The applications tested on the AP Calculus exams include average value, accumulation, finding area, finding volumes
Units – How to determine the units of a derivative and a definite integral.
Average Value of a Function – An important application of integration
Most Triangles Are Obtuse! – In fact, 81.865% of all triangles. An average value problem solved by a tenth grader.
What’s a Mean Old Average Anyway? – Helping your students with the average rate of change, the average value of a function, and the average value of a function.
Half-full and Half-empty – Visualizing the average value of a function.
Extreme Average – Exploring the average extreme value
Accumulation: Need an Amount? – Look around for a rate to integrate.
AP Accumulation Questions – A discussion of two of my favorite AP Exam questions about accumulation.
Graphing with Accumulation 1 – Using the graph of a derivative and accumulation to find extreme values without mentioning the derivative.
Graphing and Accumulation 2 – Using the graph of a derivative and accumulation to determine concavity without mentioning the derivative.
Accumulation and Differential Equations – Solving simple differential equations
Painting a Point – accumulating paint.
Area and Volume
Under is a Ling Way Down – start by using the correct terminology.
Area between Curves – The best way to think of it even if one curve is the x-axis.
Volumes of Solids with Regular Cross-sections – An important application
Volumes of Revolution – A special case of the volume problem.
Subtract the Hole from the Whole – Easier than R2 – r2
Why You Never Need Cylindrical Shells – but often they are the easiest way.
Does Simplifying Make Things Simpler? – Yes, no, and maybe.
Who’d a thunk it? – An exploration into some strange area ratios.
Visualizing Solid Figures
…but what does it look like? – Ways to see solid figures
Visualizing Solid Figures 1 – Physical models
Visualizing Solid Figures 2 = Using Winplot*
Visualizing Solid Figures 3 – The Washer Method, Winplot*
Visualizing Solid Figures 4 – Cylindrical Shells, Winplot*
Visualizing Solid Figures 5 – Comparing Washers and Shells
Logarithms – Defining the logarithm function as the inverse of the exponential function
*Winplot is an excellent graphing program which has gone out of fashion. I still use it. The program may be downloaded for free HERE. There are instructions on the internet and in my posts that refer to it.