For some high school students, SAT math is the bane of their existence. You need to learn all these foreign strings of numbers and letters, and then magically recall them once you’re sitting in a hot room for hours with your entire future weighing down on your tired shoulders. Yeah – SAT math…not the funnest thing in the world.
Our friends at Magoosh SAT have released a new ebook, Magoosh’s SAT Formula eBook, loaded with all you need to know to lighten the load and ace the math section on the SATs. The book is free with interactive elements, and comes complete with all the math formulas, study strategies, time-saving tips, and practice problems you’ll need for the SAT.
Here’s an excerpt from the intro of the book:
While formulas can be really helpful on the SAT, there are very, very few that you absolutely need to have memorized to score well. That might come as a surprise, but it’s true, and it leads us to an important thought: understanding how and why a formula works is as useful as rote memorization. In fact, it’s much better. You’ll have a better sense of when to use a formula and be more accurate in executing it if you understand the math behind it. Let’s look at a concrete case to illustrate. The distance formula is a prime example. It’s ugly…
…but it actually represents a pretty simple idea. If you have any two points on a graph (on the coordinate plane), you can make a right triangle that connects those two points as the ends of the hypotenuse. That is, you draw a diagonal line between the two points, then a straight horizontal line and a straight vertical line going through each point to make the legs of the triangle.
Then, since you’re trying to find the length of the hypotenuse, you just use the Pythagorean theorem:
(Notice that a couple very basic formulas like this one do need to be memorized.) The lengths of those legs are a and b, and the length of the hypotenuse is c.
So let’s find the length of c:
And if you’re trying to find the length of the legs (the shorter sides), you just need to know the horizontal distance between the two points, [more math], and the vertical distance between the two points, [more math]. If you replace a and b with those values, voilà: you have the distance formula.
