Past exams and exam study materials

This page describes the general structure of exams in Math 214, and provides study materials. For policies specific to the current term, see the Exam Dates and Policies Page.

Gateway Exam

A Gateway exam is a computerized exam on routine computations which may be attempted many times, to ensure that students master these fundamental skills. Many large math courses at the University of Michigan have Gateway exams. The Gateway exam for Math 214 covers elementary row operations, reduced-row echelon form, elementary matrix operations including matrix multiplication, and solving linear equations. Here is a blogpost Links to an external site. about the theory and practice of Gateways in general.

Students wishing to practice for the Gateway should go to Webwork (linked from the private Canvas page) and select PracticeMatrixOpsGW . In the current term (Fall 2024), students who wish to take the official Gateway should also do so through the WebWork interface, by selecting OfficialMatrixOpsGW, but the procedure has been different in other terms; check the private canvas page for up to date information on rules and procedures.

Midterm 1

The first midterm exam has generally covered material from Chapters 1-3 of the textbook, meaning solving linear equations, row reduction, matrices and matrix operations, linear transformations, span, linear independence, bases, image, kernel, dimension and coordinates.  Here is a more detailed study sheet:

Study sheet (not yet revised for Winter 2025) Download Study sheet (not yet revised for Winter 2025).

Here are our past exams. Note that rules regarding calculators, exactly what material can appear, and the exact timing of exams have changed from year to year. Check the exam dates and policies page for up to date information.

Midterm 2

The first midterm exam has generally covered material from Chapters 5-6 of the textbook, meaning inner products, orthogonal projection, the Gram Schmidt process, QR decomposition, least squares data fitting, and determinants. In early years, it also covered material from Chapter 7 (Eigenvalues and Eigenspaces)  Here is a more detailed study sheet:

Study sheet (Revised for Winter 2025) Download Study sheet (Revised for Winter 2025)

Here are our past exams. Note that rules regarding calculators, exactly what material can appear, and the exact timing of exams have changed from year to year. Check the exam dates and policies page for up to date information.

Final Exam

The final exam focuses on material from chapters 7 and 8 of the text book: eigenvalues and eigenvectors, diagonalization, symmetric matrices, the spectral theorem, singular value decomposition. Material from other sections will also reoccur.

Study sheet (not yet revised for Winter 2025) Download Study sheet (not yet revised for Winter 2025)

Here are our past exams. Note that rules regarding calculators, exactly what material can appear, and the exact timing of exams have changed from year to year. Check the exam dates and policies page for up to date information.