Calculus Resources

I teach AP Calculus AB using Matt Boelkin’s tremendous Active Calculus text. Here are a few resources I have created or adapted.

Desmos Activity Builders

Just a few speed graphs – These were used at the start of the year to play with some movement situations. The prompts were adapted from Exeter’s Math1.

Just a little h – This activity introduces the idea of using h in an difference quotient as a setup for the limit definition of the derivative (which is not in this activity).

What’s your limit? – Students use a graphical and numerical approach to evaluate limits. In one slide, students must try to use tables to find limits for a function they cannot see (graphically or algebraically).

What’s your limit pt 2? – Short continuation from above.

AC Section 1.2 Ex 3 – From time to time, I like to use Activity Builder to grab student responses. This is a quick one.

AC Activities 1.8 and 1.9

AC Section 1.3 Ex 1 – With a little extra added in the end on the limit definition.

AC Activity 1.10

AC Preview Activity 1.5 and Example 1.4

AC Section 1.5 Ex 1

Daylight Hours  This AB is adapted from one of the Desmos curated activities from Joshua Bowman. I tweaked it only a little. This will intro the second derivative by examining what it has to do with the equinoxes.

AC Section 1.6 Intro  Intro examples and preview activities from 1.6 (second derivative) along with some card sorts for some of the text.

AC Section 1.6 Ex 4  Just a simple collector for ex 4’s graphs. I added a few random marbleslides due to a long weekend.

Tangent Lines and Linearization  This will intro tangent lines, derivatives on desmos, and local linearization. It uses activity 1.21 from Active Calculus.

Predict with Calculus  Students will use linear approximations to predict function values. They will use the second derivative to examine how accurate an approximation may be.

Exponential Derivatives  Students will discover the only (nontrivial) function that is its own derivative. Adapted from https://www.desmos.com/calculator/7kend6oocs, which I did not write and don’t know who did!

AC Activity 2.6

Inverse Functions and Their Derivatives

Finding Maximums and Minimums  Adapted from Active Calculus Preview Activity 3.1.

Active Calculus Activity 3.2

AC Section 3.3 Ex 1

Implicit Differentiation  Can be used as a paced intro to implicit differentiation.

Extreme Value Theorem  Several examples develop the conditions for the EVT.

Related Rates  Adapted from Active Calculus Preview Activity 3.5

Graph Races  Introduction to using the area under a velocity curve as a distance traveled measure. Thanks to the Desmos Fellows and teaching faculty for help editing this one.

Rain in Maine  Preview to Riemann sums and review of sigma notation.

Riemann Sums  Left, Right, and Middle Riemann sums are used to approximate change of position. Adapted from Active Calculus Activity 4.5.

Biking from Lake Macatawa to Grand Haven  Change in position and distance traveled. Adapted from Active Calculus Section 4.1 Ex 1.

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