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Skills for a Top ACT Math Score

Skills to help you score well on the ACT Math section.
STUDY
PLAY
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
Memorize:
the laws of exponents
sohcahtoa:
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:
triangles
When calculating answers,:
never multiply and/or do long division if you can reduce first