RD Sharma Solutions for Class 9 Maths

RD Sharma Solutions for Class 9 Maths – Chapter-wise Free PDF Download Updated for (2023-24)

RD Sharma Solutions for Class 9 Maths are available in PDF format, which can be downloaded effortlessly by the students. The chapter-wise solutions are prepared in a step-wise manner to boost the exam preparations of students. The main aim is to help students self analyse the areas which require more practice from the exam point of view. With the help of RD Sharma Solutions, students can solve the exercise problems in a shorter duration, with a clear idea of the concepts.

The solutions PDF is a major reference guide to help students score well in the Class 9 examination. Solving the exercise-wise problems daily using the RD Sharma Solutions for Class 9 Maths helps students improve their problem-solving and logical thinking skills, which are important to obtain a better academic score. There are a total of 25 Chapters in the Class 9 CBSE textbook of RD Sharma.

RD Sharma Chapter-wise Solutions for Class 9 Maths

The students can access the various study materials that are available online, which include previous years’ question papers, worksheets and sample papers. Students can make use of RD Sharma Class 9 Sample Papers Solutions to get knowledge about the exam pattern of the current CBSE board.

Download Class 9 RD Sharma Solutions to speed up the exam preparations.

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

Students can use chapter-wise RD Sharma Solutions for Class 9 PDF to obtain better conceptual knowledge that is required to solve the problems of the RD Sharma textbook. The main aim is to boost confidence, which is important among students before appearing for the exams.

RD Sharma Solutions for Class 9 Maths Chapter 1 – Number System

Chapter 1 of the RD Sharma textbook provides us with the knowledge of Number Systems, including rational and irrational numbers, representing the numbers on a number line, real numbers, rationalisation and laws of exponents. Shortcut methods and tricks are provided, which include formulas that are used in solving chapter-wise problems, as per the latest CBSE syllabus.

• Number System: A number system is a system of writing in order to express numbers. It is the mathematical notation to represent numbers of a given set using digits or other symbols in a consistent manner.
• Rational Numbers: A rational number is defined as a number which is represented in the form of p/q where q ≠ 0. We can also say that any fraction fits under the category of rational numbers, where the denominator and numerator are integers, and the denominator is not equal to zero.
• Irrational Numbers: Irrational numbers are real numbers that cannot be represented as simple fractions. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.
• Real Numbers: Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”.

The exercise-wise solution links covered in this chapter are provided below.

Also, access the following resources for Class 9 Chapter 1 Number System at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 1 Number Systems
• NCERT Exemplar Solutions for Class 9 Maths Chapter 1 – Number Systems

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

Chapter 2 of the RD Sharma textbook contains problems based on important topics like Integral Exponents of a Real Number, Laws of Integral Exponents, and Rational Exponents of a Real Number. These topics are explained by experts according to the understanding level of students.

• Exponents: Exponents are used to show the repeated multiplication of a number by itself.
• Laws of exponents:

1. Product with same bases: As per this law, for any non-zero term a,

a^m×aⁿ = a^m+n

Where m and n are real numbers.

2. Quotient with same bases: As per this rule,

a^m/aⁿ = a^m-n

Where a is a non-zero term and m and n are integers.

3. Power raised to a power: According to this law, if ‘a’ is the base, then the power raised to the power of base ‘a’ gives the product of the powers raised to the base ‘a’, such as

(a^m)ⁿ = a^mn

Where a is a non-zero term and m and n are integers.

4. Product to a power: As per this rule, for two or more different bases, if the power is the same, then

aⁿ bⁿ = (ab)ⁿ

Where a is a non-zero term and n is the integer.

5. Quotient to a power: As per this law, the fraction of two different bases with the same power is represented as

aⁿ/bⁿ = (a/b)ⁿ

Where a and b are non-zero terms and n is an integer.

6. Zero Power: According to this rule, when the power of any integer is zero, then its value is equal to 1, such as;

a⁰ = 1

where ‘a’ is any non-zero term.

7. Negative Exponent Rule: According to this rule, if the exponent is negative, we can change the exponent into positive by writing the same value in the denominator, and the numerator holds the value 1.

The negative exponent rule is given as

a^-m = 1/a^m

8. Fractional Exponent Rule: The fractional exponent rule is used, if the exponent is in the fractional form. The fractional exponent rule is given by

a^1/n =

Students can find the links of solutions for exercise-wise problems that are present in this chapter.

RD Sharma Solutions for Class 9 Maths Chapter 3 – Rationalisation

Chapter 3 of the RD Sharma textbook has concepts explained in a step-wise manner. This chapter contains problems based on identities and the Rationalisation of Denominator. Various illustrative examples before each exercise help students understand the method of solving problems.

• Rationalisation of the denominator: We rationalise the denominator when the fraction given has a radical term or a surd in the denominator.
• (a + b)² = a² + b² + 2ab
• (a – b)² = a² – 2ab + b²
• (a² – b²) = (a + b) (a – b)

Given here are some of the links to exercise-wise solutions presented in Chapter 3.

RD Sharma Solutions for Class 9 Maths Chapter 4 – Algebraic Identities

This chapter consists of exercise-wise problems that are solved based on concepts like Identities, Identity for the square of a trinomial, Identity for the cube of a binomial, Sum and Difference of Cubes and One More Identity. The solutions of Algebraic Identities are well structured in an interactive manner as per the latest CBSE syllabus. Students can make use of the solutions PDF to score well in the Class 9 exams.

• (a – b)² = a² + b² – 2ab
• (a – b) (a + b) = a² – b²
• a²+ b²+2ab = (a+b)²
• (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2xz
• (a + b)³ = a³ + b³ + 3ab (a + b)
• (a – b)³ = a³ – b³ – 3ab (a – b)
• a³ + b³ = (a + b) (a² + b² – ab)
• a³ – b³ = (a – b) (a² + b² + ab)

Chapter 4 has 5 exercises and 1 VSAQ exercise whose solution links are provided below.

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

This chapter explains basic concepts like types of factorisation, factorisation as a sum or difference of two cubes, factorisation using the formulae for the cube of a binomial, and factorisation of algebraic expressions. Students can solve the exercise-wise problems of this chapter using the RD Sharma Solutions prepared by experienced faculty.

• Factorisation: Factorisation or factoring is the decomposition or breaking of an entity into a product of another entity, or factors, which, when multiplied together, gives the original number or a matrix, etc.
• Method of common factors: We take out the common factors in each term of the given expression.
• Method of grouping terms: Grouping refers to arranging the expression as like terms or similar terms.
• Factorisation using identities: Using the common identities, the given expression can be factorised.
• Factors of the form (x + a) (x + b): If the given expression is in the form of x² + (a + b) x + ab, then the factors will be (x+a) and (x + b).

The links for the exercise-wise solutions are provided below.

RD Sharma Solutions for Class 9 Maths Chapter 6 – Factorisation of Polynomials

The exercise-wise solutions are designed by experts at BYJU’S after conducting research on each topic. Chapter 6 of the RD Sharma textbook explains the major topics like definitions, zeros of a polynomial, the Remainder Theorem, the Factor Theorem and the Factorisation of polynomials using the factor theorem.

• Term: It is a number, a variable, a product of two or more variables, or a product of a number and a variable. By a single term or by a group of terms, an algebraic expression is formed.
• Coefficient: A coefficient is an integer that is written along with a variable or multiplied by the variable.  It is the numerical factor of a term having constants and variables.
• Polynomial: An expression having more than two algebraic terms, i.e., the sum (or difference) of several terms which contain different powers of the same or different variable(s).
• Degree of a Polynomial: It is the highest power of the variable in a polynomial expression.

Given below are the solution links of the exercise-wise problems covered in this chapter.

Also, access the following resources for Class 9 Chapter 6 Factorisation of Polynomials at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 2 – Polynomials
• NCERT Exemplar Class 9 Maths Solutions for Chapter 2 – Polynomials

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

The 7th chapter of the RD Sharma textbook explains to students the Axioms and Theorems, Incidence Properties, Parallel and Intersecting Lines, Line Segment, Length Axioms and Plane. The solutions are available with pictorial representation in order to make it easy for the students. The solutions PDF can be downloaded by the students, which is a major source of reference material.

Euclidean Axioms

1. Things which are equal to the same thing are equal to one another.
2. If equals are added to equals, the wholes are equal.
3. If equals are subtracted from equals, the remainders are equal.
4. Things which coincide with one another are equal to one another.
5. The whole is greater than the part.
6. Things which are double the same things are equal to one another.
7. Things which are halves of the same things are equal to one another

Solution links of the exercises prepared by experts at BYJU’S are available below.

Also, access the following resources for Class 9 Chapter 7 Introduction to Euclid’s Geometry at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry
• NCERT Exemplar Solutions for Class 9 Maths Chapter 5 – Introduction to Euclid’s Geometry

RD Sharma Solutions for Class 9 Maths Chapter 8 – Lines and Angles

The 8th chapter of the RD Sharma textbook provides students with knowledge about the types of angles and their relations and results on parallel lines. The solutions contain pictorial representations of lines and angles to make it easier for the students to grasp. The solutions PDF designed by subject matter experts helps students gain better knowledge about concepts.

• Lines: It is a one-dimensional figure which has length but no width. It is made of a set of points that is extended infinitely in opposite directions. It is found by two points in a two-dimensional plane.
• Linear Pair of Angles: Linear pair of angles are formed when two lines intersect each other at a single point. The angles are linear if they are adjacent to one another after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180° and is known as supplementary angles.
• Vertically Opposite Angles: When two lines intersect each other, then the opposite angles which are formed by intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

The links for the solutions prepared by experts at BYJU’S are provided below.

Also, access the following resources for Class 9 Chapter 8 Lines and Angles at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 6 – Lines and Angles
• NCERT Exemplar Solutions for Class 9 Maths Chapter 6 – Lines and Angles

RD Sharma Solutions for Class 9 Maths Chapter 9 – Triangle and Its Angles

Triangles and other concepts essential to determine the angles and sides are discussed here in understandable language. This chapter covers concepts like types of triangles based on angles and sides, along with the interior and exterior angles. The solutions are prepared according to the understanding level of students, which is important in solving exercise-wise problems.

• Triangle: A triangle is a three-sided polygon that has three vertices and three sides.

Types of triangles

• Scalene triangle: A scalene triangle has all three sides of different measures.
• Isosceles triangle: An isosceles triangle has two sides of equal length.
• Equilateral triangle: An equilateral triangle has all three sides equal to each other.
• Acute angled triangle: An acute-angled triangle has all angles less than 90⁰.
• Right-angled triangle: A right-angled triangle has one of the angles as 90⁰.
• Obtuse angled triangle: An obtuse angle triangle has one of its angles greater than 90⁰.

Also, access the following resources for Class 9 Chapter 9 Triangle and its Angles at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 7 – Triangles
• NCERT Exemplar Solutions for Class 9 Maths Chapter 7 – Triangles

RD Sharma Solutions for Class 9 Maths Chapter 10 – Congruent Triangles

The primary objective of providing exercise-wise solutions is to help students score well in the exams. This chapter has important concepts like the congruence of triangles, line segments, angles, congruence criteria and inequality relations. Students can make use of solutions PDF to gain a hold on concepts and score well in the exam.

1. SSS (Side-Side-Side): If all the sides of two triangles are equivalent, then triangles are said to be congruent.
2. SAS (Side-Angle-Side): If two sides and an interior angle of a triangle are equal to the corresponding sides and an interior angle of the other triangle, then both triangles are said to be congruent.
3. ASA (Angle-Side-Angle): If two angles and included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.
4. RHS (Right angle- Hypotenuse-Side): If in two right-angled triangles, the hypotenuse and any one side of a triangle are equivalent to the hypotenuse and one side of the other triangle, then both triangles are said to be congruent.

Chapter 10 exercise solution links for the topics discussed in this chapter are given below.

Also, access the following resources for Class 9 Chapter 10 Congruent Triangles at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 7 – Triangles
• NCERT Exemplar Solutions for Class 9 Maths Chapter 7 – Triangles

RD Sharma Solutions for Class 9 Maths Chapter 11 – Co-ordinate Geometry

Chapter 11 Co-ordinate Geometry tells us about the rectangular or cartesian coordinates of a point and the plotting of points. These concepts are explained in an interactive manner by the experts at BYJU’S to help students perform well in the exam. Shortcut tips and important formulas are explained to help students remember them.

• Co-ordinate Geometry: Coordinate geometry is the study of geometry using coordinate points.
• Cartesian Co-ordinate System: A Cartesian coordinate system, or Coordinate system, is mainly used to locate the position of a point, and it can be plotted as an ordered pair (x, y) called Coordinates.

Also, access the following resources for Class 9 Chapter 11 Co-ordinate Geometry at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 3 – Coordinate Geometry
• NCERT Exemplar Class 9 Maths Solutions for Chapter 3 – Coordinate Geometry

RD Sharma Solutions for Class 9 Maths Chapter 12 – Heron’s Formula

Chapter 12 Heron’s Formula of the RD Sharma textbook explains basic topics like the introduction, Heron’s formula and its applications. The solutions are prepared by teachers having experience in the education industry to improve problem-solving abilities among students.

• Heron’s Formula – It is used to determine the area of a triangle when the length of its sides is known. It is also known as the Hero’s Formula.
• Area of triangle using three sides =
  \(\begin{array}{l}\sqrt{s(s-a)(s-b)(s-c)}\end{array} \)
• Semiperimeter S = Perimeter of triangle/2 = (a + b + c)/2

Where a, b and c are the three sides of the triangle.

The solution links for the textbook problems are available below.

Also, access the following resources for Class 9 Chapter 12 Heron’s Formula at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula
• NCERT Exemplar Solutions Class 9 Mathematics Chapter 12 Heron’s Formula

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

The concepts based on Linear Equations are discussed in this chapter in simple language. This chapter consists of topics like Linear Equations in two variables, solution of a linear equation, Graph of a linear equation in two variables and equations of lines parallel to the X-axis and Y-axis.

• Linear equations: These are the equations of the first order. The linear equations are defined for the lines in the coordinate system. If the equation has a homogeneous variable of degree 1, then it is called a linear equation in one variable.
• Linear equations in two variables: It explains the geometry of lines or the graph of two lines which is plotted to solve the equations.

The exercise-wise solution links of exercises covered in this chapter are provided below.

Also, access the following resources for Class 9 Chapter 13 Linear Equations in Two Variables at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables
• NCERT Exemplar Solutions for Class 9 Maths Chapter 4 – Linear Equations in Two Variables

RD Sharma Solutions for Class 9 Maths Chapter 14 – Quadrilaterals

Quadrilaterals are one of the important concepts in Class 9, as they will be continued in higher classes as well. Chapter 14 has problems solved using important topics like Quadrilateral and some terms associated with it, Angle sum property, Types of quadrilaterals, Properties of a parallelogram, Properties of a rectangle, rhombus, a square and useful facts about a triangle.

• Quadrilaterals: A quadrilateral is a plane figure which has four edges or sides and also has four vertices or corners.
• Types of Quadrilaterals: The types of quadrilaterals are trapezium, parallelogram, squares, rectangle, rhombus and kite.

Conditions for a quadrilateral to be a parallelogram

• The opposite side of the parallelogram is of the same length.
• The opposite sides are parallel to each other.
• The diagonals of a parallelogram bisect each other.
• The opposite angles are of equal measure.
• The sum of two adjacent angles of a parallelogram is equal to 180 degrees.

The solution links to the exercises of Chapter 14 are available here.

Also, access the following resources for Class 9 Chapter 14 Quadrilaterals at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals
• NCERT Exemplar Solutions for Class 9 Maths Chapter 8 – Quadrilaterals

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

Chapter 15 of the RD Sharma textbook has 3 exercises based on important topics like figures on the same base and between the same parallels, polygonal regions and area axioms. Various shortcut methods are also available to help students grasp the formulas used in solving the problems of parallelograms and triangles. The exercise-wise problems are as per the CBSE guidelines that can be solved easily using the solutions PDF.

• Parallelogram: A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other.
• Triangle: A triangle is a three-sided polygon that has three vertices and three edges.
• Area of a parallelogram: It is the region covered by a parallelogram in a two-dimensional plane.

Area = b × h square units

Where “b” is the base and “h” is the height of the parallelogram.

• Area of a triangle: It is defined as the total region which is enclosed by the three sides of any particular triangle. It is equal to half of the base times height, i.e., A = 1/2 × b × h.

To find the area of a tri-sided polygon, we have to know its base (b) and height (h) of it.

Given below are the solution links for the exercises covered in this chapter.

Also, access the following resources for Class 9 Chapter 15 Areas of Parallelograms and Triangles at BYJU’S.

• Areas of Parallelograms and Triangles Class 9 Notes: Chapter 9
• NCERT Solutions for Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles
• NCERT Exemplar Solutions for Class 9 Maths Chapter 7 – Triangles

RD Sharma Solutions for Class 9 Maths Chapter 16 – Circles

Students can access chapter-wise solutions of the RD Sharma textbook as per the latest CBSE syllabus available in PDF format. Chapter 16 mainly deals with important definitions, arcs of a circle, chord and segment of a circle, congruence of circles and arcs, some results on equal chords, arcs and angles subtended by them and cyclic quadrilateral.

• Circle: It is a kind of ellipse in which the two foci are coincident, and the eccentricity is zero. It is termed the locus of the points, which is drawn at an equidistant from the centre.
• Concentric circles: It is defined as two or more circles that contain the same centre point. The region between the two concentric circles is of different radii called an annulus.
• Chord of a circle: It is defined as the line segment which joins any two points on the circumference of a circle.
• Segment of a circle: It is defined as the region which is bounded by a chord and a corresponding arc lying between the endpoints of the chords.

Students can download solutions to exercise-wise problems solved by subject experts from the links given below.

Also, access the following resources for Class 9 Chapter 16 Circles at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 10 Circles
• NCERT Exemplar Solutions for Class 9 Maths Chapter 10 – Circles

RD Sharma Solutions for Class 9 Maths Chapter 17 – Constructions

In this chapter, students will gain knowledge about simple and basic constructions with the help of a ruler and a pair of compasses. This chapter helps students understand basic constructions, the construction of standard angles and the construction of triangles. The solutions are explained in a step-by-step manner to help students gain conceptual knowledge, which is important from the exam point of view.

• Bisector:  It is a line that divides the line into two equal or different parts.
• Line segment: It is bounded by two distinct points on a line.
• Line segment bisector and angle bisector: A line that passes through the midpoint of the line segment is called the line segment bisector, whereas the line which passes through the apex of an angle is called an angle bisector.

Students can use the links provided below to download the solutions to exercise-wise problems covered in this chapter.

Also, access the following resources for Class 9 Chapter 17 Constructions at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 11 Constructions
• NCERT Exemplar Solutions for Class 9 Maths Chapter 11 – Constructions

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

Chapter 18 Surface Area and Volume of a Cuboid and a Cube of the RD Sharma textbook has concepts like units of measurement of area and volume, cuboid and cube, surface area and lateral surface area of a cuboid and a cube and volume of a cuboid. The team of expert faculty at BYJU’S creates solutions based on the current CBSE syllabus and guidelines. Students can avail free solutions PDF easily and refer to them while solving problems.

• The volume of a cuboid: A cuboid is a three-dimensional shape, to determine the volume of a cuboid, we have to know its Length, Width and Height.

Volume = Length × Height × Width

• Surface area of a cuboid: The total surface area of a cuboid is the sum of the areas of its six faces.

Surface Area = 2 (length.width + width.length + height.length)

• Surface area of a cube: The surface area of a cube is the area of the six squares that cover it.

Surface Area = 6(Side)²

• Volume of a cube: (Side)³

The solution links for exercises discussed in this chapter are provided below.

Also, access the following resources for Class 9 Chapter 18 Surface Area and Volume of a Cuboid and a Cube at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes
• NCERT Exemplar Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume

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

This chapter consists of important problems and formulas used in determining the surface area and volume of a right circular cylinder. The solutions contain step-wise explanations to help students score well in the board exam. Students can improve their analytical thinking and problem-solving abilities by using PDF as a major source of reference material.

• Surface area of a cylinder = 2πr (r + h)
• Volume of a cylinder = πr²h

Where r = Radius of the cylinder and

h = Height of the cylinder.

Here, the students can obtain solutions to exercises in PDF format from the links given below.

Also, access the following resources for Class 9 Chapter 19 Surface Area and Volume of a Right Circular Cylinder at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes
• NCERT Exemplar Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume

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

The main concepts discussed in this chapter are a right circular cone, surface area and volume. The set of experienced faculty at BYJU’S design the solutions keeping in mind the understanding abilities of students. The primary aim of providing chapter-wise solutions is to help students ace the exam.

• Total surface area: The total area which is occupied by the surface, including the curved part and the base(s).

Total surface area = πr(r + l)

• Curved surface area: The area which is occupied by the surface, excluding the base(s), is called a curved surface area.

Curved surface area = πrl

• Volume: The space which is occupied by an object and is measured in cubic units.

Volume = 1/3πr²h

The solutions PDF links of exercises in this chapter are available below for free download.

Also, access the following resources for Class 9 Chapter 20 Surface Area and Volume of a Right Circular Cone at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes
• NCERT Exemplar Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume

RD Sharma Solutions for Class 9 Maths Chapter 21 – Surface Area and Volume of a Sphere

In this chapter, students learn about a new geometrical figure called a sphere. It is mainly a three-dimensional object which has volume and surface area. Sphere, the section of a sphere by a plane, surface area and volume are the main concepts discussed in brief under this chapter.

• Surface area of a sphere = 4πr²
• Surface area of the hemisphere = 2πr²
• Surface area of solid hemisphere = 3πr²
• Volume of a sphere = 4/3πr³ Cubic Units

Students can access the free PDF of exercise-wise solutions from the links provided below.

Also, access the following resources for Class 9 Chapter 21 Surface Area and Volume of a Sphere at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes
• NCERT Exemplar Solutions for Class 9 Maths Chapter 13 – Surface Areas and Volume

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

The tabular representation of statistical data is necessary in order to make it easier for the observer to understand. In this chapter, students understand the steps to be followed to represent the data in tabular form. Statistics, statistical data, presentation of data, frequency distribution, construction of frequency distribution table and cumulative frequency distribution.

• Statistics: It is the study of the collection, analysis, interpretation, presentation and organisation of data.
• Presentation of Data: After the collection of data, it can be arranged in tabular form to observe their features and study them. It is known as the presentation of data.
• Array: When the raw data is arranged in an ascending or descending order of magnitude, it is known as an array or arrayed data.
• Frequency of the observation: The number of times an observation occurs in the given data is known as the frequency of the observation.

To score well in Class 9 final exam, students can download the solutions from the PDF links given below.

Also, access the following resources for Class 9 Chapter 22 Tabular Representation of Statistical Data at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 14 Statistics
• NCERT Exemplar Class 9 Maths Solutions for Chapter 14 – Statistics and Probability

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

Chapter 23 of the RD Sharma textbook has topics like graphical representation of data, bar graph, histogram and method of constructing a frequency polygon. The solutions are prepared as per the latest CBSE syllabus and exam pattern. Students can download the solutions and refer to them to solve the exercise-wise problems.

• Graphical Representation: It is the way of analysing the given numerical data. It shows the relation between ideas, data, concepts and information in a diagram.
• Bar Graph: The pictorial representation of data, in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data, is the bar graph. They are also called bar charts.
• Histogram: It is a graphical representation of a grouped frequency distribution with continuous classes. It is an area diagram that can be defined as a set of rectangles having bases along with the intervals between class boundaries and with areas proportional to frequencies in the corresponding classes.
• Frequency Polygon: A frequency polygon is identical to a histogram used to compare sets of data or to display a cumulative frequency distribution. It makes use of a line graph to represent quantitative data.

Exercise-wise solutions PDF of Chapter 23 links are provided below for free download.

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

Chapter 24 of the RD Sharma textbook explains important and basic concepts like measures of central tendency, the arithmetic mean of grouped data and the median. The concepts are explained by expert faculty at BYJU’S in simple language, which matches the understanding capacity of students.

• Central Tendency: It is the statistical measure that represents the single value of the entire distribution or a dataset. It aims to provide a correct description of the entire data in the distribution.
• Measure of Central Tendency: The central tendency of the dataset can be determined using the three important measures, namely mean, median, and mode.
• Mean: It is equal to the sum of all the values in the collection of data divided by the total number of values.

If we have n values in a set of data, i.e., x₁, x₂, x₃, ….. x_n, then the mean is

It can also be denoted as

• Median: If the data collection is arranged in ascending or descending order, the following method is applied:

If the number of values is odd, then the median is

If the number of values is even, then the median is

• Mode: The most frequent number which occurs in the data set is called the mode.

The solution links to the exercises of Chapter 24 are provided below in PDF format.

RD Sharma Solutions for Class 9 Maths Chapter 25 – Probability

Probability is an important chapter in Class 9, as the methods used here are discussed in higher classes also. The problems of this chapter are solved by subject-matter experts having vast experience in their respective fields. The concepts which are explained here are some of the terms related to probability and operations. The students can get answers to questions in the exercises of Chapter 25 by clicking on the chapter link.

• Probability: It is the measure of the likelihood of an event occurring. Many events cannot be predicted with total certainty.
• Experimental or empirical approach to probability: Experimental or empirical probability is the probability of an event based on the results of an actual experiment conducted several times.
• Trial: An experiment is repeated a fixed number of times, and each repetition is known as a trial.
• Compound Events: Contrary to the simple event, if any event consists of more than one single point of the sample space, then such an event is called a compound event.

Also, access the following resources for Class 9 Chapter 25 Probability at BYJU’S.

• NCERT Solutions for Class 9 Maths Chapter 15 Probability
• NCERT Exemplar Class 9 Maths Solutions for Chapter 14 – Statistics And Probability

Regular practice of the chapter-wise problems in the RD Sharma textbook is important to help students score well in the Class 9 exam. The faculty having vast knowledge about the concepts, have prepared chapter-wise RD Sharma Solutions for Class 9, which can be used to solve problems of higher difficulty. The illustrative examples before the exercise-wise problems in each chapter help students boost their problem-solving and time-management skills.

Benefits of RD Sharma Solutions for Class 9 Maths

• Free download is provided to the students for both chapter-wise and exercise-wise problems.
• Pictorial representation helps students to grasp the concepts in a shorter duration.
• The solutions designed by teachers are accurate and according to the current CBSE board.
• Students can self analyse their areas of weaknesses and work on them to score well in the exam.