Math Facts You Should Know for Standardized Tests

Here are some things you should know for the SAT, ACT, GMAT, GRE, or any other standardized test that tests math.

Most standardized tests given for admission to grad schools (other than physical science, medical, or engineering school) test math at a high school level.   That’s good news, in that the highest-level math you’ll be expected to know is geometry, or, in the case of the ACT, some basic trigonometry.  It’s also bad news, in that it’s still a lot of information to remember, especially if it’s been a while since you’ve taken high school math.

The SAT, and possibly some other tests, do give you a “Math Facts” section with many of these facts listed for you, but you really don’t want to have to flip back from a problem on which you are working just to look up a formula, thus breaking your train of thought and wasting a few seconds, when it’s really not that hard to memorize these formulas. The best way to memorize the facts is to work enough practice problems that you remember how you solved similar problems, including what formula you used.

So, without further ado, here are some basic math facts you should memorize before going into a standardized test.

Geometry:

Pythagorean Theorem:  

The length of the hypotenuse (longest side) of a right triangle (a triangle in which one of the angles is a right angle, or 90-degree angle) relates to the lengths of the other two sides in the following way: h2 = a2 + b2, where h is the length of the hypotenuse, and a and b are the lengths of the other two sides. You can also derive the formula for the distance between two points on a Cartesian coordinate grid using the Pythagorean Theorem – just use the points to make a right triangle, using the line between the points as the hypotenuse.

Notice that the sides of a triangle can also be the sides of squares, which is something you’re likely to see in an SAT problem.

Special Right Triangles

30-60-90 triangle:  The ratio of the lengths of the sides opposite the angles are 1,√3, and 2, respectively. That is, the shortest side is 1, the second longest side is √3  hypotenuse is 2.

45-45-90 triangle:  The ratio of the lengths of the sides opposite the angles  is 1-1-√2.

Powers To Remember  

Knowing various powers of the numbers 0 through 20, will “exponentially” increase your chances of getting a high score on a standardized test. All right, now that you’re done wincing and groaning at that awful pun, here are some powers you’ll need to know.

For Pythagorean Theorem purposes, know the squares of all numbers from 0 to 20. It’s not likely you’ll be required to know the square of any number larger than 20, unless it’s an easy one to calculate such as the square 30, 40, 50, or so on, and in the rare instances where you do, you can rely on your calculator.

You should know the powers of 2 from 0 to 10, since powers of 2 are useful for so many SAT problems (e.g., a bacterial culture that doubles the number of cells every period of time).

Higher Powers:

You really only need to know a few powers higher than 3 on the SAT. You should probably know 1 through 6 to up to the fourth power, and 7 through 9 up to the third power. (To get any power of 10, just add that number of zeroes behind it; 101 = 10, 102 =100, and so on.)

Distance Formula:

Distance = Rate X Time , so Rate = Distance/Time, Time = Distance

For example, 100 miles = 100 miles per hour (miles/hour) * 1 hour.

100 miles/hr = 100 miles/1 hr, and

1 hr = (100 miles)/ (100 miles/ 1hr) = 1 hr.

Coordinate Distance formula:

As discussed in the Pythagorean Theorem section above, the distance between two points on a Cartesian coordinate (x-y) grid, can be determined using the Pythagorean Theorem and the coordinates. The formula for the distance between points A = (x1, y1) and B = (x2, y2), which we can call AB, is:

This formula will help you with coordinate geometry (Cartesian coordinate) problems.