1. Hand out a copy of the 1991 Free Response Questions for
the A.P. Calculus AB Exam. Have students work on
question #1.
2. After 8 to 10 minutes, go over the answer. Then hand out
the 1991 Grading Standards and show students what needs
to be included in their answers.
3. Discuss coloring a map. Put several on the board and
have students determine the number of colors necessary
to color them.
Discuss the Four Color Theorem.
The Four Color Problem dates back to 1852 when Francis
Guthrie, while trying to color the map of counties of
England noticed that four colors sufficed. He asked his
brother Frederick if it was true that any map can be
colored using four colors in such a way that adjacent
regions (i.e. those sharing a common boundary segment,
not just a point) receive different colors. Frederick
Guthrie then communicated the conjecture to DeMorgan.
It wasn't until over 100 years later that this
conjecture was finally proven. It was with the help of
a computer that Appel and Haken in 1976 published their
proof of the Four Color Theorem.
4. Distribute copies of maps to color.