# T

###### 1.

## Introduction

his book is intended for students who are preparing to take either of the two

Advanced Placement Examinations in Mathematics offered by the College

Entrance Examination Board, and for their teachers. It is based on the May

course description published by the College Board, and covers the topics listed

there for both Calculus AB and Calculus BC.

Candidates who are planning to take the CLEP Examination on Calculus with

Elementary Functions are referred to the section of this Introduction on that

examination.

###### THE COURSES

Calculus AB and BC are both full-year courses in the calculus of functions of a

single variable. Both courses emphasize:

(1) student understanding of concepts and applications of calculus over

manipulation and memorization;

(2) developing the student’s ability to express functions, concepts, problems,

and conclusions analytically, graphically, numerically, and verbally, and to

understand how these are related; and

(3) using a graphing calculator as a tool for mathematical investigations and

for problem-solving.

Both courses are intended for those students who have already studied

college-preparatory mathematics: algebra, geometry, trigonometry, analytic

geometry, and elementary functions (linear, polynomial, rational, exponential,

logarithmic, trigonometric, inverse trigonometric, and piecewise). The AB

topical course outline that follows can be covered in a full high-school academic

year even if some time is allotted to studying elementary functions. The BC

course assumes that students already have a thorough knowledge of all the topics

noted above.