SAT/ACT Math Strategies Every High School Student Should Know
by Dr. Steve Warner
Hello everyone. I have been tutoring math for the SAT and the ACT for more than a decade and those of you that know me are probably aware that I place a heavy emphasis on learning test-specific strategies. One of the questions I have been asked recently is if studying for one of these tests will improve your score in the other. The answer to this is that it depends on HOW you are studying for these tests.
The ACT is definitely a more straightforward test than the SAT, in the sense that students that are very good at performing complicated algebraic and trigonometric manipulations may initially have better results in ACT math than in SAT math. Nonetheless, there are many strategies and concepts that can be used to solve both SAT and ACT problems. Today I thought I would give brief descriptions of a few important ones that can be used in a wide range of SAT and ACT math problems. Note that I have blog posts already published on each of these strategies where you can find more detailed explanations and examples. If you are preparing for the SAT or the ACT, I strongly suggest that you spend at least the next week reading each of these posts very carefully. Links to these articles are included in the content below for your convenience.
- Plugging In Answer Choices: In many math problems on the ACT and SAT 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 such as:
- the word least or greatest appears in the problem – in this case you should begin with the least or greatest answer choice.
- the middle answer choice is much more tedious to check than other answer choices – in this case you can try simpler ones first.
- 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).
- 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.
- 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
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
- Changing Averages to Sums: The SAT and ACT both 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:
- 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.
And for some more advanced material on remainder problems check out part 2
and part 3
of the article just mentioned.
If you are preparing for the SAT you may want to click on the picture of the books below to read about a special offer on 6 of my SAT math prep books.
If you are preparing for the ACT, then you may be interested in my ACT math prep book. Click on the book image below to view the book’s description on Amazon.
Steve Warner is a mathematician and test prep expert who earned his Ph.D. at Rutgers University in Pure Mathematics in May, 2001. While a graduate student, Dr. Warner won the TA Teaching Excellence Award, and he then began working as a Math Professor at Hofstra University in September, 2002. During his time at Hofstra he has taught a full range of undergraduate and graduate courses and published several articles in scholarly journals.
In 2012, Dr. Warner founded "GET 800
,” a company that offers 7 SAT math prep books, and a free 12 part email course that is customized for each student based on his or her PSAT/SAT math score. In 2013, Dr. Warner wrote his first ACT math prep book titled the “ACT Prep Red Book.”
Dr. Warner works with students individually and in group settings, he tutors both live and by video conferencing, and he offers free materials in the form of his blog, his YouTube channel, and his Facebook page where he will answer any math test prep questions at no charge.