| 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
- 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
- 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
- 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
- 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
- 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
- Basic understanding of factoring
- Basic understanding of Solving Equations
|
|
| 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
- 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
- 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
|
|
- 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
|
- Simplify rational expressions.
- Multiply rational expressions.
- Divide rational expressions.
- Add and subtract rational expressions.
- Simplify complex rational expressions.
|
| 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).
|
|
| Week 5
|
Module 4.2
|
|
- Rational Expressions.
- 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).
|
|
| Week 6
|
Module 5.1
|
|
- Understanding the Toolkit Functions for exponential functions (Module 1)
- Understanding the Domain and Range for exponential functions (Module 1)
|
- Evaluate exponential functions.
- Find the equation of an exponential function.
- Use compound interest formulas.
- Evaluate exponential functions with base e.
|
| Week 6
|
Module 5.2
|
|
|
- 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 7
|
Module 6.1
|
|
|
- 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 7
|
Module 6.2
|
|
|
- Use like bases to solve exponential equations.
- Use logarithms to solve exponential equations.
|
| Week 7
|
Module 6.2
|
|
|
- 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 8
|
Module 7.1
|
|
|
|
| Week 8
|
Module 7.1
|
|
|
|
| Week 8
|
Module 7.2
|
|
|
- Ordinary Annuity Future Values
- Annuity Due Future Values
|
| Week 8
|
Module 7.2
|
|
|
- Ordinary Annuity Future Values
- Annuity Due Future Values
|
| Week 9
|
Module 8.1
|
|
|
- Find the amount of a loan given the payments.
- Find the payments required given the loan amount.
|
| Week 9
|
Module 8.2
|
|
|
- Define a promissory note.
- Calculate unknown values for interest bearing promissory notes.
- Calculate unknown values for non interest bearing promissory notes.
|
| Week 10
|
Module 9.1
|
|
|
- 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 10
|
Module 9.1
|
|
|
- Identify the solution region of a system of two inequalities.
|
| Week 10
|
Module 9.2
|
|
|
- Define an objective function.
- Define constraint equations.
- Define feasible regions and determine corner points.
- Solve linear programming problems using a graph.
|
| Week 11
|
Module 10.1
|
|
- Basic operations with real numbers.
|
- Find the sum and difference of two matrices.
- Find the scalar multiples of a matrix.
- Find the product of two matrices.
|
| Week 11
|
Module 10.1
|
|
- Basic operations with real numbers.
|
- Find the sum and difference of two matrices.
- Find the scalar multiples of a matrix.
- Find the product of two matrices.
|
| Week 11
|
Module 10.2
|
|
|
- Find the inverse of a matrix.
- Solve a system of linear equations using inverse matrix.
|
| Week 12
|
Module 11.1
|
|
|
- Sets, elements of sets, and subsets.
- Union, intersection, and complement of sets
- Universal set and empty set
|
| Week 12
|
Module 11.1
|
|
|
- Subsets, elements of sets
- Union, intersection, and complement of sets
- Universal set and empty set
|
| Week 12
|
Module 11.2
|
|
- Sets and Subsets (Module 11.1)
- Unions and intersections of sets. (Module 11.1)
|
- Visualizing the union and intersection of sets using Venn Diagrams
- Cardinality of a set and the properties
- Finding cardinality using a Venn diagram
|
| Week 12
|
Module 11.2
|
|
|
- Cardinality of a set and the properties
- Finding cardinality using a Venn diagram
|
| Week 13
|
Module 12.1
|
|
- Basic operations with real numbers and fractions.
- Conversion between fractions, decimals, and percents.
|
- Basic probability
- Complementary events
- Odds
- Probability for independent events
|
| Week 13
|
Module 12.2
|
|
- Basic operations with real numbers and fractions.
- Conversion between fractions, decimals, and percents.
|
|
| Week 14
|
Module 13.1
|
|
|
- Conditional probability
- Probability of “and” for conditional events
|
| Week 14
|
Module 13.2
|
|
|
- Basic counting techniques and rules
- Factorial, Permutations, and Combinations
|
