RD Sharma Solutions for Class 9 Maths

Mathematics is an essential subject for students in Class 9, and RD Sharma’s Maths book is one of the most trusted resources for mastering this subject. RD Sharma’s Class 9 Maths solutions cover a wide range of topics that help students understand concepts with ease. Whether you’re struggling with algebra, geometry, or statistics, the RD Sharma book can help you build a strong foundation for your future exams.

Why Choose RD Sharma for Class 9 Maths?

RD Sharma's Class 9 Maths solutions are widely recognized for their clear and simple explanations. The book breaks down complex problems into smaller, manageable steps. The solutions provided in the book give students the right approach to solving problems, helping them not only solve exercises but also understand the concepts thoroughly.

Here’s why RD Sharma is a popular choice among students:

• Clear and Step-by-Step Solutions: RD Sharma explains each step carefully, ensuring that students understand the logic behind every problem.
• Wide Range of Topics: The book covers all topics in the Class 9 syllabus, from algebra and geometry to trigonometry and statistics.
• Helps Build a Strong Foundation: By solving RD Sharma problems, students can develop a deeper understanding of mathematical concepts, making it easier to grasp higher-level topics in future classes.
• Variety of Questions: The book provides different types of problems, from basic to advanced, ensuring that students are well-prepared for exams.

RD Sharma Chapter-wise Solutions for Class 9 Maths

Here’s a table for Class 9 Maths with chapter-wise details:

Here’s a table for RD Sharma Class 9 Maths chapters based on the list you provided:

RD Sharma Solutions for Class 9 Maths – Chapter-wise Solutions

1. Number System

This chapter introduces different types of numbers, including:

• Natural Numbers, Whole Numbers, Integers, Rational & Irrational Numbers
• Properties of Real Numbers (Closure, Commutativity, Associativity, Distributivity)
• Representation of Numbers on a Number Line
• Operations on Real Numbers (Addition, Subtraction, Multiplication, Division)
• Decimal Expansions and their classification into terminating and non-terminating decimals.

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 \( \frac{p}{q} \)

2. Exponents of Real Numbers

This chapter focuses on:

• Laws of Exponents (Multiplication, Division, Power of a Power, Negative Exponents)
• Scientific Notation of Numbers
• Application of Exponents in Real Life (e.g., astronomy, physics, and engineering)

Key Formulas:
\( a^m \times a^n = a^{m+n} \)
\( \frac{a^m}{a^n} = a^{m-n} \)
\( (a^m)^n = a^{mn} \)
\( a^0 = 1 \)

3. Rationalisation

Rationalisation refers to removing the square root (or cube root) from the denominator of an expression. Topics covered:

• Conjugates of Irrational Numbers
• Methods to Rationalise Denominators
• Applications in Algebra and Geometry

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

4. Algebraic Identities

Algebraic identities are essential tools in simplifying and solving expressions. Key topics:

• Important Identities like:
  • (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2
  • (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2
  • a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)
• Applications in Simplifying and Expanding Expressions

5. Factorisation of Algebraic Expressions

This chapter teaches breaking down algebraic expressions into their simplest components:

• Methods of Factorisation (Common Factor Method, Regrouping, Middle Term Splitting)
• Factorisation of Quadratic Expressions
• Using Factorisation in Solving Equations

Key Formulas:
\( a^2 - b^2 = (a+b)(a-b) \)
\( x^2 + (a+b)x + ab = (x+a)(x+b) \)

6. Factorisation of Polynomials

This extends factorisation to polynomials:

• Finding Zeroes of Polynomials
• Remainder Theorem and Factor Theorem
• Applications in Real-life Problems

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

7. Introduction to Euclid’s Geometry

This chapter introduces Euclid’s fundamental postulates and axioms:

• Euclid’s Definitions and Axioms
• Postulates of Geometry
• The Role of Axioms in Proving Theorems

8. Lines and Angles

This chapter discusses:

• Types of Angles (Acute, Right, Obtuse, Complementary, Supplementary)
• Pairs of Angles (Adjacent, Linear Pair, Vertically Opposite)
• Parallel Lines and Transversal Theorem
• Angle Sum Property of a Triangle

9. Triangle and Its Angles

This chapter covers:

• Properties of Triangles
• Angle Sum Property
• Types of Triangles (Equilateral, Isosceles, Scalene)
• Exterior Angle Property

10. Congruent Triangles

Congruency is crucial in geometry:

• Criteria for Congruency (SSS, SAS, ASA, RHS)
• Applications in Proving Geometric Theorems

11. Coordinate Geometry

This chapter explores:

• Cartesian Plane and Coordinate System
• Distance Formula
• Midpoint Formula
• Section Formula
• Applications in Map Reading and Navigation

12. Heron’s Formula

This formula is used for finding the area of a triangle when all three sides are known:

• Heron’s Formula: A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}
• Applications in Real-world Problems

13. Linear Equations in Two Variables

This chapter focuses on:

• Forming Linear Equations
• Graphical Representation
• Solving Simultaneous Equations (Substitution, Elimination, Graphical Method)
• Applications in Word Problems

14. Quadrilaterals

This chapter discusses:

• Types of Quadrilaterals (Parallelogram, Rhombus, Square, Rectangle, Trapezium)
• Properties of Quadrilaterals
• Midpoint Theorem and Diagonal Properties

15. Areas of Parallelograms and Triangles

This chapter focuses on:

• Formulae for Finding Areas
• Application in Real-life Problems
• Proving Theorems Using Area Concept

16. Circles

This chapter discusses:

• Basic Definitions (Radius, Diameter, Chord, Arc, Sector, Segment)
• Tangent Properties
• Number of Tangents from a Point to a Circle

17. Constructions

This chapter teaches:

• Bisecting a Line Segment
• Constructing Angles and Triangles
• Constructing Tangents to a Circle
• Real-life Applications in Architecture and Engineering

18. Surface Area and Volume of a Cuboid and Cube

Topics covered:

• Formula for Surface Area & Volume
• Real-life Applications in Packaging, Construction

19. Surface Area and Volume of a Right Circular Cylinder

This chapter covers:

• Formulae for Lateral Surface Area, Total Surface Area, and Volume
• Real-life Applications (Pipes, Cylindrical Tanks, Drums)

20. Surface Area and Volume of a Right Circular Cone

Covers:

• Formulae for Curved Surface Area, Total Surface Area, and Volume
• Real-life Applications (Ice Cream Cones, Traffic Cones)

21. Surface Area and Volume of a Sphere

This chapter includes:

• Formulae for Surface Area and Volume
• Hemispheres and Their Surface Area/Volume
• Applications in Astronomy, Earth Science, Sports

22. Tabular Representation of Statistical Data

This chapter deals with:

• Types of Data (Raw, Grouped, Ungrouped)
• Organizing Data in Tables
• Frequency Distributions

23. Graphical Representation of Statistical Data

Covers different ways to represent data visually:

• Bar Graphs
• Histograms
• Pie Charts
• Application in Economics, Research, and Surveys

24. Measures of Central Tendency

This chapter teaches:

• Mean (Average)
• Median (Middle Value)
• Mode (Most Frequent Value)
• Applications in Economics and Social Sciences

25. Probability

Probability measures the likelihood of an event occurring:

• Basic Probability Concepts
• Theoretical Probability Formula
• Simple Problems on Probability
• Applications in Gambling, Weather Forecasting, and Insurance

How RD Sharma Helps in Exam Preparation

• Practice for Better Understanding: By solving the problems in the RD Sharma book, you can practice and improve your understanding of each topic. The more you practice, the better your problem-solving skills become.
• Provides Solutions to All Exercises: The solutions provided for all exercises allow you to check your answers, ensuring that you learn the correct method to solve problems.
• Effective Time Management: By practicing with RD Sharma’s book, students can manage their time electively during exams. The book helps you improve your speed and accuracy in solving problems.
• Comprehensive Approach: RD Sharma covers all the important topics in a systematic manner, making it easier to cover the entire syllabus before exams. You can revise topics quickly by focusing on key areas.

Conclusion

RD Sharma's Class 9 Maths book is a great resource for students looking to strengthen their understanding of mathematics. The book's well-explained solutions and comprehensive coverage of topics make it an essential tool for exam preparation. If you follow the right approach and practice regularly, you’ll be well on your way to acing your Class 9 Maths exams.