Table of Contents

RD Sharma Solutions for **Class 9 Maths** are available in PDF format and can be easily downloaded by students. These solutions are organized chapter-wise and explained step-by-step to help students prepare for exams. The main goal is to help students identify which areas need more practice for better exam performance. Using RD Sharma Solutions, students can solve exercise problems faster and understand the concepts more clearly.

The solutions PDF is a helpful guide for students to score well in their **Class 9** exams. Regular practice with RD Sharma Solutions for Class 9 Maths helps students improve their problem-solving and logical thinking skills, which are important for achieving good grades. The Class 9 CBSE RD Sharma textbook contains a total of 25 chapters.

## RD Sharma Class 9 Maths Chapter-wise Solutions

Chapter-wise Solutions for RD Sharma Class 9 |

RD Sharma Class 9 Solutions Maths Chapter 1 Number System |

RD Sharma Class 9 Solutions Maths Chapter 2 Exponents of Real Numbers |

RD Sharma Class 9 Solutions Maths Chapter 3 Rationalisation |

RD Sharma Class 9 Solutions Maths Chapter 4 Algebraic Identities |

RD Sharma Class 9 Solutions Maths Chapter 5 Factorisation of Algebraic Expressions |

RD Sharma Class 9 Solutions Maths Chapter 6 Factorisation of Polynomials |

RD Sharma Class 9 Solutions Maths Chapter 7 Introduction to Euclid’s Geometry |

RD Sharma Class 9 Solutions Maths Chapter 8 Lines and Angles |

RD Sharma Class 9 Solutions Maths Chapter 9 Triangle and Its Angles |

RD Sharma Class 9 Solutions Maths Chapter 10 Congruent Triangles |

RD Sharma Class 9 Solutions Maths Chapter 11 Coordinate Geometry |

RD Sharma Class 9 Solutions Maths Chapter 12 Herons Formula |

RD Sharma Class 9 Solutions Maths Chapter 13 Linear Equations in Two Variables |

RD Sharma Class 9 Solutions Maths Chapter 14 Quadrilaterals |

RD Sharma Class 9 Solutions Maths Chapter 15 Areas of Parallelograms and Triangles |

RD Sharma Class 9 Solutions Maths Chapter 16 Circles |

RD Sharma Class 9 Solutions Maths Chapter 17 Constructions |

RD Sharma Class 9 Solutions Maths Chapter 18 Surface Area and Volume of a Cuboid and Cube |

RD Sharma Class 9 Solutions Maths Chapter 19 Surface Area and Volume of a Right Circular Cylinder |

RD Sharma Class 9 Solutions Maths Chapter 20 Surface Area and Volume of a Right Circular Cone |

RD Sharma Class 9 Solutions Maths Chapter 21 Surface Area and Volume of Sphere |

RD Sharma Class 9 Solutions Maths Chapter 22 Tabular Representation of Statistical Data |

RD Sharma Class 9 Solutions Maths Chapter 23 Graphical Representation of Statistical Data |

RD Sharma Class 9 Solutions Maths Chapter 24 Measures of Central Tendency |

RD Sharma Class 9 Solutions Maths Chapter 25 Probability |

## RD Sharma Class 9th Book PDF

## RD Sharma Solutions for Class 9 Maths – Exercise-wise Solutions

### Chapter 1: Number Systems

This chapter introduces real numbers, irrational numbers, and their decimal expansions.

**Key Formulas:**

Rational Number: \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \)

Irrational Numbers: Numbers that cannot be expressed as \( \frac{p}{q} \)

### Chapter 2: Exponents of Real Numbers

Focuses on laws of exponents and their applications.

**Key Formulas:**

\( a^m \times a^n = a^{m+n} \)

\( \frac{a^m}{a^n} = a^{m-n} \)

\( (a^m)^n = a^{mn} \)

\( a^0 = 1 \)

### Chapter 3: Rationalisation

Rationalizing the denominator of irrational numbers.

**Key Formulas:**

For \( \frac{1}{\sqrt{a}} \), multiply by \( \frac{\sqrt{a}}{\sqrt{a}} \)

For \( \frac{1}{a+\sqrt{b}} \), multiply by \( \frac{a-\sqrt{b}}{a-\sqrt{b}} \)

### Chapter 4: Algebraic Identities

Expands on various algebraic identities.

**Key Formulas:**

\( (a+b)^2 = a^2 + 2ab + b^2 \)

\( (a-b)^2 = a^2 – 2ab – b^2 \)

\( (a+b)(a-b) = a^2 – b^2 \)

\( (x+a)(x+b) = x^2 + (a+b)x + ab \)

### Chapter 5: Factorisation of Algebraic Expressions

Techniques to factorize algebraic expressions.

**Key Formulas:**

\( a^2 – b^2 = (a+b)(a-b) \)

\( x^2 + (a+b)x + ab = (x+a)(x+b) \)

### Chapter 6: Factorisation of Polynomials

Factorizing polynomials using factor theorem and remainder theorem.

**Key Formulas:**

If \( f(x) \) is a polynomial, and \( f(a) = 0 \), then \( (x-a) \) is a factor of \( f(x) \).

### Chapter 7: Introduction to Euclid’s Geometry

Basic concepts and definitions related to Euclidean geometry.

**Key Concepts:**

Axioms and postulates

Definitions of point, line, and plane

### Chapter 8: Lines and Angles

Properties of lines and angles, including parallel lines and transversal.

**Key Formulas:**

Sum of angles in a triangle = \( 180^\circ \)

Vertically opposite angles are equal

### Chapter 9: Triangle and its Angles

Properties of triangles and their angles.

**Key Formulas:**

Pythagoras Theorem: \( a^2 + b^2 = c^2 \) (for right-angled triangles)

Exterior angle theorem: Exterior angle = sum of opposite interior angles

### Chapter 10: Congruent Triangles

Conditions for the congruence of triangles.

**Key Concepts:**

RHS (Right angle-Hypotenuse-Side)

### Chapter 11: Coordinate Geometry

Basic concepts of the coordinate plane and plotting points.

**Key Formulas:**

Distance formula: \( \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \)

Midpoint formula: \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)

### Chapter 12: Heron’s Formula

Calculating the area of a triangle using Heron’s formula.

**Key Formulas:**

\( s = \frac{a+b+c}{2} \) (semi-perimeter)

Area \( = \sqrt{s(s-a)(s-b)(s-c)} \)

### Chapter 13: Linear Equations in Two Variables

Solving linear equations in two variables.

**Key Formulas:**

General form: \( ax + by + c = 0 \)

Solution: Intersection point of two lines

### Chapter 14: Quadrilaterals

Properties and types of quadrilaterals.

**Key Concepts:**

Sum of interior angles = \( 360^\circ \)

Parallelogram: Opposite sides and angles are equal

### Chapter 15: Areas of Parallelograms and Triangles

Calculating areas of parallelograms and triangles.

**Key Formulas:**

Area of parallelogram = base \( \times \) height

Area of triangle = \( \frac{1}{2} \times \) base \( \times \) height

### Chapter 16: Circles

Basic properties of circles and related theorems.

**Key Formulas:**

Circumference = \( 2\pi r \)

Area = \( \pi r^2 \)

### Chapter 17: Constructions

Construction of geometric figures using a compass and straightedge.

**Key Concepts:**

Constructing perpendicular bisectors and angle bisectors

### Chapter 18: Surface Areas and Volumes

Calculating surface areas and volumes of 3D shapes.

**Key Formulas:**

Surface area of a cube = \( 6a^2 \)

Volume of a cube = \( a^3 \)

Surface area of a cylinder = \( 2\pi rh + 2\pi r^2 \)

Volume of a cylinder = \( \pi r^2 h \)

### Chapter 19: Statistics

Collection, presentation, and interpretation of data.

**Key Formulas:**

Mean = \( \frac{\text{Sum of all observations}}{\text{Number of observations}} \)

Median: Middle value when data is arranged in ascending or descending order

Mode: Most frequently occurring value

### Chapter 20: Probability

Basic concepts of probability.

**Key Formulas: **Probability of an event \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \)

More Resources for Class 9

NCERT Solutions for Class 9

NCERT Solutions for Class 9 Maths

## RD Sharma Class 9 Maths FAQs

### Which is the toughest chapter in class 9 maths?

Many students find 'Linear Equations in Two Variables' to be the toughest chapter in class 9 maths.

### Which is better, RD Sharma or RS Aggarwal for class 9?

RD Sharma is better for detailed explanations and RS Aggarwal is good for practice problems.

### Which is the most scoring chapter in class 9 maths?

'Surface Areas and Volumes' is often considered the most scoring chapter in class 9 maths.

### Which is the hardest chapter in Maths class 9?

The chapter on 'Linear Equations in Two Variables' is commonly seen as the hardest.

### Is RD Sharma important for class 9th?

Yes, RD Sharma is important as it offers thorough explanations and numerous practice questions.