CHAPTER 1 NUMBER SYSTEMS
1) NATURAL NUMBERS
- Mixed Operations in Natural Numbers Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , from 12:30 to 24:00 VIDEO 90 ,
- Calculate The Sum of Consecutive Natural Numbers Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , VIDEO 6 , from 24:30 to end VIDEO 90 , from 00:00 to 17:00 VIDEO 91 ,
- Problem About The Sum of Consecutive Natural/Odd/Even Numbers
- Extra Lesson general natural numbers with 6th grade VIDEO 90 , VIDEO 91 ,
CHAPTER 2 MODULAR ARITHMETIC
1) CLOCK ARITHMETIC AND MODULAR
2) OPERATIONS IN MODULAR ARITHMETIC
3) BINARY OPERATIONS
CHAPTER 3 EXPONENTS AND RADICALS
1) REAL NUMBERS
2) ABSOLUTE VALUE
3) EXPONENTS WITH REAL NUMBERS
- Exponential Equations
4) SQUARE ROOTS
-Properties of square roots
-Simplifing square roots
-Multiplying and dividing square roots
-Adding and subtracting square roots Video 8 ,
-Comparing the square roots Video 1 ,
-Square root of irrational sum / A Special case for square roots Video 1 ,
5) RATIONAL EXPONENTS
6) RADICALS
7) RADICAL EQUATIONS
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CHAPTER 4 SETS
1) THE CONCEPT OF SETS Video 1 ,
a) Sets
b) Representing Sets Vid 1 , Vid 2 ,
c) Number of Elements
d) Types of Sets
e) Subsets
-Subsets Including or Not Including Distinct Elements Vid 1 ,
-Subsets With Distinct Number of Elements Vid 1 ,
The Number of Subsets By Pascal's Triangle
2) OPERATIONS ON SETS
a) Union of Sets
b) Intersection of Sets
c) Complement of a Set
d) Difference of Two Sets
3) APPLICATIONS ON SETS (Using set properties for solving written problems)
-SURVEY PROBLEMS about sets union, intersection, difference, complement Vid 1 , Vid 2 , Vid 3 ,
The number of elements of union of two sets
The number of elements of union of three sets
4) MATHEMATICAL QUANTIFIERS
Universal quantifier; '' for all, for every ''
Existential quantifier; '' for some, at least one ''
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CHAPTER 5 FUNCTIONS
1) RELATIONS
Ordered Pairs
Cartesian Product
Analytic Plane
Relations
Definition of Functions
2) INTRODUCTION TO FUNCTIONS
Finding Results for a Given Function
-Finding Results for The Piece-wise Defined Function Vid 1 ,
Types by Checking Domain and Range
One to One - Into - Onto
Drawing Graph of First Degree Functions
Domain of Functions
Even Odd Functions
Increasing, Decreasing and Constant Functions
Reading Graph of Functions Video 1 ,
3) OPERATIONS ON FUNCTIONS
Basic Operations
Composition of Functions Vid 1 , Video 1 , Video 2 , Video 3 ,
Inverse of Functions Vid 1 , Video 1 ,
-Finding Results for The Inverse of a Function Vid 1 ,
4) GRAPHS OF FUNCTIONS (optional)
Transformation of Graphs
a) Vertical Shift b) Horizontal Shift c) Reflection d) Vertical Stretch and Shrink d) Horizontal Stretch and Shrink
Graphs of Elementary Functions
Exponential, Radical, Rational, Absolute Value
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CHAPTER 6 POLYNOMIALS
1) ALGEBRAIC EXPRESSIONS
2) POLYNOMIALS
-Equal polynomials Vid 1 ,
-Constant and Zero polynomial Vid 1 ,
-Polynomial functions Vid 1 ,
A. ADDING POLYNOMIALS
B. SUBTRACTING POLYNOMIALS
C. MULTIPLYING POLYNOMIALS Vid 1 ,
D. DIVIDING POLYNOMIALS
1. Dividing a Polynomial by a Monomial Vid 1 ,
2. Dividing Two Polynomials (long division of polynomials) Vid 1 ,
3. Synthetic Division (Horner’s Method)
a. Dividing by x – c
b. Dividing by ax + b
4. Finding the Remainder Vid 1 ,
5. Finding the Remainder of Division by xn + a
E. BINOMIAL EXPANSION OF POLYNOMIALS Vid 1 ,
3) BINOMIAL EXPANSION
4) BASIC IDENTITIES
-Square of a Binomial
-Cube of a Binomial
-Difference of Two Squares (Factorization)
-Sum of Two Cubes (Factorization)
-Difference of Two Cubes (Factorization) (mixed)
5) FACTORIZATION OF POLYNOMIALS
-Taking Out a Common Factor
-Factoring by Grouping
-Factorization Identities (You can find them in previous part. Last three of basic identities are about factorization.)
-Factoring Trinomials Video 12 , Video 13 , using perfect square method
*All factoring methods mixed Vid 1 ,
6) SIMPLIFYING RATIONAL EXPRESSIONS WITH POLYNOMIALS Vid 1 , helpful videos video 26 ,
-Adding and Subtracting Rational Expressions Vid 1 ,
CHAPTER 7 QUADRATICS
1) SOLVING QUADRATIC EQUATIONS
a) by Factoring
b) by Completing Perfect Square
c) by Quadratic Formula
d) Discriminant
-all methods mixed Vid 1 ,
e) Solving Problems
2) VIETA’S THEOREM Vid 1 ,
3) DERIVING QUADRATIC EQUATIONS
4) EQUATIONS REDUCIBLE TO QUADRATIC FORM
a) Equations With Different Degree (Changing Unknown)(using substitution with t) Vid 1 ,
b) Equations Involving Products and Quotients Vid 1 ,
c) Equations Involving Radicals
d) Equations Involving Absolute Value
Systems of Quadratic Equations
5) QUADRATIC INEQUALITIES Vid 1 ,
-Inequalities reducible to quadratics Vid 1 ,
6) SYSTEMS OF INEQUALITIES
7) GRAPHS OF QUADRATIC FUNCTIONS
-Sketching a Graph Vid 1 ,
CHAPTER 8 COMPLEX NUMBERS
1) A
1)
a)
b)
2)
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2) B
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A)
1)
2)
B)
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CHAPTER 9 COUNTING PRINCIPLES AND PROBABILITY
1) Counting Principles
A. THE ADDITION PRINCIPLE
B. SYSTEMATIC LISTING
1) Simple Listing
2) Using a Product Table
3) Using a Tree Diagram
C. THE MULTIPLICATION PRINCIPLE Vid 1 ,
2) Permutation
A. FACTORIAL NOTATION
B. PERMUTATIONS OF n ELEMENTS
C. PERMUTATIONS OF r ELEMENTS SELECTED FROM n ELEMENTS Vid 1 ,
D. PERMUTATIONS WITH RESTRICTIONS
1) Permutations with Grouped Elements
2) Permutations with Identical Elements Vid 1 ,
3) Circular Permutation
3) Combination Vid 1 , Vid 2 , Vid 3 ,
4) Probability Vid 1 , Vid 2 , Vid 3 ,
*Counting Principles and Probability
CHAPTER 10 PERIMETERS AND AREAS OF PLANE FIGURES
1) POLYGONS AND THEIR PROPERTIES
2) ANGLES OF A POLYGON
3) QUADRILATERALS & TYPES OF QUADRILATERALS
A. PARALLELOGRAM
B. RECTANGLE
C. SQUARE
D. RHOMBUS
E. KITE
F. TRAPEZOID
CHAPTER 11 STATISTICS
1) BASIC CONCEPTS OF STATISTICS
2) PRESENTING AND INTERPRETING DATA
3) STATISTICAL MEASURES
1. Mean
2. Median
3. Mode
4. Range
I watched only a few from start. These videos explain everything even the part you don't need in high school. You may want to watch them to have general idea. Video 0 , Video 1 , Video 2 , Video 3 , Video 4 , Video 5 , Video 6 , Video 7 , Video 8 , Video 9 , Video 10 , Video 11 , Video 12 , Video 13 , Video 14 , Video 15 , Video 16 , Video 17 ,
1) Frequency Distribution Video 1 ,Graphing Histogram, Dots Video 2 , Group Frequency Video 3 , Video 4 , Mean - Median - Mode Video 5 , Video 6 , Video 7 ,
2)? Percentiles and Dispersion Video 8 , Video 9 , Video 10 , we don't have this part in our book
3) Ranges and standard deviation Video 11 , Normal Distribution Video 12 , Video 13 ,
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CHAPTER 12 LOGIC
Video 1 ,
1) PROPOSITIONS
Truth Values of Propositions
Equivalent Propositions
Negation of Propositions
Negations of Symbols
Truth Table
2) COMPOUND PROPOSITIONS
a) Conjunction
b) Disjunction
Common Properties of Conjunction and Disjunction:
c) Conditional
d) Biconditional
-Finding results of compound propositions with numbers Vid 1 , Vid 2 , Vid 3 ,
-Simplifying compound propositions with letters Vid 1 , Vid 2 , Vid 3 ,
-Proving equivalence of compound propositions with truth table Vid 1 ,
3) TAUTOLOGY AND CONTRADICTION
-Proving tautology or contradiction with truth table Vid 1 ,
4) ELECTRICAL CIRCUITS (optional)
5) MATHEMATICAL INDUCTION (optional)
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