# College Math

College Math provides basic college level math and lays the foundation for further studies in higher mathematics. Students explore the fundamentals of numbers and number systems before moving onto algebra. Students examine probability, statistics, and logic through a mathematical lens. Topics in this course include properties of numbers and number systems, factors, divisibility, and prime factorization, unit conversion, algebraic conventions and notation, using variables in a variety of settings, simplifying algebraic terms and expressions, factoring algebraic terms and expressions, solving linear equations and inequalities, representing and interpreting functions, graphing functions, combinations and permutations, statistical probabilities of events, analytical representation and interpretation of data, measures of central tendency, interest rates, present value and future value, properties of triangles, quadrilaterals, and circles, parallel and perpendicular lines, logical operations, and set relationships.

The course includes module pre-assessments and assessments, interactive exercises, videos, flashcards, and games that appeal to a variety of learning styles. Case studies give students opportunities to use critical thinking skills and apply their knowledge to real-world ethical scenarios.

## Module 1: Numbers and Number Systems

• Describe and identify integers and their properties
• Recognize rational and irrational numbers and applications of both
• Factor integers
• Recognize divisibility between numbers
• Identify prime and composite numbers
• Perform prime factorization
• Understand the properties of odd and even numbers
• Generalize operations that are being performed with odd and even numbers
• Use the fundamental theorem of arithmetic
• Visually represent intervals and sets on the number line
• Apply and use the mathematical concepts of absolute value and order
• Apply the concepts of numbers and number systems

## Module 2: Algebra Basics

• Recognize variables
• Understand how to use variables in mathematical expressions
• Perform addition and subtraction, using variables with known values
• Perform multiplication and division, using variables with known values
• Evaluate expressions with one or more variables
• Use formulas that involve variables
• Evaluate an expression or formula by plugging in varying values for an expression
• Identify like terms
• Combine like terms
• Simplify a long algebraic expression by combining like terms
• Use the distributive property
• Factor an algebraic expression

## Module 3: Algebra and Functions

• Understand and use linear equations and inequalities
• Solve linear algebraic equations and inequalities
• Use and solve systems of linear equations by analytic methods
• Graph and solve systems of linear equations
• Interpret, represent, and evaluate functions numerically
• Graph functions and evaluate and interpret those graphs
• Translate functions on the coordinate plane
• Perform horizontal and vertical reflections of functions
• Identify symmetry of functions about the x- and y-axes, as well as the origin
• Identify and graphically represent both linear and exponential growth
• Apply the concepts of algebra and functions

## Module 4: Counting and Probability

• Use the multiplication rule to solve counting problems
• Understand probabilities and their applications
• Calculate probabilities from word problems
• Determine probabilities using combinations and permutations
• Find probabilities using unions and intersections
• Understand what independent events are
• Determine probabilities of mutually exclusive events from number and word problems
• Calculate probabilities using complementary events
• Use conditional probabilities
• Calculate expected values
• Apply the concepts of counting and probability

## Module 5: Data Analysis and Statistics

• Select appropriate graphic methods for displaying descriptive statistics
• Explain the fundamental concepts of inferential statistics and their real-world application
• Evaluate a scenario in order to determine the appropriate statistic to use
• Apply fundamental statistics to a real-world situation
• Evaluate the appropriateness of statistics used
• Use statistics to identify the most appropriate decision alternative
• Translate statistical data into a graphical presentation based on a brief case study

## Module 6: Financial Mathematics

• Use mathematics in finance, including percents and percent change
• Evaluate economic transactions using math, including markups and discounts
• Report and evaluate financial decisions and companies using profit, loss, and other financial mathematics
• Calculate simple interest and compound interest
• Use mathematical techniques to calculate and evaluate continuous interest and effective interest rates
• Use financial mathematics in banking problems using effective annual yield and annual percentage rate
• Understand present and future value
• Apply the concepts of financial mathematics

## Module 7: Geometry

• Identify the properties of triangles
• Use the Pythagorean theorem
• Calculate the perimeter and area of triangles
• Recognize triangle types and similarities
• Identify the properties of quadrilaterals
• Calculate the perimeter and area of quadrilaterals
• Recognize quadrilateral types and similarities
• Use and understand the properties and applications of parallel and perpendicular lines
• Identify the properties of circles
• Calculate the circumference and area of circles
• Use and understand the properties of central angles, inscribed angles, and sectors
• Apply the concepts of geometry

## Module 8: Logic and Sets

• Distinguish between argument form and argument content
• Construct truth tables
• Define various logical relationships and determine when they are applicable in translation
• Identify the truth conditions of different logical statement types: negations, disjunctions, conjunctions, implications and equivalences
• Symbolize English statements using the language of formal logic
• Symbolize English arguments using the language of formal logic