## Writing Review Sheets

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I was re-reading the post Writing Tests recently, and thinking about how I prepare for exams. In particular, I was thinking about how I prepare students for exams, and one way that has worked well for me is giving an Outline of Topics as a review sheet.

This isn’t how I originally designed review sheets. My original review sheets were lists of topics and lists of questions, but in an effort to be thorough I included as much as possible: my very first review sheet was four pages, dense with bullets and possible questions. My students were completely overwhelmed. I quickly realized that this wasn’t working for anyone, including me, and eventually settled on the outline review sheet.

My review sheets now run 1-2 pages, and they do consist of occasional examples, but for the most part they simply organize the past several weeks of material into a hierarchy. My first Calculus I review sheet, for example, starts off:

I. Functions

A. Words, graphs, tables, equations (incl. absolute value and piecewise)
B. Independent variable and dependent variable
C. Domain and Range
D. Increasing and Decreasing
E. Function composition
Ex.

Cars run most efficiently at intermediate speeds (around 55mph). We can view gas mileage (miles per gallon) as a function of speed.
What is the independent variable? Dependent variable? Domain? Range? What would a graph of this function look like?

II. Specific Types of Functions

A. Linear Functions

i) Find the equation of the line through two points (e.g. (2,1) and (5,10))
ii) Find the equation of the line through a point parallel/perpendicular to a line
(e.g. through (2,1) perpendicular to 4xy = 3)

B. Trig Functions

i) Ratios of right sides of triangles
ii) How the trig functions are related to each other
(e.g. cscx = 1/sinx)
iii) General shape of each curve plus where it is positive/negative
iv) Connection with a circle
(x = rcosθ, y = rsinθ)

For the students, this helps them see what I think of as the main topics and what I think of as subtopics. They seem to have enough information to study, but not so much that they’re overwhelmed; at the same time, the outline is vague enough that I have the freedom to ask questions in many different ways. In addition, I have a pre-made outline of what the test should look like, and one that’s easy to adjust the next time I teach the class.