Hey Guys! Are you looking to get a 700, a 750, possibly even an 800 math SAT score?
Well, in order to do that … you’re gonna need to know a few SAT formulas.
But don’t worry, not these! We’ll start with something a bit more practical. You can use
this super handy formula to answer any percent increase or decrease problem. Let’s suppose your
favorite football player’s jersey went for $150 in 2020. But now it’s 2021 and it goes for $180.
What’s the percent increase in the price of the jersey? $150 would be
the old price and $180 would be the new price. The percent increase formula is just new minus
old over old times 100%, so just substitute 180 in for New and 150 in for Old and you get 20%.
Next up is the difference of two squares formula. Suppose a minus b is 10 and a squared minus b
squared is 20, and they ask you for a plus b. Just use the difference of two squares formula!
Replace the a squared minus b squared side of the formula with 20 and a minus b with 10,
since both those values were given. Then just divide both sides by 10 to solve for a plus b,
and BAM there’s your answer: a plus b equals 2. Here’s a slope formula you might not have
seen before. If you have a line in Ax + By = C form, then the slope is just negative A over B.
Let’s try this on a real SAT question. Which of the following lines is perpendicular
to the line 5x minus 3y equals 7 ? First let’s use the formula to get the slope of 5x minus 3y = 7.
It would be the negative of 5 over negative 3, which is 5/3. The perpendicular slope is
the negative reciprocal, so it’s negative 3/5. Whichever answer choice has that slope is our
answer! Choice A would be negative 3 over negative 5 which is 3/5, so cross it out. Choice B would be
-6/5, so cross it out. Choice C would be 6/5, so cross it out. And finally choice D would be -3/5,
so there’s our answer! This is the vertex form of a parabola – and it’s on almost every SAT, usually
reserved for the hard SAT math questions. The arc beneath the first platform of the Eiffel Tower
is actually a parabola. And this is the vertex form of a parabola. The vertex is located at
coordinates h comma k. Suppose you were told that the equation modeling this arc was given as shown.
Two things you could find out from this equation would be the height of the arc from the ground
and the length of the base of the arc. To answer that, just get the vertex, which would be at 150
comma 150. The height is the y-coordinate of the vertex, which is 150 feet. And the base would be
twice the x-coordinate of the vertex, or 300 ft. The last of our SAT math formulas, which
was the one featured in the thumbnail…is useful for trig on SAT. The formula is sinx = cos(90-x).
Let’s take a closer look. Suppose you had a right triangle with angles 40 degrees
and 50 degrees. We’ll label side a opposite the 40 degree angle and side c will be the hypotenuse.
Let’s take the sine of the 40 degree angle. That would be opposite over hypotenuse,
or a over c. Now something cool happens when you take the cosine of the 50 degree angle. You would
do adjacent over hypotenuse, which comes out to a over c again! So that means, in general
the sine of x is equal to the cosine of 90 minus x. And vice versa. In other words, if two angles
add up to 90 degrees, then the sine of one of those angles equals the cosine of the other.
So here are your formulas for SAT math that we covered in this video. Since they are NOT given
on the SAT, you need to memorize them and get in a lot of SAT math practice so they become automatic.
More SAT math formulas videos will be coming soon, but in the meantime
be sure to check out my other SAT math tips videos. Thanks for watching and see you soon!