SPU Mathematics

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 pre-calculus 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 Algebra and Trigonometry (MAT 1110).  NOTE: This exam is NOT the same as the Math Proficiency Exam that is given to all incoming freshmen.

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 (in Adobe PDF format; the free Adobe Acrobat Reader is required to view and print these exercises).  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 pre-calculus 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 acquire skills needed 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; and

• use Maple to effectively to explore and solve calculus problems.

In addition to the specific skill-oriented objectives above, students should

• have a better overall conceptual understanding of functions and their graphical, numerical, analytical, and verbal representations; 

• understand derivatives as rates of change;

• have improved skills at problem solving and critical thinking: at dissecting a complex problem, determining steps in its solution, finding the solution, and testing whether it is reasonable; and

• be able to 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 6th 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 Graphing Calculators and Computers

• 2.1 The Tangent and Velocity Problems

• 2.2 The Limit of a Function

• 2.3 Calculating Limits Using the Limit Laws

• 2.4 The Precise Definition of a Limit

• 2.5 Continuity

• 3.1 Derivatives and Rates of Change

• 3.2 The Derivative as a Function

• 3.3 Differentiation Formulas

• 3.4 Derivatives of Trigonometric Functions

• 3.5 The Chain Rule

• 3.6 Implicit Differentiation

• 3.7 Rates of Change in the Natural & Social Sciences

• 3.8 Related Rates

• 3.9 Linear Approximations and Differentials

• 4.1 Maximum & Minimum Values

• 4.2 The Mean Value Theorem

• 4.3 How Derivatives Affect the Shape of a Graph

• 4.4 Limits at Infinity; Horizontal Asymptotes

• 4.5 Summary of Curve Sketching

• 4.6 Graphing with Calculus and Calculators

• 4.7 Optimization Problems

• 4.8 Newton's Method

• 4.9 Antiderivatives

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

  • Basic matrix operations and solutions of systems of linear equations

  • Computer labs with Maple