Course

Objective:

Learning Outcomes:

• Identify sets and properties of real numbers
• 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
• Define polynomials
• Demonstrate addition, subtraction, multiplication, and division of rational expressions
• Use the properties of equality
• Solve linear and rational equations
• Analyze and solve geometric, motion, and business problems
• Perform operations on complex numbers
• Calculate the absolute value of a complex number
• Solve polynomial and other equations by factoring
• Demonstrate knowledge of linear, compound, quadratic, and rational inequalities
• Define and use absolute value
• Solve equations with two absolute values
• Calculate the slope of a line
• Locate the x- and y- intercepts of a graph
• Apply knowledge to solve proportions
• Evaluate a function
• Graph a quadratic function
• Recall the characteristics of polynomial functions and construct a graph
• Use vertical and horizontal translations to graph functions
• Use vertical and horizontal stretching and shrinking to graph functions
• Locate the domain of a rational number. Identify vertical and horizontal asymptotes of rational functions
• Construct functions as compositions
• Recall the definition of a one-to-one function
• Analyze and verify inverse functions
• Illustrate graphing exponential functions
• Evaluate common and natural logarithms
• Use logarithms to solve geology, population growth, and charging a battery problems
• Use logarithms to analyze problems in electronics and physiology issues
• Use the Remainder Theorem and the Factor Theorem
• Recall the fundamental Theorem of Algebra
• Locate rational roots of polynomial equations
• Apply the Intermediate Value Theorem and the Bisection Method
• Demonstrate mastery of Gauss-Jordan elimination method
• Solve an inconsistent system
• Analyze applications using matrices
• Demonstrate competency in applying a system of equations by matrix inversion
• Evaluate determinants of higher order matrices
• Decompose a fraction when various denominator issues are present
• Develop a graph of systems of inequalities
• Formulate an equation of a circle
• Restate the definition of an ellipse
• Solve applied problems using ellipses
• Use Pascal's Triangle to expand a binomial
• Define and use factorial notation
• Define and use arithmetic sequences
• Solve problems involving geometric sequences and series
• Solve permutation and combination problems
• Develop the analytical skills of the student in order to better comprehend various algebraic theories and applications
• Define natural-number exponents
• Demonstrate addition, subtraction, multiplication, and division of polynomials
• Explain factoring out a common monomial
• Factor trinomials
• Define rational expressions
• Solve number, geometric, and investment problems
• Calculate quadratic equations using the Quadratic Formula, factoring and the Square Root Property
• Demonstrate graphing linear equations, vertical and horizontal lines, and find distance between two points
• Use the slope to solve applications
• Write equations of parallel and perpendicular lines
• Use point-slope form and slope-intercept form to write an equation of a line
• Identify the center and radius of a circle
• Use combined variation to solve problems
• Describe the concept of a function
• Graph a function by plotting points
• Recognize the characteristics of a quadratic function
• Explain when a graph has a missing point
• Evaluate composite functions
• Solve compound interest problems
• Recognize, approximate and simplify exponential expressions
• Solve radioactive decay and Malthusian population growth problems
• Use like bases to solve exponential equations
• Demonstrate knowledge of synthetic division to address various problems
• Apply Decartes' Rules of Signs
• Solve applications
• Show how to solve systems using the graphing method, substitution method, and addition method
• Add and subtract matrices
• Use determinants to solve systems of equations
• Solve linear programming problems
• Construct graphs of circles and parabolas
• Prepare equations of hyperbolas
• Solve problems using systems of nonlinear equations
• Define and use sequences
• Define a series
• Define and use geometric sequences
• State the Principle of Mathematical Induction
• Compute probabilities
• Use the Multiplication Property of Probabilities

General Topics: