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NUMBER SYSTEMS
Introduction
1.0 What are Rational Numbers
QUIZ-What are Rational Numbers?
Irrational Numbers
1.1 What are Irrational Numbers and Why do we need them
QUIZ-What are Irrational Numbers and Why do we need them?
1.2 How do we Prove the Existence of Irrational Numbers
QUIZ-How do we Prove the Existence of Irrational Numbers?
1.3 What are Irrational Numbers
QUIZ-What are Irrational Numbers?
1.4 How do we Plot Irrational Numbers on a Number Line
How do we Plot Irrational Numbers on a Number Line
1.5 How do we Plot Root 2 on a Number Line
How do we Plot Root 2 on a Number Line
1.6 How do we Plot Root 3 on a Number Line
How do we Plot Root 3 on a Number Line
1.7 How do we Plot Root 5 on a Number Line Part 1
How do we Plot Root 5 on a Number Line Part 1
1.8 How do we Plot Root 5 on a Number Line Part 2
How do we Plot Root 5 on a Number Line Part 2
1.9 How do we plot Root 6 and Root 7 on a Number Line
How do we plot Root 6 and Root 7 on a Number Line
Real Numbers and their Decimal Expansions
1.10 What are Real Numbers
1.11 What are the Different Categories of numbers that come under Real Numbers
1.12 Decimal Representation of Rational Numbers
1.13 What are Recurring Decimal Numbers
1.14 How can we tell if a Rational Number is a Terminating or a Non Terminating Recurring Decimal
1.15 How do we Write a Terminating Decimal in the form P by Q
1.16 How do we Write a Non Terminating Recurring Decimal in the form P by Q Part 1
1.17 How do we Write a Non Terminating Recurring Decimal in the form P by Q Part 2
1.18 How do we Write a Non Terminating Recurring Decimal in the form P by Q (Shortcut) Part 3
Operations on Real Numbers
1.19 Addition and Subtraction of Real Numbers Part 1
1.20 Addition and Subtraction of Real Numbers Part 2
1.21 Addition and Subtraction of Real Numbers Part 3
1.22 Multiplication and Division of Real Numbers (Order 2) Part 1
1.23 Multiplication and Division of Real Numbers (Order 2) Part 2
1.24 How do we Represent Root X on a Number Line Part 1
1.25 How do we Represent Root X on a Number Line Part 2
1.26 How do we Represent Root X on a Number Line Part 3
1.27 What is Rationalisation of the Denominator
1.28 What is a Rationalising Factor (Conjugate)
1.29 How do we Rationalise an Irrational Number (Two terms)
1.30 Writing Nth root of A in Exponential Form
1.31 Multiplication and Division of Real Numbers (Order greater than 2) Part 1
1.32 Multiplication and Division of Real Numbers (Order greater than 2) Part 2
Laws of Exponents for Real Numbers
1.33 What are Exponents
1.34 What are Fractional Exponents
POLYNOMIALS
Introduction
What is a Polynomial
Constant Polynomial and Zero Polynomial
Polynomials in One Variable
How do we know if an Expression is a Polynomial or Not
Polynomial or Not - Examples
What are the Different Forms of Polynomials
What is the Degree of a Polynomial
How do we Find the Value of a Polynomial
Zeroes of a Polynomial
What is the Zero of a Polynomial
What is the General Form of the Zero of a First Degree Polynomial
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
Finding Zeroes - Example
Remainder Theorem
What are Factors
What is Factorisation of Polynomials
How do we know if a Polynomial is a Factor of Another Polynomial Part 1
How do we know if a Polynomial is a Factor of Another Polynomial Part 2
How do we Divide a Polynomial by a Monomial (Review)
Remainder and Factor Theorem
Factorisation of Polynomials
How do we Factorise a Quadratic Polynomial Part 1
How do we Factorise a Quadratic Polynomial Part 2
Algebraic Identities
How do we Factorise Polynomials using Identities Part 1
How do we Factorise Polynomials using Identities Part 2
How do we Factorise Polynomials using Identities Part 3
Factorization using Identities
COORDINATE GEOMETRY
Introduction
How do we give a Point on a Plane an Identity
How do we give a Point on a Plane an Identity
What are the X and Y axes
What are the X and Y axes
Cartesian System
What is the Cartesian Coordinate System
What is the Cartesian Coordinate System
What is the Cartesian Plane
What is the Cartesian Plane
Plotting a Point in the Plane if its Coordinates are Given
What are Co-ordinates
What are Co-ordinates
What is a Graph Paper and how does it help us
What is a Graph Paper and how does it help us
LINEAR EQUATION IN TWO VARIABLES
Linear Equations
What are Linear Equations in Two Variables
What are Linear Equations in Two Variables
Linear Equations in Two variables - Example
What is a System of Linear Equations in Variables
Graph of a Linear Equation in Two Variables
What is the Equation of the X and Y axes
How do we draw Graphs of Equations
What are Linear Equations in Two Variables
How do we draw the Graph of a Linear Equation in Two Variables
How do we solve Two Linear Equations using Graphs
Equations of Lines Parallel to the x-axis and y-axis
What is the Equation of a Line Parallel to the X axis
What is the Equation of a Line Parallel to the Y axis
INTRODUCTION TO EUCLID'S GEOMETRY
Origin of Geometry
Origin of Geometry and Basic definitions - Part 1
Origin of Geometry and Basic definitions - Part 2
Euclid's Definitions
What is a Point
What are Rays, Lines and Line Segments
What is a Plane
What are the Different Kinds of Shapes and Figures
Euclid's Axioms
Euclid's Geometry - Axioms - Part 1
Euclid's Geometry - Axioms - Part 2
Euclid's Postulates
Euclid’s first four postulates
Equivalent Versions of Euclid’s Fifth Postulate
Important Theorem and Equivalent version of Euclid’s 5th postulate
Euclid’s fifth postulate & its Equivalent version
LINES AND ANGLES
Basic Terms and Definitions
What is a Line
How many Lines can be Drawn Passing through 1, 2 or 3 points
Intersecting Lines and Non-intersecting Lines
What are Intersecting Lines
What are Coplanar Points and Lines
In how many ways can Three Lines Intersect
Pairs of Angles
Which are the Different Types of Angles
Pairs of Angles
What are Adjacent Angles
Non-common arms of adjacent angles with the sum 180 degrees
What are Complementary Angles
What are Supplementary and Vertically Opposite Angles
Parallel Lines and a Transversal
What are the Different Angles Formed by a Transversal with Two Parallel Lines
What is the Alternate Angles Test
What is the Converse of the Alternate Angles Test
What is the Corresponding Angles Test and it's Converse
What is the Consecutive Interior Angles Test and it's Converse
Lines Parallel to the Same Line
Prove that if Two Lines are Parallel to a Line then they are also Parallel to Each Other
Perpendicular Transversals
Angle Sum Property of a Triangle
What is the Sum of the Angles of a Triangle
How does the Sum of Angles of a Triangle measure 180 degrees
What is the Relation of an Exterior Angle of a Triangle with its Interior Angles
Exterior Angles of a Triangle - Example
TRIANGLES
Congruence of Triangles
What are Congruent Figures
What are Congruent Figures
When are Two Triangles Congruent
When are Two Triangles Congruent
Correspondence between Vertices of Congruent Triangles
Correspondence between Sides and Angles of Congruent Triangles
Criteria for Congruence of Triangles
What is the SAS Condition for Congruence
What is the ASA Condition for Congruence
What is the AAS Congruence Condition
Some Properties of a Triangle
What is the Isosceles Triangle Theorem How do we Prove it
What is the Converse of the Isosceles Triangle Theorem
How do we Prove the Converse of the Isosceles Triangle Theorem
Some More Criteria for Congruence of Triangles
What is the SSS Condition for Congruence
SSS Congruence Condition - Example
What is the RHS Condition for Congruence
Inequalities in a Triangle
What is the Triangle Inequality Theorem
Triangle Inequality Theorem - Example
Sum of Lengths of the Sides of a Triangle is Greater than Twice the Length of the Side joining a Vertex to the Opposite Side
QUADRILATERALS
Introduction
What is a Quadrilateral
Angle Sum Property of a Quadrilateral
What are the Different Pairs of Sides and Angles in a Quadrilateral
What are the Different Pairs of Sides and Angles in a Quadrilateral?
What is the Sum of Angles of a Quadrilateral
What is the Sum of Angles of a Quadrilateral?
Types of Quadrilaterals
What are Trapeziums and Kites
What are Trapeziums and Kites?
What is a Parallelogram and what are its Special Cases
What is a Parallelogram and what are its Special Cases
Properties of a Parallelogram
What are the Different Properties of Quadrilaterals we will look at
What are the Different Properties of Quadrilaterals we will look at
How do we Prove that the Opposite Sides of a Parallelogram are Equal
How do we Prove that the Opposite Sides of a Parallelogram are Equal
How to prove that a quadrilateral having each pair of opposite sides equal is a parallelogram
How to prove that a quadrilateral having a pair of opposite sides equal and parallel is a parallelogram
How do we Prove that the Opposite Angles of a Parallelogram are Equal
How do we Prove that the Opposite Angles of a Parallelogram are Equal
How to prove that a quadrilateral having each pair of opposite angles equal is a parallelogram
How do we Prove that the Diagonals of a Parallelogram Bisect each other
How to prove that if the diagonals of a quadrilateral bisect each other then it is a parallelogram
How do we Prove that the Diagonals of a Rectangle are Equal
How do we Prove that the Diagonals of a Rhombus Bisect each other are Right Angles
Properties of a Rhombus - Example
Another Condition for a Quadrilateral to be a Parallelogram
How to prove that a quadrilateral having a pair of opposite sides equal and parallel is a parallelogram
The Mid-point Theorem
How to prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side
How to prove that a line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side
AREA OF PARALLELOGRAM TRIANGLE
Introduction
Areas Of Parallelograms And Triangles - Congruent Figures
Areas Of Parallelograms And Triangles - Congruent Figures
Parallelograms on the Same Base and between the Same Parallels
Parallelograms on the Same Base and between the Same Parallel Lines - Part 1
Parallelograms on the Same Base and between the Same Parallel Lines - Part 1
Parallelograms on the Same Base and between the Same Parallel Lines - Part 2
Parallelograms on the Same Base and between the Same Parallel Lines - Part 2
Triangles on the Same Base and between the Same Parallels
A Triangle and a Parallelogram on the Same Base between the Same Parallel Lines
A Triangle and a Parallelogram on the Same Base between the Same Parallel Lines
Triangles Having The Same Base And Between The Same Two Parallel Lines
Triangles Having The Same Base And Between The Same Two Parallel Lines
Triangles having the same base and between the same two parallels - Converse
Triangles having the same base and between the same two parallels - Converse
CIRCLES
Circles and Its Related Terms : A Review
What is a Circle
How do we Define a Circle
What are the different regions associated with a circle
What is the Circumference
What is Pi
What is the Area of a Circle Part 1
What is the Area of a Circle Part 2
What is a chord
What is the distance of a chord from the centre What does a chord divide a circle into
Angle Subtended by a Chord at a Point
How do we Prove that Congruent Chords of a Circle Subtend Congruent Angles at the Centre
How do we prove that chords subtending equal angles at the centre are equal
Perpendicular from the Centre to a Chord
How do we Prove that the Perpendicular from the Centre of the Circle to the Chord bisects the Chord
How do we Prove that the Line joining the Centre of the Circle and the Midpoint of the Chord is Perpendicular to that Chord
Circle through 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
Equal Chords and Their Distances from the Centre
How do we prove that equal chords are equidistant from the centre
How do we Prove that the Chords which are Equidistant from the Centre are Equal
Angle Subtended by an Arc of a Circle
How is the angle formed by an arc at the centre related to the angle formed by the arc in the remaining part of the circle
Can we prove that the Angle formed by an Arc at the Centre is Twice that formed by the Arc in the remaining part of the Circle
What is the angle of a Segment?
What are Concyclic Points
Concyclic Points - Proof
Cyclic Quadrilaterals
What is the Sum of the Measure of Opposite Angles in a Cyclic Quadrilateral
How do we Prove that the Opposite Angles of a Cyclic Quadrilateral add up to 180 degrees
What is the Quadrilateral which has its Opposite Angles add up to 180 degrees called
How do we Prove that if the Sum of Opposite Angles of a Quadrilateral is 180 degrees, then it is Cyclic
CONSTRUCTION
Basic Constructions
How do we Construct an Angle Bisector
How do we Construct an Angle Bisector
Logic behind the Construction of an Angle Bisector
Logic behind the Construction of an Angle Bisector
How do we Construct a Perpendicular Bisector of a Line Segment
Logic behind the Construction of a Perpendicular Bisector of a Line Segment
Logic behind the Construction of a Perpendicular Bisector of a Line Segment
How do we Construct a 60 Degree Angle
How do we Construct a 60 Degree Angle
Some Constructions of Triangles
How to construct a triangle, given its base, a base angle and sum of other two sides
How to construct a triangle, given its base, a base angle and sum of other two sides
How to construct a triangle given its base, a base angle and the difference of the other two sides
How to construct a triangle given its base, a base angle and the difference of the other two sides
How to construct a triangle, given its perimeter and its two base angles
How to construct a triangle, given its perimeter and its two base angles
HERON'S FORMULA
Area of a Triangle — by Heron’s Formula
What is Heron's Formula
What is Heron's Formula
Heron's Formula - An Example
Heron's Formula - An Example
SURFACE AREA AND VOLUME
Surface Area and Volume of a Cube and Cuboid
What is the Surface Area of a Cuboid
What is the Surface Area of a Cuboid
What is the Surface Area of a Cube
What is the Surface Area of a Cube
What is the Volume of a Cuboid Part 1
What is the Volume of a Cuboid Part 1
What is the Volume of a Cuboid Part 2
What is the Volume of a Cuboid Part 2
Volume of a Cuboid - Example
Volume of a Cuboid - Example
Surface Area of a Cuboid - Example
Surface Area of a Cuboid - Example
Surface Area and Volume of a Cylinder
What is a Cylinder
What is a Cylinder
What is the Surface Area of a Cylinder
What is the Surface Area of a Cylinder
What is the Volume of a Cylinder
What is the Volume of a Cylinder
What is the Volume of a Pizza
What is the Volume of a Pizza
Volume of a Cylinder - Example
Volume of a Cylinder - Example
A Cylinder within a Cylinder - Example
A Cylinder within a Cylinder - Example
Surface Area and Volume of a Right Circular Cone
What is a Right Circular Cone
What is a Right Circular Cone
What is the Surface Area of a Right Circular Cone
What is the Surface Area of a Right Circular Cone
What is the Volume of a Cone
What is the Volume of a Cone
Volume of a cone - Example
Volume of a cone - Example
Surface Area of a Cone - Example
Surface Area of a Cone - Example
Surface Area and Volume of a Sphere
What is a Sphere
What is a Sphere
What is the Surface Area and Volume of a Sphere
What is the Surface Area and Volume of a Sphere
What is a Spherical Shell
What is a Spherical Shell?
Volume and Surface Area of a Sphere - Example
Volume and Surface Area of a Sphere - Example
Surface Area of a Sphere - Example
Surface Area of a Sphere - Example
STATISTICS
Collection of Data
How do we Classify Data
How do we Classify Data
What are Tally Marks
What are Tally Marks
Presentation of Data
What is Ungrouped Frequency Distribution
What is Ungrouped Frequency Distribution
What is Grouped Frequency Distribution Part 1
What is Grouped Frequency Distribution Part 2
What is Grouped Frequency Distribution Part 2
Graphical Representation of Data
What are Bar graphs
What are Bar graphs
Bar Graph - Example
Bar Graph - Example
How do we Draw a Bar Graph Example 1
How do we Draw a Bar Graph Example 1
How do we Draw a Bar Graph Example 2
How do we Draw a Bar Graph Example 2
What is a Histogram
What is a Histogram
How do we draw Histograms for Discontinuous Class Intervals
How do we draw Histograms for Discontinuous Class Intervals
What is a Frequency Polygon
What is a Frequency Polygon
How do we Draw a Frequency Polygon using a Histogram
How do we Draw a Frequency Polygon using a Histogram
How do we Draw a Frequency Polygon without using a Histogram
How do we Draw a Frequency Polygon without using a Histogram
Measures of Central Tendency
What is the Arithmetic Mean
What is the Arithmetic Mean
What are the Properties of Arithmetic Mean
How do we Find the Mean of Ungrouped Data
What is Combined Arithmetic Mean
What is Combined Arithmetic Mean
What are Mean, Median and Mode
What are Mean, Median and Mode
Mean, Median, Mode - Example
Mean, Median, Mode - Example
How do we Find the Median
How do we Find the Median
How do we Find the Median of an Ungrouped Frequency Distribution Part 1
How do we Find the Median of an Ungrouped Frequency Distribution Part 1
How do we Find the Median of an Ungrouped Frequency Distribution Part 2
How do we Find the Median of an Ungrouped Frequency Distribution Part 2
What are the Different Types of Mode
What are the Different Types of Mode
Why do we need Median - Example
Why do we need Median - Example
What is Skewness
What is Skewness
Why do we need Mode - Example
Why do we need Mode - Example
PROBABILITY
Introduction
What is Probability
QUIZ-What is Probability?
Probability – an Experimental Approach
What are Equally Likely Events (Tossing a Coin)
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?
Preview - Class IX MATHS
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