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by Dr. Steve Warner
I have been tutoring math for standardized tests such as the SAT, ACT and GRE for a long time now and those of you that know me are well aware that I place a heavy emphasis on learning test-specific strategies. One question I get very often is “Does studying math for one of these standardized tests help to improve your score on the others?” The answer to this question is that it depends on HOW you are studying for these tests.
The newly revised SAT is a lot more like the ACT than its predecessor, but there are still many differences. If you are interested in seeing a summary of these differences, check out the following article: The Differences Between the ACT and the SAT
The GRE is probably most similar to an older version of the SAT. Despite many differences among the three exams, there are many strategies and concepts that can be used to solve ACT, SAT and GRE math problems. Today I would like to give brief descriptions of some important ones that can be used on a wide range of ACT, SAT and GRE math problems. Note that I already have blog posts published on each of these strategies where you can find more detailed explanations and examples. I have included links to these more detailed articles below for your convenience. If you are preparing for one of these standardized tests, I strongly suggest that you spend at least a week reading each of these posts very carefully.
1. Plugging in Answer Choices: In many math problems on standardized tests you can get the answer simply by trying each answer choice one by one until you find the one that works. I usually recommend starting with the middle answer choice because answers are most often given in increasing or decreasing order. There are a few exceptions to this rule of “starting in the middle” such as:
a. the word least or greatest appears in the problem – in this case you should begin with the least or greatest answer choice.
b. the middle answer choice is much more tedious to check than other answer choices – in this case you can try simpler ones first.
c. you have a strong intuition that a specific answer choice will work – then by all means try that one (but do not use this if least or greatest appears in the problem).
For more information on this strategy use this link: Plugging In Answer Choices
2. Taking Guesses: This strategy is similar to the last one except this time you will be choosing your own guesses instead of using the ones in the answer choices (this can be especially useful for grid-ins on the SAT, but it sometimes also works well in multiple choice questions). Try to make the best guess you can, but don’t waste time thinking too hard. It’s okay to start with a completely random guess and then begin making more informed guesses until you zero in on the answer.
For more information on this strategy use this link: Taking Guesses
And for an additional more advanced example take a look here: Taking a Guess – A Harder Example
3. Picking Numbers: This strategy involves replacing one or more unknowns in a problem by specific numbers. For example, by changing all the letters to numbers in a “hard to read” problem, the question usually begins to make a lot more sense. Just be careful and make sure that you understand all the guidelines.
You can find these guidelines (as well as some examples) here: Picking Numbers
This strategy works well with percent problems: Picking Numbers to Solve Percent Problems
After learning these strategies some students begin to have trouble deciding which one to use on specific problems. If this sounds like you, then you should read the following article: When to Use the Most Common Math Strategies
4. Changing Averages to Sums: The SAT, ACT and GRE all love to test students with problems involving averages. But most of the time they do not want you to compute the average. Instead they GIVE YOU the average and ask you to find something else. Knowing the following formula will go a long way in helping you solve these problems quickly and easily:
Sum = Average · Number
For more information on this formula and how to apply it, use this link: Changing Averages to Sums
5. Calculator Algorithm for Finding Remainders: Too many students attempt to find a remainder by performing a simple division in their calculator. They then might do something random like take the first digit to the right of the decimal point for their answer. This does not give you a remainder, but there are some very simple algorithms that you can perform on your calculator that will give you a remainder.
For details look here: Can We Solve Remainder Problems Without Using Long Division?
And for some more advanced material on remainder problems check out part 2 and part 3 of the article just mentioned.
Note that this last strategy is no longer very useful for the SAT, but it is still very important for the ACT and GRE.
If you are preparing for a standardized test such as the SAT, ACT or GRE, you may want to take a look at the Get 800 collection of test prep books. Click on the picture below for more information.
-Dr. Steve
GET 800
Dr. Steve Warner is a Math Professor, math tutor, and author and publisher of the “GET 800” series of college test prep books for the SAT, ACT, GRE, AP Calculus exams, SAT Subject Tests, and SHSAT.