Math for Non-Mathheads
Feel like you’re bad at SAT math? Strongly dislike it? Actively fear it? Even if you don’t normally stick a pencil behind your ear, spend free time programming your graphing calculator, or ask the teacher if the class can “do the hard problem,” you can still do well on SAT math.
The key is to not get intimidated. The SAT wants you to think it’s testing you on really hard math, but it’s not. There’s no calculus. No pre-calculus. No trigonometry. Only arithmetic, algebra, and geometry—subjects you’ve probably already had. And within those three subjects, the SAT only tests a limited number of concepts.
In geometry, for example, the SAT focuses on the three basic shapes: rectangles (don’t forget that all squares are rectangles!), triangles, and circles. And for each of these shapes, the SAT only tests a few basic aspects.
Take the triangle, a shape the SAT loves:
|area||A = ½ bh|
|perimeter||P = s1 + s2 + s3|
|angle measure||Rule of 180 (the three angle measures add up to 180)|
|side length in a right triangle||Pythagorean Theorem (a2 + b2 = c2) or its shortcuts:|
1) special right triangles (30-60-90, 45-45-90);
2) Pythagorean triples (e.g., 3-4-5, 5-12-13)
If you’ve studied the concepts above, you know they’re pretty straightforward. But if the SAT gave you the base and height of a triangle and asked you for the area, it would be too easy (you’d just have to plug into the area formula, which the SAT provides you). So, to trip you up, the SAT tests these relatively easy concepts in difficult ways.
An isosceles right triangle has an area of 12.5. What is the height of the triangle?
Given the area, you can work backwards to find the height:
A = ½ bh
12.5 = ½ bh
But we still have two variables, which makes it impossible to solve for h. Every word is key, however: “isosceles” means two sides are equal, and since neither leg can be equal to the hypotenuse, the two legs (the base and the height) must equal each other. So we can replace b with h:
12.5 = ½ hh or 12.5 = ½ h2
Divide both sides by ½ (which is the same as multiplying by 2/1):
25 = h2
And, finally, take the square root of each side:
5 = h
Notice that while the concepts involved here—height and area of a triangle—aren’t too complex, the problem is tricky. But if you practice working forwards and backwards with the various algebraic and geometric formulas the SAT tests, you’ll be able to keep your pencil moving and work your way to correct answers.