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Skills for a Top ACT Math Score

Skills to help you score well on the ACT Math section.
When you see variables or unknowns in the question and numbers in the answers:
Use the Answers. Convert fractions, pi, or √ to decimals.
"What is m in terms of p and q" is just a fancy way of saying:
solve for m or use algebra to get m alone
When you see vertical angles, a linear pair, or a triangle,:
calculate the measure of all angles
When you see two parallel lines that are crossed by another line, eight angles are formed and:
all of the bigger-looking angles are equal, and all of the smaller-looking angles are equal
When you see "then x=?":
complete the algebra or just Use The Answers
When you see a triangle with two equal sides:
mark the two opposite angles as equal. (3 equal sides means 3 equal 60 degree angles)
When you see and expression like (2x - 5) (5x - 4):
use FOIL (First Outer Inner Last)
Anytime you see a math vocabulary term:
underline it
The key to charts and graphs is:
to read the intro material and the "note" if there is one, and to expect an average, percent, and/or probability question about the data
f(3) means:
plug 3 in for x
When a picture is described, but not shown, :
draw it
When something can be factored, foiled, reduced, or simplified:
do it
the laws of exponents
some other horse caught another horse taking oats away; sin=opp/hyp, cos=adj/hyp, tan=opp/adj
If one side of a triangle is the diameter of a circle, and the opposite vertex is on the circle, then:
the triangle is right with its right angle opposite the diameter
An arithmetic sequence is a sequence of numbers where a certain number is:
ADDED to each term to arrive at the next
A geometric sequence is a sequence of numbers where a certain number is:
MULTIPLIED by each term to arrive at the next
A log is just a fancy way of writing exponents. For example,:
log(base 5) of 25 = 2 means 5^2 = 25
The key to complex number questions is to treat i like a normal variable, and then:
in the final step, replace i^2 with -1
Cancel quantities to:
make the problem simpler
Know how to find unknown quantities (areas, lengths, arc and angle measurements) from:
known quantities (the whole equals the sum of its parts)
Use specific numerical examples to:
prove or disprove your guess
When each choice must be tested:
start with the last choice and work backward
Try not to make tedious calculations:
since there is usually an easier way
Draw or extend lines in a diagram to:
make the problem easier (also, label unknown quantities)
Watch out for questions that:
seem very easy but that can be tricky (beware of choice A as a "lure" choice)
Know and use facts about:
When calculating answers,:
never multiply and/or do long division if you can reduce first