CHAPTER 1 LOGIC Video 1 ,
1) PROPOSITIONS
– Truth Values of Propositions
– Equivalent Propositions
– Negation of Propositions
– Negations of Symbols
– Truth Table
2) COMPOUND PROPOSITIONS
A) CONJUNCTION '' AND ''
B) DISJUNCTION '' OR ''
Common Properties of Conjunction and Disjunction:
C) CONDITIONAL '' IF ...... THEN ...... ''
D) BICONDITIONAL '' ...... IF AND ONLY IF ...... ''
– 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
5) MATHEMATICAL QUANTIFIERS
6) MATHEMATICAL INDUCTION
CHAPTER 2 SETS
1) GENERAL TERMS 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) SET OPERATIONS
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 ''
CHAPTER 3 FUNCTIONS
1) RELATIONS
A) ORDERED PAIRS
B) CARTESIAN PRODUCT
C) ANALYTIC PLANE
D) RELATIONS
E) 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
A) BASIC OPERATIONS
B) Composition of FunctionsCOMPOSITION OF FUNCTIONS Vid 1 , Video 1 , Video 2 , Video 3 ,
C) INVERSE OF FUNCTIONS Vid 1 , Video 1 ,
– Finding Results for The Inverse of a Function Vid 1 ,
4) GRAPHS OF FUNCTIONS (optional)
A) TRANSFORMATION OF GRAPHS
1) Vertical Shift
2) Horizontal Shift
3) Reflection
4) Vertical Stretch and Shrink
5) Horizontal Stretch and Shrink
B) GRAPHS OF ELEMENTARY FUNCTIONS
1) Exponential,
2) Radical,
3) Rational,
4) Absolute Value
CHAPTER 4 EXPONENTS - RADICALS
1) EXPONENTS
Calculating Exponents
Simplifying Simple Exponents
Multiplying and Dividing Exponents
Adding Subtracting Exponents
Simple Exponential Equations
Additional Types of Examples with Exponents
2) RADICAL EXPRESSIONS
General Properties
Square Roots
– Properties of square roots
– Simplifying square roots
– Comparing the square roots Video 1 ,
– Adding and subtracting square roots Video 1 ,
– Multiplying and dividing square roots
3) RATIONALIZING DENOMINATOR
4) NTH ROOT OF A NUMBER
Simplifying nth Root
Operations on nth Root
5) RATIONAL NUMBER EXPONENTS
6) RADICAL EQUATIONS
7) SQUARE ROOT OF IRRATIONAL SUM / A SPECIAL CASE FOR SQUARE ROOTS Video 1 ,
CHAPTER 5 POLYNOMIALS
1) DEFINITION OF POLYNOMIALS
*Constant polynomial and zero polynomial Vid 1 ,
*Polynomial Functions Vid 1 ,
*Constant term
*Sum of the coefficients
* Equal Polynomials Vid 1 ,
2) OPERATIONS ON POLYNOMIALS
a. Adding and Subtracting Polynomials
b. Multiplying Polynomials Vid 1 ,
c. Dividing Polynomials
1. Dividing a Polynomial by a Monomial Vid 1 ,
2. Dividing Two Polynomials (long division) Vid 1 ,
3. Horner's Method (Synthetic Division)
a. Dividing by x – c
b. Dividing by ax + b
4. Finding the Remainder of Division by x – a Vid 1 ,
5. Finding the Remainder of Division by xn + a
3) BINOMIAL EXPANSION Vid 1 ,
– Square of a Binomial
– Cube of a Binomial
4) FACTORING POLYNOMIALS
FACTORING METHODS
A) Taking Common Factor Out
B) Grouping
C) Factoring Trinomials ax2 + bx + c
*1) If a=1 Video 12 ,
*2) If a≠1 Video 13 ,
D) Factoring Perfect Square Trinomials
E) Completing the Square
F) Using Identities
– Difference of Two Squares
– Sum of Two Cubes
– Difference of Two Cubes
G) Factoring Binomials of the Form
*All factoring methods mixed examples Vid 1 ,
5) RATIONAL EXPRESSIONS WITH POLYNOMIALS
a) Simplifying Rational Expressions Vid 1 ,
b) Adding Subtracting Rational Expressions Vid 1 ,
c) Decomposing Rational Expressions (Partial Fractions)
General About Algebraic Expressions helpful videos video 26 ,
CHAPTER 6 NUMBER SYSTEMS
1) 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 ,
Mixed Operations on Natural Numbers
Even and Odd Numbers
Calculate The Sum of Consecutive Natural Numbers (The Gauss Formula) 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 ,
Consecutive Even-Odd Numbers
The Sum Formula For Arithmetic Progression
– Extra Lesson general natural numbers with 6th grade VIDEO 90 , VIDEO 91 ,
2) DIVISIBILITY
Finding Digits by Checking Divisibility
Prime Factorization
Greatest Common Factor
Least Common Multiple
3) INTEGERS
Mixed Operations on Integers
Linear Equations With Integers
4) RATIONAL AND IRRATIONAL NUMBERS
Fractional and Decimal Forms of a Rational Number
Repeating Decimals in Rational Form
4 Operations on Rational Numbers
Types of Fraction
Mixed Operations on Rational Numbers
Mixed Fractions
Linear Equations With Rational Numbers
5) REAL NUMBERS
6) MODULAR ARITHMETIC
Modular Arithmetic for 4 operations
Written Problems about Modular Arithmetic
Modular Equations
Find the remainder of large exponents with Modular Arithmetic
CHAPTER 7 COMPLEX NUMBERS
1) THE IMAGINARY UNIT i
Powers of Imaginary Unit
2) COMPLEX NUMBERS BASIC(STANDARD) FORM
Equal Complex Numbers
Square Roots of a Complex Number
3) EQUATIONS WITH IMAGINARY ROOTS
4) THE COMPLEX PLANE
5) CONJUGATE OF A COMPLEX NUMBER
6) BASIC OPERATIONS IN COMPLEX NUMBER
Adding Subtracting Complex Numbers
Multiplying Complex Numbers
Powers of 1+i and 1–i
Dividing Complex Numbers
Multiplicative Inverse of a Complex Number
7) MODULUS OF A COMPLEX NUMBER
8) DISTANCE BETWEEN 2 COMPLEX NUMBERS ON COMPLEX PLANE
9) POLAR COORDINATE SYSTEM 11TH GRADE
CHAPTER 8 COUNTING PRINCIPLES AND PROBABILITY (Combinatorics)
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) PERMUTATIONS
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) COMBINATIONS Vid 1 , Vid 2 , Vid 3 ,
4) PROBABILITY 11TH GRADE Vid 1 , Vid 2 , Vid 3 ,
*Counting Principles and Probability
CHAPTER 9 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 Including Quadratic Equations
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
e) 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 of Parabola Vid 1 ,
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
4) CIRCULAR REGIONS
Area of circular regions
Area of a ring
CHAPTER 11 STATISTICS
1) BASIC CONCEPTS OF STATISTICS
2) PRESENTING AND INTERPRETING DATA
3) STATISTICAL MEASURES
A) MEAN
B) MEDIAN
C) MODE
D) 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 ,
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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VID1, VID2, VID3, VID4, VID5, VID6, VID7, VID8, VID9, VID10, VID11, VID12, VID13, VID14, VID15, VID16,