Preposition At

A) Use "at" to indicate that one's vision is fixed upon something.
  1. look at
  2. look back at
  3. glance at
  4. stare at
  5. gaze at
B) Use "at" to indicate precise location within one's field of vision.
  1. point at
  2. aim at
C) Use "at" to show that something is the target of a moving object set forth in motion by a person, equipment, or a machine.
  1. shoot at
  2. fire at
  3. throw at
  4. toss at
  5. hurl at
D) Someone is the target of language that expresses displeasure, annoyance, anger, or some other negative feeling.
  1. shout at
  2. snap at
  3. yell at
  4. swear at  
E) Someone is the target of one’s facial expressions.
  1. laugh at
  2. smile at
  3. wink at
  4. make eyes at
F) The target is what one means to say, express, or indicate.
  1. drive at “something” – mean something – indicate something
  2. get at “something”
  3. hint at
G) A negative idea or thought is a target.
  1. cringe at the thought of “something”
  2. balk at
H) Make something the target of one's movement.
  1. take a swing at “someone”
  2. lunge at
  3. come at “someone” with “something”
  4. run at
I) A correct answer is a target.
  1. take a stab at something – guess
  2. guess at
J) Something is the target of one’s effort.
  1. work at “something”
  2. make an attempt at “something”
  3. try hard at “something
K) Idiomatic expressions
  1. jump at the chance
  2. throw money at “something”
  3. sling mud at “someone”
  4. thumb your nose at “something”
  5. be nothing to sneeze at
  6. chip away at “something”
  7. get at “something”
L) Use "at" to show that someone or something is the target of one's emotion as indicated by an adjective.

Semi-fixed expressions - be + adjective + at “something”
  1. be amazed at “something” or “someone”
  2. be surprised at “something” or “someone”
  3. be angry at “someone” 
M) An activity or something one does is the target of one's degree of skill or proficiency. 
  1. good at "something"
  2. bad at "something" 
  3. excellent at "something"
  4. horrible at "something"
  5. great at "something"
  6. terrible at "something".