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ALGEBRA 1* and 2

Lesson with an (*) are Algebra 1 Lessons. Lessons without and (*) are Algebra 2 Lessons.

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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)

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 Coinditions 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, Subracting, Multiplying and Dividing Polynomials 1*
2.- Adding, Subracting, Multiplying and Dividing Polynomials 2*
3.- Properties of Exponents. Adding, Subracting, Multiplying and Dividing.*
4.- Rational Exponents and Radicals. Adding, Subtracting, Multiplying and Dividing.*
5.- Radical Equations and Inequalities. Determining valid domain and solution.*
6.- Complex Numbers. Adding, Subracting, Multiplying and Dividing.

CHAPTER 5

ANALITIC GEOMETRY

CONICS: PARABOLA, CIRCLE, ELLIPSE, HYPERBOLE

1.- Quadratic Functions.*
2.- Distance Formula, and Midpoint Formula.*
3.- Parabola: From Graph to Equation and From Equation to Graph.
4.- Circle: From Graph to Equation and From Equation to Graph.
5.- Ellipse: From Graph to Equation and From Equation to Graph.
6.- Hyperbole: From Graph to Equation and From Equation to Graph.
7.- Conic Sections ad Theinr Generator
8.- Conic Sections and The General Equation for Conics.
9.- Inequalities with All Conics.

CHAPTER 6

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.

INSIDE EACH LESSON YOU MAY DO AS THIS GRAPHIC SHOWS

CHAPTER 7

REAL WORLD APPLICATIONS AND PROOFS

FOR CONICS AND POLYNOMIAL FUNCTIONS AND INEQUALITIES

1.-Inequalities Real World Applications.*
2.- Ellipse Formula Proof.
3.- Hyperbole Formula Proof.
4.- Parabola Formula Proof.
5.- A Ball Up to a Ramp Generates a Parabolic Model.*
6.- Animation for the Ball Up to a Ramp (Vernier LabPro 2)
7.- Geometry and Algebra to Represent Arithmetic with Polynomials using Base 10 or Foam Prisms.*

CHAPTER 8

RATIONAL EQUATIONS, EXPONENTIAL AND LOGARITMIC EQUATIONS

AND AN INTRODUCTION TO SEQUENCES AND SERIES (ARITHMETIC AND GEOMETRIC)

1.- Rational Equations.*
2.- Exponential and Logarithmic Equations.
3.- Arithmetic and Geometic 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

7.- Trigonometry An In Depth Approach to Sine, Cosine, Tangent, Cotangent, Secant and Cosecant: Trigonometry Ratios and Their Graphs and Real World Applications.
8.- Trigonometry Identities. Sum and Difference, Double Angle and Half Angle. PROOFS

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