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