AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

AP Calculus

This course can help prepare students who wish to continue their math education after high school, as well as students who wish to perform exceptionally well on the Math portion of the SAT exam. The level of aptitude in this subject will assist students wishing to excel on the SAT and in college courses.

According to the College Board’s website, advanced placement Calculus focuses primarily on differential and integral components of Calculus, with minimal time spent on the basics of Calculus. Students wishing to take this class should complete four years of secondary mathematics, namely Algebra, Geometry, Trigonometry, and other courses covering elementary functions. Having experience in these different areas of study will help students as they enter Calculus, and assist them once they begin learning about higher functions of math as well.

AP Calculus AB, also called AB Calc, is an advanced placement calculus exam taken by some United States high school students. It comes after Precalculus, which is known as Introduction to Analysis in some places, and is the first calculus course offered at most schools. An AP Calculus AB course is typically equivalent to one semester of college calculus. The material includes limits, differentiation, integration, applications of the previous, and other topics covered in standard college calculus courses.

AP Calculus BC, sometimes called BC Calc, includes all of the topics in AP Calculus AB, as well as convergence tests for series, Taylor and/or Maclaurin series, parametric, vector, polar functions, and curve length. In addition, L'Hôpital's rule, improper integrals, and using partial fractions to integrate rational functions are commonly taught in this course. Students in AP Calculus BC generally receive two semesters of Advanced Placement in mathematics.

Students should have a basic handle on linear functions, rational functions, polynomials, and logarithms. Students should also be familiar with the different properties of these functions as well. They should know the algebra of these functions, the graphs of these functions, and the language of these functions in order to succeed in learning about more complex theories.

AP Calculus is a serious course and includes many course goals. According to the College Board’s website, by the time students take their AP Calculus exam (or the SAT exam) they should be prepared to do the following:

  • Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should also recognize and understand the connections between these representations and be able to express them orally and in writing.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation, and they should be able to use derivatives as a means to solve a variety of problems and equations.
  • Understand the meaning of the definite integral, both as a limit of the Riemann sums and as a net accumulation of change. They should be able to use integrals to solve a variety of equations.
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
  • Communicate mathematics in a variety of ways. Students should be able to communicate mathematics both orally and in written form, explaining solutions to a various problems.
  • Model a written description of a physical situation with a function, a differential equation, or an integral, and understand the steps taken in the situation itself.
  • Use technology to help solve problems, experiment, interpret results to mathematical problems, and verify conclusions to various equations and situations.
  • Determine the rationality of solutions, including sign, size, relative accuracy, and units of measurement. Students should also be prepared to express this orally and in written form.
  • Develop and appreciation for calculus as a coherent body of knowledge and as a human accomplishment.
  • Use study notes and other basic study techniques in conjunction with textbooks such as Barron’s AP Calculus or Kaplan’s AP Calculus.

Students interested in enrolling in an AP Calculus course should remember that that taking college level courses requires a commitment of their time and energy. Since AP courses are designed to be college level courses, they require the same amount of time that a college student would dedicate to them in order to receive a good grade. Students who commit themselves to their AP classes will see a large payoff in their grades as well as their confidence in school.

Students who wish to get into the college or university of their choice should definitely consider taking Advanced Placement courses. Not only do AP courses look excellent on college transcripts, they can also prepare students for the workload they’ll be dealing with in a college atmosphere. Most importantly, student can also earn college credit before they even graduate high school. This can save students and their family’s valuable time and money. The more students do to prepare themselves for college, the more successful their college education will be. So, students wishing to get a jump on their college career should consider taking advantage of the Advanced Placement course program in their school

Calculus Topics Covered:

Subject X2: 

Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!