The SAT Prep Black Book
SAT Math Quick Summary
This is a one-page summary of the major relevant concepts. Use it to evaluate your comprehension or jog your memory. For a more in-depth treatment of these ideas, see the rest of the section.
The Big Secret: SAT Math tests very simple things in very strange ways.
The concepts in the SAT Math section must be limited because of standardization. No trig or advanced stats—just arithmetic, algebra, and geometry. Refer to the SAT Math Toolbox if necessary.
Focus on the definitions and properties of the concepts in each question, not on formulas.
All SAT Math is “easy,” and each question can be done in 30 seconds or less if you find the fastest solution. If your solution is very complicated, you’re probably doing the question wrong.
Look for shortcuts, things that cancel out, equivalent terms, etc. Leave expressions as fractions and radicals, instead of decimals, for easier canceling and substitution.
Diagrams are assumed to be to scale unless the question says otherwise. Taking a close look can often help to eliminate wrong answers or even point to the right one without doing any math.
Diagrams that aren't drawn to scale often yield important information if you redraw them to scale.
Every question contains all the information you need to answer it (unless “not enough information” is an answer choice, in which case there may not be enough information), even if it doesn't seem like that. If you understand every word in the question, then you know enough to mark the right answer.
Some common wrong answer patterns include choices that are:
ohalf or double the right answer
oin a series with the right answer
oa number that you have to find “on the way” to the answer
osimilar in appearance to the right answer
I recommend a step-by-step process called the Math Path for questions that are hard to figure out:
oRead the question carefully and consider the words. This is the most important step.
oConsider any diagrams—scale, missing dimensions, etc.
oConsider answer choices (if there are any)—relationships with each other and with question.
oWhat areas of math are involved? What can the SAT test in those areas? (Math Toolbox.)
oIn light of steps 1 - 4, look for a solution that would take 30 seconds or less, ideally.
oSolve the problem.
oCheck your work with the answer choices. “Carelessness” costs more people more points than any other single thing does.
Note that we think about the question holistically before we actually start solving it.
Ignore the order of difficulty, which is based on people who don’t know what they’re doing. You can make careless mistakes on any question, and every question has a simple, direct solution.
See the example solutions in this Black Book for demonstrations of these ideas.