CHAPTER 1 TRIGONOMETRY
How to memorize the trigonometric table Video 1 , Video 2 ,
A) Trigonometric Theorems
1) The Law Of Sine
2) The Law Of Cosine
3) Formulas For The Area Of a Triangle,
B) Trigonometric Formulas
1) Sum and Difference Formulas Video 1 , Video 2 , Video 3 , Video 4 ,
-Shape(Figure) Examples Vid 1 ,
2) Double-Angle Formulas
3) Half-Angle Formulas
4) Reduction Formulas
5) Sum To Product Formulas
6) Product To Sum Formulas
C) Trigonometric Functions
1) The Sine Function
2) The Cosine Function
3) The Tangent Function
4) The Cotangent Function
5) The Secant and the Cosecant Functions
6) "Periodic Functions"
7) Periods Of Trigonometric Functions
GRAPHS OF TRIGONOMETRIC FUNCTIONS
8) Graph Translations
INVERSE TRIGONOMETRIC FUNCTIONS
9) The Arcsine And The Arccosine Functions
10) The Arctangent and The Arccotangent Functions
-Finding results of inverse trigonometric ratios Vid 1 ,
D) Trigonometric Equations
1) Basic Formulas Vid 1 ,
2) Factorizing Equations
2) Equations with A Common Ratio
3) Linear Equations In Sinx And Cosx
4) Homogeneus Equations In Sinx And Cosx
5) Maximum And Minimum Values Of a Trigonometric Functions
6) Further Trigonometric Equations
E) Trigonometric Inequalities
1) Basic Trigonometric Inequalities Vid 1 , Vid 2 ,
2) Advanced Trigonometric Inequalities
CHAPTER 2 POLYGONS
1) Basic Concepts of Polygons
2) Quadrilaterals
1) PARALLELOGRAM
2) RHOMBUS
3) RECTANGLE
4) SQUARE
5) TRAPEZOID
6) KITE
CHAPTER 3 LOGARITHMS AND EXPONENTIAL
a EXPONENTS AND EXPONENTIAL FUNCTIONS
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1. EXPONENTS
A. INTEGER EXPONENTS
-Simplifying Rational Exponential Expression Vid 1 ,
-Adding Subtracting Exponential Expressions Vid 1 ,
-Adding Subtracting Exponential Expressions and Simplifying Vid 1 ,
-Substituting Exponential in Another Similar One Special Type Example Vid 1 ,
B. ROOTS AND RADICAL EXPRESSIONS
-Perfect square examples simplify + 4 operations Vid 1 ,
-Moving Exponential Expressions Out of the Square Root Vid 1 ,
-Adding and Subtracting Square Roots Vid 1 ,
-Multiplying Sum or Difference of Square Roots Vid 1 ,
-Rationalizing a Denominator Vid 1 ,
-Moving Exponential Expressions Out of the Radicals Vid 1 ,
-Working with Rational Exponents Vid 1 ,
-Multiplying Dividing Radicals by Rational Exponents Vid 1 ,
-Radical Equations
type 1 Vid 1 ,
C. RATIONAL EXPONENTS
D. REAL EXPONENTS
–The Number e
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2. EXPONENTIAL FUNCTIONS
A. BASIC CONCEPT
B. GRAPHS OF EXPONENTIAL FUNCTIONS
C. PROPERTIES OF EXPONENTIAL FUNCTIONS
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3. SIMPLE VARIATIONS OF EXPONENTIAL FUNCTIONS (OPTIONAL)
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4. APPLICATIONS OF EXPONENTIAL FUNCTIONS
A. EXPONENTIAL GROWTH
B. EXPONENTIAL DECAY
C. COMPOUND INTEREST
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b LOGARITHMS AND LOGARITHMIC FUNCTIONS
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1. LOGARITHMS
A. BASIC CONCEPT Vid 1 ,
B. TYPES OF LOGARITHM
1. Common Logarithms
2. Natural Logarithms
C. PROPERTIES OF LOGARITHMS
1. Changing the Base of a Logarithm
-Using Properties of Logarithm Examples Vid 1 - Vid 2 - Vid 3 (Express a log in terms of another), Vid 4 - Vid 5 (Simplify a log by changing base and number into exponential form),
-Adding Subtracting same base logarithm using properties Vid 1 ,
-Adding Subtracting different base logarithm using properties Vid 1 ,
-Simplifying multiplication of logarithms Vid 1 ,
-Properties of Logarithm replace base and log Vid 1 ,
D. USING A TABLE OF LOGARITHMS
1. Parts of Logarithm
2. Using a Table of Logarithms
–Table of Logarithms
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2. LOGARITHMIC FUNCTIONS
A. BASIC CONCEPT
B. GRAPHS OF LOGARITHMIC FUNCTIONS Vid 1 ,
C. PROPERTIES OF LOGARITHMIC FUNCTIONS
1. Sign of a Logarithmic Function
2. Inverse of a Logarithmic Function Vid 1 ,
3. Monotone Property of Logarithmic Functions
–Logarithmic Spirals
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3. SIMPLE VARIATIONS OF LOGARITHMIC FUNCTIONS (OPTIONAL)
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4. APPLICATIONS OF LOGARITHMIC FUNCTIONS
A. THE RICHTER SCALE
B. THE pH SCALE
C. THE DECIBEL SCALE
–Estimating World Population
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c EXPONENTIAL AND LOGARITHMIC EQUATIONS & INEQUALITIES
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1. EXPONENTIAL EQUATIONS AND INEQUALITIES
A. EXPONENTIAL EQUATIONS
1. Equations of the Form af(x) = ag(x) Vid 1 , (type 1)
2. Equations of the Form af(x) = b (type 2)
3. Equations of the Form af(x) = bg(x) Vid 1 , (type 3)
4. Working with Exponential Equations
5. Exponential Equations with a Unique Solution
6. Equations of the Form f(x)g(x) = f(x)h(x) Vid 1 , (type 4)
7. Exponential Equations with Parameters
B. EXPONENTIAL INEQUALITIES
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2. LOGARITHMIC EQUATIONS AND INEQUALITIES
A. LOGARITHMIC EQUATIONS
1. Equations of the Form logf(x) g(x) = b
2. Equations of the Form logf(x) g(x) = logf(x) h(x)
3. Working with Logarithmic Equations
4. Equations with Logarithms to Different Bases
5. Logarithmic Equations with a Unique Solution
6. Logarithmic Equations with Parameters
B. LOGARITHMIC INEQUALITIES
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3. SYSTEMS OF EQUATIONS AND INEQUALITIES
A. SYSTEMS OF EQUATIONS
B. SYSTEMS OF INEQUALITIES
–The Slide Rule
–What is a Logarithm?
CHAPTER 4 CIRCLES
1) Basic Concepts
1) Circles
2) Chords
3) Arcs
4) Tangents
2) Angles and Circles
1) Inscribed Angles and Arcs
2) Angles Formed by Secants
3) Angles Formed by Tangents
4) Angles Formed by Chords,
3) Segments and Circles
1) Segments Formed by Tangents
2) Segments Formed by Secants
3) Segments Formed by Chords
4) Areas of Circular Regions
1) Area of Circular Region,
2) Area of Sector
3) Area of Ring
CHAPTER 5 ANALYTIC ANALYSIS OF LINES AND CIRCLE
1) Points and Lines on Coordinate Plane
1) Coordinate Plane,
2) Distance Between Two Points,
3) Midpoint of Line Segment,
4) Centroid of a Triangle,
5) Area of Triangle,
6) Dividing a Line Segment With a Given Ratio Vid1 , Vid2 , Vid3 , Vid4 , Vid5 ,
7) Slope of a Line,
8) Equation of a Line
9) Finding the Slope of a Line with a Given Equation,
10) Relative Positions of Two Lines,
11) Distance from a Point to a Line,
12) The Angle Between Two Lines
13) Symmetry of a Point
2) Equation of a Circle on Coordinate plane
1) Equation of Circle
2) Positions of Lines and Circles
CHAPTER 6 MATRICES AND DETERMINANTS
1) Matrices
1) Basic concepts,equal matrices
2) Sum and difference of matrices
3) Product of matrices
4) Transpose of a matrix
5) Inverse of a matrix
2) Determinant
1) Determinant of a matrix 2x2
2) Determinant of a matrix 3x3
3) Properties of determinants,
4) Solving system of linear equations with three unknowns (Cramer's method)
5) Area of Triangle, Lines in the Plane
CHAPTER 7 COUNTING PRINCIPLES AND PROBABILITY
1) Counting Principles
1) The Addition Principle,
2) Systematic Listing,
3) Systematic Listing,
2) Permutation
1) Factorial Notation,
2) Permutations of n Elements,
3) Permutations of r Elements Selected from n elements
3) Combination
1) Combinations of r Elements Selected from n elements
4) Probability
1) Basic Concepts and Definitions of Probability,
2) Working with Probability,
3) Counting Principles and Probability
CHAPTER 8 SOLIDS
1) Prism
2) Pyramid
3) Cylinder
4) Cone
5) Sphere
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CHAPTER 1