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RATIONAL NUMBERS
Introduction
1.1 Natural and Whole Numbers (Review)
Natural and Whole Numbers (Review)
1.2 What are Integers
What are Integers
What are the Other Properties of Rational Numbers?
1.3 What are Rational Numbers
What are Rational Numbers
1.4 Fractions and Integers - Are they Rational Numbers
1.5 What are Positive and Negative Rational Numbers
1.6 What is the Closure property of Rational Numbers
1.7 What is the Commutative Property of Rational Numbers
1.8 What is the Associative Property of Rational Numbers
1.9 What are Additive and Multiplicative identities
1.10 What is the Zero Property
1.11 What are the Other Properties of Rational Numbers
1.12 How do we Add Two Rational Numbers Part 1
1.13 How do we Add Two Rational Numbers Part 2
1.15 How do we Subtract Two Rational Numbers
1.16 How do we Multiply Two Rational Numbers Part 1
1.17 How do we Multiply Two Rational Numbers Part 2
1.18 How do we Divide Two Rational Numbers Part 1
1.19 How do we Divide Two Rational Numbers Part 2
Representation of Rational Numbers on the Number Line
1.20 Rational Numbers on a Number Line - Part 1
1.21 Rational Numbers on a Number Line - Part 2
1.22 Rational Numbers on a Number Line - Part 3
Rational Numbers between Two Rational Numbers
1.23 How many Rational Numbers exist between Two Rational Numbers
1.24 How many Rational Numbers exist between Two Rational Numbers (Logic)
1.25 How many Rational Numbers exist between Two Rational Numbers (Finding Averages)
1.26 How do we Find Rational Numbers between Two Rational Numbers (Examples Part 1)
1.27 How do we Find Rational Numbers between Two Rational Numbers (Examples Part 2)
LINEAR EQUATIONS ONE VARIBLE
Introduction
What is a Linear Equation in One Variable
Solving Equations which have Linear Expressions on one Side and Numbers on the other Side
How do we Use the Inverse Method to Solve a Linear Equation
How do we Use the Transpose Method to Solve a Linear Equation
Some Applications
Forming Equations - Find the Number
Forming Equations - Find the Parts
Forming Equations - Find the Length and Breadth of a Rectangle
Forming Equations - Inheritance
Forming Equations - Consecutive Integers
Forming Equations - Consecutive Even Integers
Forming Equations - Find the Digits, and then the Number
Some More Applications
Forming Equations - Find the Present Age
Forming Equations - Find the Present Age (Table Method)
Reducing Equations to Simpler Form
Forming Equations - Find the Fraction
Forming Equations - Find the Number of Coins
UNDERSTANDING QUADRILATERALS
Introduction
What is a Quadrilateral
What are the Different Pairs of Sides and Angles in a Quadrilateral
Polygons
What is a Polygon
What is a Regular Polygon
Types of polygons
Angle sum property
Sum of Exterior Angles of a Polygon
Sum of the Measures of the Exterior Angles of a Polygon
What is the Relation of an Exterior Angle of a Triangle with its Interior Angles
Exterior Angles of a Triangle - Example
Kinds of Quadrilaterals
What are Trapeziums and Kites
What is a Parallelogram and what are its Special Cases
The Quadrilaterals Tree
What are the Different Properties of Quadrilaterals we will look at
How do we Prove that the Diagonals of an Isosceles Trapezium are Equal
How do we Prove that the Diagonals of a Kite are Perpendicular to each other
How do we Prove that the Opposite Sides of a Parallelogram are Equal
How do we Prove that the Opposite Angles of a Parallelogram are Equal
How do we Prove that the Diagonals of a Parallelogram Bisect each other
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
Some Special Parallelograms
A Summary of the Properties of a few Special Quadrilaterals
Properties of a Rhombus - Example
PRACTICAL GEOMETRY
Introduction
Practical Geometry - Introduction
Constructing a Quadrilateral
Constructing a Quadrilateral - With lengths of 4 sides and the diagonal
Constructing a Quadrilateral - With lengths of 3 sides and 2 diagonals
Constructing a Quadrilateral - With lengths of 3 sides and 2 included angles
Constructing a Quadrilateral - With lengths of 2 adjacent sides and 3 angles
Some Special Cases
Constructing Quadrilaterals - Special Cases
DATA HANDLING
Organising Data
How do we Classify Data
What are Tally Marks
Grouping Data
What are Bar graphs
Bar Graph - Example
How do we Draw a Bar Graph Example 1
How do we Draw a Bar Graph Example 2
What are Joint Bar Graphs
How do we Draw a Joint Bar Graph
How do we Draw a Percentage Bar Diagram
Percentage Bar Diagram - Example
What is Ungrouped Frequency Distribution
What is Grouped Frequency Distribution Part 1
What is Grouped Frequency Distribution Part 2
How do we form Class Intervals
What is the Continuous Form of Grouping
Circle Graph or Pie Chart
What are Pie Charts
How do we Construct a Pie Chart Part 1
How do we Construct a Pie Chart Part 2
How do we Interpret a Pie Chart
What is a Histogram
How do we draw Histograms for Discontinuous Class Intervals
Chance and Probability
What is Probability
What are Equally Likely Events (Tossing a Coin)
What are Equally Likely Events (Throwing a die)
When are two Events Not Equally Likely What are Impossible and Certain Events
SQUARES AND SQUARE ROOTS
Properties of Square Numbers
Properties of Square Numbers
Some More Interesting Patterns
Adding triangular numbers
Numbers between square numbers
Adding odd numbers
A sum of consecutive natural numbers
Product of two consecutive even or odd natural numbers
Some more patterns in square numbers
Finding the Square of a Number
Finding the Square of a Number
What is the Square of a Number
Pythagorean triplets
Square Roots
What are Square Roots
Finding square root through repeated subtraction
How do we Find the Square Root of a Number using the Prime Factorisation Method Part 1
How do we Find the Square Root of a Number using the Prime Factorisation Method Part 2
How do we Find the Square Root of a Number using the Long Division Method Part 1
How do we Find the Square Root of a Number using the Long Division Method Part 2
How do we Find the Square Root of a Number using the Long Division Method Part 3
How do we Find the Square Root of a Number using the Long Division Method Part 4
Estimating Square Root
Approximating Roots
Square Roots of Decimals
Square Roots of Decimals
CUBES AND CUBE ROOTS
Cubes
Introduction to Cubes
Adding consecutive odd numbers and difference between cubes of consecutive natural numbers
Smallest multiple that is a perfect cube
Cube Roots
What is the Cube of a Number
What is the Cube Root of a Number
How do we Find the Cube Root of a Number using the Prime Factorisation Method
How do we Find the Cube Root of a Large Number (in a few seconds)
COMPARING QUANTITIES
Recalling Ratios and Percentages
What is a Ratio
What is Percentage
Percentage - Example
Finding the Increase or Decrease Per cent
Percentage of a Quantity - Example 1
Percentage Increase or Decrease - Example 2
Finding Discounts
What do we mean by Discount
How do we Find a Percentage of a Given Quantity
Prices Related to Buying and Selling (Profit and Loss)
What do we mean by Profit and Loss
What do we mean by Cost Price and Selling Price
What are Overhead Costs
What do we mean by Profit Percentage and Loss Percentage
Example - How do we find the Cost Price when we are given the Loss Percentage
Sales Tax/Value Added Tax/Goods and Services Tax
What do we mean by Sales Tax
Discount and Sales Tax Example
Compound Interest
Simple Interest - Basics
Simple Interest vs Compound Interest
Deducing a Formula for Compound Interest
How do we Derive the Compound Interest formula
Rate Compounded Annually or Half Yearly (Semi Annually)
What is Half Yearly Compounding
What is Quarterly Compounding
Applications of Compound Interest Formula
Compound Interest Example
ALGEBRAIC EXPRESSIONS AND IDENTITIES
What are Expressions?
What is an Equation
Terms, Factors and Coefficients
What are Terms
How do we Count the Number of Terms in an Algebraic Expression
What are Like and Unlike Terms
When can Terms be Added or Subtracted
Monomials, Binomials and Polynomials
Heard of the Polynomial Store
What is Factorisation of Polynomials
Addition and Subtraction of Algebraic Expressions
How do we Add Two Polynomials
How do we Subtract One Polynomial from Another
How do we Add Two Polynomials using the COLUMN method Part 1
How do we Add Two Polynomials using the COLUMN method Part 2
How do we Subtract a Polynomial from Another using the COLUMN method Part 1
How do we Subtract a Polynomial from Another using the COLUMN method Part 2
Multiplication of Algebraic Expressions: Introduction
Multiplication of Algebraic Expressions Introduction
Multiplying a Monomial by a Monomial
How do we Multiply Two Monomials
Multiplying a Monomial by a Polynomial
How do we Multiply a Monomial with a Binomial
Multiplying a monomial by a trinomial
Multiplying a Polynomial by a Polynomial
How do we Multiply Two Polynomials
Multiplying a binomial by a binomial
Multiplying a binomial by a trinomial
What is an Identity?
What is an Identity
Standard Identities
First Identity (Square of a Binomial)
How do we Prove the First Identity
Second Identity (Square of a Binomial)
How do we Prove the Second Identity
Third Identity (Difference of Squares)
How do we Prove the Third Identity
VISUALISING SOLID SHAPES
Views of 3D-Shapes
Viewing 3 Dimensional Shapes
Faces, Edges and Vertices
What is a Cuboid
What is a Cube
Cylinder and Sphere
What is a Cone
What is a Prism
What is a Pyramid
MENSURATION
Let us Recall
What is the Perimeter of a Rectangle
What is the Perimeter of a Square and a Triangle
What is the Area of a Square and a Rectangle
What is the Perimeter of a Parallelogram
What is the Circumference of a Circle
How do we Find the Area of an Irregular Figure
Area of a Rectangle - Example
What is the Area of a Triangle
What is the Area of a Circle Part 1
Paths in a Park - Example
Area of Trapezium
How do we Find the Area of a Trapezium
Area of a General Quadrilateral
Area of a General Polygon
What is the Area of a Parallelogram
Area of a Parallelogram - Example
How do we Find the Area of a Rhombus
Area of a Polygon
What is the Area of a Regular Polygon (Pentagon) in terms of its Inradius?
Surface Area & Volume of a Cube, Cuboid
What do we mean by Volume and Surface Area
What is the Surface Area of a Cuboid
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 2
Volume of a Cuboid - Example
Surface Area of a Cuboid - Example
Surface Area & Volume of a Cylinder
What is a Cylinder
What is the Surface Area of a Cylinder
What is the Volume of a Cylinder
What is the Volume of a Pizza
Volume of a Cylinder - Example
A Cylinder within a Cylinder - Example
EXPONENTS AND POWERS
Introduction
What are Exponents
Powers with Negative Exponents
What are Negative Exponents
Laws of Exponents
What is the Product Law of Exponents
What is the Quotient Law of Exponents
What is the Power Law of Exponents
What are the Power of Product and the Power of Quotient Property
Use of Exponents to Express Small Numbers in Standard Form
Powers of 10 - Part 1
Powers of 10 - Part 2
Powers of 10 - Part 3
DIRECT AND INVERSE PROPORTION
Introduction
What is Proportion
Direct Proportion
Direct Variation - Example
What is Direct Variation Part 1
What is Direct Variation Part 2
Inverse Proportion
What is Indirect Variation Part 1
What is Indirect Variation Part 2
FACTORISATION
Introduction
What are Factors
Factors of a term
What is Factorisation?
What is Factorisation of Polynomials
How do we Factorise Polynomials using Grouping Part 1
How do we Factorise Polynomials using Grouping Part 2
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
How do we Factorise a Quadratic Polynomial Part 1
How do we Factorise a Quadratic Polynomial Part 2
How do we Factorise a Quadratic Polynomial Part 3
How do we Factorise a Quadratic Polynomial Part 4
How do we Factorise a Quadratic Polynomial Part 5
Division of Algebraic Expressions
How do we Divide One Monomial by Another
How do we Divide a Polynomial by a Monomial
How do we Divide a Polynomial by a Monomial Part 1
How do we Divide a Polynomial by a Monomial Part 2
How do we Divide a Polynomial by a Binomial
Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)
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
INTRODUCTION TO GRAPHS
A Bar Graph
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 2
What are Joint Bar Graphs
How do we Draw a Joint Bar Graph
A Pie Chart
What are Pie Charts
How do we Interpret a Pie Chart
How do we Construct a Pie Chart Part 1
How do we Construct a Pie Chart Part 2
Histogram
What is a Histogram
How do we draw Histograms for Discontinuous Class Intervals
Frequency Polygon
What is a Frequency Polygon
How do we Draw a Frequency Polygon using a Histogram
How do we Draw a Frequency Polygon without using a Histogram
Linear Graphs
A line graph
Location of a point
What are Co-ordinates
Some Applications
Independent variable and dependent variable - Quantity and Cost
Independent variable and dependent variable - Principal and Simple Interest
Independent variable and dependent variable - Time and Distance
PLAYING ITH NUMBERS
Numbers in General Form
Numbers in General Form
Numbers in General Form
Games with Numbers
Games with Numbers
Games with Numbers
Letters for Digits
Letters for Digits
Letters for Digits
Tests of Divisibility
Divisibility Rules (2, 4 and 8)
Divisibility Rules (2, 4 and 8)
Divisibility Rules (5 and 10)
Divisibility Rules (5 and 10)
Divisibility Rules (3, 6 and 9)
Divisibility Rules (3, 6 and 9)
Divisibility Rules (11)
Divisibility Rules (11)