The SAT abounds with “Ex-“ words. It’s easy to get them mixed up, so pay careful attention!
This word sounds like example, which is helpful considering this word means the typical or perfect example of something. So if somebody is an exemplar you want to make sure you follow their example.
To be really excited about something (yeah, I got into Stanford on a full-ride) is to exult. Indeed, many people were exulting all around me (and on my Facebook post) about how Duke won the championship (I apparently know a lot of ex-Duke folk). Of course, if you get into a college as esteemed as Duke, you’ll probably want to exult too.
This word can mean to make a physical effort (he exerted every ounce of his being to make it up the mountain). It can also mean to exercise an influence over another thing. Okay, that’s kind of a weird definition so let me give you a couple of examples:
Gravity exerts a far stronger effect on Earth than it does on Mars, where if we were on the surface we could jump and get more hang time than Michael Jordan.
The SAT is exerting a negative influence on my brain—I think it’s going to implode!
You can do it = motivational
You can do it, because I believe doing so will make you a better person = exhortative
You can see that the second example differs slightly because there is an emphasis on doing the right thing (the first sentence can be urging you to rob a bank). The verb exhort means to urge in a constructive manner.