Mathematical Reasoning | Compound Statements lesson Plan and Notes :: Danielitte

Maths ( 104-11 )

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Sets

Introduction

Introduction
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Sets And Their Representations

Sets And Their Representations
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The Empty Set

The Empty Set
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Finite And Infinite Sets

Finite And Infinite Sets
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Equal Sets

Equal Sets
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Sub Sets

Subsets Of Set Of Real Numbers
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Intervals As Subsets Of R
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Power Set

Power Set
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Universal Set

Universal Set
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Venn Diagrams

Venn Diagrams
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Operations On Sets

Union Of Sets
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Intersection Of Sets
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Difference Of Sets
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Complement Of A Set

Complement Of A Set
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Practical Problems On Union And Intersection Of Two Sets

Practical Problems On Union And Intersection Of Two Sets
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Relations And Functions

Introduction

Introduction
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Cartesian Products Of Sets

Cartesian Products Of Sets
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Relations

Relations
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Functions

Some Functions And Their Graphs
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Algebra Of Real Numbers
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Trigonometric Functions

Introduction

Introduction
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Angles

Degree Measure
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Radian Measure
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Relation Between Radian And Real Numbers
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Relation Between Degree And Radian
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Trigonometric Functions

Trigonometric Functions
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Sign Of Trigonometric Functions
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Domain And Range Of Trigonometric Functions
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Trigonometric Functions Of Sum And Difference Of Two Angles

Trigonometric Functions Of Sum And Difference Of Two Angles
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Trigonometric Equations

Trigonometric Equations
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Principle Of Mathematical Induction

Introduction

Introduction
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Motivation

Motivation
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The Principle Of Mathematical Induction

The Principle Of Mathematical Induction
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Some Examples
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Complex Numbers And Quadratic Equations

Introduction

Introduction
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Complex Numbers

Complex Numbers
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Algebra Of Complex Numbers

Algebra Of Complex Numbers
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The Modulus And The Conjugate Of A Complex Number

The Modulus And The Conjugate Of A Complex Number
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Argand Plane And Polar Representation

Argand Plane And Polar Representation
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Quadratic Equations

Quadratic Equations
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Linear Inequalities

Introduction

Introduction
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Inequalities

Inequalities
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Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation

Algebraic Solutions Of Linear Inequalities In One Variable And Their Graphical Representation
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Graphical Solution Of Linear Inequalities In Two Variables

Graphical Solution Of Linear Inequalities In Two Variables
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Solution Of System Of Linear Inequalities In Two Variables

Solution Of System Of Linear Inequalities In Two Variables
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Permutations And Combinations

Introduction

Introduction
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Fundamental Principle Of Counting

Fundamental Principle Of Counting
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Permutations

Permutations When All The Objects Are Distinct
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Factorial Notation
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Derivation Of The Formula For 'P'
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Permutations When All The Objects Are Not Distinct Objects
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Combinations

Combinations
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Binomial Theorem

Introduction

Introduction
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Binomial Theorem For Positive Integral Indices

Binomial Theorem For Positive Integral Indices
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Binomial Theorem For Any Positive Integer N
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Some Special Cases
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General And Middle Terms

General And Middle Terms
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Sequences And Series

Introduction

Introduction
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Sequences

Sequences
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Series

Series
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Arithmetic Progression

Arithmetic Progression
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Arithmetic Mean
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Geometric Progression

Geometric Progression
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General Term Of A G.P
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Sum To N Terms Of A G.P
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Geometric Mean (G.M)
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Relationship Between A.M And G.M

Relationship Between A.M And G.M
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Sum To N Terms Of Special Series

Sum To N Terms Of Special Series
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Straight Lines

Introduction

Introduction
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Slope Of A Line

Slope Of A Line
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Slope Of A Line When Coordinates Of Any Two Points On The Line Are Given
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Conditions For Parallelism And Perpendicularity Of Lines In Terms Of Their Slopes
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Angle Between Two Lines
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Collinearity Of Three Points
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Various Forms Of The Equation Of A Line

Horizontal And Vertical Lines
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Point Slope Form
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Two-Point Form
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Slope-Intercept Form
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Intercept Form
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Normal Form
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General Equation Of A Line

Different Forms Of Ax + By + C = 0
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Distance Of A Point From A Line

Distance Between Two Parallel Lines
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Conic Section

Introduction

Introduction
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Sections Of A Cone

Circle, Ellipse, Parabola And Hyperbola
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Degenerated Conic Sections
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Circle

Circle
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Parabola

Standard Equation Of Parabola
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Latus Rectum
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Ellipse

Relationship Between Semi-Major Axis, Semi-Minor Axis And The Distance Of The Focus From The Centre Of The Ellipse
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Special Cases Of An Ellipse
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Eccentricity
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Standard Equation Of An Ellipse
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Latus Rectum
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Hyperbola

Hyperbola
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Eccentricity
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Standard Equation Of Hyperbola
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Latus Rectum
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Introduction To Three Dimensional Geometry

Introduction

Introduction
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Coordinate Axes And Coordinate Planes In Three Dimensional Space

Coordinate Axes And Coordinate Planes In Three Dimensional Space
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Coordinates Of A Point In Space

Coordinates Of A Point In Space
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Distance Between Two Points

Distance Between Two Points
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Section Formula

Section Formula
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Limits And Derivatives

Introduction

Introduction
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Intuitive Idea Of Derivatives

Intuitive Idea Of Derivatives
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Limits

Limits
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Algebra Of Limits
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Limits Of Polynomials And Rational Functions
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Limits Of Trigonometric Functions

Limits Of Trigonometric Functions
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Derivatives

Derivatives
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Algebra Of Derivative Of Functions
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Derivative Of Polynomial And Trigonometric Functions
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Mathematical Reasoning

Introduction

Introduction
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Statement

Statement
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New Statements From Old

Negation Of A Statement
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Compound Statements
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Special Words/Phrases

The Word "And"
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The Word "Or"
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Quantifiers
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Implications

Contrapositive And Converse
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Validating Statements

Validating Statements
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By Contradiction
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Statistics

Introduction

Introduction
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Measures Of Dispersion

Measures Of Dispersion
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Range

Range
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Mean Deviation

Mean Deviation
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Mean Deviation For Ungrouped Data
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Mean Deviation For Grouped Data
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Limitation Of Mean Deviation
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Variance And Standard Deviation

Variance And Standard Deviation
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Standard Deviation
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Standard Deviation Of A Discrete Frequency Distribution
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Standard Deviation Of A Continuous Frequency Distribution
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Shortcut Method To Find Variance And Standard Deviation
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Analysis Of Frequency Distribution

Analysis Of Frequency Distribution
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Comparison Of Two Frequency Distributions With Same Mean
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Probability

Introduction

Introduction
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Random Experiment

Outcomes And Sample Space
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Event

Event
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Occurrence Of Event
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Types Of Event
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Algebra Of Events
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Mutually Exclusive Events
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Exhaustive Events
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Axiomatic Approach To Probability

Axiomatic Approach To Probability
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Probability Of An Event
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Probabilities Of Equally Likely Outcomes
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Probability Of The Event 'A' Or 'B'
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Probability Of Event 'Not A'
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Shape

Shape

Shape

Shape

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New Statements From Old

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