Mathematics Class X

Real Numbers
12 Topics | 4 Quizzes
What are Real Numbers?
Integers
Rational Numbers
Irrational Numbers
Natural Numbers
Whole Numbers
Integers
Euclid’s Division Lemma
Algorithm
Euclid’s Division Algorithm
Application of lemma
Fundamental theorem of Arithmetic
Concept Checkers-Real Numbers-Class X
Practice Questions-Real Numbers-Class X
Practice Questions 2-Real Numbers-Class X
Olympiad Questions-Real Numbers-Class X
Polynomials
13 Topics | 4 Quizzes
Polynomials
Degree of a Polynomial
Types of polynomials based on the number of terms
Types of Polynomials based on Degree
Value of Polynomial
Zero of a Polynomial
Graph of a Linear Polynomial
Graph of Quadratic Polynomial
Factorisation of Polynomials
Splitting the middle term:
Relationship between Zeroes and Coefficients of a Polynomial
Division Algorithm
Algebraic Identities
Practice Questions 2 – Polynomials – Class X
Olympiad Questions – Polynomials – Class X
Concept Checkers – Polynomials – Class X
Practice Questions – Polynomials – Class X
Pair of Linear Equations in Two Variables
4 Topics | 4 Quizzes
Linear Equations
Pair of Linear Equations
Graphical method of solution of a pair of Linear Equations
Algebraic Methods of Solving a Pair of Linear Equations
Practice Questions 2 – Pair of Linear Equations in Two Variables – Class X
Olympiad Questions – Pair of Linear Equations in Two Variables – Class X
Concept Checkers – Pair of Linear Equations in Two variables – Class X
Practice Questions – Pair of Linear Equations in Two Variables – Class X
Quadratic Equations
7 Topics | 4 Quizzes
Quadratic Polynomial
Quadratic Equation
Standard form of Quadratic Equation
Types of Quadratic Equations
Roots of a Quadratic Equation
Methods to solve the Quadratic Equations
Nature of Roots
Practice Questions 2 – Quadratic Equations – Class X
Olympiad Questions – Quadratic Equations – Class X
Concept Checkers – Quadratic Equations – Class X
Concept Checkers – Quadratic Equation – Class X
Arithmetic Progressions
5 Topics | 4 Quizzes
Arithmetic Progressions
Finite or Infinite Arithmetic Progressions
The general form of an AP
Arithmetic Series
Sum of first n terms of an Arithmetic series
Olympiad Questions-Arithmetic Progression-ClassX
Practice Questions 2-Arithmetic Progression-ClassX
Concept Checkers – Arithmetic Progressions – Class X
Practice Questions – Arithmetic Progressions – Class X
Triangles
8 Topics | 4 Quizzes
Triangle
Based on the length
Based on the angle
Centers of the Triangle
Similarity Criteria of Triangles
Basic Proportionality Theorem (Thales Theorem)
Converse of Basic Proportionality Theorem
Pythagoras Theorem (Baudhayan Theorem)
Practice Questions 2-Triangles-ClassX
Olympiad Questions-Triangles-ClassX
Concept Checkers – Triangles – Class X
Practice Questions – Triangles – Class X
Coordinate Geometry
9 Topics | 4 Quizzes
Cartesian coordinate system
Equation of a Straight Line
Distance formula
Section formula
Mid-point formula
Centroid of a Triangle
Area of a triangle given its vertices
Collinearity Condition
Using section formula
Concept Checkers – Coordinate Geometry – Class X
Practice Questions – Coordinate Geometry – Class X
Practice Questions 2-Coordinate Geometry-ClassX
Olympiad Questions-Coordinate Geometry-ClassX
Introduction to Trigonometry
7 Topics | 4 Quizzes
Trigonometry
Trigonometric Ratios
Relation between Trigonometric Ratios
Trigonometric Ratios of Some Specific Angles
Trigonometric Ratios of Complementary Angles
Range of Trigonometric Ratios from 0 to 90 degrees
Trigonometric Identities
Practice Questions 2-Introduction to Trigonometry-Class X
Olympiad Questions-Introduction to Trigonometry-Class X
Concept Checkers -Trigonometry – Class X
Practice Questions -Trigonometry – Class X
Some Applications of Trigonometry
5 Topics | 2 Quizzes
APPLICATION OF TRIGONOMETRY
Line of Sight
Horizontal Line
Angle of Elevation
Angle of Depression
Practice Questions-Some Applications of Trigonometry-Class X
Olympiad Questions-Some Applications of Trigonometry-Class X
Circles
5 Topics | 2 Quizzes
Introduction to Circles
Circle and line in a plane
Tangent to a Circle
Circle Theorems
Length of a tangent
Olympiad Questions-Circles-Class X
Practice Questions-Circles-Class X
Constructions
3 Topics | 2 Quizzes
Introduction
Division of a Line Segment
Construction of a Triangle similar to a given Triangle as per given Scale
Concept Checkers – Construction – Class X
Practice Questions-Construction-Class X
Areas Related to Circles
5 Topics | 3 Quizzes
Areas related to Circle
Area of a Sector of a Circle
Perimeter and Area of the Semi-circle
Areas of Segments of the Circle
Areas of Combinations of Plane Figures
Concept Checkers-Areas Related to Circles-Class X
Practice Questions-Areas Related to Circles-Class X
Olympiad Questions-Areas Related to Circles-Class X
Surface Areas and Volumes
4 Topics | 2 Quizzes
Introduction
Volume of a combination of solids
Conversion of Solid from One Shape to Another
Frustum of a Cone
Olympiad Questions-Surface area and volume-Class X
Practice Questions-Surface area and volumes-Class X
Statistics
8 Topics | 2 Quizzes
Introduction
Types of Data
Frequency
Mean of Grouped Data (Without Class-Interval)
Mean of Grouped Data (With Class-Interval)
Mode of Grouped Data
Median of Grouped Data
Graphical Representation of Cumulative Frequency Distribution
Practice Questions-Statistics-Class X
Olympiad Questions-Statistics-Class X
Probability
4 Topics | 1 Quiz
Introduction
Sum of Probabilities
Sure or Certain Event
Complementary Events
Olympiad Questions-Probability-Class X
Mock Test 1-Class X
Mock Test 2 – Class X
Mock Test 3 – Class X
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Euclid’s Division Lemma

Mathematics Class X Real Numbers Euclid’s Division Lemma

It is basically the restatement of the usual division system. The formal statement for this is-

For each pair of given positive integers a and b, there exist unique whole numbers q and r which satisfies the relation

 a = bq + r, 0 ≤ r < b, where q and r can also be Zero.

Where ‘a’ is a dividend, ‘b’ is divisor, ‘q’ is quotient and ‘r’ is remainder.

∴ Dividend = (Divisor \times Quotient) + Remainder

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