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**Topics for Calculus Mastery Quizzes**

I. Derivatives. Questions are of two types:
a. Given a function (graph, table, or formula) __determine the derivative__
at a point or x-value. (For the graph question, the derivative is approximated.)

b. Given a function (graph, table, or formula) __determine where the
derivative is__ negative, positive, -1, 0, +1, or greater than 1. The
answer is an x-value or set of x-values.

Four questions total. example1,
example2
II. Find limits (one-sided and two-sided). The variable may approach a
finite value (number) or infinity or negative infinity .
Three questions: one graph, one table, one formula. example1,
example2
III. Applications of the derivative. Questions will be of two types:
a. Given a time-distance graph describe (in words) the trip of the
object.

b. Given a function (as a formula), which describes a *real *situation,
answer questions. Questions may include the following:

i. Determine the derivative at a point or x-value, and describe what
this means.

ii. Determine where the derivative is negative, positive, or some specific
value (such as +1, 0, or -2), and describe what this means. Your answer
will be an x-value or set of x-values.

iii. Find maximum or minimum points and describe what these mean.

Four questions. One written description and three questions on the application.
example
IV. Integrals and their applications. Three questions:
a. Evaluate a definite or indefinite integral (formula* given).

b. Given a function (as a formula*), which describes a *real *situation,
evaluate a definite integral and

c. explain what it means.

*Formulas on the mastery quiz are just polynomials. example
Graphing calculators and computers not allowed on all mastery quizzes.
Four-function calculators *are *allowed.
Some questions may require an approximate answer.

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James R. Olsen, Western Illinois University

E-mail: `jr-olsen@wiu.edu`

*updated Dec. 11, 2001*