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# NCERT Solutions for Class 9 Maths [2023] PDF - All Chapters - Free PDF Download

Class 9

Hey are you a class 9 Student and looking for ways to Download NCERT Solutions for Class 9 Maths PDF to start your Preparations? If yes then Don’t worry you are at the right place.

If you want to score high in your class 9 Maths Exam [2023] then it is very important for you to have a good knowledge of all the important topics, so to learn and practice those topics you can use eSaral NCERT Solutions.

In this post We have listed NCERT Solutions for Class 9 Maths all Chapters in PDF Form that are prepared by Kota’s top IITian’s Faculties in a well Structured Format by keeping Simplicity in mind.

So, Without Wasting More Time Lets start.

## Table of content

• NCERT Class 9 Math Syllabus with Marks

•  Benefits of NCERT Solutions For Class 9 Math

• Geometry Formulas

• Algebra Identities

• Surface Area and Volume

• Heron’s Formula

• Polynomial Formula

• Statistics (Measure of Central Tendency)

• Probability Formulas

• Common mistakes that students make while solving NCERT class 9 Maths problems

• FAqs

## Chapter 1 - Number Systems

Number Systems - This chapter introduces students to the properties of real numbers and their various types such as rational, irrational, and integers. It also covers the laws of exponents and the representation of real numbers on a number line.

## Chapter 2 - Polynomials

This chapter deals with the basics of polynomials, their degree, and division. It also covers the factorization of polynomials and the relationship between the roots and coefficients of a quadratic equation.

## Chapter 3 - Coordinate Geometry

This chapter introduces students to the Cartesian plane and the concept of coordinates. It covers the distance formula, the section formula, and the midpoint formula.

## Chapter 4 - Linear Equations in Two Variables

Linear Equations in Two Variables - This chapter teaches how to solve linear equations with two variables. It covers the methods of graphical representation and substitution.

## Chapter 5 - Introduction to Euclid's Geometry

Introduction to Euclid's Geometry - This chapter explains the five postulates of Euclid's Geometry and their applications. It also covers the concept of axioms and the construction of geometric figures.

## Chapter 6 - Lines and Angles

This chapter covers various types of lines, angles, and their properties. It covers the angle sum property of triangles and the parallel lines and transversals.

## Chapter 7 - Triangles

Triangles - This chapter deals with the properties of triangles and their congruence. It covers the Pythagorean Theorem, the criteria for congruence, and the inequalities in a triangle..

This chapter discusses the properties of various types of quadrilaterals such as parallelograms, rhombus, and trapeziums. It also covers the angle sum property of a quadrilateral.

## Chapter 9 - Areas of Parallelograms and Triangles

In Chapter 9 you will learn about the Areas of Parallelograms and Triangles. There are three Exercise in this chapter which will help you to understand deeply about the Areas of Parallelograms and Triangles.

## Chapter 10 - Circles

This chapter deals with the properties of circles and their various elements such as radius, diameter, and chords. It covers the tangent and secant properties of circles.

## Chapter 11 - Constructions

This chapter covers the construction of various geometric figures such as angles, triangles, quadrilaterals, and circles using a compass and a ruler.

## Chapter 12 - Heron’s Formula

In this Chapter you will learn about the Heron’s Formula. This chapter introduces Heron's formula for the area of a triangle and covers its derivation and applications.

## Chapter 13 - Surface Area and Volumes

This chapter deals with the surface area and volume of various 3-dimensional shapes such as cubes, cuboids, cylinders, cones, and spheres.

## Chapter 14 - Statistics

This chapter introduces the concept of statistics and covers the collection, presentation, and analysis of data. It also covers the measures of central tendency such as mean, median, and mode

## Chapter 15 - Probability

This chapter deals with the basics of probability and covers the concepts of experiments, outcomes, and events. It also covers the addition and multiplication rules of probability..

### NCERT Class 9 Math Syllabus with Marks

 S No. Units Marks 1 Number Systems 10 2 Algebra 20 3 Coordinate Geometry 04 4 Geometry 27 5 Mensuration 13 6 Statistics and Probability 06

## Benefits of NCERT Solutions For Class 9 Math

1. Provides comprehensive coverage of all chapters: NCERT solutions for Class 9 Maths PDF cover all the chapters of the NCERT Maths textbook in a comprehensive manner. This ensures that students have access to a complete set of solutions to all the problems in the textbook.

2. Helps in understanding concepts: The step-by-step approach in NCERT solutions for Class 9 Maths PDF helps students understand the concepts better. This is especially helpful for students who may find certain topics difficult to comprehend.

3. Boosts problem-solving skills: The solutions provide students with a clear understanding of how to approach and solve problems. This helps in building their problem-solving skills and confidence.

4. Improves exam preparation: NCERT solutions for Class 9 Maths PDF are designed to complement the NCERT textbook and are aligned with the CBSE syllabus. This makes them an excellent resource for exam preparation and helps students score well in their exams.

5. Builds a strong foundation for higher studies: A thorough understanding of Maths at the Class 9 level is essential for higher studies in the field of Science, Technology, Engineering, and Mathematics (STEM). NCERT solutions for Class 9 Maths PDF provide students with a strong foundation in the subject and prepare them for higher studies.

In conclusion, NCERT solutions for Class 9 Maths PDF are an essential resource for any student who wants to excel in Maths. They provide comprehensive coverage of all chapters, help in understanding concepts, boost problem-solving skills, improve exam preparation, and build a strong foundation for higher studies.

## Important Math Formulas and Equations for Class 9

Here are Class 9 Maths all formulas which are important from an exam perspective

### Geometry Formulas

 Geometrical Shapes Area (A) Perimeter Rectangle A = Length x Width P =  2(Length + Width) Triangle A = ½ x Breadth x Height P = Sum of all the three sides of a triangle Trapezoid A = ½ x Height x (b₁ x b₂) P = Sum of all the sides of a trapezoid Parallelogram, A = Breadth x Height P = 2( a+ b) Here. a = side B = base Circle A = πr² P = 2 πr

### Algebra Identities

 (x + β)² = x²  +  β²  +  2 x β (x - β)² = x²  +  β²  - 2 x β (x + θ) (x - θ) =  x² - θ² (x + α)(x + θ) =  x²  +   (α + θ)x  +  αθ (x +  α)(x - θ) =  x²  +  (α - θ)x   -  αθ (x - α)(x + θ) =  x²  +  (θ - α)x  -  xθ (x - α)(x - θ) = x²  -  (α + θ)x   + αq (α + θ)³  = α³ + θ³  +  3αθ(α + θ) (α - θ)³ =  α³  + θ³ - 3αθ(α - θ) (α + β + θ)²  = α² + β² + θ² + 2αβ + 2βθ + 2αθ (α + β - θ)²  = α² + β² + θ² + 2αβ - 2βθ - 2αθ (α - β + θ)²  = α² + β² + θ²- 2αβ - 2βθ + 2αθ (α - β - θ)²  = α² + β² + θ² - 2αβ + 2βθ - 2αθ (x)³ + (β)³ = ( x + β) (x² - xβ + β) (x)³ - (β)³ = ( x + β) (x² - xβ + β)

### Surface Area and Volume

 Shape Surface Area (A) Volume (V) Cuboid 2 = (lb + bh + hl),  Here, l = length,  b = Breadth, h = height V = Length x  Breadth x Height Cube A = 6 side² V = Side³ Cylinder A = 2πr( h + r) Here, r = radius of circular cylinder H = height of a cylinder V = πr²H Cone A = πr( L + r) Here,  l = slant height  r = Radius of base Also, l² = h² + r², where h is the cone's height V = ½ πr² Sphere A = 4πr² V = 4/3πr³

### Heron’s Formula

 Area of Triangle with 3 sides √s(s-a)(s-b)(s-c) Here, s = semi perimeter A,b, c are the sides of triangle Semi Perimeter S = ( a + b + c)/2

### Polynomial Formula

 P (x) = anxn + an- 1xn- 1 - an- 2xn- 1 + …… ax + a0

### Statistics (Measure of Central Tendency)

 Mean Sum of all the observations/ Total Number of Observations Median For odd observations = ((n+1)/2)th observations Here, n is he total number of observations For even Observations - ((n/2)th + ((n/2) +1)th)/2 observations Mode Value which occur most frequently in a adata

### Probability Formulas

 Empirical Probability = Number of Trails With Expected Outcomes/ Total Number of Trials

### Common mistakes that students make while solving NCERT class 9 Maths problems

Common mistakes that students make while solving Maths problems in Class 9 and how to avoid them include:

1. Calculation errors: Students may make careless errors while performing basic arithmetic operations such as addition, subtraction, multiplication, and division. To avoid such errors, students should double-check their calculations and use a calculator wherever necessary.

2. Not understanding the problem: Sometimes students do not understand the problem or misinterpret it. This can result in incorrect solutions. To avoid this mistake, students should read the problem carefully and identify what is being asked before attempting to solve it.

3. Skipping steps: Students often skip important steps while solving problems. This can result in an incorrect answer or an incomplete solution. To avoid this mistake, students should follow the steps in the textbook or NCERT solutions and ensure that they do not miss any steps.

4. Incorrect use of formulae: Students may use incorrect formulae or use the right formulae incorrectly. This can lead to a wrong answer or an incomplete solution. To avoid this mistake, students should practice using formulae in a variety of problems and make sure they understand how and when to apply them.

5. Lack of practice: Lack of practice can result in poor performance in exams. To avoid this mistake, students should practice regularly and solve a variety of problems from textbooks, NCERT solutions, and other resources.

### How many chapters are there in NCERT Class 9 Maths?

There are a total of 15 chapters present in the NCERT Class 9 Maths. Chapter 1- Number System, 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 These are the chapters in Class 9 of NCERT Maths. And you need to cover all the chapters to get full marks in your final exam

### Are these NCERT Solutions enough to score better in the Class 9 Maths Board Exam?

NCERT Solutions for Class 9 Maths are an excellent resource for exam preparation and can help students score well in the Class 9 Maths Board Exam. However, it is important to note that scoring well in the Board Exam requires more than just knowing the solutions to the textbook problems. Students should also practice solving previous years' Board Exam papers and sample papers to get an idea of the type of questions asked and the exam pattern. This will help them understand the marking scheme and time management skills needed to complete the exam within the given time frame.

### Which are the important chapters in CBSE Class 9 Maths?

1. Polynomials 2. Circles 3. Surface Areas and Volumes 4. Triangles 5. Areas of Parallelograms and Triangles 6. Quadrilaterals

### Can you use any other method for solving questions apart from the one provided in the NCERT Solutions for Class 9 Maths pdf?

Yes, students can use other methods to solve problems apart from the ones provided in the NCERT Solutions for Class 9 Maths pdf. In fact, Mathematics is a subject that offers multiple methods to solve a problem, and students are encouraged to explore different methods and choose the one that works best for them. While the NCERT Solutions provide a standard method to solve problems, there may be alternative ways to solve the same problem. Students should try to understand the concept behind the solution and see if they can come up with a different approach that is easier or more efficient

If you have any Confusion related to NCERT Solutions for Class 9 Maths PDF then feel free to ask in the comments section down below.

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