How Can I Learn All of Sal's Math Tricks

Alright, I don't know when your SAT is, if it's June 1st this year then you won't have time.  First off memorize the unit circle so you can recall it instantly.  Next memorize and practice the trig identities.  Make sure you at least have the 11 x 11 multiplication table memorized, possibly up to 13 by 13.  I know they tended to stop at 10 x 10 but the extra little bit helps. 
a x b = |a||b|sin(theta), he is doing quick symbolic and integer math in his head.  Treating things like sqrt(2) and sqrt(3) as variables.

Other little tricks with fractions and simple arithmetic can be learned by practicing a LOT. 

I used to be able to do some of that.  That particular problem would have taken me a lot more time to do even though I had finished Calculus 3, Differential Equations and Linear Algebra before I finished Highschool over 20 years ago.

sal is the god of math (real)