Week 
Sections 
Topics 
Prerequisite Skills 
Student Learning Outcomes

Week 1

Fundamentals


 Basic mathematical symbols and terminology
 Basic arithmetic skills

Students will be able to correctly identify the algebraic properties:
 Additive & Multiplicative identity
 Additive & Multiplicative inverse
 Commutative property
 Associative property
 Distributive property
Students will be able to correctly explain the algebraic properties of numbers and correctly apply these properties in procedural explanations of:
 Solving mathematical equations
 Simplifying/evaluating mathematical expressions

Week 2

Fundamentals


 Basic mathematical symbols and terminology
 Basic arithmetic skills
 Basic understanding of Algebraic Properties

Students will be able to add, subtract fractions:
 Determine common denominators and equivalent fractions
 Work with proper and improper fractions
 Simplify to lowest terms
Students will be able to multiply, and divide fractions:
 Work with proper and improper fractions
 Simplify to lowest terms

Week 2

Fundamentals


 Basic mathematical symbols and terminology
 Basic arithmetic skills
 Basic understanding of Algebraic Properties

Students will be able to:
 Identify factored vs nonfactored forms of a polynomial
 Successfully factor binomials & trinomials and difference of squares into two binomial terms
 Factor out GCF
 Multiply and / or distribute to check their factors are correct
 Differentiate between factors and terms of a polynomial expression

Week 3

Module 1.1


 Basic mathematical symbols and terminology
 Basic arithmetic skills
 Basic understanding of Algebraic Properties
 Understanding of the Cartesian coordinate system

Students will be able to:
 Solving linear equations in one variable
 Determine a linear equation
 Write and interpret a linear equation
 Graph a linear equation

Week 3

Module 1.2



Students will be able to:
 Solve systems of equations by graphing.
 Solve systems of equations by substitution.
 Solve systems of equations by elimination
 Identify inconsistent systems of equations containing two variables.
 Express the solution of a system of dependent equations containing two variables.

Week 4

Module 2.1



Students will be able to:
 Determine whether a relation represents a function.

Week 4

Module 2.2


 Basic understanding of Functions (Module 2.1)

Students will be able to:
 Find the value of a Functions
 Graph the functions listed in the library of functions.
 Determine whether a function is onetoone.
 Use the vertical line test to identify functions.

Week 4

Module 2.2



Students will be able to:
 Find the domain of a function defined by an equation.

Week 4

Module 2.2



Students will be able to:
 Find the range of a function defined by an equation.

Week 4

Module 2.2


 Basic understanding of Functions (Module 2.1)

Students will be able to:
 Identify the basic toolkit functions
 Determine Domain and Range for the basic toolkit functions (Module 2.2)

Week 5

Module 3.1



Students will be able to:
 Combine functions using Algebraic Properties
 Create a new function by composition of functions
 Evaluate composite functions
 Find the domain of a composite function
 Decompose a composite function into its component functions

Week 5

Module 3.2



Students will be to able to:
 Verify inverse functions using Algebraic Properties
 Determine the domain and range of an inverse function, and restrict the domain of a function to make it onetoone
 Find or evaluate the inverse of a function
 Use the graph of a onetoone function to graph its inverse function on the same axes

Week 6

Module 4.1


 Basic mathematical symbols and terminology
 Basic arithmetic skills
 Basic understanding of Algebraic Properties

Students will be able to:
 Use the product rule for exponents.
 Use the quotient rule for exponents.
 Use the power rule for exponents.

Week 6

Module 4.2



Students will be able to:
 Determine the difference between Linear and Exponential Functions (Module 1.1)
 Evaluate exponential functions.
 Find the equation of an exponential function.
 Evaluate exponential functions with base e.
 Evaluate exponential functions with base 10.
 Graph exponential functions.

Week 7

Module 5.1



Students will be to able:
 Rewriting from exponential form to logarithmic form and vice versa
 y=b^x\equiv\log_b(y)=x
 Use the product rule for logarithms.
 Use the quotient rule for logarithms.
 Use the power rule for logarithms.
 Expand logarithmic expressions.
 Condense logarithmic expressions.
 Use the changeofbase formula for logarithms.

Week 7

Module 5.2



Students will be able to:
 Evaluate logarithms.
 Use common logarithms.
 Use natural logarithms.
 Graph logarithmic functions.

Week 8

Module 6.2



Students will be able to:
 Determine complex number solutions
 Determine solutions of quadratic equations using factoring techniques
 Determine solutions of quadratic equations using Quadratic Formula

Week 8

Module 6.2



Students will be able to:
 Basic understanding of a polynomial expression.
 Recognize characteristics of parabolas
 Understand how the graph of a parabola is related to its quadratic function
 Determine a quadratic function's minimum or maximum value
 Solve problems involving a quadratic function's minimum or maximum value

Week 9

Module 7.1



Students will be able to:
 Identify polynomial functions.
 Identify the degree and leading coefficients of polynomial functions.
 Use long division to divide polynomials
 Use synthetic division to divide polynomials

Week 9

Module 7.2



Students will be able to:
 Evaluate a polynomial using the Remainder Theorem
 Use the Factor Theorem to solve a polynomial equation
 Use the Rational Zero Theorem to find rational zeros
 Find zeros of a polynomial function
 Solve realworld applications of polynomial equations

Week 10

Module 8.1



Students will be able to:
 Find the average rate of change of a function.
 Use a graph to determine where a function is increasing, decreasing, or constant.
 Use a graph to locate local maxima and local minima.
 Use a graph to locate the absolute maximum and absolute minimum.
 Identify end behavior of power functions.

Week 10

Module 8.2



Students will be able to:
 Recognize characteristics of graphs of polynomial functions
 Use Factoring to find zeros of polynomial functions
 Identify zeros and their multiplicities
 Determine end behavior of polynomial functions
 Understand the relationship between degree and turning points
 Graph polynomial functions

Week 11

Module 9.1


 The student understands that zero in the denominator of a fraction is undefined.
 Basic understanding of Fractions (Fundamentals)

Students will be able to:
 Simplify rational expressions.
 Multiply rational expressions.
 Divide rational expressions.
 Add and subtract rational expressions.

Week 11

Module 9.2



Students will be able to:
 Identify and graph vertical asymptotes
 Identify and graph horizontal asymptotes
 Determine behavior of rational functions around vertical asymptotes
 Find the domains of rational functions
 Graph rational functions

Week 12

Module 10.1



Students will be able to:
 Graph functions using vertical and horizontal shifts
 Graph functions using reflections about the xaxis and the yaxis

Week 12

Module 10.2



Students will be able to:
 Determine whether a function is even, odd, or neither
 Graph functions using compressions and stretches
 Combine transformations
