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Tangent & Area Explorer
The Fundamental Theorem, live
Drag a point along a curve to read its slope, then shade the accumulated area — derivative and integral, connected before your eyes.
Scored investigations
Playing with a simulation is not the same as earning a point. These take your own measurements from this lab into a real AP free response, graded against the rubric.
Measure how a Taylor error grows away from the center
Unit 10 · Infinite Sequences and Series · Quantitative reasoning · 8 pts
Verify an integration-by-parts result numerically
Unit 6 · Integration and Accumulation of Change · Model reasoning · 8 pts
Watch an exponential lose a race it is guaranteed to win
Unit 1 · Limits and Continuity · Data analysis · 8 pts
Find the point where a function attains its own average value
Unit 8 · Applications of Integration · Experimental design · 8 pts
Verify the Fundamental Theorem numerically
Unit 6 · Integration and Accumulation of Change · Model reasoning · 8 pts
Locate a maximum of an accumulation function from the graph of f
Unit 6 · Integration and Accumulation of Change · Data analysis · 8 pts
Measure what "increasing at a decreasing rate" looks like
Unit 5 · Analytical Applications of Differentiation · Quantitative reasoning · 8 pts
Connect a derivative, its zeros, and an accumulation function
Units 5–6 · Analytical applications and integration · Quantitative reasoning · 6 pts
Test whether a secant slope equals the tangent slope at the midpoint
Unit 1 · Polynomial & rational functions · Model reasoning · 9 pts
Determine concavity and locate an inflection point from the tangent slope
Unit 1 · Polynomial & rational functions · Data analysis · 9 pts
Establish what distinguishes an exponential function from a power function
Unit 2 · Exponential & logarithmic functions · Quantitative reasoning · 9 pts
Relate a sinusoid to its own rate of change
Unit 3 · Trigonometric & polar functions · Data analysis · 9 pts
Booting the lab…