The AP Calculus exams include a substantial amount of integration. So it’s very important to be familiar with integrals, numerous integration methods, and the interpretations and applications of integration. In this short article, we’ll take a look at some of the most common integrals on the test. For a quick review of integration (or, antidifferentiation), […]
Author Archive  Shaun Ault

Shaun earned his Ph. D. in mathematics from The Ohio State University in 2008 (Go Bucks!!). He received his BA in Mathematics with a minor in computer science from Oberlin College in 2002. In addition, Shaun earned a B. Mus. from the Oberlin Conservatory in the same year, with a major in music composition. Shaun still loves music  almost as much as math!  and he (thinks he) can play piano, guitar, and bass. Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!
Interpreting Slope Fields: AP Calculus Exam Review
Slope fields show up on both the AP Calculus AB and BC tests. While at first this topic might seem daunting, the questions on the test are actually quite straightforward. Just keep one thing in mind: Go with the flow! A slope field shows the direction of flow for solutions to a differential equation. What […]
What is Logarithmic Differentiation? AP Calc Review
What is logarithmic differentiation? Basically, it’s a calculus tool that helps you to find derivatives of complicated functions involving a lot of multiplication, division, or powers. This review article walks you through the methods and provides plenty of example problems to help you succeed on the AP Calculus exams! Properties of Logarithms First of all, […]
Linear Approximation: AP Calculus Exam Review
What is linear approximation? Basically, it’s a method from calculus used to “straighten out” the graph of a function near a particular point. Scientists often use linear approximation to understand complicated relationships among variables. In this review article, we’ll explore the methods and applications of linear approximation. We’ll also take a look at plenty of […]
AP Calculus Review: Average Value of Functions
The average of a set of data is typically defined as the sum of the values divided by the number of data points. But what if you have infinitely many data points? What is the average value of a function? Read on to find out! Average Value of Functions Suppose f is a continuous function […]
AP Calculus Review: Differential Equations
A differential equation is a relation that involves an unknown function and its derivative. There are many kinds of differential equations and tons of specialized techniques we may use to solve them. Fortunately, on the AP Calculus exams you will only encounter a handful of the most basic kinds. Basic Differential Equations: Integration You have […]
AP Calculus Review: Optimization
This review article is all about optimization. Here, you’ll learn the tools and techniques for setting up and solving these often difficult problems. And along the way, we’ll work out a few examples! Optimization The method of optimization uses derivatives to find maximum or minimum values. However, the functions that need to be optimized typically […]
AP Calculus Review: Applications of Derivatives
Calculus is primarily the study of rates of change. However, there are numerous applications of derivatives beyond just finding rates and velocities. In this review article, we will highlight the most important applications of derivatives for the AP Calculus AB/BC exams. Applications of Derivatives Here is a list of some of the essential derivative applications. […]
AP Calculus Review: Derivatives of Inverse Functions
One of the trickiest topics on the AP Calculus AB/BC exam is the concept of inverse functions and their derivatives. In this review article, we’ll see how a powerful theorem can be used to find the derivatives of inverse functions. Then we’ll talk about the more common inverses and their derivatives. What are Inverse Functions? […]
AP Calculus Review: Shell Method
The Shell Method is a technique for finding the volume of a solid of revolution. Just as in the Disk/Washer Method (see AP Calculus Review: Disk and Washer Methods), the exact answer results from a certain integral. In this article, we’ll review the shell method and show how it solves volume problems on the AP […]