Algebra: Introduction

Beginning of Algebra
Where did the word 'Algebra' come from
What is 'Algebra'
'Arithmetic' vs 'Algebra'
Who is an 'Algebraist'
Indian name for 'Algebra'
Usages of Algebra

Algebra: Constants and Variables

Introduction
Two types of numbers in Algebra
What is a 'Constant'
What is a 'Variable'
What is a 'Literal'
'Constant' vs 'Variable'
Constants with 'unknown' values
Fundamental operations on variables
Why can we perform operations on variables
Shorter way to write product of variables
Repeated multiplication (or Exponentiation) of variables
A variable to the power zero (0)
Repeated addition (or Multiplication) of variables
Properties of operations on variables

Algebra: Algebraic Expressions

Algebraic expression - Introduction
What is an 'Algebraic expression'
'Arithmetic expression' vs Algebraic expression'
What are 'terms'
How to identify 'terms' in an algebraic expression
'Constant term' in an algebraic expression
'Factors' of a term
Tree diagram
'Numerical factor' and 'Variable factor'
What are 'Coefficients'
'Numerical coefficient' and 'Literal coefficient'
What are 'Like terms'
What are 'Unlike terms'
How to add or subtract 'terms'
How to add or subtract 'like terms'
How to add or subtract 'Unlike terms'
How to add or subtract 'Algebraic expressions'
How to multiply 'terms'
How to multiply two 'algebraic expressions'
Finding the value of an algebraic expression

Algebra: Polynomials

Polynomial - Introduction
A variable to the power whole number
(Constant) X (A variable to the power whole number)
What is a 'Polynomial in 1 variable'
What is a 'Constant polynomial'
'Terms' of a polynomial
'Coefficients' of terms of a polynomial
'Degree' of a polynomial in 1 variable
Summary of concepts
Classification of polynomials
What is a 'Linear polynomial'
What is a 'Quadratic polynomial'
What is a 'Cubic polynomial'
'Constant polynomial' - Revisited
Summary of polynomials based on 'degree'
Degree table of polynomials
Classifying polynomials on 'Number of terms'
Polynomials in more than 1 variable

Algebra: Linear equation in 1 variable

What are 'variables' and 'constants'
What is an 'Expression'
Problem session - variables, constants and expressions
What is an 'Equation'
Parts of an equation
What is 'Equation in 1 variable'
Problem session - On identifying equation in 1 variable
Problem session - On identifying equation in 1 variable
What is 'Linear equation in 1 variable'
Problem session - Identifying 'Linear equation in 1 variable'
'Solution' or 'root' of an equation - Part 1
'Solution' or 'root' of an equation - part 2
'Solution' or 'root' of an equation - part 3
Number of roots of an equation
Plotting the roots of an equation
'Solution' or 'root' of a L.E.1.V.
Why is a Linear equation called 'Linear'
Problem session - Understanding the meaning of solution
Problem session - Understanding the meaning of solution
Problem session - Understanding the meaning of solution
What is 'Solving a L.E.1.V'
Two methods of solving LE1V
Trial and Error method of solving L.E.1.V.
Problem session - Trial and Error method
Problem session - Trial and Error method
Demerits of Trial and Error method
An equation as a weighing balance
Properties of a balanced equation
Gist of properties of balanced equation
Systematic method of solving L.E.1.V.
Problem session - Systematic method - Part 1
What is 'Transposition'
Problem session - Systematic method - Part 2
Problem session - Systematic method - Part 3
Problem session - Systematic method - Part 4
Problem session - Systematic method - Part 5
Problem session - Systematic method - Part 6
Problem session - Systematic method - Part 7
Setting up an equation
Problem session - Converting statements to equations
Problem session - Setting up equations
Problem session - Word problems
Problem session - Word problems
Problem session - Word problems
Checking the solution
Problem session - Checking the solution
Plotting the solution of LE1V
Problem session - Plotting solution of LE1V
Standard form of a LE1V
Problem session - Writing LE1V in standard form
Problem session - Overall chapter in one session
Revision of the chapter - Part 1
Revision of the chapter - Part 2
Revision of the chapter - Part 3
Revision of the chapter - Part 4
Revision of the chapter - Part 5
Revision of the chapter - Part 6
Revision of the chapter - Part 7

Plane Geometry: Introduction

Break up of the word 'Geometry'
What is 'Geometry'
How did Geometry evolve
2 Types of Geometries
Which Geometry will we study
Geometry of the Universe
Who is the 'Father of Geometry'
Who gave the 'first known proof'
Who is a 'Geometer'

Plane Geometry: Meaning of 'Axioms' & 'Theorems'

Two types of 'Statements' in Mathematics
Axioms or Postulates
Theorems or Propositions

Plane Geometry: Plane

What is a 'Plane'

Plane Geometry: Point

Definition of 'Point'
Why is a 'Point' not defined in Geometry
A Point is a 'Primitive Object'
Characteristics of a Point
How to represent a Point
How to draw a Point on paper
How to denote a Point
Practical examples of a Point

Plane Geometry: Line Segment

Definition of a Line-segment
Definition of a Line-segment from a Line
Another word for Line-segment
How to denote a Line-segment
'Line-segment AB' vs 'Line-segment BA'
The length of a Line-segment
Characteristics of a Line-segment
How to compare lengths of Line-segments
Practical examples of Line-segments

Plane Geometry: Line

Definition of 'Line'
Why is a 'Line' not defined in Geometry
Line is a 'Primitive Object'
What is a 'Straight Line'
Defining a line from a Line-segment
Defining a Line from 'Intersecting planes'
Complete picture of a Line cannot be drawn
How to denote a Line
'Line AB' vs 'Line BA'
Characteristics of a Line
How many Lines can be drawn passing through 1 given point
How many Lines can be drawn passing through 2 given points
Two points fix a line
What are Collinear points
What are Non-collinear points
What are Concurrent lines
Practical examples of lines

Plane Geometry: Ray

What is a 'Ray'
Definition of a 'Ray' from a 'Line'
Definition of a 'Ray' from a 'Line-segment'
About the complete picture of a Ray
How to denote a Ray
Starting point of a Ray AB
'Ray AB' vs 'Ray BA'
Number of rays that can be drawn from a 'Starting point'
Ray from 2 given points
Characteristics of a ray
Practical examples of rays

Plane Geometry: 'line' vs 'line Segment' vs 'Ray'

'Line' vs 'Line segment' vs 'Ray'

Plane Geometry: Angle

Origin of the word 'Angle'
What is an 'Angle'
Symbol for Angle
How to denote an angle
What is the 'Measure of an angle'
How to denote the 'Measure of an angle'
What is 'One Complete Revolution'
What is 'Complete angle' or 'Full angle'
What is 'Straight angle'
What is 'Right angle'
'Three-fourth' of a revolution has no special name
Relation among a 'Complete angle', a 'Straight angle' and a 'Right angle'
Comparison among a 'Complete angle', a 'Straight angle' and a 'Right angle'
Systems of measuring angle
Centesimal system (French system)
Sexagesimal system (English system)
Circular system
Degree measurement of a complete angle, a straight angle and a right angle
Types of angles
Examples of 7 types of angles
Comparison among 7 types of angles
Automatic formation of Reflex angle
Distinction between an angle and its reflex counterpart
Two important results
How to compare angles
Instrument to measure an angle
An angle leads to 3 divisions of a region
Practical examples of angles

Plane Geometry: Pairs of Angles

Pairs of Angles
Complementary angles
Supplementary angles
Adjacent angles
Linear pair of angles
Linear Pair Axiom
Vertically opposite angles
Theorem concerning 'Vertically opposite angles'
'Linear pair axiom' vs 'Vertically opposite angles theorem'

Plane Geometry: Pairs of Lines

Pairs of Lines - Introduction
Parallel Lines
Intersecting Lines
Perpendicular Lines
'Perpendicular bisector' of a line segment
What are 'Transversals'
Angles made by a transversal
'Exterior Angles' made by a transversal
'Interior Angles' made by a transversal
Pairs of exterior angles on same side of transversal
Pairs of interior angles on same side of transversal
Pairs of corresponding angles formed by a transversal
Pairs of Alternate interior angles formed by a transversal
Pairs of Alternate exterior angles formed by a transversal
Revision of all types of angles formed by transversal

Plane Geometry: Parallel lines & a Transversal

Parallel lines and a transversal - Introduction
Corresponding angles axiom
Alternate angle theorem
Proof of 'Alternate angle theorem'
Theorem regarding interior angles on same side of transversal
Proof of theorem regarding interior angles on same side of transversal
Most important result (for competitions)

Plane Geometry: Curve

What is a 'Curve'
Two types of curves
What is 'Open curve'
What is 'Closed curve'
What is 'Simple curve'
What is 'Simple Closed Curve'
A 'Simple Closed Curve' leads to 3 divisions of a region

Plane Geometry: Polygon

What is a 'Polygon'
What are 'Sides' or 'Edges' of a polygon
What are 'Vertices' or 'Corners' of a polygon
What are 'Adjacent sides' of a polygon
What are 'Adjacent vertices' of a polygon
What is 'Diagonal' of a polygon
A polygon leads to 3 divisions of a region
Angles in a polygon
What are 'Adjacent angles' in a polygon
Quick recapitulation
Types of Polygons
What is 'Convex polygon'
What is 'Concave polygon'
Names of some polygons
Types of Convex polygon
What is 'Regular polygon'
What is 'Irregular polygon'

Plane Geometry: Triangle

e Geometry: Triangle
What is a 'Triangle'
How to denote a triangle
'Interior', 'On' and 'Exterior' of a triangle
'Sides' of a Triangle
'Vertices' of a Triangle
'Adjacent sides' of a Triangle
'Adjacent vertices' of a Triangle
Sides opposite to vertices
Vertices opposite to sides
Interior angles of a triangle
Exterior angles of a triangle
'Diagonals' of a triangle
Elements in a triangle
'Angle sum property' of a triangle
'Exterior angle property' of a triangle
Types of triangles
Types of triangles based on 'sides'
Types of triangles based on 'angles'
Inequalities in a triangle - Introduction
Inequalities in a triangle - The 1st inequality
Inequalities in a triangle - The 2nd inequality
Inequalities in a triangle - 1st and 2nd inequalities
Inequalities in a triangle - The 3rd inequality
Inequalities in a triangle - The 4th inequality
Bound on a side of a triangle
Special lines and special line-segments in a triangle
'Medians' in a triangle
'Centroid' or 'Gravity centre' of a triangle
'Altitudes' in a triangle
'Orthocenter' of a triangle
'Interior angle bisectors' in a triangle
'Incentre' of a triangle
'Side perpendicular bisectors' in a triangle
'Circumcenter' of a triangle
All 4 centres in a sample triangle
Right-angled triangle
Pythagoras theorem

Plane Geometry: Quadrilateral

What is a 'Quadrilateral'
'Interior', 'On' and 'Exterior' of a quadrilateral
'Sides' or 'Edges' of a Quadrilateral
'Vertices' or 'Corners' of a Quadrilateral
'Adjacent sides' of a Quadrilateral
'Adjacent vertices' of a Quadrilateral
'Opposite sides' of a Quadrilateral
'Opposite vertices' of a Quadrilateral
'Interior angles' of a Quadrilateral
'Exterior angles' of a Quadrilateral
'Adjacent interior angles' of a Quadrilateral
'Opposite interior angles' of a Quadrilateral
'Diagonals' of a Quadrilateral
Elements in a Quadrilateral
Two types of quadrilaterals
Angle sum property of a quadrilateral
5 Types of quadrilaterals
What is a 'Trapezium'
What is a 'Parallelogram'
What is a 'Rhombus'
What is a 'Rectangle'
What is a 'Square'
'Family tree' of quadrilaterals

Plane Geometry: Circle

Introduction to Circle
What is a 'Circle'
A circle is a 'Simple closed curve'
A circle leads to 3 divisions of a region
What is 'Centre' of a circle
What is 'Radius' of a circle
Distance of a point from the centre of a circle
What is 'Chord' of a circle
What is 'Diameter' of a circle
What is 'Arc' of a circle
What is 'Circumference' of a circle
What is 'Semi-circle'
'Chord associated with an arc' and vice-versa
What is 'Sector'
Two types of quadrilaterals
Differences in diagrams of 'Arc', 'Segment' and 'Sector'
What is 'Semi-circular region'
'Quadrant' of a circle
Circles passing through 1 given point in a plane
Circles passing through 2 given points in a plane
Circle passing through 3 given points in a plane
What are 'Concentric circles' and 'Annulus'
What is a 'Cyclic quadrilateral'
What is a 'Secant'
'Chord associated with a secant' and vice-versa
What is a 'Tangent'
Number of tangents from a point to a circle
Which Instrument is used to construct a circle

3 Dimensional geometry

What is a 1D shape
What is a 2D shape
What is a 3D shape
Five 3D shapes that we will study
What is a 'Cuboid'
What is a 'Cube'
What is a 'Cylinder'
What is a 'Cone'
What is a 'Sphere'
Problem session - Mixed problems

Symmetry

Two types of symmetries
What is 'mirror image' of an object
How to draw 'mirror images' - Introduction
How to draw mirror image of a 'point'
Problem session - Mirror image of a 'point'
How to draw mirror image of a 'plane figure'
Problem session - Mirror image of a 'plane figure'
What is 'Linear symmetry'
Test of 'Linear symmetry'
Problem session - Line of symmetry
Problem session - Line of symmetry
Problem session - Line of symmetry
Problem session - Line of symmetry
Line of symmetries of some standard figures
Problem session - Line of symmetry
Problem session - Line of symmetry
Problem session - Line of symmetry
Line of symmetries of English alphabets
Problem session - Symmetries of Alphabets

Geometrical constructions

Introduction to 'Geometrical Constructions'
Constructing a circle of given radius
Previous construction on notebook
Constructing a line segment of given length
Previous construction on notebook
Constructing a copy of a given line segment
Previous construction on notebook
Constructing the perpendicular bisector of a line segment
Previous construction on notebook
Constructing an equilateral triangle
Previous construction on notebook
Constructing a perpendicular to a line through a point on it
Construction 7 on copy
Constructing a perpendicular to a line through a point not on it
Construction 8 on copy
Constructing an angle using protractor
Constructing an angle using protractor
Constructing a copy of a given angle
Constructing a copy of a given angle
Constructing bisector of a given angle
Constructing bisector of a given angle
Constructing 60 deg, 120 deg, 180 deg and 90 deg
Constructing 60 deg, 120 deg, 180 deg and 90 deg
Constructing multiples of 15 degrees
Constructing multiples of 15 degrees

Mensuration

What is 'Mensuration'
What is 'perimeter'
Problem session - Finding perimeter
Perimeter of some standard figures
Problem session - Perimeter of rectangle
Problem session - Perimeter or rectangle
Problem session - Perimeter of square
Problem session - Perimeter of miscellaneous shapes
What is 'area'
Area of rectangle and square
Problem session - Rectangle and square
Problem session - Square
Problem session - Rectangle and square
Problem session - Rectangle and square
Circle - Circumference and area
Problem session - Mensuration of circle
Estimating area by counting squares
Problem session - Estimating area by counting squares

Statistics

What is 'Data'
The word 'statistics'
Meaning of the word 'statistics' as plural noun
Meaning of the word 'Statistics' as singular noun
Definition of 'Statistics'
Stages of statistical study
Stage 1 - Collection of data
Stage 2 - Organisation of data
What is 'Array'
What is 'Frequency distribution table'
Problem session - Tally Marks
'Array' vs 'Frequency distribution table'
Problem session - 'Array' and 'Frequency distribution table'
Problem session - Interconverting 'Array' and 'Freq dist table'
Problem session - 'Tally Marks' and 'Frequency'
Problem session - Frequency distribution table
Stage 3 - Presentation of data
What is 'Pictograph'
Problem session - Pictograph
Problem session - Pictograph
Problem session - Pictograph
Demerits of 'Pictograph'
What is 'Bar graph'
Problem session - Bar graph 1
Problem session - Bar graph 2
Problem session - Bar graph 3
Problem session - Bar graph 4
Problem session - Bar graph 5
Stages 4 and 5 - Analysis and interpretation of data
What is 'Mean'
How to calculate 'mean'
What is 'Median'
How to calculate 'median'
What is 'Mode'
How to calculate 'mode'
What is 'Range'
How to calculate 'range'
Problem session - Mean, median, mode, range
Problem session - Mean, median, mode, range
Problem session - Mean, median, mode, range
Problem session - Mean, median, mode, range
Properties of mean, median and mode

Trigonometry: Introduction

Trigonometry - Introduction
Division of the word 'Trigonometry'
What is 'Trigonometry'
What will we study in 'Trigonometry'

Trigonometry: The required background

The required background
Basics of a right angled triangle
How to identify 'sides' opposite to 'angles' in a triangle
Problem session - Identifying 'sides' opposite to 'angles'
How to identify 'hypotenuse'
Problem session - Identifying the 'hypotenuse'
Side adjacent to an acute angle in a right angled triangle
Problem session - Mixed
'Ratios of sides' in a right angled triangle
Problem session - Writing all the 6 ratios of pairs of sides

Trigonometry: Trigonometric ratios of acute angles

Introduction to Trigonometric ratios
Glimpse to Trigonometric ratios
Definition of Trigonometric ratios
How to find the 'sine' of an acute angle of a right triangle
Problem session - Finding 'sine'
How to find the 'cosine' of an acute angle of a right triangle
Problem session - Finding 'cosine'
How to find the 'tangent' of an acute angle of a right triangle
Problem session - Finding 'tangent'
How to find the 'cosecant', 'secant' and 'cotangent'
Problem session - Finding 'cosecant', 'secant', 'cotangent'
Problem session - Finding all trigonometric ratios
Problem session - Finding all trigonometric ratios

Coordinate Geometry

What is coordinate geometry
Another name of coordinate geometry
Problem session
Who invented coordinate geometry
What are 'Coordinate axes'
What is 'x-axis'
What is 'y-axis'
Problem session - On coordinate axes
What is 'Origin'
What is 'coordinate plane'
What are 'Quadrants'
What is 'x-coordinate' or 'abscissa' of a point
What is 'y-coordinate' or 'ordinate' of a point
'Cartesian coordinates' of a point - Part 1
'Cartesian coordinates' of a point - Part 2
Summary of coordintates of a point
Problem session - Writing and plotting coordinates
Problem session - Writing Abscissa
Problem session - Writing Ordinate
Problem session - Writing coordinates
Problem session - Origin
Problem session - Finding distances from axes
Problem session - x-axis and abscissa
Problem session - y-axis and ordinate
Problem session - Deciding quadrants
Problem session - Deciding quadrants
Most commonly used coordinate systems
What is 'Cartesian coordinate system'
Problem session - Reading coordinates from graph
Problem session - Plotting coordinates in the coordinate plane
Address of a 'point' on a 'line'
Address of a 'point' in a 'plane'
Problem session - A short problem

Introduction to Logarithm

Who introduced Logarithm
How to denote a Logarithm
Problem session - Identifying valid logarithms
How to read a Logarithm
Problem session - Reading logarithms
'Base' and 'Argument' of a Logarithm
Problem session - Finding 'Base' and 'Argument'
What is Logarithm
How to evaluate a Logarithm
d
Logarithm is inverse of exponentiation
What does a Logarithm find
Problem session - converting exponents to logs
Problem session - converting Logs to exponents
Types of Logarithms
Usages (Applications) of Logarithms
Multiplication using Logarithm

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Mastering the Fundamentals of Math (Mathematics) : Part 2

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The syllabus

Algebra: Introduction

Algebra: Constants and Variables

Algebra: Algebraic Expressions

Algebra: Polynomials

Algebra: Linear equation in 1 variable

Plane Geometry: Introduction

Plane Geometry: Meaning of 'Axioms' & 'Theorems'

Plane Geometry: Plane

Plane Geometry: Point

Plane Geometry: Line Segment

Plane Geometry: Line

Plane Geometry: Ray

Plane Geometry: 'line' vs 'line Segment' vs 'Ray'

Plane Geometry: Angle

Plane Geometry: Pairs of Angles

Plane Geometry: Pairs of Lines

Plane Geometry: Parallel lines & a Transversal

Plane Geometry: Curve

Plane Geometry: Polygon

Plane Geometry: Triangle

Plane Geometry: Quadrilateral

Plane Geometry: Circle

3 Dimensional geometry

Symmetry

Geometrical constructions

Mensuration

Statistics

Trigonometry: Introduction

Trigonometry: The required background

Trigonometry: Trigonometric ratios of acute angles

Coordinate Geometry

Introduction to Logarithm

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