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 |
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messy/nasty algebra =>simple clear arithmetic |
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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 |
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eg total number of marbles in a jar, total miles to travel in a trip |
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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 |
DATA ANALYSIS
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. |
Median |
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. |
Mode |
the number that appears the most. (Remember: Mode sounds like most.) |
Range |
highest-lowest |
Rate pie =average |
car speed, work done, average pie |
Percent translatiom |
percent: /100; of: x; what x; is are equals: = |
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5 is what percent of 80? 5=x*80/100 |
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what percent of 5 is 80? x*5/100=80 |
PERCENTS increase and decrease |
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100* difference / original amt |
Growth and decay |
final amount = original amount (1 ± rate)number of changes |
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population growth, radioactive decay, and credit payments |
RATIOS AND PROPORTIONS |
fraction=part/whole; ratio=part/part, part+part=100 |
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sometimes : fraction/ratio => decimal |
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ratio box [p,p,w]*[r,m,a]: fill in known ->calc unknown |
direct proportion/variation |
x1/y1=x2/y2 |
inverse proportion/variation |
x1y1=x2y2 |
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