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Precalculus Online Course with Trigonometry for Academic Credit

Precalculus is a catch-all phrase for all of the algebra and trigonometry usually studied in high school. The topics of any standard Precalculus course will include:

  • Solving Equations (both easy and more difficult)
  • Linear Equations
  • Quadratic Equations
  • The Quadratic Formula
  • Polynomials
  • Factoring Polynomials
  • Rational Polynomials
  • Functions
  • Exponential and Logarithmic Functions
  • Trigonometry Concepts
  • Trigonometric Functions
  • Systems of Equations - Linear and More Complicated Equations
  • Complex Numbers
  • Equations and Inequalities
  • Conic Sections

Completion of the Distance Calculus @ Roger Williams University Math 136 - Precalculus course earns 4 academic credit semester hours, earning an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.

Online Precalculus Course for College Credit Introductory Video

Distance Calculus @ Roger Williams University - Math 136 - Precalculus is a self-paced, asynchronous, live-lecture-free, high-tech, empirical, investigation-driven approach to the traditional topics of high-school (and lower college) Precalculus.

The Distance Calculus Approach To Precalculus

Our online Precalculus course Math 136 from Distance Calculus @ Roger Williams University has the following educational assumptions and goals:

  • Adult Students
    Distance Calculus is intended for adult students (although we do have advanced High School students in the upper courses like Multivariable Calculus, Differential Equations, Linear Algebra, and Probability Theory), and our Precalculus course is designed for adult learners - especially those looking to continue into our Engineering Calculus sequence.
  • Rote Learning Should Be Left in High School
    All Distance Calculus students have already gone through high school. Repeating such a high school "rote skills" Precalculus course seems unlikely to produce success to adult learners
  • Computer Algebra and Graphing Throughout The Curriculum
    As all Distance Calculus courses are based upon curricula written in LiveMath and/or Mathematica - both powerful computer algebra and graphing systems, we extend these tools in the Precalculus course which change the nature of the curriculum, far more than just using a simple graphing calculator as an ancillary tool to a traditional "rote" curriculum
  • Empirical Learning
    Instead of a "proofs-based" Precalculus course, we use the powerful computer algebra and graphing platform LiveMath to conduct graphical, numerical, and algebraic experiments - like you would in a biology or chemistry or physics laboratory - to empirically investigate the topics of traditional high school precalculus. "Rote" learning is replaced with investigating the topics much more thoroughly using modern technical tools at a much deeper level, because the "Do these 1-99 odd factoring problems" is now replaced with "Use Factor Command" - and then we ask when we can use factoring, what it does for us, and what do we do when we cannot factor!
  • Asynchronous Studying
    This means that the course happens on your schedule, not at fixed times. You may work as intensely as you wish, take a break for a week or two, and then resume, all on your needs.
  • Mastery Learning
    The student will learn the current module of material thoroughly before moving on to the next topic. This eliminates the "slippery slope" problem of not mastering a previous topic when faced with a new topic.
  • Synchronous Communications
    The majority of communcation between the student and the instructors will occur via Chat, so that problems, questions, issues, that come up are solved in real time.
  • ChalkTalk Video
    Video presentations of problems solved manually, "by hand", providing the basis of the classical study of precalculus topics - we have a balance of 80% Computer Algebra and 20% By Hand Manual Computations split of the problems. There are core problems that all students who complete a Precalculus course should be able to do by hand, which is reinforced by the Computer Algebra assignments.

Examples of Distance Calculus Unique Approach in Precalculus

Many prospective students will have completed Algebra at some level in high school, perhaps many years ago, and they are looking for a comprehensive course on Precalculus before they start the Engineering Calculus I sequence. Below we list a few topics that demonstrate the enhanced curriculum of our Precalculus course, which studies the same topics as high school Algebra and Trigonometry, but we are able to go to much deeper levels of investigation because of the usage of the computer algebra platform LiveMath.

  • Factoring A Polynomial By Graphing Analysis
    Factoring is now made rather trivial using LiveMath's Factor command:
    factoring a degree 5 polynomial
    You would never attempt to factor such a polynomial in high school algebra class by hand! After we make the standard connection to the x-axis crossings/touches for this polynomial function graphed:
    graph a factored degree 5 polynomial
    We then ask the question in reverse:
    Suppose you are given the graph of a function whose algebraic formula you do not know - can you reconstruct the algebraic formula (assuming it is a polynomial function) from just the graph?
    graph an formula-unknown polynomial function


  • How Complex Roots Affect A Polynomial Function Graph
    Here's what looks to be a degree 4 polynomial function - can we find its algebraic formula?
    graph of polynomial function with complex roots
    Only problem is: there are only 2 real x-axis crossings! That function wiggles, but not far enough down to actually cross the x-axis! Turns out this wiggle is the affect of complex roots at work. But we can still analyze this graphically by vertically translating the graph down to force that wiggle to cross the x-axis (and cross at nice roots, too!):
    vertical translation of polynomial function with complex roots
    From that translation we can get 4 real roots, create the factorization, and then ... don't forget ... reverse the vertical translation back up, and voila!
    determine polynomial formula of graph with complex roots


  • Conic Sections - Parabolas in 3D Animations
    Remember parabolas, hyperbolas, ellipses in high school algebra? Well, they never looked this cool in 3D animations on those little TI-83 calculators!
    animation of cone being sliced by plane
    In our Precalculus course, the equations and analytical geometry study of parabolas, hyperbolas, and ellipses takes on a 3D feel, where we study much harder problems: how do we convert these slicing equations into standard form, and rotate everything "just so" to get the standard equations to pop out?

Other Online Precalculus Courses vs. Distance Calculus

The Distance Calculus Precalculus online course was created as a support course for our Calculus I - Engineering Calculus sequence. Many students who need to complete Calculus I or higher in the engineering sequence are often not prepared for starting Calculus I - especially the considerably-different Calculus I online course offered via Distance Calculus.

There are many Precalculus online courses available around the internet. In almost all cases, these other Precalculus online courses are just a re-hash of the high school algebra II and trigonometry experience - more of the same - endless hand-calculation problem sets ("1-99 odd"), perhaps with usage of a graphing calculator (high school Precalculus courses now routinely include the Texas Instrument TI-83 or similar graphing calculators), and probably with a multiple choice engine where your instructor becomes an automated machine checking answers instead of a human being.

These other online Precalculus online courses all share the same process: a paper or e-paper textbook is provided to the student, and long problem sets of factoring polynomials, applying the quadratic formula, interpreting word problems into solvable equations, etc.

The Educational term for these courses is: learning by rote - doing a hand-technique over and over again, until the technical process is imprinted in your mind. Many students who go through these types of precalculus courses are so trained that when they see an equation like the following:

x2 + 5x - 8 = 0
They immediately say "Oh, I know the quadratic formula:"

\(\frac {-b\pm\sqrt{b^2 - 4ac}}{2a}\)

But often these students are completely stumped what to do if the equation instead looks like this:

x3 + 5x + 8 = e2x
There often is a disconnect between generally solving equations for (numerical) solutions, and applying (historical) formulas that work only in special cases (purely quadratic equations).

Many students are very successful at "rote" Precalculus courses. As almost all of the other Precalculus online courses on the internet are exactly these "rote" courses, if you are looking for such a "plug-and-chug" Precalculus online course, you have many options, and Distance Calculus is not for you.

If, on the other hand, diving back into another high-school-like Precalculus "rote" course does not sound appealing to you, then read on about our Distance Calculus Precalculus online course.

Roger Williams University Course Catalog Listing - Math 136 - Precalculus

MATH 136: Precalculus [4 credit hours]

Course Description: The focus of this course is on functions, which are of central importance in Calculus. Topics include definitions, properties, and applications of algebraic, inverse, exponential, logarithmic and trigonometric functions.

Prerequisite: High School Algebra
Detailed Course Syllabus in PDF

Precalculus Syllabus Topics Online Course

  1. Solving Basic Equations
    1. Solving (easy) equations in 1 variable
    2. What if you can't solve for x?
    3. Finding solutions numerically
    4. Finding solutions graphically
    5. Solving equations of more than 1 variable
  2. Functions
    1. Function notation
    2. Data sets
    3. Graphing functions
    4. Data sets and smooth curves
    5. Domain and Range
    6. Algebraic combinations of functions
  3. Linear Functions
    1. Algebraic definition
    2. Slope
    3. Graphing linear functions by hand
    4. Properties of linear functions
    5. Linear data sets
  4. Quadratic Functions
    1. Algebraic definition
    2. Graphing and Properties of Quadratic Functions
    3. Solving quadratic equations algebraically:Factoring
    4. Solving quadratic equations algebraically:Quadratic formula
    5. Solving quadratic equations numerically and graphically
    6. Complex Numbers
    7. Quadratic data sets
  5. Power and Polynomial Functions
    1. Algebraic definition
    2. Graphing and Properties of Polynomial Functions
    3. Solving polynomial equations algebraically: factoring
    4. Solving polynomial equations numerically and graphically
    5. Fundamental Theorem of Algebra
    6. Radicals and fractional exponents
  6. Rational Polynomial Functions
    1. Algebraic definition
    2. Graphing and Properties of Rational Polynomial Functions
    3. Solving rational polynomial equations algebraically: factoring
    4. Solving rational polynomial equations numerically and graphically
  7. Inequalities, Systems of Equations
    1. Inequalities of 1 variable
    2. Inequalities of 2 variables
    3. System of Equations in 2 variables
  8. Introduction to Matrices
    1. Inverses
    2. Determinants
    3. Cramer's Rule
  9. Exponential Functions
    1. Algebraic definition
    2. Graphing and Properties of Exponential Functions
    3. Solving exponential equations numerically and graphically
    4. Exponential Growth and Applications
    5. Data sets and exponential functions
  10. Logarithmic Functions
    1. Inverse Functions
    2. Algebraic Definition
    3. Graphing and Properties of Logarithmic Functions
    4. Solving exponential and logarithmic equations algebraically
    5. Solving logarithmic equations numerically and graphically
    6. Logarithmic Growth and Applications
    7. Data sets and logarithmic functions
  11. Trigonometry
    1. Geometry of Right Triangles
    2. The Unit Circle
    3. The (Circular) Trigonometric Functions
    4. Graphing and properties of trigonometric functions:frequency, amplitude, shifting
    5. Radians and degrees
    6. Trigonometric identities
    7. Inverse Trigonometric functions
    8. Solving Trigonometric equations algebraically
    9. Solving Trigonometric equations graphically and numerically
    10. Applications of trigonometry
    11. Laws of sines and cosines
    12. DeMoivre's Theorem
  12. Analytic Geometry
    1. The Cone
    2. Parabolae, Hyperbolae, Ellipsi
    3. Polar Coordinates
    4. Parametric Equations and Graphs
  13. Sequences and Series
    1. Sequences
    2. Summation
    3. Arithmetic and Geometric Sequences and Series

Precalculus Online Course Example Learning Movies

One of the ongoing themes of the Precalculus curriculum is bridging between the classical approach to Precalculus with pen/paper - or chalk on a chalkboard - and using the modern LiveMath computer algebra and graphing platform. Often the video assignments come in pairs, with the same core topic explained in both ChalkTalk format and also in LiveMath format.

Introduction to Cubic Functions

Solving Equations and Inequalities

Complex Number Multiplication and Division

Exponential and Logarithm Functions

Trigonometric Functions

Student Work Assignments

Students will complete a variety of types of homework assignments, including:

  • Written Solution Sets
    Students will complete written solution sets, take a photo with your phone, and turn them in on-line for grading. These problem sets will be from the classical side of the precalculus curriculum - the "math you need to be able to do by hand."


  • Computer Algebra Notebook Solution Sets
    Students will complete notebook questions in using LiveMath software dealing with more modern types of questions in Precalculus requiring technological approaches.


  • Video Solution Sets
    Students will complete some Video Solutions of various problems, and turn these videos in on-line for grading, expanding upon both types of solution sets with more of a "Now You Explain It".

Similar to our Distance Calculus course structure, this course is based upon heavy amounts of communication between the student and the instructional team. All assignments are based upon the mastery learning model, and turned in recursively back-and-forth between student and instructor until 100% mastery is achieved.

This is an excellent course for the computer novice. Even if checking your email is a not a "natural" activity for you, the Distance Precalculus course is an excellent way to simultaneously prepare for Calculus, and conquer whatever computer "phobia" fears you may have.

Distance Calculus - Student Reviews

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Date Posted: Jan 13, 2020
Review by: Anonymous
Courses Completed: Calculus II
Review: This is the most interactive and productive online course I have ever taken. I had taken calculus before but never understood some of the underlying concepts until I took this course. If you want to really learn calculus in a way that will stay with you for the rest of your life, take this course.
Transferred Credits to: The college of New Jersey

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Date Posted: Jun 6, 2020
Review by: Douglas Z.
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
Review: I loved these courses. So in depth and comprehensive. The mix of software and math curriculum was tremendously helpful to my future studies and career in engineering. I highly recommend these courses if you are bored of textbook courses.
Transferred Credits to: University of Massachusetts, Amherst

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Date Posted: Mar 16, 2020
Review by: Malia K.
Courses Completed: Applied Calculus
Review: Course was good and fast. I don't like math so I can't say it was fun or anything. Grader was very nice. Software was ok.
Transferred Credits to: University of Maine

Frequently Asked Questions

No, not really. The student is expected to have "High School Algebra" but nearly all U.S. college/university students have taken High School Algebra, probably Algebra II, as that is a universal requirement for college/university. We do start at the very beginning, and assume that even though you have taken High School Algebra, you may not remember much of it.

Yes. Precalculus is often called "Precalculus With Trigonometry" to remind everyone of the trigonometry component. Essentially Precalculus is, as the name suggests, the course you take before Calculus I.

No. Precalculus is a prerequisite for the higher Calculus I STEM sequence; not for the lower Applied Calculus, single-semester course on calculus.

Well not from Distance Calculus! Our Precalculus course is quite progressive, exploring the topics of Precalculus with a laboratory-minded approach, using graphical, algebraic, and numerical tools to have a refreshing investigation (or re-investigation) of the topics of Precalculus, including Trigonometry.

Yes, All Distance Calculus courses are offered through Roger Williams University in Providence, Rhode Island, USA, which is regionally accredited (the highest accreditation) through New England Commission of Higher Education (NECHE).