UNIT I

EQUATIONS AND INEQUALITIES IN ONE VARIABLE

• Expressions and Formulas:  Working with order of operations, use of formulas from geometry and from algebra.

• Real Numbers: Learn the properties of real numbers and the number line. Simplifying expressions using these properties.

• Equations, Including Absolute Value Equations: Learn to use the properties of equality to solve one variable linear equations and inequalities.

• Inequalities and Absolute Value Inequalities: Learn to apply the properties of inequality to solve inequalities and absolute value inequalities.

UNIT II

INTRODUCTION TO LINEAR EQUATIONS

• Relations, Functions and Linear Equations: Study the definition of relations and functions. Use of mapping, tables, ordered sets and graph to represent relations and functions. Learn how to apply the vertical test to identify a function. Determine the difference between discrete vs. continues functions. Definition of linear equations and the Standard Form.

• 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)

• Two Variable Linear Inequalities and Absolute Value Inequalities.  Solving two variable inequalities by shading above o below the graph to indicate the solution set.

• Systems of Linear Inequalities and Introduction to Linear Programming and Its Applications.  Learn how to solve systems of two variable linear inequalities. This concept it is extended to introduce concepts as solution region, feasible region, and maximum and minimum of the optimization function. Solution of linear programming problems.

UNIT III

MANIPULATING POLYNOMIALS

• Polynomials:  Learn to apply the properties of exponents to simplify polynomial expressions.
• Adding polynomials:  Learn to add and subtract polynomials. Horizontal and vertical formats.

• Manipulate Radicals and Rational Exponents. Learn to simplify expressions that contain radicals and rational exponents.

• Radical Equations and Inequalities. Study how to solve radical equations and inequalities.

UNIT IV

QUADRATIC FUNCTIONS

• Quadratic Functions and Its Roots.  Solve quadratic functions using several methods. For example: By factoring, completing the square and by use of the Quadratic Formula.

• Discriminant, Product and Sum of Roots. Determine the number of roots of a quadratic equations. How to verify the solution with the product and sum of its roots.