The SAT math test is unlike any math test you've taken before. It's designed to take concepts you're used to and make you apply them in new (and often strange) ways. It's tricky, but with attention to detail and knowledge of the basic formulas and concepts covered by the test, you can improve your score.
So what formulas do you need to have memorized for the SAT math section before the day of the test? In this complete guide, I'll cover every critical formula you MUST know before you sit down for the test. I'll also explain them in case you need to jog your memory about how a formula works. If you understand every formula in this list, you'll save yourself valuable time on the test and probably get a few extra questions correct.
This is exactly what you'll see at the beginning of both math sections (the calculator and no calculator section). It can be easy to look right past it, so familiarize yourself with the formulas now to avoid wasting time on test day.
You are given 12 formulas on the test itself and three geometry laws. It can be helpful and save you time and effort to memorize the given formulas, but it is ultimately unnecessary, as they are given on every SAT math section.
You are only given geometry formulas, so prioritize memorizing your algebra and trigonometry formulas before test day (we'll cover these in the next section). You should focus most of your study effort on algebra anyways, because geometry makes up just 10% (or less) of the questions on each test.
Nonetheless, you do need to know what the given geometry formulas mean. The explanations of those formulas are as follows:
Law: the number of degrees in a circle is 360
Law: the number of radians in a circle is $2π$
Law: the number of degrees in a triangle is 180
Gear up that brain because here come the formulas you have to memorize.
For most of the formulas on this list, you'll simply need to buckle down and memorize them (sorry). Some of them, however, can be useful to know but are ultimately unnecessary to memorize, as their results can be calculated via other means. (It's still useful to know these, though, so treat them seriously.)
We've broken the list into "Need to Know" and "Good to Know," depending on if you are a formula-loving test taker or a fewer-formulas-the-better kind of test taker.
$$√[(x_2 - x_1)^2 + (y_2 - y_1)^2]$$
You don't need this formula, as you can simply graph your points and then create a right triangle from them. The distance will be the hypotenuse, which you can find via the Pythagorean Theorem.
Note: If you know how to complete the square, then you don't need to memorize the quadratic equation. However, if you're not completely comfortable with completing the square, then it's relatively easy to memorize the quadratic formula and have it ready. I recommend memorizing it to the tune of either "Pop Goes the Weasel" or "Row, Row, Row Your Boat".
Trigonometry was added to the SAT in 2016. Though it makes up less than 5% of math questions, you won't be able to answer the trigonometry questions without knowing the following formulas.
$sin(x)$= Measure of the opposite side to the angle / Measure of the hypotenuse
In the figure above, the sine of the labeled angle would be $a/h$.
$cos(x)$= Measure of the adjacent side to the angle / Measure of the hypotenuse
In the figure above, the cosine of the labeled angle would be $b/h$.
$tan(x)$= Measure of the opposite side to the angle / Measure of the adjacent side to the angle
In the figure above, the tangent of the labeled angle would be $a/b$.
Sine equals Opposite over Hypotenuse
Cosine equals Adjacent over Hypotenuse
Tangent equals Opposite over Adjacent
Though these are all the formulas you'll need (the ones you're given as well as the ones you need to memorize), this list doesn't cover every aspect of SAT Math. You'll also need to understand how to factor equations, how to manipulate and solve for absolute values, and how to manipulate and use exponents.
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Whether you’re prepping with us or on your own, though, keep in mind that knowing the formulas outlined in this article doesn’t mean you’re all set for SAT Math. While memorizing them is important, you also need to practice applying these formulas to answer questions, so that you know when it makes sense to use them.
For instance, if you're asked to calculate how likely it is that a white marble would be drawn from a jar that contains three white marbles and four black marbles, it's easy enough to realize you need to take this probability formula:
and use it to find the answer:
$\text"Probability of a white marble" = 3/7$
On the SAT math section, however, you will also run into more complex probability questions like this one:
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