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Precalculus

Precalculus prepares students for future courses in mathematics and science courses. Utilizing an in-depth discussion and application of basic concepts of calculus, we provide students with foundational practice and skills upon which trigonometric understanding and basic calculus knowledge can be built. Precalculus includes a complete interactive text, practice problems, captioned videos, problem sets, practice exams, and online assessments.

 

Lumen Learning’s Precalculus consists of the following resources:

  • Online Homework Manager (OHM): A flexible, user-friendly math homework system with customizable learning content, assessments, and activities you can tailor to fit your needs. Request an OHM instructor account.
  • Outcome-aligned OER: Designed to replace expensive textbooks, this course curates open educational resources (OER) aligned with learning outcomes. Teach as-is or customize to fit your needs.
  • LMS Integration: This course may be delivered with seamless LMS integration and automatic grade return for Canvas, Blackboard, Brightspace, and Moodle.
  • Accessibility: Lumen is 100% committed to providing learning materials that are accessible to all learners. Lumen course materials are mobile-friendly.

 

Lumen Learning applies learning science research to the design of affordable digital courseware to engage students and empower them in building a strong foundation in Mathematics. OHM has fully digital course materials focused on hands-on practice, customizable template courses, interactive full e-text with immediate feedback that stands alone or integrates seamlessly into Brightspace, Canvas, Blackboard, or Moodle.

 

Contributors: Lumen Learning vetted and improved a variety of sources including Prealgebra by Jay Abramson.

 

Course Content

Module 1: Introduction to Functions

  • Identify and evaluate functions
  • Calculate the domain and range of a function
  • Describe change behaviors of graphs
  • Evaluate composite functions
  • Transform functions
  • Solve absolute value functions
  • Find inverse functions

Module 2: Linear Functions

  • Evaluate linear functions
  • Graph linear functions
  • Model real world scenarios with linear functions
  • Use linear models of data to make predictions

Module 3: Polynomial and Rational Functions

  • Simplify complex number expressions
  • Understand quadratic functions
  • Identify power functions and polynomial functions
  • Graph polynomial functions
  • Divide polynomial functions
  • Find the zeros of polynomial equations
  • Graph rational functions
  • Find inverse functions
  • Solve direct, indirect, and joint variation problems

Module 4: Exponential and Logarithmic Functions

  • Evaluate exponential functions
  • Graph exponential functions
  • Use logarithmic functions
  • Graph logarithmic functions
  • Expand and condense logarithmic expressions
  • Solve exponential and logarithmic equations
  • Use exponential and logarithmic models
  • Fit exponential models to data

Module 5: Systems of Equations and Inequalities

  • Evaluate systems of linear and non-linear equations with both two and three variables
  • Solve systems of linear equations in two variables
  • Solve systems of linear equations in three variables
  • Solve and graph systems of nonlinear equations and inequalities
  • Decompose partial fractions
  • Evaluate matrices and matrix operations
  • Write and solve systems with Gaussian Elimination
  • Solve systems with inverses
  • Solve systems with Cramer’s rule

Module 6: Sequences, Probability, and Counting Theory

  • Write the terms of a sequence
  • Evaluate arithmetic sequences
  • Evaluate geometric sequences
  • Find the terms of a series
  • Solve counting problems
  • Use the binomial theorem
  • Compute probabilities

 

Module 7: Trigonometric Functions

  • Evaluate trigonometric functions using angles and right triangles
  • Find and use angles
  • Evaluate sine and cosine functions
  • Understand other trigonometric functions
  • Use right triangle trigonometry

Module 8: Periodic Functions

  • Graph sine and cosine functions
  • Analyze and graph other trigonometric functions
  • Use inverse trigonometric functions

Module 9: Trigonometric Identities and Equations

  • Solve trigonometric equations using identities
  • Solve trigonometric equations with identities
  • Use sum and difference formulas
  • Use double-angle, half-angle, and reduction formulas
  • Use sum-to-product and product-to-sum formulas
  • Solve trigonometric equations
  • Model trigonometric equations

Module 10: Further Applications of Trigonometry

  • Apply trigonometric rules to evaluate more complex graphs and equations
  • Solve non-right triangles using the Law of Sines
  • Solve non-right triangles using the Law of Cosines
  • Identify and use polar coordinates
  • Graph polar equations
  • Evaluate the polar form of complex numbers
  • Find parametric equations
  • Graph parametric equations
  • Perform vector operations

Module 11: Analytic Geometry

  • Analyze the graphs and equations of conic sections
  • Evaluate ellipses
  • Evaluate hyperbolas
  • Evaluate parabolas
  • Evaluate the rotation of axes
  • Evaluate conic sections in polar coordinates

Module 12: Introduction to Calculus

  • Describe how to find limits and derivatives of functions
  • Find limits using graphs and tables
  • Find limits using properties
  • Determine continuity of functions
  • Find the derivative of a function

What People Are Saying

“OHM saves me time grading and is a good study tool for my students.” – Solomon Willis, Cleveland Community College

 

 

 

“I just love the ease of use and ability to edit what I need in a course.” – Shirley Sinacore, Sullivan County Community College

 

“Since using OHM, I have time to help a larger number of students pass the course. It’s also easy for students to understand how to use.” – Jean Greear, Wytheville Community College

Teaching with Lumen Course Materials

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  • Replace expensive textbooks | Ready-to-adopt open educational resources (OER) include text, videos, simulations, self-checks, and other interactives.
  • Choose affordability | Low cost to students.
  • Use better content | Continuous, data-driven improvements make OER content more effective at supporting learning.
  • Simplify access | Easy access to course materials in your LMS (Blackboard, Canvas, D2L, and Moodle) plus automatic grade return.
  • Improve student outcomes | Research shows Lumen course materials can improve academic performance, passing rates, and course completion.

FOR INSTRUCTORS

  • Connect with students | Instructor and student tools designed to help strengthen communication.
  • Save time | Start with curated, outcome-aligned OER and supplemental instructor resources like quiz banks, assignments, slide decks, etc. 
  • Customize your course | Freedom to tailor course content to fit your learning outcomes and instructional approach.
  • Enjoy awesome support | Faculty-friendly onboarding, training, and support. 
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FOR STUDENTS

  • Learn by doing | Online homework, self-check activities, and other interactive tools strengthen learning.
  • Engage from day one | Avoid falling behind with access to course materials from the first day of class.
  • Retain materials | Download a digital copy of course content to keep forever.
  • Become a better learner | Real-time feedback guides students on where to focus and how to improve.

Are you ready to get started with Lumen Learning digital courseware?

Great! Fill out our Explore a Course form, and our team will contact you promptly.