AP Test Prep
College Board

Differentiability of Piecewise Defined Functions

For Teachers 10th - 12th
Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...
AP Test Prep
College Board

Beginning the Year with Local Linearity

For Teachers 10th - 12th
Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...
AP Test Prep
College Board

Reasoning from Tabular Data

For Teachers 10th - 12th
Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...
AP Test Prep
College Board

Frozen in Time

For Teachers 10th - 12th
Take a closer look at increasing and decreasing behavior by zooming in on graphs. An AP® Calculus reference document examines how increasing/decreasing behavior should be considered in terms of intervals rather than points. The resource...
AP Test Prep
College Board

AP Calculus: Slope Fields

For Teachers 10th - 12th
Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...