College Algebra (OpenStax)

College Algebra (OpenStax)

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.