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REAL NUMBERS
Introduction
1.0 What are Real Numbers
QUIZ-What are Real Numbers?
1.1 What are the Different Categories of numbers that come under Real Numbers
QUIZ-What are the Different Categories of numbers that come under Real Numbers?
Euclid’s Division Lemma
1.2 Euclids Division Lemma
QUIZ-Euclid’s Division Lemma
1.3 Euclids Division Algorithm
QUIZ-Euclid’s Division Algorithm
The Fundamental Theorem of Arithmetic
1.4 What is the Factor Tree Approach to Find the Prime Factors of a Number
QUIZ-What is the Factor Tree Approach to Find the Prime Factors of a Number?
1.5 Factor Tree Approach - Examples
QUIZ-Factor Tree Approach - Examples
1.6 How do we Find the HCF and LCM of 2 numbers Part 1
QUIZ-How do we Find the HCF and LCM of 2 numbers? Part 1
1.7 How do we Find the HCF and LCM of 2 numbers Part 2
QUIZ-How do we Find the HCF and LCM of 2 numbers? Part 2
1.8 A quick way to Find the HCF and LCM of 2 numbers
QUIZ-A quick way to Find the HCF and LCM of 2 numbers
1.9 How do we Find the HCF and LCM of 3 numbers
QUIZ-How do we Find the HCF and LCM of 3 numbers?
1.10 Fundamental Theorem of Arithmetic
QUIZ-Fundamental Theorem of Arithmetic
Revisiting Irrational Numbers
1.11 What are Irrational Numbers and Why do we need them
QUIZ-What are Irrational Numbers and Why do we need them?
1.12 If a prime number 'p' divides a square number 'a', then will it even divide 'a'
QUIZ-If a prime number 'p' divides a square number 'a', then will it even divide 'a'
1.13 How do we Prove the Existence of Irrational Numbers
QUIZ-How do we Prove the Existence of Irrational Numbers?
1.14 What are Irrational Numbers
QUIZ-What are Irrational Numbers?
Revisiting Rational Numbers and Their Decimal Expansions
1.15 What are Rational Numbers
QUIZ-What are Rational Numbers?
1.16 Fractions and Integers - Are they Rational Numbers
QUIZ-Fractions and Integers - Are they Rational Numbers?
1.17 What are Positive and Negative Rational Numbers
QUIZ-What are Positive and Negative Rational Numbers?
1.18 What is the Standard Form (Simplest Form) of a Rational Number
QUIZ-What is the Standard Form (Simplest Form) of a Rational Number?
1.19 Rational Numbers - Examples of Standard Form
QUIZ-Rational Numbers - Examples of Standard Form
1.20 How do we Convert a Decimal to a Fraction
QUIZ-How do we Convert a Decimal to a Fraction?
1.21 How do we Convert a Fraction to a Decimal Part 1
QUIZ-How do we Convert a Fraction to a Decimal? Part 1
1.22 How do we Convert a Fraction to a Decimal Part 2
QUIZ-How do we Convert a Fraction to a Decimal? Part 2
1.23 How do we Convert a Fraction to a Decimal Part 3
QUIZ-How do we Convert a Fraction to a Decimal? Part 3
1.24 How can we tell if a Rational Number is a Terminating or a Non Terminating Recurring Decimal
QUIZ-How can we tell if a Rational Number is a Terminating or a Non Terminating Recurring Decimal?
Practice Test
POLYNOMIALS
Introduction
What is a Polynomial
QUIZ-What is a Polynomial?
What is the Degree of a Polynomial?
QUIZ-What is the Degree of a Polynomial?
How do we Find the Value of a Polynomial
QUIZ-How do we Find the Value of a Polynomial?
Geometrical Meaning of the Zeroes of a Polynomial
Zeroes of a Linear Polynomial - Geometrical Meaning
QUIZ-Zeroes of a Linear Polynomial - Geometrical Meaning
Zeroes of a Quadratic Polynomial - Geometrical Meaning
QUIZ-Zeroes of a Quadratic Polynomial - Geometrical Meaning
Zeroes of a Cubic Polynomial - Geometrical Meaning
QUIZ-Zeroes of a Cubic Polynomial - Geometrical Meaning
Relationship between Zeroes and Coefficients of a Polynomial
What is the Zero of a Polynomial
QUIZ-What is the Zero of a Polynomial?
What is the General Form of the Zero of a First Degree Polynomial
QUIZ-What is the General Form of the Zero of a First Degree Polynomial?
How do we Find the Zeroes of a Quadratic Polynomial
QUIZ-How do we Find the Zeroes of a Quadratic Polynomial?
How do we Find the Sum and Product of the Zeroes of a Quadratic Polynomial
QUIZ-How do we Find the Sum and Product of the Zeroes of a Quadratic Polynomial?
Finding Zeroes - Example
QUIZ-Finding Zeroes - Example
Relationship between zeroes and coefficients of Cubic polynomials
QUIZ-Relationship between zeroes and coefficients of Cubic polynomials
Division Algorithm for Polynomials
How do we Divide a Polynomial by a Binomial
Pair of Linear Equations in Two Variables
Pair of Linear Equations in Two Variables
Linear Equations in 2 Variables - Review
QUIZ-Linear Equations in 2 Variables - Review
Linear Equations in 2 Variables - Pairs
QUIZ-Linear Equations in 2 Variables - Pairs
Graphical Method of Solution of a Pair of Linear Equations
Linear Equations in 2 Variables - Graphs 01
QUIZ-Linear Equations in 2 Variables – Graphs 01
Linear Equations in 2 Variables - Graphs 02
QUIZ-Linear Equations in 2 Variables – Graphs 02
Linear Equations in 2 Variables - Graphs 03
QUIZ-Linear Equations in 2 Variables – Graphs 03
Linear Equations in 2 Variables - Graphs 04
QUIZ-Linear Equations in 2 Variables – Graphs 04
Algebraic Methods of Solving a Pair of Linear Equations
Linear Equations in 2 Variables - Algebraic Methods
QUIZ-Linear Equations in 2 Variables – Algebraic Methods
How do we use 'Elimination by Substitution' to Solve Linear Equations in Two Variables
QUIZ-How do we use 'Elimination by Substitution' to Solve Linear Equations in Two Variables?
How do we Add Two Linear Equations to Eliminate One Variable
QUIZ-How do we Add Two Linear Equations to Eliminate One Variable?
Cross - Multiplication Method
Linear Equations in 2 Variables - Cross Multiplication Method
QUIZ-Linear Equations in 2 Variables – Cross Multiplication Method
Equations Reducible to a Pair of Linear Equations in Two Variables
Linear Equations in 2 Variables - Non-Linear equations
QUIZ-Linear Equations in 2 Variables – Non-Linear equations?
How do we Modify Two Linear Equations to Eliminate One Variable
QUIZ-How do we Modify Two Linear Equations to Eliminate One Variable?
How do we Modify just One Linear Equation to Eliminate One Variable
QUIZ-How do we Modify just One Linear Equation to Eliminate One Variable?
Word Problems
Linear Equations in 2 Variables - Word Problems
QUIZ-Linear Equations in 2 Variables – Word Problems
Linear Equations in 2 Variables - Word Problems 2
Quadratic Equations
Quadratic Equations
Quadratic Equations - Basics
QUIZ-Quadratic Equations - Basics
Representing Quadratic Equations
Representing Quadratic Equations
Quadratic Equation or not
Quadratic Equation or not
Solution of a Quadratic Equation by Factorisation
Solution of a Quadratic Equation
Solution of a Quadratic Equation
Solution of a Quadratic Equation - Part 1
Solution of a Quadratic Equation - Part 1
Solution of a Quadratic Equation by Completing the Square
Completing the Square Method - Part 1
Completing the Square Method - Part 1
Completing the Square Method - Part 2
Completing the Square Method - Part 2
Completing the Square Method - Part 3
Completing the Square Method - Part 3
Completing the Square Method - Part 4
Completing the Square Method - Part 4
Completing the Square Method - Part 5
Completing the Square Method - Part 5
Quadratic Formula
Quadratic Formula
Quadratic Formula - Examples (Part 1)
Quadratic Formula - Examples (Part 1)
Quadratic Formula - Examples (Part 2)
Quadratic Formula - Examples (Part 2)
Nature of Roots
Nature of Roots
Nature of Roots
Nature of Roots - Examples
Nature of Roots - Examples
Arithmetic Progression
Arithmetic Progressions
What are Terms
QUIZ-What are Terms?
What is a Sequence
QUIZ-What is a Sequence?
Examples of Sequences
Examples of Sequences
nth Term of an AP
Arithmetic Progression and Geometric Progression
Arithmetic Progression and Geometric Progression
Sequence - Examples (Part 1)
Sequence - Examples (Part 1)
Sequence - Examples (Part 2)
Sequence - Examples (Part 2)
Series - Basics
Series - Basics
Triangles
Similar Figures
What are Similar Figures
QUIZ-What are Similar Figures?
When are Two Triangles Similar
QUIZ-When are Two Triangles Similar?
Similarity of Triangles
Basic proportionality theorem
QUIZ-Basic proportionality theorem
Converse of Basic proportionality theorem
QUIZ-Converse of Basic proportionality theorem
Criteria for Similarity of Triangles
What is the AAA Condition for Similarity of Triangles
QUIZ-What is the AAA Condition for Similarity of Triangles?
THALES THEOREM
QUIZ-THALES THEOREM
What is the AA Condition for Similarity of Triangles
QUIZ-What is the AA Condition for Similarity of Triangles?
What is the SSS Condition for Similarity of Triangles
QUIZ-What is the SSS Condition for Similarity of Triangles?
SSS similarity criterion for two triangles
QUIZ-SSS similarity criterion for two triangles
What is the Converse of the SSS Condition for Similarity
QUIZ-What is the Converse of the SSS Condition for Similarity?
What is the SAS Condition for Congruence
QUIZ-What is the SAS Condition for Congruence?
SAS similarity criterion for two triangles
QUIZ-SAS similarity criterion for two triangles
Areas of Similar Triangles
Similarity in Triangles
QUIZ-Similarity in Triangles
Areas of Similar triangles
QUIZ-Areas of Similar triangles
Pythagoras Theorem
How do we Derive the Pythagoras Theorem Part 1
QUIZ-How do we Derive the Pythagoras Theorem? Part 1
How do we Derive the Pythagoras Theorem Part 2
QUIZ-How do we Derive the Pythagoras Theorem? Part 2
How do we Derive the Pythagoras Theorem Part 3
QUIZ-How do we Derive the Pythagoras Theorem? Part 3
Similarity in a right-angled triangle
QUIZ-Similarity in a right-angled triangle
Pythagoras theorem
QUIZ-Pythagoras theorem
CONVERSE OF PYTHAGORAS THEOREM
QUIZ-CONVERSE OF PYTHAGORAS THEOREM
Coordinate Geometry
Distance Formula
How do we Find the Distance between Two Points on a Number Line
QUIZ-How do we Find the Distance between Two Points on a Number Line?
How do we Find the Distance between Two Points on the Same Axis
QUIZ-How do we Find the Distance between Two Points on the Same Axis?
How do we Find the Distance between Two Points which Form a Line Parallel to an Axis
QUIZ-How do we Find the Distance between Two Points which Form a Line Parallel to an Axis?
How do we Find the Distance between any Two Points on the XY plane
QUIZ-How do we Find the Distance between any Two Points on the XY plane?
What is the Distance Formula
QUIZ-What is the Distance Formula?
Distance between any Two Points - Example
QUIZ-Distance between any Two Points - Example
Section Formula
What is the Section Formula for Internal Division
QUIZ-What is the Section Formula for Internal Division?
How do we Prove the Section Formula for Internal Division
QUIZ-How do we Prove the Section Formula for Internal Division?
What is the Midpoint Formula
QUIZ-What is the Midpoint Formula?
Midpoint Formula - Example
QUIZ-Midpoint Formula - Example
What is the Section Formula for External Division
QUIZ-What is the Section Formula for External Division?
How do we Prove the Section Formula for External Division
QUIZ-How do we Prove the Section Formula for External Division?
Area of a Triangle
How do we Find the Area of a Triangle given the Coordinates of its Vertices
QUIZ-How do we Find the Area of a Triangle given the Coordinates of its Vertices?
Area of a Triangle given the Coordinates of its Vertices - Proof
QUIZ-Area of a Triangle given the Coordinates of its Vertices - Proof
What is Heron's Formula
QUIZ-What is Heron's Formula?
Heron's Formula - An Example
QUIZ-Heron's Formula - An Example
Introduction to Trigonometry
Introduction
What is Trigonometry
QUIZ-What is Trigonometry?
What is the Reference Angle
QUIZ-What is the Reference Angle?
Trigonometric Ratios
What is a Function Basics
QUIZ-What is a Function? Basics
What is the Sine Function
QUIZ-What is the Sine Function?
Which are the Three Functions in Trigonometry
QUIZ-Which are the Three Functions in Trigonometry?
What is the Unit Circle Part 1
QUIZ-What is the Unit Circle? Part 1
What is the Unit Circle Part 2
QUIZ-What is the Unit Circle? Part 2
Which are the Six Functions in Trigonometry
QUIZ-Which are the Six Functions in Trigonometry?
How do we Find the Value of all Functions Given the Value of Just One
QUIZ-How do we Find the Value of all Functions Given the Value of Just One?
Trigonometric Ratios of Some Specific Angles
30-60-90 Triangle in Trigonometry
QUIZ-30-60-90 Triangle in Trigonometry
What are the Values of the Trigonometric Functions for the 30 Degree Angle
QUIZ-What are the Values of the Trigonometric Functions for the 30 Degree Angle?
What are the Values of the Trigonometric Functions for the 60 Degrees Angle
QUIZ-What are the Values of the Trigonometric Functions for the 60 Degrees Angle?
45-45-90 Triangle in Trigonometry
QUIZ-45-45-90 Triangle in Trigonometry
What are the Values of the Trigonometric Functions for the 45 Degrees Angle
QUIZ-What are the Values of the Trigonometric Functions for the 45 Degrees Angle?
What are the Values of the Trigonometric Functions for the 0 and 90 Degree Angles
QUIZ-What are the Values of the Trigonometric Functions for the 0 and 90 Degree Angles?
Trigonometric Ratios of Complementary Angles
Complementary Angles - Part 1
QUIZ-Complementary Angles - Part 1
Complementary Angles - Part 2
QUIZ-Complementary Angles - Part 2
Trigonometric Identities
Which are the Different Identities in Trigonometry
QUIZ-Which are the Different Identities in Trigonometry?
What is the Super Hexagon
QUIZ-What is the Super Hexagon?
Applications of Trigonometry
Basics
Applications of Trigonometry - Basics
Applications of Trigonometry - Basics
Problems
Applications of Trigonometry - Problems Part 1
Applications of Trigonometry - Problems Part 1
Applications of Trigonometry - Problems Part 2
Applications of Trigonometry - Problems Part 2
Angle of Elevation and Angle of Depression
Angle of Elevation and Angle of Depression
Applications of Trigonometry - Problems Part 3
Applications of Trigonometry - Problems Part 3
Applications of Trigonometry - Problems Part 4
Applications of Trigonometry - Problems Part 4
Applications of Trigonometry - Problems Part 5
Applications of Trigonometry - Problems Part 5
Circles
Introduction
In how many ways can Circle and Lines lie on a Plane
In how many ways can Circle and Lines lie on a Plane
How many Circles can pass through One point, Two points, or Three points
How many Circles can pass through One point, Two points, or Three points
How do we prove that only one circle can pass through three non collinear points
How do we prove that only one circle can pass through three non collinear points
Tangent to a Circle
Construction of a Tangent to a Circle
Construction of a Tangent to a Circle
Tangent is perpendicular to the radius
Tangent is perpendicular to the radius
Number of Tangents from a Point on a Circle
Lengths of tangents from an external point to a circle are equal
Lengths of tangents from an external point to a circle are equal
Construction
Division of a Line Segment
Division of a Line Segment - Part 1
Division of a Line Segment - Part 1
Division of a Line Segment - Part 2
Division of a Line Segment - Part 2
Construction of a Similar Triangle - Part 1
Construction of a Similar Triangle - Part 1
Construction of a Similar Triangle - Part 2
Construction of a Similar Triangle - Part 2
Construction of Tangents to a Circle
Construction of a Tangent to a Circle
Construction of a Tangent to a Circle
Areas related to Circles
Introduction
What is the Circumference
QUIZ-What is the Circumference?
Perimeter and Area of a Circle — A Review
What is Pi
QUIZ-What is Pi?
What is the Area of a Circle Part 1
QUIZ-What is the Area of a Circle? Part 1
What is the Area of a Circle Part 2
QUIZ-What is the Area of a Circle? Part 2
Areas of Sector and Segment of a Circle
What are segments What are their types
QUIZ-What are segments? What are their types?
What is the angle of a Segment
QUIZ-What is the angle of a Segment?
What is the measure of the angle formed in a Semi Circle
QUIZ-What is the measure of the angle formed in a Semi Circle?
What are sectors What are their types
QUIZ-What are sectors? What are their types?
What is the area of a sector
QUIZ-What is the area of a sector?
How to find the area of segment of a circle
QUIZ-How to find the area of segment of a circle?
What is the length of an arc
QUIZ-What is the length of an arc?
Surface Area Volume
Introduction
Solid Shapes
Solid Shapes
Surface Area of a Combination of Solids
Finding Surface Areas - Part 1
Finding Surface Areas - Part 1
Finding Surface Areas - Part 2
Finding Surface Areas - Part 2
Surface Area of a Tent
Surface Area of a Tent
Volume of a Combination of Solids
Volume of Test tube
Volume of Test tube
Volume of a Pen stand
Volume of a Pen stand
Surface area and volume of a Gulab Jamun!
Surface area and volume of a Gulab Jamun!
Conversion of Solid from One Shape to Another
Conversion of one solid into another
Conversion of one solid into another
Frustum of a Cone
Frustum of a cone - Part 1
Frustum of a cone - Part 1
Frustum of a cone - Part 2
Frustum of a cone - Part 2
Examples on Frustum of a cone
Examples on Frustum of a cone
Statistics
Introduction
What are Mean, Median and Mode
What are Mean, Median and Mode
Mean of Grouped Data
What is the Arithmetic Mean
What is the Arithmetic Mean
How do we Find the Mean of Ungrouped Data
Mean using the Step Deviation Method - Part 1
Mean using the Step Deviation Method - Part 1
Mode of Grouped Data
What is Grouped Frequency Distribution Part 1
What is Grouped Frequency Distribution Part 1
What is Grouped Frequency Distribution Part 2
What is Grouped Frequency Distribution Part 2
How do we form Class Intervals
How do we form Class Intervals
What is the Continuous Form of Grouping
What is the Continuous Form of Grouping
Mode of Grouped data
modes of grouped data
Median of Grouped Data
How do we Find the Median
How do we Find the Median
What is Cumulative Frequency (Less than type)
What is Cumulative Frequency (Less than type)
What is Cumulative Frequency (More than type)
What is Cumulative Frequency (More than type)
Median of Grouped data
Median of Grouped data
Empirical relationship between the measure of central tendencies
Empirical relationship between the measure of central tendencies
Graphical Representation of Cumulative Frequency Distribution
Graphical representation of cumulative frequency distribution
Graphical representation of cumulative frequency distribution
Obtaining Median from Ogives
Obtaining Median from Ogives
Probability
Introduction
What is Probability
QUIZ-What is Probability?
Probability — A Theoretical Approach
What are Equally Likely Events (Tossing a Coin)
QUIZ-What are Equally Likely Events? (Tossing a Coin)
What are Equally Likely Events (Throwing a die)
QUIZ-What are Equally Likely Events? (Throwing a die)
When are two Events Not Equally Likely What are Impossible and Certain Events
QUIZ-When are two Events Not Equally Likely? What are Impossible and Certain Events?
What is the Probability Line
QUIZ-What is the Probability Line?
Sample Space, Sample Points, Events
QUIZ-Sample Space; Sample Points; Events
Mutually exclusive Events
What are Mutually Exclusive Events
QUIZ-What are Mutually Exclusive Events?
Mutually Exclusive Events - Example
QUIZ-Mutually Exclusive Events - Example
Coins and Dice Examples
What is the Probability of Getting a Sum of 11 When Two Dice are Rolled
QUIZ-What is the Probability of Getting a Sum of 11 When Two Dice are Rolled?
How many Possibilities Exist When Two Coins are Tossed Together
QUIZ-How many Possibilities Exist When Two Coins are Tossed Together?
How many Possibilities Exist When Two Dice are Thrown Together
QUIZ-How many Possibilities Exist When Two Dice are Thrown Together?
Two Coins are Tossed - Example
QUIZ-Two Coins are Tossed - Example
Two Dice are Thrown - Example 1
QUIZ-Two Dice are Thrown - Example 1
Two Dice are Thrown - Example 2
QUIZ-Two Dice are Thrown - Example 2
Which door would you pick
QUIZ-Which door would you pick?
Deck of cards and probability
QUIZ-Deck of cards and probability