probability of getting a bad egg and the total number of eggs. Using these two values and the formula of probability, we can easily find the number of bad eggs (by multipling probability to the total number of eggs).

A cyclic quadrilateral is a quadrilateral whose all the vertices lie on a single circle. In a cyclic quadrilateral, the sum of opposite angles is equals to 180 degree. In the video, angle CAD and angle DBC would be equal as angles in same segment subtend equal angles.

In this video, we are given two sides and the perimeter. Using the sides and the perimeter, we can find the value of third side.

Remainder Theorem : Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.

An equilateral triangle is a triangle, in which all the three sides are equal. Heron’s formula is used to find out the area of the triangle when we don’t know the angles between the sides . In this video, we know the perimeter (i.e. 180 cm) and given that all the sides are equal.

In this video,Shravan Lodhi, a graduate from IIT Bombay has explained a very quick and easy method of rationalizing the denominator of a number.