Department of Mathematics

Exam Formula Sheets

Each exam will have a formula sheet that will aid students during the exams. Copies of the formula sheets are available here for students to reference while studying.

These formula sheets are not all inclusive. There may be additional formulae, techniques, and strategies that would be benificial for you to know from memory.

Exam Creation Strategy

When selecting problems to put on exams the writers will first use the WeBWorK homework problems as guides. Students should expect a decent number of problems on the exams to have similar wording or structure as the problems on WeBWorK. It is therefore recommended in addition to practice exams and other study techniques students also review the WeBWorK homework and are able to complete these problems in a timely manner. Note: this does NOT guarantee that all or even most problems on the exam will be WeBWorK problems.

More Challenging Problem(s)

One of the undergraduate learning goals at Michigan State University is to develop analytical thinking by synthesizing and applying course content. Each exam will have a page (near the end) of more challenging problems (typically 1 or 2) to accomplish this goal. To prepare for these type of problems it is recommended that students study the concepts in detail rather than repeating specific types of problems. These challenging problems are meant to assess your ability to make connections between concepts and synthesize core ideas.

Uniform Midterm Exam Content

These are the guidelines that the exam writers are given: The exam is 90 minutes long and will cover the following sections

Exam Date Sections Covered
Exam 1 Monday February 19th 12.1 - 14.5
Exam 2 Monday April 9th 14.6 - 16.6

The exam is out of 100 points maximum and will typically have the following breakdown in terms of types of questions:

Type Quantity Points
Multiple Choice 9 Questions 4 Points/Problem
Standard Response 4 Pages 14 Points/Page
More Challenging Problem(s) 1 Page 14 Points
TOTAL 106

Note that despite there being 106 points in total the maximum score is 100 points. Any points over 100 will be discarded.

Priority 1

The below topics are considered the core topics covered by Exam 1 and are therefore more likely to appear on the exam.
  • Linearization/Tangent Plane
  • 12.5 Type problems. Including both dot and cross product
  • Domain/Range/Level curves
  • Limits
  • Parametrization
  • Derivatives and integrals of vector functions
  • Chain rule

Priority 2

All other topics/sections covered by Exam 1.
  • Some of these other topics are less likely to appear as standard response questions but may show up as multiple choice questions.

Priority 1

The below topics are considered the core topics covered by Exam 2 and are therefore more likely to appear on the exam.
  • Maximum and minimum values
  • Multiple Integrals
    • Rectangular Double or Triple
    • Polar/Cylindrical
    • Spherical
  • Line integrals
    • Scalar functions
    • Vector fields
    • Green's theorem
  • Fundamental Theorem of Line Integrals
  • Surface Area
    • Parametric surface
    • Explicit surface

Priority 2

All other topics/sections covered by Exam 2.
  • Some of these other topics are less likely to appear as standard response questions but may show up as multiple choice questions.

Final Exam Content

These are the guidelines that the exam writers are given: The final exam is 120 minutes long and will cover everything!

Exam Date Sections Covered
Final Exam Tuesday, May 1st ALL
The final exam is out of 100 points maximum and will have the following breakdown in terms of types of questions:

Type Quantity Points
Multiple Choice 12 Questions 3 Points/Problem
Standard Response 5 Pages 12 Points/Page
More Challenging Problem(s) 1 Page 12 Points
TOTAL 108

Note that despite there being 108 points in total the maximum score is 100 points. Any points over 100 will be discarded.

Priority 1

The below topics are considered the core topics covered by Final Exam and are therefore more likely to appear on the exam.
  • Surface area or surface integral
    • Parametric surface
    • Explicit surface
  • Divergence Theorem
  • Stokes' Theorem
  • Maximum and minimum values
  • Line integrals
    • Scalar functions
    • Vector fields
    • Green's theorem
  • Limits
  • Parametrization
  • Derivatives and integrals of vector functions
  • Chain rule
  • Linearization/Tangent Plane
  • 12.5 Type problem. May include both dot and cross product
  • Domain/Range/Level curves
  • Integrals
    • Rectangular Double or Triple
    • Polar/Cylindrical
    • Spherical
    • Fundamental Theorem of Line Integrals

Priority 2

All other topics/sections.
  • Some of these other topics are less likely to appear as standard response questions but may show up as multiple choice questions.