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,
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,
III. Applications of the derivative. Questions will be of two types:
a. Given a time-distance graph describe (in words) the trip of the
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
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.
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
updated Dec. 11, 2001