


Math IC Algebra Strategies
There are several ways to answer most algebra problems.
You could try to solve a problem by using standard algebra and setting
up and solving an equation. Alternatively, you could try to avoid
algebra and simply plug the answer choices back into the question
until one of them works out. Or you can pick numbers to substitute
into the various expressions given as answer choices.
None of these methods is necessarily better than the others.
Remain flexible in your approach to each question and choose the
method that best suits the problem. For a problem you know how to
solve, using algebra is probably the quickest method. In contrast,
a tough problem that you are unsure how to solve might become easy
if you try to plug in some answers. When you study your practice
tests and look over the algebra questions you got wrong, you should
think about the method you employed. Did you plug in answers when
you should have used algebra? Did you use algebra when you should
have plugged in answers?
We’ll lay out for you the different problemsolving
approaches and tell you all you need to know about them. Then you
can decide for yourself which method to choose.
Let’s use a sample algebra problem to illustrate these
separate approaches:

Using Algebra
This question is a simple rate problem that can be solved
with a few basic equations. Since traveling time = distance speed, it took him:
to drive to Giambia City. To find the duration
of his flight, we use the same rate formula:
It took the player:
longer to drive. D is the correct answer.
Plugging In Answers
Sometimes you might not be sure how to approach a problem
or don’t have the time to think out the proper equations. In such
instances, plugging in might be the best method for you, especially
as you come across the more difficult questions at the end of the
test. All you have to do is substitute the answer choices back into
the problem, and see whether the given information holds true.
The process of plugging in is simple. First, you should
make full use of the fact that the answer choices on Math IC are
always presented in ascending value. So start by plugging in answer
choice C, since if it doesn’t turn out to be the answer,
you can usually tell whether to try a smaller or larger answer choice.
Now, to solve the question: it takes the baseball player 25050 = 5 hours to drive to Giambia
City. So, if it takes him C 4 hours more to drive,
than it takes him 5 – 4 = 1 hour to fly back to Jasonville. But
the question tells us that in 1 hour, he could fly 500 miles. Therefore,
it must take him longer than 4 hours more to drive than to fly.
Next, we try D 4.5. It takes him 5 – 4.5 = .5 hours
to fly, which means that he travels 500 .5 = 250 miles on his flight. D is
the answer.
Picking Numbers
Picking numbers is a variation of plugging in and should
only be used when the answer choices contain variables. A modified
version of our original sample question shows what kind of problems
might lend themselves to picking numbers.

This question asks you to figure out which set of variables
in the answer choices is the right one. But thinking in terms of
variables can be confusing to some people. Picking numbers allows
you to transform variables into concrete numbers.
To use the picking numbers method, you need to select
numbers and plug them into the answer choices. You’re essentially
testing the relationships between the variables in each given answer
and ensuring they remain true. It doesn’t matter what specific numbers
you plug into a problem. The same answer choice will always surface
as long as you plug in consistently and follow all guidelines given
by the problem.
For example, in the baseball player problem, let m =
5, v = 100, and p = 10. Clearly,
these numbers aren’t realistic (who flies at 10 miles an hour?),
but your goal is to pick easytomanipulate numbers. Using our numbers,
it takes the baseball player 1005 = 20 hours to drive and 10010 = 10 hours to fly. So, it takes
him 20 – 10 = 10 hours longer to drive. After plugging m, v, and
p into all the answer choices, we find that only D produces
an answer of 10.
Very rarely, more than one answer choice will result in
the correct answer for the first set of numbers you picked. When
this occurs, simply plug in a different set of numbers. You will
almost never have to plug in more than two sets of numbers.
When picking numbers, you must check through all the answer
solutions with your chosen numbers. Obviously, this will slow you
down, but that’s the price you pay for using this method. Picking
numbers gives you a mechanical method of solving tricky problems,
and it also allows you to check your math for careless calculations,
but it is timeconsuming.
Finally, when you are picking numbers, avoid 0, 1, or
any numbers that appear in the answer choices. Picking these numbers
can overly simplify the expressions you are dealing with and cause
you to pick the wrong answer.
The Bottom Line
As you can see, there is no “right” method to solving
all algebra problems. Some methods work best some times, and others
work best at other times. Part of your practice for the Math IC
test will be to get comfortable with algebra questions so that you
can choose which method you want to use for every question.
Now, we’ll review the algebra topics covered in the Math
IC Subject Test.
EquationSolving
There are a number of algebraic terms you should know
in order to be able to talk and think about algebra:
 Variable. An unknown quantity, written as a letter. The letters x and y are the most commonly used letters for variables, but a variable can be represented by any letter in the English alphabet. Greek letters are also used quite often. Variables will sometimes represent specified quantities, like apples or dollars, for example. Other times, a specific meaning won’t be attached to them. You’ll need to manipulate variables just to show that you understand certain algebraic principles.
 Constant. A quantity that does not change. In other words, a number.
 Term. The product of a constant and a variable. Another way to define a term is as any quantity that is separated from other quantities by addition or subtraction. For example, in the equation below, the left side contains four terms {x^{3}, 2x^{2}, –7x, 4} and the right side contains two terms {x, –1}. The constants, 4 and –1, are considered terms because they are considered coefficients of variables raised to the zero power. For constant 4, 4 = 4x^{0}. So every term, including constants, is the product of a constant and a variable raised to some power.
 Expression. Any combination of terms. An expression can be as simple as a single constant term, like 5. Or an expression can be as complicated as the sum or difference of many terms, each of which is a combination of constants and variables, such as {(x^{2} + 2)^{3} – 6x} ⁄ 7x^{5}. Expressions don’t include an equal sign, which is what differentiates expressions from equations. Expressions therefore cannot be solved; they can only be simplified.
 Equation. Two expressions linked by an equal sign. A lot of the algebra that you’ll have to perform on the SAT II Math tests will consist of solving an equation with one variable. Most of this chapter, in fact, deals with different techniques for simplifying expressions and solving different types of equations. First, we’ll review how to write an equation.
