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.
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.
\( a^m \times a^n = a^{m+n} \)
\( \frac{a^m}{a^n} = a^{m-n} \)
\( (a^m)^n = a^{mn} \)
\( a^0 = 1 \)
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.
\( a^2 – b^2 = (a+b)(a-b) \)
\( x^2 + (a+b)x + ab = (x+a)(x+b) \)
Chapter 6: Factorisation of Polynomials
Factorizing polynomials using factor theorem and remainder theorem.
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.
Axioms and postulates
Definitions of point, line, and plane
Chapter 8: Lines and Angles
Properties of lines and angles, including parallel lines and transversal.
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.
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.
RHS (Right angle-Hypotenuse-Side)
Chapter 11: Coordinate Geometry
Basic concepts of the coordinate plane and plotting points.
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.
\( s = \frac{a+b+c}{2} \) (semi-perimeter)
Area \( = \sqrt{s(s-a)(s-b)(s-c)} \)
Chapter 13: Linear Equations in Two Variables
Solving linear equations in two variables.
General form: \( ax + by + c = 0 \)
Solution: Intersection point of two lines
Chapter 14: Quadrilaterals
Properties and types of quadrilaterals.
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.
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.
Circumference = \( 2\pi r \)
Area = \( \pi r^2 \)
Chapter 17: Constructions
Construction of geometric figures using a compass and straightedge.
Constructing perpendicular bisectors and angle bisectors
Chapter 18: Surface Areas and Volumes
Calculating surface areas and volumes of 3D shapes.
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.
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.
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