MindEdge has enhanced OpenStax’s College Algebra learning resource, which exposes students to topics in algebra. Students explore the mathematics while simultaneously applying this knowledge to real-world scenarios. Students solve various problems through the lens of a statistician, using a variety of tools to develop solutions.

The course includes pretests and self-assessments, interactive exercises, graphics, and games that appeal to a variety of learning styles. Open ended questions that apply topics to real world problems give students opportunities to apply critical thinking skills to real-world mathematics scenarios.

MindEdge has enhanced OpenStax courses with interactive games, video commentary, adaptive learning segments, additional practice questions, and a robust question database.

## Module 1: Learning Outcomes

- Determine whether a relation represents a function
- Find the value of a function
- Determine whether a function is one-to-one
- Use the vertical line test to identify functions
- Graph the functions listed in the library of functions
- Graph functions using vertical and horizontal shifts
- Graph functions using reflections about the x-axis axis and the y-axis
- Determine whether a function is even, odd, or neither from its graph
- Graph functions using compressions and stretches
- Combine transformations
- Graph an absolute value function
- Solve an absolute value equation
- 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
- Represent a linear function
- Determine whether a linear function is increasing, decreasing, or constant
- Interpret slope as a rate of change
- Write and interpret an equation for a linear function
- Graph linear functions
- Determine whether lines are parallel or perpendicular
- Write the equation of a line parallel or perpendicular to a given line
- Build linear models from verbal descriptions
- Model a set of data with a linear function.

## Module 2: Learning Outcomes

- 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
- Identify power functions
- Identify end behavior of power functions
- Identify polynomial functions
- Identify the degree and leading coefficient of polynomial functions
- 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
- Use the Intermediate Value Theorem
- 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
- Use the Linear Factorization Theorem to find polynomials with given zeros
- Use Descartes’ Rule of Signs
- Solve real-world applications of polynomial equation
- Use arrow notation
- Solve applied problems involving rational functions
- Find the domains of rational functions
- Identify vertical asymptotes
- Identify horizontal asymptotes
- Graph rational functions
- Find the inverse of an invertible polynomial function
- Restrict the domain to find the inverse of a polynomial function.

## Module 3: Learning Outcomes

- Evaluate exponential functions
- Find the equation of an exponential function
- Use compound interest formulas
- Evaluate exponential functions with base e
- Graph exponential functions
- Graph exponential functions using transformations
- Convert from logarithmic to exponential form
- Convert from exponential to logarithmic form
- Evaluate logarithms
- Use common logarithms
- Use natural logarithms
- Identify the domain of a logarithmic function
- Graph logarithmic functions
- 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
- Use like bases to solve exponential equations
- Use logarithms to solve exponential equations
- 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
- Model exponential growth and decay
- Use Newton’s Law of Cooling
- Use logistic-growth models
- Choose an appropriate model for data
- Express an exponential model in base e

## Module 4: Learning Outcomes

- Write the terms of a sequence defined by an explicit formula
- Write the terms of a sequence defined by a recursive formula
- Use factorial notation
- Find the common difference for an arithmetic sequence
- Write terms of an arithmetic sequence
- Use a recursive formula for an arithmetic sequence
- Use an explicit formula for an arithmetic sequence
- Find the common ratio for a geometric sequence
- List the terms of a geometric sequence
- Use a recursive formula for a geometric sequence
- Use an explicit formula for a geometric sequence
- Use summation notation
- Use the formula for the sum of the first n terms of an arithmetic series
- Use the formula for the sum of the first n terms of a geometric series
- Use the formula for the sum of an infinite geometric series
- Solve annuity problems
- Solve counting problems using the Addition Principle
- Solve counting problems using the Multiplication Principle
- Solve counting problems using permutations involving n distinct objects
- Solve counting problems using combinations
- Find the number of subsets of a given set
- Solve counting problems using permutations involving n non-distinct objects
- Apply the Binomial Theorem
- Construct probability models
- Compute probabilities of equally likely outcomes
- Compute probabilities of the union of two events
- Use the complement rule to find probabilities
- Compute probability using counting theory.

## Module 5: Learning Outcomes

- Solve systems of three equations in three variables
- Identify inconsistent systems of equations containing three variables
- Express the solution of a system of dependent equations containing three variables
- Solve systems of equations by graphing
- Solve systems of equations by substitution
- Solve systems of equations by addition
- Identify inconsistent systems of equations containing two variables
- Express the solution of a system of dependent equations containing two variables
- Find the sum and difference of two matrices
- Find scalar multiples of a matrix
- Find the product of two matrices
- Write the augmented matrix of a system of equations
- Write the system of equations from an augmented matrix
- Perform row operations on a matrix
- Solve a system of linear equations using matrices
- Find the inverse of a matrix
- Solve a system of linear equations using an inverse matrix
- Evaluate 2 × 2 determinants
- Use Cramer’s Rule to solve a system of equations in two variables
- Evaluate 3 × 3 determinants
- Use Cramer’s Rule to solve a system of three equations in three variables
- Know the properties of determinants.