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