Class 9 mathematics is the foundation of Class X and beyond. In fact, post Class XII, students endeavoring to get into IIT or other top engineering institutes have to revise mathematics from Class 9 if their concepts are not clear. Everything that you learned until Class 8 is now applied to more complex theories and concepts. However, on the bright side, if you put the effort to understand all these concepts and solve problems based on them, then you will not face any major roadblocks in the subject ahead. The RD Sharma Class 9 Solutions for maths is an excellent guide to handhold you and help you learn all new concepts with relative ease.

## Importance of RD Sharma Solutions for Class 9 Maths

RD Sharma is well-known for simplifying concepts and writing comprehensive explanations in mathematics. Every year, hundreds of students benefit from the Solutions and boost their scores. While maths is scary for most students, RD Sharma makes it simpler by providing a step-by-step method of understanding it and solving problems.Â RD Sharma Class 9 Solutions for Maths offers detailed solutions for all types of questions and helps you get better prepared for the examination.

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### Chapters under RD Sharma Solutions for Class 9 Maths

- Chapter 1: Number System
- Chapter 2: Exponents Of Real Numbers
- Chapter 3: Rationalization
- Chapter 4:Â Algebraic Identities
- Chapter 5: Factorization Of Algebraic Expressions
- Chapter 6: Factorization Of Polynomials
- Chapter 7:Â Introduction To Euclidâ€™s Geometry
- Chapter 8: Lines And Angles
- Chapter 9: Triangle And Its Angles
- Chapter 10: Congruent Triangles
- Chapter 11: Coordinate Geometry
- Chapter 12: Herons Formula
- Chapter 13: Linear Equations In Two Variables
- Chapter 14: Quadrilaterals
- Chapter 15: Areas Of Parallelograms And Triangles
- Chapter 16: Circles
- Chapter 17: Constructions
- Chapter 18: Surface Area And Volume Of A Cuboid And Cube
- Chapter 18: Volume and Surface Area Of a Right Circular Cylinder
- Chapter 20: Surface Area And Volume Of a Right Circular Cone
- Chapter 21: Surface Area And Volume Of Sphere
- Chapter 22: Tabular Representation Of Statistical Data
- Chapter 23: Graphical Representation Of Statistical Data
- Chapter 24: Measures Of Central Tendency
- Chapter 25: Probability

#### RD Sharma Solutions for Class 9 MathsÂ Chapter 1: Number System

In Class 9 maths, Chapter 1 will introduce you to the Number Systems. It will introduce you to Irrational Numbers, Real Numbers & their decimal expansions, how to represent real numbers on the number line, and operations on real numbers. This is an important chapter as it will allow you to understand further chapters easily.

#### RD Sharma Solutions for Class 9 MathsÂ Chapter 2: Exponents Of Real Numbers

Chapter 2 is a continuation of Chapter 1 where you will use the understanding of real numbers and their operations to grasp the concept of Exponents of Real Numbers. You will learn certain laws about these exponents and solve problems based on them.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 3: Rationalisation

The third chapter will help you familiarise yourself with identities and the rationalization of the denominator. The book provides a detailed guide on how to rationalize the denominator and solve problems based on the concept.

#### RD Sharma Solutions for Class 9 Maths Chapter 4: Algebraic Identities

Chapter 4 talks about Algebraic Identities and problems based on various concepts that you learned during Class 8. These concepts include the identity for the square of a trinomial, cube of the binomial, sum and difference of cubes, etc.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 5: Factorization Of Algebraic Expressions

Chapter 5 will teach you about factorizing algebraic expressions like monomials and polynomials using identities. You will also get to practice factorization as the sum of cubes.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 6: Factorization Of Polynomials

In Chapter 6, you will learn about polynomials in one variable, zeroes of a polynomial, remainder theorem, and Factor Theorem. You will also solve some problems based on these theorems and concepts.

#### RD Sharma Solutions for Class 9 Maths Chapter 7: Introduction To Euclidâ€™s Geometry

Euclid’s Geometry established the foundation for understanding axioms, postulates, and their applications. In Chapter 7 you will understand the concept of Euclid’s Geometry including certain definitions and his famous five postulates.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 8: Lines And Angles

Chapter 8 is all about understanding basic terms and definitions of lines and angles, intersecting and non-intersecting lines, pairs of angles, parallel lines, transversal, lines parallel to the same line, and angle sum property of a triangle.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 9: Triangle And Its Angles

In Chapter 9, you will learn about the properties of a triangle, some essential theorems, inequalities in a triangle, and some problems based on these concepts and theorems.

#### RD Sharma Solutions for Class 9 Maths Chapter 10: Congruent Triangles

In continuation with the last chapter, in Chapter 10, you will understand all about congruent triangles, the criteria for the congruence of triangles, axioms and theorems based on these concepts, and problems to help understand it better.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 11: Coordinate Geometry

Coordinate Geometry, Chapter 11 explains the Cartesian system in detail and teaches you how to plot a point in a plane if you have the coordinates. Another important chapter to ensure that your basics are in place.

#### RD Sharma Solutions for Class 9 Maths Chapter 12: Herons Formula

In this chapter, you will learn about the famous Heron’s formula to calculate the area of a triangle and solve some problems using it too. Further, you will also learn about the application of Heron’s formula for calculating the area of a quadrilateral.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 13: Linear Equations In Two Variables

While you already know about linear equations in one variable, this chapter is about linear equations in two variables. You will learn the basics, solution of a linear equation, the graph of a linear equation in two variables, and equations of lines parallel to the X and Y-axis.

#### RD SharmaÂ Solutions for Class 9 MathsChapter 14: Quadrilaterals

Chapter 14 is all about quadrilaterals, the angle sum property of a quadrilateral, types of quadrilaterals, properties of a parallelogram, and the mid-point theorem. You will also solve some problems based on these concepts and theorems.

#### RD Sharma Â Solutions for Class 9 Maths Chapter 15: Areas Of Parallelograms And Triangles

In this chapter, you will understand how to calculate the area of a parallelogram and triangle. You will learn about figures on the same base and between the same parallels, parallelograms on the same base and between the same parallels, and trianglesÂ on the same base and between the same parallels.

#### RD Sharma Â Solutions for Class 9 Maths Chapter 16: Circles

This chapter on Circles will teach you about all the terms related to circles, the angle that a chord subtends at a point, perpendicular from the center to a chord, circle through three points, equal chords and their distances from the center, the angle that an arc of the circle subtends, and cyclic quadrilaterals.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 17: Constructions

While you have already learned about constructingÂ a circle, the perpendicular bisector of aÂ line segment, different angles, and the bisector of a given angle, this year you will understand what makes these constructions valid.

#### RD SharmaÂ Â Solutions for Class 9 Maths Chapter 18: Surface Area And Volume Of A Cuboid And Cube

In Class 8, you learned about the basics of calculating the volume and surface area of a cuboid and a cube. While the concept is simple, solving difficult problems can take time. In this chapter, you will practice some difficult problems on this topic.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 19: Volume and Surface Area Of a Right Circular Cylinder

In Class 8, you learned about the basics of calculating the volume and surface area of a right circular cylinder. While the concept is simple, solving difficult problems can take time. In this chapter, you will practice some difficult problems on this topic.

#### RD Sharma Solutions for Class 9 Maths Chapter 20: Surface Area And Volume Of a Right Circular Cone

This is a new concept – a right circular cone. In Chapter 20, you will learn about calculating the surface area and volume of a right circular cone.Â You will also understand the practical applications of this concept.

#### RD Sharma Solutions for Class 9 Maths Chapter 21: Surface Area And Volume Of Sphere

This is also a new concept – a right circular cone. In Chapter 20, you will learn about calculating the surface area and volume of a sphere.Â You will also understand the practical applications of this concept.

#### RD Sharma Â Solutions for Class 9 Maths Chapter 22: Tabular Representation Of Statistical Data

When you collect information or data, you have to tabulate it to make it easier to understand and analyze. Chapter 22 will help you understand data collection and the tabular representation of data.

#### RD SharmaÂ Solutions for Class 9 Maths Chapter 23 Graphical Representation Of Statistical Data

Apart from presenting data in a structured tabular format, you also need to learn how to present the data in a graphical format. In this chapter, you will learn about the graphical representation of statistical data. This includes bar graphs, histograms, and also frequency polygons.

#### RD Sharma Â Solutions for Class 9 Maths Chapter 24: Measures Of Central Tendency

After understanding the tabular and graphical representation of data, you must also know how to make sense of it. This chapter will teach you about Central Tendency to help understand data. You will solve some complex problems to get better at making sense of a table or a graph.

#### RD SharmaÂ Â Solutions for Class 9 Maths Chapter 25 Probability

The last chapter introduced you to the concept of probability. It also teaches you about the experimental approach to probability – a concept that you will use next year.

**Solved Questions from RD Sharma Solutions for Class 9 MathsÂ **

**Question 1**:Â Â Factorise the given polynomial expression: a^{3} + a – 3a^{2} – 3

**Answer**: Rearranging the expression, we get:

a^{3} – 3a^{2} +Â aÂ – 3

= a^{2}(a – 3) + 1(a – 3)

= (a – 3) (a^{2} + 1)

âˆ´Â a^{3} + a – 3a^{2} – 3 =Â (a – 3) (a^{2} + 1)

**Question 2**:Â Identify constant, linear, quadratic and cubic polynomials from the following polynomial:Â p(a)=2a^{2}Â âˆ’ a + 4.

**Answer**: The degree of p(a) is 2. Therefore, this is a quadratic polynomial.

**Question 3**:Â Express the following linear equation in the form ax+by+c=0 and indicate the values of a,b and c in each case:

âˆ’2x+3y=12.

**Answer**:

We can writeÂ âˆ’2x+3y=12 asÂ âˆ’2x+3y-12=0

Comparing the given equation with ax+by+c=0, we get:

a = -2

b = 9

c = -12

**Question 4**:Â The external dimensions of a closed wooden box are 48cm,36cm,30cm. The box is made of 1.5cm thick wood. How many bricks of size 6cmÃ—3cmÃ—0.75cm can be put in this box?

**Answer**:

The volume of the box = (48 – 3)Â Ã— (36 – 3)Â Ã— (30 – 3) = 38880 cm^{3}

*Please note that we subtracted ‘3’ because we have the outer dimensions of the box and the thickness of the wood is 1.5 cm. Therefore, to get the inner dimensions of the box, we need to subtract the thickness of the wood from the outer dimensions of the box.*

The volume of a brick = 6Â Ã— 3Â Ã— 0.75 = 1.35 cm^{3}

The the number of bricks = 38880/13.5 = 2970

**FAQs related to RD Sharma Solutions for Class 9 Maths**

**Q1. Can I completely rely on the RD Sharma Class 9 Solutions for maths or should I get a textbook too?**

Answer: The RD Sharma Class 9 Solutions for maths are comprehensive and cover the entire syllabus. However, we would recommend keeping a textbook handy as additional reference material.

Q2. Is the RD Sharma book tough?

Answer: The book covers problems with varying difficulty levels. If you solve this book, you will be able to solve all types of problems based on the topic.

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