UNIT I

EQUATIONS AND INEQUALITIES IN ONE VARIABLE

• Working with Expressions and Formulas: Order of operations, formulas, area formulas and quadratic formula.

• Understanding Real Numbers: Number line, number sets, properties of numbers (commutative, associative, distributive...), simplifying expressions.

• Solving Equations, Including Absolute Value Equations: Properties of equality, solution of one variable linear equations, absolute value equations.

• Solving Inequalities, Including Absolute Value Inequalities: Properties of inequality, solution of one variable linear inequalities and absolute value inequalities.

UNIT II

INTRODUCTION TO LINEAR EQUATIONS

• Understanding Relations and Functions and Linear Equations: Definition of relation and function, representation of relations as mapping, table, ordered set, and graph. State domain and range. Identify a function (vertical line test), discrete vs. continuous function, identification of linear equations, standard form for two variable linear equations.

• Learning About Slope: Slope formula (run vs. rise and two points), falling to the right, horizontal, vertical, negative and positive cases for the slope. Slope of parallel and perpendicular lines.

• Working With Systems of Linear Equations: Slope intercept form and point-slope form problems that involve a point and slope, two points, etc. Solving systems of two variable linear equations by substitution, linear combinations and graphing. Introduction to special functions (step function, constant function, identity function and absolute value function)

• Solving Two Variable Linear Inequalities Including Absolute Value Inequalities. Learn where to shade above or below the ´line. Is it a broken line or a solid one?

UNIT III 

SOLVING SYSTEMS OF LINEAR EQUATIONS

• Using Determinants to Solve Equations In Two Variables and Solving Equations In Three Variables: Second order determinant, Cramer's rule, and systems of three variable linear equations.

• Solving Systems of Linear Inequalities. Introduction to Linear Programming and Its Applications. It covers solution of two variable linear inequalities, including absolute value ones. Solution region and feasible region, maximum and minimum of an optimization function and linear programming problems.

• Using Matrices to Solve Systems of Equations with inverse and Augmented. Covers addition and subtraction of matrices, multiplication of matrices and inverse of a matrix.

UNIT IV 

MANIPULATING POLYNOMIALS

• Working with Polynomials: Properties of Exponents.
• Working with Polynomials: Adding, Subtracting, Multiplying, Dividing and Factoring. Include modeling with algebra tiles and blocks. F.O.I.L., synthetic division and Greatest Common Factor.

• Learning to Manipulate Radicals and Rational Exponents. It teaches about rational exponents and how they relate to radicals. Roots of real numbers and radical expressions.

• Solution for Radical Equations and Inequalities.  Learn how to solve equations and inequalities with radicals.

• Learning About COMPLEX NUMBERS. Imaginary roots, simplify expressions with imaginary numbers, simplify complex numbers and expressions. Iterations.

UNIT V

QUADRATIC FUNCTIONS

• Learning About Quadratic Functions and Its Roots. Solution of quadratic equations by graphing, by graphing features, by factoring, by quadratic formula and by completing the square.

• Discriminant and Product and Sum of Roots. Learn how to determine if a quadratic equation has one, two, or none real roots, and how to verify the solution using the product and sum of the roots.

UNIT VI 

UNDERSTANDING CONIC SECTIONS

• Working With Distance and Midpoint Formulas. Lesson that teaches how to use the distance formula, how to find the midpoint with two endpoints, and endpoint of a segment given the midpoint and one endpoint.

• Parabola: Formula and Graphing. Learn how to use the vertex and general formulas of horizontal and vertical parabolas, and how to find the equation given the graph.

• Circles: Formula and Graphing. This lesson is aimed at teaching how to use the standard and general formulas of a circle, and how to use the distance and midpoint formulas to find the equation of a circle.

• Ellipses: Formula and Graphing.Learn the formal definition of an ellipse, and how to use the general and standard formulas of vertical and horizontal ellipses, and how to determine the equation from the graph.

• Hyperbolas: Formula and Graphing. Equation For Conics: It teaches how to graph the standard and general forms of horizontal and vertical hyperbolas, and how to get the equation of the graph of a hyperbola and its asymptotes using the point-slope formula. It finalizes teaching how to determine from the general equation for conics, which conic a given equation represents.

• Solving Systems of Equations and Inequalities That Involve Conics. Learn how to solve systems that involve circles, parabolas, ellipses and hyperbolas in equations and inequalities.

UNIT VII 

LEARNING ABOUT POLYNOMIAL FUNCTIONS

• Working With Polynomials To Find Zeros. Find out if binomial is a factor of a polynomial by using synthetic division, and find the factors of a polynomial given one factor. Learn to apply the remainder and factor theorems to find zeros, and the Descarte's rule of signs to find out the number of positive, negative and imaginary zeros. Learn to find the polynomial equation for a given number of zeros.

• Applying The Rational Zero Theorem to Find The Zeros in a Polynomial Function. This is done using a synthetic division table to find out if the possible zeros are in fact solutions of the polynomial equation.

• Can Quadratic Techniques Solve Polynomial Equations? Learn to use the quadratic equations to solve equations of an even degree.

• Composition e Inverse In Polynomial Functions.   Find the composition of a given pair  of functions or a relation. Learn to find the inverse function of a linear equation. Find out the result of the composition of a function and its inverse function.

UNIT VIII 

LEARNING ABOUT RATIONAL EXPRESSIONS 

AND EQUATIONS

• Solving Rational Equations.   This lesson teaches how to simpify rational expressions and how to find the LCD and apply this to find the solution of rational equations.

UNIT IX 

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

• Working with Exponential and Logarithmic Functions. Learn how to use the properties of rational exponents and radicals to simplify expressions with radical exponents. Learn how to apply the properties of logarithms to solve logarithmic equations and inequalities. Find the logarithms and antilogarithms of numbers and learn about exponential and natural logarithms.

UNIT X 

ARITHMETIC AND GEOMETRIC SERIES

• Working with Arithmetic and Geometric Sequences and Series.Find the terms of arithmetic and geometric series and learn to calculate the sum, including infinte geometric series.

UNIT XI 

LEARNING PROBABILITY

• The Counting Principle.This lesson teaches how to find out the number of outcomes for a set of events happening  in succession one after the other. Students may see the outcomes for each digit or letter position.

• Permutations and Combinations. In this lesson students will learn the difference between a permutation and a combination, and how repeated elements or circular arrangements will affect the number of outcomes.

• An Introduction to Probability. This lesson presents the formal and informal definitions of probability. Students learn how to find probabilities using a spinner, a dice and a deck of cards. Students also apply probability to problems involving permutations and combinations.

• Dependent and Independent Probability. Great lesson to learn about dependent and independent probability and exclusive and inclusive events and how they affect the probability of an event. Students will understand when they add probabilities and when they multiply them.

• Binomial Experiments and Their Probabilities. In this lesson students will learn about the binomial theorem and how it may used to find the probabilities of binomial experiments and simulations.

• Experimental and Geometric Probability. Learn in an easy way how to find experimental probability from data gathered from a survey, and how to find probability using the ratio of lengths, areas and volumes.