Upon successful completion of the course, students will be able to: identify sets and properties of real numbers; define natural- number exponents; apply the rules of exponents  and the rules for order of operations to evaluate expressions; define rational exponents whose numerators are one and whose numerators are not one; evaluate a variable expression; simplify a variable expression using addition, multiplication, and the Distributive Property; translate a verbal expression into a variable expression; determine whether a given number is a solution of an equation; solve an equation in the form x+a=b; solve an equation in the form ax=b; solve uniform motion problems; solve applications using formulas; solve problems involving angles; solve value mixture problems; solve percent mixture problems; define polynomials, demonstrate addition, subtraction, multiplication, and division of polynomials; explain factoring out of a common monomial; factor trinomials; factor the difference of two squares and perfect square trinomial; define rational expressions; demonstrate addition, subtraction, multiplication, and division of rational expressions; simplify complex fractions;  solve equations containing fractions; solve literal equations for one of the variables; demonstrate graphing linear equations, vertical and horizontal lines, and fine distance between two points; calculate the slope of a line; use the slope to solve application; write equations of parallel and perpendicular lines; use point-slope and slope-intercept form to write an equation of a title; locate the “x- and y-“ intercepts of a graph; to solve a system of linear equations by graphing, substitution method, and additions method; solve investment problems; solve application problems using two variables; to solve problems having inequalities; to solve an inequality using the addition property and multiplication property of inequalities; graph an inequality in two variables; to simplify numerical radical expressions; solve an equation containing a radical expression; calculate quadratic equations using the quadratic formulas, factoring and the Square Root Property; solve a quadratic equation by completing the square; and develop  analytical skills in order to better comprehend various algebraic theories and applications.