Placement Exam Topics

Students that have obtained a 4 or 5 on the BC Calculus AP exam are eligible to take the Calculus Placement Exam.

The mathematics placement exam (for placing out of Calculus I, into Calculus II) tests students for:

1) a well-developed sense of the concept of function according to the rigorous definition, specifically when applied to real valued functions of one real variable (which is also the context for everything below);

2) ability to use limits in order to determine geometric properties of the graph, e.g., continuity/discontinuity and asymptotic trend;

3) expert familiarity with the standard rules for computing limits (e.g., through reduction and evaluation), through usual arithmetic including the composition formalism; also, Rule of L'Hopital;

4) expert familiarity with the standard rules for computing derivatives, including arithmetic laws and the chain rule;

5) ability to solve related rates, implicit differentiation, and optimization problems from beginning to end, including precise justification when appropriate;

6) ability to use the differential calculus to study the graph of a function (e.g., geometric information deduced from the first and second derivatives);

7) a good precise understanding of the fundamental theorem of calculus;

8) knowledge of the standard techniques of integration;

9) facility with computing improper definite integrals resulting from discontinuity or unboundedness of the domain of integration.

Suggested reference textbook for topics enumerated above:

Thomas, George B. (as revised by Weir, Maurice D. and Hass, Joel). Calculus. Twelfth Edition. Addison-Wesley, 2010. For

(1) see ch. 1;
(2) see ch. 2;
(3) see ch. 2 & 7;
(4) see ch. 3 & 7;
(5) see ch. 3 & 4;
(6) see ch. 4;
(7) see ch. 5;
(8) see ch. 8;
(9) see ch. 8.

Students may also find the following text useful for a discussion of these topics:

Stein, Sherman K. and Barcellos, Anthony. Calculus and Analytic Geometry. Fifth Edition. Mc. Graw-Hill, Inc. 1992.



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