Skills for a Top ACT Math Score

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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)

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

plug 3 in for x

draw it

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)

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)

triangles

never multiply and/or do long division if you can reduce first

Example: