Have you wondered how you can go really fast on the SAT math section? Maybe you’ve run out of time, or you wish you just had 5 more minutes to answer that final question. If so, we’ve compiled some SAT Math shortcuts that cover some of the more challenging types of questions you’ll find on the test.
#1: Polynomial Remainder Theorem
Sometimes even top students get stuck on polynomial division problems because they don’t know where to start! First, let’s take a look at the question in the video. We’ll notice the expression is divided by (x-3). Then, when we look at each answer choice, we see that every answer also ends with an (x-3) divisor. This means the question is not fully divisible by (x-3), and the number over the divisor is a remainder. Once we establish a remainder, it’s time for one of our SAT math shortcuts: Remainder theorem!
You can answer this with long division, but using the Polynomial Remainder theorem is faster. In order for this to work, all remainders in the answer choices must be distinct. Then, the Polynomial Remainder theorem states that if we divide a polynomial by (x-a), the remainder will be the result if we plug in a where x is in the equation. So, for the example in the video, a=3, and to find the remainder, you just have to plug in 3 for every x in the equation. This gives you the remainder -2. Also, if there’s no remainder, plugging in a for x will lead to a result of zero.
#2: Interpreting Linear Functions
This is one of our SAT math shortcuts that helps when linear equations are mapped onto word problems. Remember linear equations usually take the form of y=mx+b. Our first tip is to remember that added items always share the same label. For example, in our video example we know that that in the equation 0.5c+60p= 315, the 315 stands for dollars. This means each part of the equation represents dollar amount. This can help to eliminate some answer choices.
Our second tip for these types of questions is to look for the words: per, for each, or for every. These words will always mean to divide, which almost always indicates some sort of rate. If we look at our y=mx+b equation, we know that m usually represents the rate, and it’s followed by the variable x. Remember though, when you’re looking at your answer choices, not to forget our first tip! You may think an answer is correct because it represents rate, but you need to double check that every part of your equation is still sharing the same label (such as dollars or tons).
#3: Special Products- The Difference of Squares
For our final SAT math shortcuts, remember your Special Products formulas! Knowing Special Products isn’t just a speed tip. These formulas are necessary to get some of the trickier questions correct on your exam. Special Products equations include: The Square of A Difference, The Square of a Sum, and The Difference of Squares. You can find out more about all of these equations in our books The Best ACT Math Books Ever.
For now, we will focus on The Difference of Squares. Here’s the pattern: a2 – b2 = (a-b)(a+b)
The Difference of Square will be the formula that comes up the most often. Remember that if you foil out a2 – ba + ba – b2 , then the two ‘ba’ parts of your equation end up canceling out. That’s how you end up with the a2 – b2. The Difference of Squares formula can be the most difficult to see, which is why it’s important for you to memorize! Whenever you see a tricky polynomial formula, remember to go through the Special Products formulas to help you find your answer faster!
