 The problems are not easy, so you are encouraged to discuss them in small groups, ask for hints on Piazza or during office hours etc. However your submitted solutions must be written by yourself.
 Your written solutions must be readable:
use full sentences
example: "we will use (a,b) to denote the coordinates of the center of the circle in question" is always preferred to "center: (a,b)", which is in turn preferred to just using a and b as the coordinates of the center without ever mentioning it).
Illustrate your solution with relevant pictures
for instance if a problem asks for equations of two circles, the solution most likely will include a diagram with two circles on it.
Use appropriate connectors between phrases
example: "...the equation of a circle with center (a,b) and radius 3 is (xa)^{2}+(yb)^{2}=9. In order for the point (1,2) to lie on this circle, it must be true that (1a)^{2}+(2b)^{2}=9. Expanding this we get 12a+a^{2}+44b+b^{2}=9, or, rearranging the terms, a^{2}2a+b^{2}4b=4. Next we notice that..." is preferred to something like "circle: (xa)^{2}+(yb)^{2}=9. (1,2) on it: (1a)^{2}+(2b)^{2}=9. 12a+a^{2}+44b+b^{2}=9. a^{2}2a+b^{2}4b=4". You can see for yourself that the first one is readable, while the latter one isn't.
Slow down when writing the final version of you solution: it will make you think a little more about your solution and make your handwriting easier to read.
Try to read your own solution once it is written down: often you will see a way to improve it. This is normal. Do not resist the urge. In fact rewriting, not writing, is what improves your writing skills the most.

