RD Sharma Class 10 Solutions 2022 For Term 1 & Term 2 | Free PDF

RD Sharma Class 10 Solutions 2022 For Term 1 & Term 2: The RD Sharma Class 10 pdf Maths book is intended for students enrolled in the Central Board of Secondary Education (CBSE). NCERT Rules were followed in the preparation of RD Sharma Solutions.

RD Sharma Class 10 Solutions solved by KopyKitab’s CBSE Class 10 Maths experts following up the (NCERT) CBSE guidelines. In Class 10 Maths, students can easily improve their scores.

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Chapter-Wise Class 10 RD Sharma Solutions 2022 For Term 1 & Term 2

• RD Sharma Class 10 Solutions Chapter 1 Real Numbers
• RD Sharma Class 10 Solutions Chapter 2 Polynomials
• RD Sharma Class 10 Solutions Chapter 3 Pair of Linear Equations in Two Variables
• RD Sharma Class 10 Solutions Chapter 4 Triangles
• RD Sharma Class 10 Solutions Chapter 5 Trigonometric Ratios
• RD Sharma Class 10 Solutions Chapter 6 Trigonometric Identities
• RD Sharma Class 10 Solutions Chapter 7 Statistics
• RD Sharma Class 10 Solutions Chapter 8 Quadratic Equations
• RD Sharma Class 10 Solutions Chapter 9 Arithmetic Progressions
• RD Sharma Class 10 Solutions Chapter 10 Circles
• RD Sharma Class 10 Solutions Chapter 11 Constructions
• RD Sharma Class 10 Solutions Chapter 12 Some Applications of Trigonometry
• RD Sharma Class 10 Solutions Chapter 13 Probability
• RD Sharma Class 10 Solutions Chapter 14 Co-ordinate Geometry
• RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles
• RD Sharma Class 10 Solutions Chapter 16 Surface Areas and Volumes

Detailed Chapter-wise CBSE Class 10 RD Sharma Solutions 2022 For Term 1 & Term 2

Chapter 1 – Real Numbers

Important Topics covered in Real Numbers RD Sharma Solutions are Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, Fundamental Theorem of Arithmetic Motivating Through Examples, Introduction of Real Numbers, Proofs of Irrationality, Real Numbers Examples and Solutions, Revisiting Irrational Numbers, Revisiting Rational Numbers and Their Decimal Expansions.

• Euclid’s division lemma: If we have two positive integers a and b, there should be whole numbers q and r that satisfy the equation – a = bq + r, where 0 ≤ r < b where a is the dividend and b is the divisor.
• Euclid’s division algorithm: It is the technique used to determine the HCF of two given positive integers.
• Fundamental Theorem of Arithmetic: Every composite number can be factorized as a product of primes, and this factorization is unique, apart from the order in which the prime factors occur.

Chapter 2 – Polynomials

Major Topics covered in RD Sharma Polynomials Solutions are Division Algorithm for Polynomials, Geometrical Meaning of the Zeroes of a Polynomial, Introduction to Polynomials, Polynomials Examples and Solutions, Relationship Between Zeroes and Coefficients of a Polynomial.

RD Sharma Class 10 Solutions Polynomials | Important Concepts

• Polynomial – Let x be a variable, n be a positive integer and a₁, a₂, a₃ ……… a_n be constants (real numbers), then f (x) = a_n xⁿ + a_n-1 x^n-1 + a_n-2 x^n-2 + ……… + a₁x+ a₀ is called a polynomial in variable x.
• a_n xⁿ, a_n-1 x^n-1, a_n-2 x^n-2 ……… a₁x, a₀ are known as the terms of the polynomial, and a_n, a_n-1 …….a₁, a₀ are their coefficients.
• Degree of Polynomial – The exponent of the highest degree term in a polynomial is known as its degree.
• Constant Polynomial – A polynomial of degree zero (0) is called a constant polynomial.
• Linear Polynomial – A polynomial of degree 1 is called the linear polynomial.
• A linear polynomial may be a monomial or a binomial having one term or two terms respectively e.g., ax or ax + b.
• Zero of a Polynomial: For any polynomial p(x), if p(k) = 0, k is called a zero of polynomial p(x).
• A number of zeroes/roots of a polynomial p(x) is always equal to or less than the degree of polynomial p(x).
• If a polynomial p(x) is divided by (x — a), then remainder will be p(a) = r.
• If a polynomial p(x) is divisible by (x — a), then p(a) = O.

Chapter 3 – Pair of Linear Equations In Two Variables

• Linear equation: An equation of the form ax + by + c = O, where a, b, c all are real numbers and a ≠ 0, b ≠ 0, is known as a linear equation in two variables x and y. Its graph is always a straight line.
• System of Simultaneous Linear Equations: A pair of linear equations in two variables a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂= 0 is said to form a system of simultaneous linear equations, where a₁, a₂, b₁, b₂, c₁, c₂ are real numbers.
• A pair of values of x and y which satisfy each of the equations is called a solution or root of the system.
• If the system has at least one solution, it is called consistent and if the system has no solution, it is called inconsistent.
• A pair of linear equations in two variables can be solved by the :
  Graphical method— To solve a pair of linear equations in two variables by Graphical method, we first draw the lines represented by them.
• If the pair of lines intersect at a point, then we say that the pair is consistent and the coordinates of the point provide us the unique solution.
• If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.
• If the pair of lines are coincident, then it has infinitely many solutions-each point on the line being of solution. In this case, we say that the pair of lines equations is consistent with infinitely many solutions.
• Algebraic method—To solve a pair of linear equations in two variables algebraically, we have (i) Substitution method (ii) Elimination method (iii) Cross-multiplication method.

Chapter 4 – Triangles

Some Topics covered in Pair of Linear Equations RD Sharma solutions for Maths are Algebraic Conditions for Number of Solutions, Consistency of Pair of Linear Equations, Cramer’S Rule, Cross – Multiplication Method, Determinant of Order Two, Elimination Method, Equations Reducible to a Pair of Linear Equations in Two Variables.

• The similarity of geometric figures: Two geometric figures are said to be similar if they have the same sides, angles, or mirror of the figures.
• Similar triangles: If the two pairs of corresponding angles in two triangles are congruent, then both the triangles are said to be similar.
• Proportionality: The equality between two ratios i.e., a/b = c/d where a and b are in the same proportion as c and d.

Chapter 5 – RD Sharma Class 10 Solutions Trigonometric Ratios 

• Trigometric Ratios: In the right angled triangle AMP, Base = AM = x, Perpendicular = PM = y, and Hypotenuse = AP = r.
• It should be noted that sin θ is an abbreviation for “sine of angle θ”, it is not the product of sin and θ. Similar is the case for other trigonometric ratios.
• The trigonometric ratios are defined for an acute angle θ.
• The trigonometric ratios depend only on the value of angle θ.

Chapter 6 – Trigonometric Identities

Important Topics covered in Quadratic Equations are Formula for Solving a Quadratic Equation, Nature of Roots, Quadratic Equations, Quadratic Equations Examples and Solutions, Relation Between Roots of the Equation and Coefficient of the Terms in the Equation Equations Reducible to Quadratic Form, Relationship Between Discriminant and Nature of Roots.

RD Sharma Class 10 Solutions Trigonometric Identities | Important Definition

• Trigonometrical Identity: An equation, involving trigonometric ratios of an angle and which is true for all values of the angle, is called a trigonometrical identity.

Chapter 7 – Statistics

Topics covered in Statistics are Applications of Ogives in Determination of Median, Frequency Polygon, Graphical Representation of Cumulative Frequency Distribution, Graphical Representation of Histograms, Histograms, Inclusive and Exclusive Type of Tables, Introduction of Statistics, Introduction to Normal Distribution, Mean of Grouped Data.

• Statistics: The collection, organization, analysis, interpretation and presentation of numerical data is called statistics.
• Mean: It is done by adding all the numbers in the data set and then dividing by the number of values.
• Median: The middle value when a data set is ordered from least to greatest.
• Mode: The number which occurs most frequently in a data set.
• Frequency distribution: The overview of all different values in some variables and the number of times they occur.

8 – Quadratic Equations 

The exercise problems in this chapter mostly include various methods for determining their zeros or roots, as well as certain applications of quadratic equations in real-world situations. Students’ exam preparation will be aided by the availability of solutions in PDF format. 

• Quadratic equations: The quadratic polynomials when equated to zero are the quadratic equations.
• Standard form of quadratic equation: ax² + bx + c = 0.

Chapter 9 – Arithmetic Progressions

Topics covered in Arithmetic Progression are Application in Solving Daily Life Problems, Arithmetic Mean, Arithmetic Progression, Arithmetic Progression Examples, and Solutions, Arithmetic Progressions Examples and Solutions, Derivation of the nth Term.

RD Sharma Class 10 Solutions Arithmetic Progression

• Sequence: A sequence is an arrangement of terms, which are formed according to some definite patterns. From a definite pattern, we can find the general term (in terms of n).
• Terms: The elements in a sequence are called terms. A sequence is generally written as t_n, where t_n is the n^th term and t₁, t₂, … are first, second,… terms of the sequence.
• Finite Sequence: A sequence containing a finite number of terms is called a finite sequence.
• Infinite Sequence: A sequence containing an infinite number of terms is called an infinite sequence.
• Arithmetic Progression (AP): Arithmetic progression is a sequence in which each term, except the first term, differs from its preceding term by a fixed number (constant). The constant or fixed number is called the common difference of the arithmetic progression.
• Generally, an arithmetic progression with first term a and common difference d is represented as a, a + d, a + 2d, a + 3d, ….
• To find n^th Term of an AP: The nth term of an AP with first term a and common difference d is given by t_n = a + (n – 1) d.

Chapter 10 – Circles

Topics covered in Circles are Angle Subtended by the Arc to the Centre, Angle Subtended by the Arc to the Point on the Circle, Circles Examples and Solutions, Circles passing through one, two, three points, Converse of Cyclic Quadrilateral Theorem, Converse of Tangent Theorem, Converse of Theorem of the Angle Between Tangent and Secant, Corollaries of Inscribed Angle Theorem, Corollary of Cyclic Quadrilateral Theorem, Cyclic Properties.

Cyclic Quadrilateral, Inscribed Angle, Inscribed Angle Theorem, Intercepted Arc, Introduction to an Arc, Introduction to Circles, Number of Tangents from a Point on a Circle, Number of Tangents from a Point to a Circle, Property of Sum of Measures of Arcs, Tangent Properties – If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers, Tangents and Its Properties, Tangent – Secant Theorem.

Chapter 11 – Constructions

Topics covered in Constructions are Basic Geometric Constructions, Construction of Tangents to a Circle, Construction of Tangent to the Circle from the Point on the Circle, Construction of Tangent Without Using Centre, Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given, Constructions Examples and Solutions, Division of a Line Segment, To Construct Tangents to a Circle from a Point Outside the Circle.

• Constructions: Drawing lines and shapes using various geometrical instruments.
• Angle: The amount of turn between two lines from their common point.
• Length: The size of a line segment is called the length.

Chapter 12 – Some Applications of Trigonometry

Major Topics covered in RD Sharma Maths Solutions for Trigonometry are Angles in Standard Position, Application of Trigonometry, Heights and Distances, Trigonometric Identities, Trigonometric Ratios in Terms of Coordinates of Point, Trigonometric Ratios of Complementary Angles, Trigonometry Ratio of Zero Degree and Negative Angles.

• Trigonometry: It is a branch of Mathematics that deals with the relationship between angles and side lengths of triangles.
• Height of a triangle: It is the length of a perpendicular line segment that originates on a side and intersects the opposite angle.

Chapter 13 – Probability

Topics covered in Probability are Addition Theorem, Concept Or Properties of Probability, Equally Likely Outcomes, Introduction to Probability, Probability – A Theoretical Approach, Probability Examples, and Solutions, Probability of an Event, Random Experiments, Sample Space, Simple Problems on Single Events, Type of Event – Complementary, Type of Event – Elementry, Type of Event – Exclusive, Type of Event – Exhaustive.

• Probability: The numerical description of how likely an event will occur.
• Event: It is an outcome or defined collection of outcomes of a random experiment.

Chapter 14 – Coordinate Geometry

Topics covered in Co-Ordinate Geometry are Area of a Triangle, Centroid Formula, Concepts of Coordinate Geometry, Coordinate Geometry Examples and Solutions, Co-ordinates of the Midpoint of a Segment, Distance Formula, Division of a Line Segment, General Equation of a Line, Graphs of Linear Equations, Intercepts Made by a Line, Section Formula, Slope of a Line, Standard Forms of Equation of a Line.

• Coordinate Geometry: Study of geometry using coordinate systems.
• Distance between two points: The distance between two points in a geometric shape can be determined by using the distance formula which is an application of the Pythagoras theorem.
• Section formula: It is used to determine the ratio in which a line segment is divided by a point externally or internally.

Chapter 15 – Areas Related To Circles

Topics covered in Areas Related to Circles are Angle Subtended by the Arc to the Centre, Angle Subtended by the Arc to the Point on the Circle, Areas of Combinations of Plane Figures, Areas of Sector and Segment of a Circle, Areas Related to Circles Examples and Solutions, Circles passing through one, two, three points, Converse of Cyclic Quadrilateral Theorem, Converse of Tangent Theorem, Converse of Theorem of the Angle Between Tangent and Secant.

• Area of circular regions: The area of a circle is pi times the radius squared.
• Sector: A part of the circle which is made of an arc of the circle along with its two radii.
• Segment: It is the region bounded by the arc and the intercepted arc of the circle. 

Chapter 16 – Surface Area and Volume

Topics covered in Surface Areas and Volumes are Conversion of Solid from One Shape to Another, Frustum of a Cone, Introduction of Surface Areas and Volumes, Surface Area of a Combination of Solids, Surface Areas and Volumes Examples and Solutions, Volume of a Combination of Solids.

• Surface area: The region occupied by the surface of the object.
• Volume: The amount of space that is available in the object.

Why RD Sharma Class 10 Solutions 2022 For Term 1 & Term 2?

• Easy to understand
• Available in PDF format which can be downloaded and easily accessed
• The effectiveness of the explanation for each and every topic in RD Sharma Class 10 Solutions helps the students in improving their speed as well as accuracy.
• Helps in the preparation of many Competitive exams like NTSE and Olympiads.
• Helps students to ingrain a habit of regular practicing. 
• A unique presentation of the topics.
• RD Sharma Class 10 Solutions is enough to score the best marks in the Class 10 Board Exam.

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