Calculus
Placement Exam
All students are required to take the Calculus
Placement Exam prior to enrolling in MAT 1234 (Calculus I). This
placement exam, which is administered online, covers
precalculus algebra and trigonometry skills that are necessary for success
in Calculus. Calculators are not permitted on the exam. Scores on the exam will be used to determine
appropriate placement, typically in either Calculus I (MAT 1234) or
Precalculus (MAT 1110).
Students currently enrolled at SPU who wish
to register for MAT 1234 should go to
http://www.spu.edu/depts/sas/oltesting.html to sign up to take the
placement exam. Newly admitted students will receive information
about taking the placement exam before coming to campus for early
registration.
Some
exercises to help you review some key ideas of algebra and trigonometry
are available here.
Note that this review does not cover every type of problem that might be on
the placement exam. It is also not intended as a sample of what the exam will
look like; it is merely intended as a good starting point for reviewing your
precalculus skills. Solutions for the
practice exercises are also available.
Course
Objectives for MAT 1234: Calculus I
This first course in calculus emphasizes
limits and derivatives of functions of one variable. The primary aims of the course are to
help students develop new problem solving and critical reasoning skills and
to prepare them for further study in mathematics, the physical sciences, or
engineering. By the end of the course, students should be able to:

compute limits by
graphical, numerical, and analytical methods;

mechanically calculate
derivatives of algebraic and trigonometric functions and combinations of
functions;

use derivatives to
sketch graphs and solve applied problems;

represent functions graphically, numerically,
analytically, and verbally;

interpret derivatives
as rates of change;

solve systems of linear equations;

perform matrix arithmetic;

use Maple effectively to explore and solve calculus problems;

analyze and solve complex problems; and

provide
clear written explanations of the ideas behind key concepts from the
course.
Students should also gain an increased
appreciation of mathematics as part of the language of science and as a
study in itself.
Course
Content
The standard
material to be covered in Calculus I from the 7th edition of Stewart's
Calculus is listed below. Individual instructors may make minor
modifications to this list.

1.1 Four Ways to Represent a Function

1.2 Mathematical Models: A Catalog of
Essential Functions

1.3 New Functions from Old Functions

1.4 The Tangent and Velocity Problems

1.5 The Limit of a Function

1.6 Calculating Limits Using the Limit
Laws

1.7 The Precise Definition of a Limit

1.8 Continuity

2.1 Derivatives and Rates of Change

2.2 The Derivative as a Function

2.3 Differentiation Formulas

2.4 Derivatives of Trigonometric
Functions

2.5 The Chain Rule

2.6 Implicit Differentiation

2.7 Rates of Change in the Natural &
Social Sciences

2.8 Related Rates

2.9 Linear Approximations and
Differentials

3.1 Maximum & Minimum Values

3.2 The Mean Value Theorem

3.3 How Derivatives Affect the Shape of
a Graph

3.4 Limits at Infinity; Horizontal
Asymptotes

3.5 Summary of Curve Sketching

3.6 Graphing with Calculus and
Calculators

3.7 Optimization Problems

3.8 Newton's Method

3.9 Antiderivatives

In addition to the sections above from
the main textbook, there will be some supplementary materials:
