| Date |
Sections |
Topics |
Prerequisite Skills |
Student Learning Outcomes
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of order of operations
|
Review of:
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic understanding of Order of Operations (Module R)
- Basic understanding of exponents and radicals
- Basic understanding of factoring polynomials and definition of a factor
- Understanding operations with fractions
|
Review the following radical expression concepts:
- evaluate square roots
- use the product rule to simplify square roots
- use the quotient rule to simplify square roots
- add and subtract square roots
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Order of Operations (Module R)
- Basic understanding of exponents
|
Review the following rules of exponents:
- product rule
- quotient rule
- power rule
- zero exponent rule
- negative rule
Review how to find the power of a product and a quotient
Review how to simplify exponential expressions
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Order of Operations (Module R)
- Basic prime factorization
- Basic understanding of factoring
|
Review factoring techniques for the following type of polynomials:
- factor the greatest common factor of a polynomial
- factor a trinomial
- factor by grouping
- factor a perfect square trinomial
- factor a difference of squares
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Order of Operations (Module R)
- Basic understanding of factoring
|
Review the following linear equation topics:
- Basic mathematical symbols and terminology
- solving linear equations in one variable
- finding a linear equation
- write and interpret a linear equation
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Order of Operations (Module R)
- Basic understanding of factoring
|
Review the following linear inequality topics:
- use interval notation
- use properties of inequalities
- solve inequalities in one variable algebraically
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of Order of Operations (Module R)
- Basic understanding of factoring
- Basic understanding of Solving Equations (Module R)
|
|
| Week 1
|
Module R
|
|
- Basic mathematical symbols and terminology
- Basic arithmetic skills
- Basic understanding of order of operations
- Basic understanding of factoring
- Basic understanding of solving Linear Equations (Module R)
- Understanding of the Cartesian coordinate system
|
|
| Week 2
|
Module 1.1
|
|
|
- Determine whether a relation represents a function.
|
| Week 2
|
Module 1.1
|
|
|
- Find the value of a Functions
- Graph the functions listed in the library of functions.
- Determine whether a function is one-to-one.
- Use the vertical line test to identify functions.
|
| Week 2
|
Module 1.2
|
|
- Basic understanding of interval notation (Module R: Inequalities)
|
- Find the domain of a function defined by an equation.
- Graph piecewise-defined functions.
|
| Week 2
|
Module 1.2
|
|
- Basic understanding of interval notation (Module R: Inequalities)
|
- Find the domain of a function defined by an equation.
- Graph piecewise-defined functions.
|
| Week 2
|
Module 1.2
|
|
- Basic understanding of Cartesian coordinate system (Module R: Graphs)
- Basic understanding of interval notation (Module R: Inequalities)
|
- Identify the basic toolkit functions
- Determine Domain and Range for the basic toolkit functions (Module 1.2)
- Graph the basic toolkit functions. (Module R)
|
| Week 3
|
Module 2.1
|
|
- Basic understanding of power expressions.
- The student recalls the Graphs and equations of Toolkit Functions, and their associated Domains and Ranges (Module 1).
- The student understands where the x-intercept and y-intercept are located given a graph.
- The student understands interval notation for Domain and Range (Module 1).
- The student can substitute values for variables in an Equations and solve for an unknown (Module R)
|
- Identify power functions.
- Identify end behavior of power functions.
- Identify polynomial functions.
- Identify the degree and leading coefficients of polynomial functions.
|
| Week 3
|
Module 2.1
|
|
- Basic understanding of a polynomial expression.
- The student recalls the Graphs and equations of Toolkit Functions, and their associated domains and ranges (Module 1).
- The student understands where the x-intercept and y-intercept are located given a graph.
- The student understands interval notation for Domain and Range (Module 1).
- The student can substitute values for variables in an Equations and solve for an unknown (Module R).
|
- Identify polynomial functions.
- Identify the degree and leading coefficients of polynomial functions.
|
| Week 3
|
Module 2.2
|
|
- Fundamentals of Polynomials (Module 2.1)
- The student understands the difference between a maximum and minimum.
|
- 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 4
|
Module 3.1
|
|
- Basic understanding of multiplying and dividing fractions.
- Basic understanding of simplifying fractions by common factors.
- Basic understanding of the rules of exponents. (Module R: Simplifying Exponents)
- Basic understanding of Factoring Polynomials (Module R)
|
- Use long division to divide polynomials
- Use synthetic division to divide polynomials
|
| Week 4
|
Module 3.2
|
|
- Basic understanding of multiplying and dividing fractions.
- Basic understanding of simplifying fractions by common factors.
- Basic understanding of Factoring Polynomials (Module R)
- Basic understanding of Functions (Module 1.1)
- Basic understanding of Solving Equations (Module R)
|
- 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 real-world applications of polynomial equations
|
| Week 5
|
Module 4.1
|
|
- The student understands that zero in the denominator of a fraction is undefined.
- The student recalls the Graphs and equations of Toolkit Functions, and their associated Domains and Ranges (Module 1.2 & R).
|
|
| Week 5
|
Module 4.2
|
|
|
- Solving applied problems involving Polynomial Functions. (Module 2.1)
- Use arrow notation.
- Solve applied problems involving rational functions.
- Find the Domain of rational functions.
- Identify vertical asymptotes.
- Identify horizontal asymptotes.
|
| Week 6
|
Module 5.1
|
|
|
- Recognize characteristics of graphs of polynomial functions
- Use factoring to find zeros of polynomial functions
- Identify zeros and their multiplicities
- Determine end behavior
- Understand the relationship between degree and turning points
- Graph polynomial functions
|
| Week 6
|
Module 5.2
|
|
|
- Identify and graph vertical asymptotes
- Identify and graph horizontal asymptotes
- Determine behavior of rational functions around vertical asymptotes
- Graph rational functions
|
| Week 7
|
Module 6
|
|
|
- Graph functions using vertical and horizontal shifts
- Graph functions using reflections about the x-axis and the y-axis
- Determine whether a function is even, odd, or neither from it's graph
- Graph functions using compressions and stretches
- Combine transformations
|
| Week 8
|
Module 7.1
|
|
|
- Combine functions using algebraic operations
- 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 8
|
Module 7.2
|
|
|
- Verify inverse functions
- Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one
- Find or evaluate the inverse of a function
- Use the graph of a one-to-one function to graph its inverse function on the same axes
|
| Week 9
|
Module 8.1
|
|
|
- Evaluate exponential functions.
- Find the equation of an exponential function.
- Use compound interest formulas.
- Evaluate exponential functions with base e.
|
| Week 9
|
Module 8.2
|
|
|
- Rewriting from exponential form to logarithmic form and vice versa
- -y=b^x\equiv\log_b(y)=x
- Evaluate logarithms.
- Use common logarithms.
- Use natural logarithms.
|
| Week 10
|
Module 9.1
|
|
|
- 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 change-of-base formula for logarithms.
|
| Week 10
|
Module 9.2
|
|
|
- Use like bases to solve exponential equations.
- Use logarithms to solve exponential equations.
|
| Week 10
|
Module 9.2
|
|
|
- Use the definition of a logarithm to solve logarithmic equations.
- Use the one-to-one property of logarithms to solve logarithmic equations.
- Solve applied problems involving exponential and logarithmic equations.
|
| Week 11
|
Module 10
|
|
|
- Model exponential growth and decay
- Use Newton's Law of Cooling
- Choose an appropriate model for data
- Express an exponential model in base e
|
| Week 11
|
Module 10
|
|
|
- Use logistic-growth models
- Choose an appropriate model for data
|
| Week 12
|
Module 11
|
|
|
- Solve direct variation problems
- Solve inverse variation problems
- Solve problems involving joint variation
|
| Week 13
|
Module 12.1
|
|
|
- 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 13
|
Module 12.2
|
|
|
- Solve systems of equations in three variables
- Identify inconsistent systems of equations containing three variables
- Express solutions of a system of dependent equations containing three variables
|
