Explorations in Calculus has been written as an enrichment
supplement to an AP calculus course. Graphing calculators have revolutionized the teaching and learning of mathematics. Graphs are a very important component of calculus and are crucial in helping students visualize and gain insight into traditional calculus topics. Calculations can reduce time spent on “paper and pencil” methods and increase time spent on concepts, problem solving and application.
The exploratory exercises incorporate the TI-84 or the TINspire
CAS calculator and were created to guide and encourage
• discover and explore patterns and then describe them;
• do a problem analytically (paper and pencil) and support results numerically and/or
graphically (with graphing calculator);
• do a problem numerically/graphically (with graphing calculator) and then confirm the results
analytically (paper and pencil);
• do a problem numerically and/or graphically beause paper and pencil methods are impractical
(too time consuming) or impossible.
Each of the 17 explorations starts with a set of Solved Problems followed by a set of Exercises.
The Solved problems are examples that provide a context for instructions that one might
encounter in the exercises, but they also contain useful mathematical hints and lessons as well.
The explorations in this book are not designed to teach you how to use your calculator.
However, when an exploration requires you to perform a complicated calculator operation, you
will be referred to the APPENDIX, where the specific keystrokes are described in detail for the or the
TI-84 in APPENDIX A and for the TI-Nspire in APPENDIX B.