236 MCGRAW-HILL’S SAT
What Is Mapping?
Mapping a problem means orientingyourself to the
problem and representing its information. It’s like
pulling out a map before you start a trip. The map
shows you where you’re going but not how to get
there. On some tough SAT math problems, half the
battle is “mapping”—orienting yourself to the problem
and figuring out what it’s asking.
Tips for mapping tough SAT math problems:- Write out any diagrams, equations,or tables
that represent the key information in the
problem. You don’t get neatness points on
the SAT—good test-takers scribble all over
the test booklet. Writing things down helps
you to keep track of the information as well
as your thought process. - Notice any restrictions on the unknowns.
For instance, do they have to be integersor
positive numbers or multiples of some
number? Are they measures of anglesor
segmentsor areasin a figure? Underline key
restrictions. - Know the definitions of special terms such
as primes, integers, factors, multiples,
perimeter, and so on, and underline these
terms when you see them. - Notice whether any unknowns can take any
values that you choose or have only one par-
ticularvalue that you have to find. You can
solve many complicated-looking problems
by just choosing values for the unknowns! - Read carefully and notice exactlywhat the
problem is asking for. Does it ask you to
solve an equation? Find the value of an ex-
pression? Find an area? Underline what
the problem is asking you to find so that
you don’t lose track of it. - Notice whether the question is multiple-
choice, and if so, notice the range of the an-
swer choices. If the answers are far apart,
you might be able to just estimatean answer
to zero in on the right choice. Also, notice
how the choices are expressed. Are they frac-
tions, decimals, radicals, algebraic expres-
sions? Noticing this often helps you to see
what you have to do to get the answer.
Lesson 1:MappingProblems
Watch for the Common Mix-Ups
Even the best students sometimes miss questions be-
cause they misinterpret key terms in the problem. You
can avoid this by underlining these key terms and
thinking about the terms they are commonly confused
with.•A perimeteris the distance around a figure.
Don’t confuse it with area,which is the num-
ber of square units that fit inside a figure.- The circumference formulafor a circle
isc= 2πr. Don’t confuse it with the area
formulaof a circle, which is a= πr^2. To
avoid confusing them, remember that
area is always measured in square units, so
its formula contains the “square.” - An odd numberis any integer not divisible
by 2. Don’t confuse it with a negative num-
ber,which is any number less than 0. These
two are commonly confused because both
of these words have a “bad” tone. - An even numberis any integer divisible by 2.
Don’t confuse it with an integerin general,
which is any positive or negative whole
number. These two are commonly confused
because when we talk of a number dividing
another “evenly,” we really mean that it goes
in an integernumber of times, not necessar-
ily an evennumber of times.
•A productis the result of a multiplication.
Don’t confuse it with a sum, which is the
result of addition.
Don’t Rush—Avoid Quick GimmicksAlways read the whole problem carefully
before deciding how to solve it. SAT math
questions—especially medium and hard-level
ones—are designed to trap students who don't
read carefully or who pigeon-hole questions
too quickly. Getting an answer quickly doesn’t
help if it’s the wrong answer.