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SAT Math Techniques ch10 Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Plugging In Your Own Numbers (PIYON)

Whenever you see a problem with variables in the answer choices, Plug In.
in terms of; equivalent form
messy/­nasty algebra =>s­imple clear arithmetic
Try 1, verify with 0 or 2; be careful the number must be in the domain
if answers are percents or fractional parts of some unknown quantity
try Plugging In: percent = 100*di­ff/­ori­ginal
eg total number of marbles in a jar, total miles to travel in a trip
ratio percent =>p­lugin ==>­number, 10% =>10

PLUGGING IN THE ANSWERS (PITA): answer is a number

If the average (arith­metic mean) of 8 and x is equal to the average of 5, 9, and x, what is the value of x ?
Don’t try to solve problems like this by writing equations and solving for x or y. Plugging In the Answers lets you use arithmetic instead of algebra, so you’re less likely to make errors.
Start from either end(gr­eatest or least) or middle­(mean)
if answer has very small/big number, try bigger­/sm­aller first


The Average Pie
[total­,avg,n] When calcul­ating averages, always find the total. It’s the one piece of inform­ation that ETS loves to withhold.
To find the median of a set containing an even number of items, take the average of the two middle numbers after putting the numbers in order.
the number that appears the most. (Remember: Mode sounds like most.)
Rate pie =average
car speed, work done, average pie
Percent transl­atiom
percent: /100; of: x; what x; is are equals: =
5 is what percent of 80? 5=x*80/100
what percent of 5 is 80? x*5/100=80
PERCENTS increase and decrease
100* difference / original amt
Growth and decay
final amount = original amount (1 ± rate)number of changes
population growth, radioa­ctive decay, and credit payments
fracti­on=­par­t/w­hole; ratio=­par­t/part, part+p­art=100
sometimes : fracti­on/­ratio => decimal
ratio box [p,p,w­]*[­r,m,a]: fill in known ->calc unknown
direct propor­tio­n/v­ari­ation
inverse propor­tio­n/v­ari­ation