We'll mainly be using the math department's 53 worksheets, which can be found here.
Worksheet solutions! Some of us GSIs are collaborating on these. They were initially written by Qiaochu Yuan, Catherine Cannizzo, and myself, for Professor Hutchings' Spring 2014 section of Math 53. Therefore we included some solutions to his previous midterms and finals.
Solutions to Worksheet 1.
Solutions to Worksheet 2.
Solutions to Worksheet 3.
Some parametric equations that are good to know: circles and ellipses, line segments, some notion of what happens when you replace t by a function of t (e.g. if t^2). Some polar equations that are good to know: circles, what happens when you multiply the theta in sine or cosine by an integer, some notion of what can happen when you add a positive number to a polar curve. I can't promise that this list will be exhaustive, but I hope it helps. Play with an online graphing tool.
Solutions to Worksheet 4.
Solutions to Worksheet 5.
Solutions to Worksheet 6.
Solutions to Worksheet 8.
Solutions to Worksheet 9.
Solutions to Worksheet 10.
Solutions to Worksheet 11.
Solutions to Worksheet 12.
Solutions to Worksheet 13.
Solutions to Worksheet 14.
Solutions to Worksheet 15.
Solutions to Worksheet 16.
Solutions to Worksheet 17.
Solutions to Worksheet 18.
Solutions to Worksheet 19.
Solutions to Worksheet 20.
Solutions to Hutchings' 2003 Midterm 2.
Solutions to Hutchings' 2007 Midterm 2. Here is the test itself.
Solutions to Worksheet 25.
Solutions to Worksheet 26.
Solutions to Worksheet 27.
Solutions to Worksheet 31.
Solutions to Worksheet 32.
Solutions to a 2007 final (the one given in May I think). Solutions to another 2007 final (the one given in December I think). Solutions to the 2003 final. These are linked to the professor's website, under "Past Courses" and "53 Fall 2008."