CHAPTER 1
EXPRESSIONS AND FORMULAS
ONE VARIABLE EQUATIONS AND INEQUALITIES
|
| 1.- Expressions and Formulas: Order of Operations.* |
| 2.- Real Numbers: Properties of Numbers, and Number Sets.* |
| 3.- One Variable Linear Equations Including Absolute Value.* |
| 4.- One Variable Linear Inequalities Including Absolute Value.* (For Inequalities Real World Applications lesson.* See chapter 7) |
| 5.-Inequalities Real World Applications.* |
CHAPTER 2
RELATIONS AND FUNCTIONS
SYSTEMS OF TWO VARIABLE EQUATIONS AND INEQUALITIES
|
| 1.- Relations and Functions.* |
| 2.- Introduction to Slope of a Line.* |
| 3.- Two Variable Systems of Linear Equations.* |
| 4.- Two Variable Systems of Linear Inequalities.* |
CHAPTER 3
OTHER WAYS TO SOLVE SYSTEMS OF LINEAR EQUATIONS
LINEAR PROGRAMING
|
| 1.- Using Determinants to Solve Systems of Linear Equations: Cramer's Rule. |
| 2.- Using Augmented Matrix to Solve Systems of Linear Equations. Introduction of Matrices and their operations. |
| 3.- Linear Programing: Using a Set of Conditions to Create a Polygon and Using the Vertices to Optimize an Optimizing Function. |
CHAPTER 4
ARITHMATIC OF POLYNOMIALS AND PROPERTIES OF EXPONENTS
RADICAL EQUATIONS AND ONE INTRODUCTION TO COMPLEX NUMBERS.
|
| 1.- Adding, Substracting, Multiplying and Dividing Polynomials 1* |
| 2.- Adding, Substracting, Multiplying and Dividing Polynomials 2* |
| 3.- Algebra Tiles Adding Polynomials* (modeling: Concrete to abstract) |
| 4.- Algebra Tiles Multiplying and factoring Polynomials* (modeling: Concrete to abstract) |
| 5.- Properties of Exponents. Adding, Subtracting, Multiplying and Dividing.* |
| 6.- Simplifying Numeric Rational and Irrational Radicals.. Learn to simplify numerical radical expressions, multiply and divide them. |
| 7.- Rational Exponents and Radicals. Adding, Subtracting, Multiplying and Dividing. Including expressions with variables. |
| 8.- Radical Equations and Inequalities. Determining valid domain and solution.* |
| 9.- Complex Numbers. Adding, Subtracting, Multiplying and Dividing. |
CHAPTER 5
ANALYTIC GEOMETRY
CONICS: PARABOLA, CIRCLE, ELLIPSE, HYPERBOLE
|
| 1.- Quadratic Functions.* |
| 2.- Discriminant and Sum & Product of Roots.* |
| 3.- Distance Formula, and Midpoint Formula.* |
| 4.- Parabola: From Graph to Equation and From Equation to Graph. |
| 5.- Circle: From Graph to Equation and From Equation to Graph. |
| 6.- Ellipse: From Graph to Equation and From Equation to Graph. |
| 7.- Hyperbole: From Graph to Equation and From Equation to Graph. |
| 10.- Inequalities with All Conics. |
CHAPTER 6
REAL WORLD APPLICATIONS AND PROOFS
FOR CONICS AND POLYNOMIAL FUNCTIONS AND INEQUALITIES
|
| 1.- Conic Sections ad Their Generator |
| 2.- Conic Sections and The General Equation for Conics. |
| 3.- Parabola Formula Proof. |
| 4.- Ellipse Formula Proof. |
| 5.- Hyperbole Formula Proof. |
| 6.- A Ball Up to a Ramp Generates a Parabolic Model.* |
| 7.- Animation for the Ball Up to a Ramp (Vernier LabPro 2) |
| 8.- Finding the Maximum Area of a Rectangle with 24 wood sticks. Quadratic Model: Parabola* |
| 9.- Geometry and Algebra to Represent Arithmetic with Polynomials using Base 10 or Foam Prisms.* |
CHAPTER 7
FUNCTIONS THAT INVOLVE POLYNOMIALS
|
| 1.- Polynomials and Zeros, Roots or Solutions (Intersections with x-axis) |
| 2.- Mathematical Models Activity that Yields Polynomial Functions. |
| 3.- Rational Zero Theorem |
| 4.- Quadratic Technics to Solve Polynomial Functions of Higher Degree. |
| 5.- Composition of Functions, and Inverse of Functions. |
| 6.- Pascal's Triangle for Binomial expansion visual and with combinations formula. |
|
INSIDE EACH LESSON YOU MAY DO AS THIS GRAPHIC SHOWS
|
CHAPTER 8
RATIONAL EQUATIONS, EXPONENTIAL AND LOGARITMIC EQUATIONS
AND AN INTRODUCTION TO SEQUENCES AND SERIES (ARITHMETIC AND GEOMETRIC)
|
| 1.- Rational Equations.* |
| 2.- Base Number Systems Introduction: Base 10 to Base 2, Binary and Base 20. Converting between basis and Basic Math Operations with Properties of Real Numbers and Properties of Equality. |
| 3.- Base Number Systems Introduction: Arithmetic Operations |
| 4.- Arithmetic Operations With Base 16 or Hexadecimal in particular Multiplications |
| 5.- Arithmetic Operations With Base Different than base 10: Divisions |
| 6.- Exponential and Logarithmic Equations. |
| 7.- Arithmetic and Geometric Sequences and Series. |
CHAPTER 9
PROBABILITY AND STATISTICS TOPICS
(Topics in these lessons are also in the section for statistics)
|
| 1.- Measures of Central Tendency and Dispersion: Mean, Median and Mode. Standard Deviation and Variance. |
| 2.- Counting Principle. |
| 3- Combinations and Permutations. |
| 4.- Experimental Probability (Introduction) |
| 5.- Adding Probabilities (Module "OR") and Multiplying Probabilities (Module "AND") (From Informal to Formal) |
| 6- Binomial Probability. Calculated with the formula, the tables and with Ti-83 Texas Instrument Calculator. |
| 7- Normal Distribution: Introduction to Standard Normal Distribution and Z-score |
CHAPTER 10
PLAYING DICE, CARDS AND THE WHEEL OF FORTUNE.
A HANDS ON APPROACH TO LEARN PROBABILITY.
|
| 1.- Real World Probability with a Spinning Wheel. (You fill in the tables) |
| 2.- Real World Probability with a Spinning Wheel (Tables already fill) |
| 3.- Real World Probability with Dice and Cards (You fill the tables) |
| 3.- Real World Probability with Dice and Cards (Tables already fill) |
CHAPTER 11
ADVANCED TOPICS OF TRIGONOMETRY
|
| 1.- Trigonometry An In Depth Approach to Sine, Cosine, Tangent, Cotangent, Secant and Cosecant: Trigonometry Ratios and Their Graphs and Real World Applications. |
| 2.- Trigonometric Graphing of Functions with an emphasis in parameters. |
| 3.- Trigonometry Identities. Sum and Difference, Double Angle and Half Angle. PROOFS |
| 4.- Graphing Polar Functions: Limazon, Cardioid, Even or odd number of Leaves Rose (odd and even), Leminiscate, etc |
| 5.- Complex Roots and their graphs: with emphasis on phases and solution polygons. (Same lesson posted in trigonometry as Modeling in Trigonometry title.) |
