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 easy-to-manipulate numbers. Using our numbers, it takes the baseball player 100
5 = 20 hours to drive and 100
10 = 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.
5 = 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 time-consuming.
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.
Equation-Solving
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 {x3, 2x2, –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 = 4x0. 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 {(x2 + 2)3 – 6x} ⁄ 7x5. 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.