Calculus, Precalculus, and Post Calculus

Depending on the high school you go to and the intensity of your curriculum, these three words may pop up from time to time as mathematics courses. In fact, some of these are prerequisites for other courses as well, such as Precalculus to Calculus, Calculus to a course such as AP Physics C, and Calculus to Post Calculus courses. In this post, we’ll explain these three options, and talk about what you can do to prepare for them.


Precalculus

This is the course before Calculus, and is usually taken after Algebra 2. While some schools may teach Precalculus material in Algebra and skip this course, many still recommend you take Precalculus before taking Calculus itself. 

Here is the curriculum for Precalculus:

  1. Functions and Graphs

  2. Equations and Inequalities

  3. Lines and Rates of Change

  4. Sequences and Series

  5. Polynomials

  6. Exponential and Logarithmic Functions

  7. Geometry

  8. Vectors and Matrices

  9. Probability and Statistics

From our previous article on Algebra 2, it is evident that there are some topics that are covered in both Algebra 2 and Precalculus. However, there are still differences, especially as some of these topics will be more complex than anything from Algebra 2. For example, these include rates of change and probability and statistics. 


Calculus

Calculus is the only section of the three that have Advanced Placement tests on the subject: AP Calculus AB and AP Calculus BC. Calculus is defined as the “branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus)” by Brittanica. Thus, there are two main parts to Calculus: differentials and integrals. While AP Calculus AB will cover both of these, AP Calculus BC goes into more complex sections, including differentiating/integrating series or sequences, among other topics. To get a better sense of the differences between these two AP’s, here are the respective curriculums from Collegeboard:

Here is the curriculum for AP Calculus AB:

  1. Limits and Continuity

  2. Differentiation: Definition and Fundamental Properties

  3. Differentiation: Composite, Implicit, and Inverse Functions

  4. Contextual Applications of Differentiation

  5. Analytical Applications of Differentiation

  6. Integration and Accumulation of Change

  7. Differential Equations

  8. Applications of Integration

Here is the curriculum for AP Calculus BC:

  1. Limits and Continuity

  2. Differentiation: Definition and Fundamental Properties

  3. Differentiation: Composite, Implicit, and Inverse Functions

  4. Contextual Applications of Differentiation

  5. Analytical Applications of Differentiation

  6. Integration and Accumulation of Change

  7. Differential Equations

  8. Applications of Integration

  9. Parametric Equations, Polar Coordinates, and Vector-Valued Functions

  10. Infinite Sequences and Series

As you can see, AP Calculus BC has all of the same material as AP Calculus AB, but also has two additional topics about more complex functions, and also sequences and series. In your school, these two choices will most likely be both available to you. In some cases, schools may prefer you to take both of them, first AP Calculus AB then AP Calculus BC, but usually, schools will prefer you to choose one. 


Post Calculus

After the AP Calculuses, schools will usually offer Post Calculus courses. These include but are not limited to Linear Algebra, Differential Equations, and Multivariable Calculus. Depending on when you finish Calculus AB/BC, you may want to take one of these more advanced courses, but it is not completely necessary. In most cases, you will learn these Post Calculus courses in college or university as well.


Resources and Preparation

With that being said, all of these different levels to mathematics may be complex and difficult for students, especially when having to learn completely new material. Thus, how can we help students to prepare for these courses? Well, by reading this blog, you have already gotten a sense of what will be taught throughout the years, and if that’s not enough, you can always buy a preparation book or even take a tutoring class. 

For more help and information on these subjects, check out this link, where we offer courses preparing for both Precalculus (from Algebra 2) and AP Calculus. 


Calculus, Precalculus, and Post Calculus
7EDU Impact Academy 21 July, 2021
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