RD SharmaRD Sharma Class 9 PDF Book With Solutions

RD Sharma Class 9 PDF Book With Solutions

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.

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    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:
    SSS (Side-Side-Side)
    SAS (Side-Angle-Side)
    ASA (Angle-Side-Angle)
    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.

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