AP Calculus AB

From: $104.00 / month for 8 months

Prerequisite: See course description below.

Grades: 11th–12th

Live Class: Wed 3:00–4:00 p.m. ET

Dates: August 25th–May 13th

Price:  $749

Instructor: Kristen Lauria

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Course Description

See Reviews of Instructor Kristen Lauria


Course Syllabus

The AP Calculus AB course endeavors to demonstrate the relevance and pervasiveness of math and mathematical thinking in today’s world. Per the AP Curriculum Guidelines*, in this course students will:

  • Be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal, and should understand the connections among these representations.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and should be able to use derivatives to solve a variety of problems.
  • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and should be able to use integrals to solve a variety of problems.
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
  • Be able to communicate mathematics and explain solutions to problems both verbally and in written sentences.
  • Be able to model a written description of a physical situation with a function, a differential equation, or an integral.
  • Be able to use technology to help solve problems, experiment, interpret results, and support conclusions.
  • Be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
  • Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment

*Source: College Board AP Calculus AB Course Description

Course Structure

AP Calculus AB students have daily assignments; they consist of watching video lectures and solving problems related to the unit of study. Lectures will be delivered solely through videos available on the class webpage as this is a flipped classroom (read more about that here).

Students are expected to take detailed notes on video lectures and to complete the embedded quizzes, which will be the basis for class discussion and work the following day. The embedded quizzes are not graded for correctness, only for completion; the goal is for them to serve as a learning check and to address clarifying questions for class. It is imperative that students attempt each problem assigned. A detailed solution sheet will be provided with each assignment, so there is never an excuse to have nothing written down for an assigned problem. It is also expected that students will show all work. Correct answers without proper support may receive no credit on the free-response section of the AP Exam.

Following class discussion of an assignment, students are expected to make any necessary corrections for homework. Homework grades will be based on viewing of the video lectures and completing all assigned problems. Additionally, turned in quiz/test corrections will be required for all assessments.

Who should enroll?

This class is for 11th—12th graders.

Before studying Calculus, all students should complete the equivalent of four years of secondary mathematics designed for college-bound students: courses that should prepare them with a strong foundation in reasoning with algebraic symbols and working with algebraic structures.

Prospective Calculus students should take courses in which they study Algebra, Geometry, Trigonometry, Analytic Geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, and piecewise-defined functions. In particular, before studying Calculus, students must be familiar with the properties of functions, the composition of functions, the algebra of functions, and the graphs of functions.

Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and descriptors such as increasing and decreasing). They should also know how the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at the numbers 0, 30°, 45°, 60°, 180° and their multiples.

*Source: College Board AP Calculus AB Course Description

Students will need to complete a summer assignment showing proficiency in earlier math. This assignment can be found in the Syllabus.

Technology Requirements

  • High speed, broadband Internet
  • Sound card and microphone (for live sessions)
  • Streaming video capabilities to watch recorded lectures

Evaluation and Feedback

I believe homework and projects are the best tool for students to practice the skills they are learning, and I grade homework/provide feedback so they learn as they continue working toward mastery. Assignments are generally graded within 5 days of submission. Grades are based on a combination of homework, quizzes, labs, and exams/projects. Students are also given a participation grade to account for timeliness of completing assignments, class participation, and effort. Communication will take place as needed through email, and announcements and responses to student messages are generally within a few hours.


Once registered, you will receive a welcome email within 24 hours. Throughout the course, parents will only be contacted if issues arise, as I try to encourage students to take ownership of the class and contact me directly if they have any concerns. At midterm and close of the course progress reports will be sent to parents. Parents are always welcome to contact me with any issues or concerns, as they are partners in this endeavor.

View Course Application

Required Texts


  • OpenStax Calculus Volume 1, ISBN 13: 978-1-938168-02-4
  • OpenStax Calculus Volume 2, ISBN 13: ISBN-13: 978-1-938168-06-2

Also available for free at: https://openstax.org/books/calculus-volume-1/ and https://openstax.org/books/calculus-volume-2/


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Instructor Bio

Kristen Lauria

Kristen Lauria is a lifelong student who has become the teacher.  In second grade she was found stealing teacher’s editions from her public-school classroom to teach her younger best friend at home. She’s since progressed to buying her materials legally, but her love of teaching hasn’t wavered.  She spent 4 years in the Navy learning about nuclear reactors and went on to finish her BS in Physics with a minor in Math graduating Cum Laude.  She also was inducted into the physics honor society, Sigma Pi Sigma, having attained a GPA in Physics of over 3.0.  She has her MS in Teaching, Learning, and Curriculum from Drexel University and is certified to teach physics and chemistry in the state of Pennsylvania.

In addition to teaching for Aim Academy, she also homeschools her own 2 children in middle school, counsels her adult stepchildren in what adulting really means, and helps her husband with restoring their 200-year-old farmhouse one slow-moving project at a time.  She also runs her own tutoring company and teaches at her local homeschool co-op.  In her free time (which is rather scarce at the moment) she loves to read and spend time outside enjoying God’s creation.  The teacher is now becoming the student as well, as Kristen is beginning a PhD program at Lehigh University to further hone her teaching skills and improve the integration of technology to bring the material alive for her students.

She hopes to share her love of math and science with all of her students here at Aim Academy.  While she can’t change the difficulty of what students learn in her classes, she will do her best to make them approachable and interesting.  She hopes to show her students how everything they will encounter in their textbooks will apply to their own lives; not just in the future, but today.

Email: knlauria@aimacademy.online

All classes taught by Kristen Lauria