Rough Rules for Math

Eight years ago, I wrote this to a student. I've changed my mind on a few things, like when to bubble, but otherwise this advice holds true

Phil’s SAT Math Reminders:

1. SLOW DOWN – you have plenty of time to score well. Remember that getting a 70% gets a 600! 
2. SLOW DOWN - Breath deeply during the exam. Take breaks to take deep breaths, your brain NEEDS the oxygen & it helps to control your nerves.
3. SLOW DOWN - I have tutored hundreds of students and overwhelmingly mistakes are made in haste.
4. WRITE DOWN YOUR WORK - do not do every math problem in your head. Get your hands involved.
5. Time yourself as practice. Practice doing math problems for 15, 20 and 25 minutes. Set a timer so that you can get a feel for the length of the sections.
6. Mark your answers in your test booklet and then transcribe them onto the bubble sheet as you are about to turn the page to the next set. This "batch processing" is the most efficient. 
7. RTFQ – Read The Flippin Question; before each question, take a deep breath and then read the entire question. Too many mistakes are made when students start attempting an answer BEFORE they even read the entire question. Too many mistakes are made by reading into the question. Get your hands on as many SAT practice tests as you can; form a study group with friends and each buy one of the big books with only practice tests - Barrons, Kaplan, Princeton Review. Read the question style.
8. W? – WHAT is the question asking? Make sure that you know what you are solving for. If it is past half way, there is probably two steps and you have to solve for one thing and then use that answer to solve for real answer. You can bet that 9 times out of 10, the first answer and all permutations of it are in the answer choices.
9. Know the RATIO BOX or RATIO GRID; you can solve the four hardest word problems on the SAT: 1. Ratio’s; 2. Work; 3. Solutions (as in Acid solution); 4. Time-Speed-Distance. Princeton Review has a great Ratio box; my more thorough box will be posted shortly.
10. Average – Arithmetic mean [Mean, Median, Mode]
11. Probability – simply have to practice these.
12. Permutations - how many ways can seven runners finish a race: 7! = 7*6*5*4*3*2*1
13. Time = Speed x Distance these can be very tricky; I will be posting about 50 of these so that you can get plenty of practice
14. Plug In! – If there are variables in the question & variables in the answer, put in your own numbers and see which one works.
15. Backsolve – for multiple choice questions the answers are right in front of you, set up your equation & put the answer choices into the equation. It is best to start with choice C and then move up or down. [answers are in ascending or descending order]
16. Eliminate wrong answers through: Process of elimination. Eliminate wrong answers. Get rid of a few choices that are obviously wrong. You may get to the right answer without even having to do the problem. If you are stuck, pick one of the remaining and move on.
17. GUESS!!!!! --- If you can estimate or eliminate possible wrong answers, guess! For Grid-ins, there is very little chance of simply guessing the answer but it doesn't count against you so mark something down. 
18. Spend time wisely – do your best on the hard problems, but remember answering an easy or medium problem correctly is worth the same amount as the hardest problem. Did I say slow down and breath deeply yet?
19. Three Dimensional (3-D) problems usually have a two dimensional answer. There is usually a quick trick with 3-D.
20. Special triangles. Know them, cold. They WILL BE on the test. 3-4-5; 5-12-13; equilateral; isosceles;30-60-90; 45-45-90.
21. Sum of the interior angles of a polygon, 180(n-2), where n=number of sides.
22. Rules of Divisibility, 2, 3, 4, 5, 6, 9 are the most common.
23. REMAINDER – look up the remainder problem and practice it. You have probably not done a remainder problem for several years. NOTE: a calculator will not help you on a remainder problem as much as knowing how to solve it.
24. SLOPE INTERCEPT FORM  y = mx + b; solve for slope (m); parallel slopes, perpendicular slopes, lines in a coordinate plane, midpoints, rise/run.
25. Make a ruler out of your answer sheet and measure the figures, most are drawn to scale.
26. Algebraic factoring; usually not that hard so don’t over think it.
27. 180 degrees on a line; 360 degrees about a point - This question is on every test. Funky multi-step intersecting lines and triangles; find the 180’s! 
28. Circles, circumference, diameter, radius, tangent, area, arc’s. Practice, practice, practice. These are all easy, so they have to word the problems with tricks.
29. Quadratic & Parabolas.
30. Exponents. Rules of adding, multiplying and raising to a another power. Squares & cubes.
31. INTEGER – get to know & love this word, it WILL BE on the SAT that you take.
32. Consecutive, even, odd, prime integers on the number line.
33. Digits; Distinct numbers; real numbers; rational numbers; factor; multiple; remainder; prime – know them.
34. Arithmetic rules for evens/odds e+ e = e; o + o = e; o x o = o, etc
35. Read the question thoroughly, take your time and aim to get the first 2/3 of each section correct – that’s a 600!
36. Order of Operations – PEMDAS
37. Memorize the instructions and the given formulas. Please at least read them over. They are given for a reason, they WILL BE used. So get used to them and make note of your practice problems that use the given formulas. Using your time wisely means being able to see when this formulas will be used and NOT having to turn back the page to search for them.
38. Write down each step as if this was middle school and you were getting graded on your work.  Joe Cool does math in his head and skips steps. Write down every miserable step to avoid simple math mistakes. You have the time to get a 600! So use the time and get the easy and medium difficulty questions.
39. Distributive law
40. Adding/subtracting/multiplying/dividing fractions. The answer choices are in fractions, so a calculator may not be an advantage.