The ACT repeats a lot of questions. 75-80% of the questions are the same types of questions test after test after test. If you want to master the ACT Math section, you need to divide and conquer, so master the question types one by one.
If you know just these seven question types, you’re nearly halfway towards a perfect score. I will cover these question types one by one in subsequent posts with practice problems and worksheets. There will be about 25 types all together. Here are the Top Seven most common math questions, in no particular order:
1. The Distance Formula Question
You will need to commit this formula to memory. Plug in two coordinates, (x1,y1) and (x2,y2), into this. You will usually see this within a circle question. For example, the ACT will give you the coordinates of the endpoints of a circle’s diameter. Then, the ACT will ask you to find the length of the diameter or radius.
2. The FOIL Question
Remember FOIL? First, Outside, Inside, Last.
3. The Combo Parallelogram/Trapezoid Area Problem
I’ve seen three or four questions like this on a single test. The ACT loves this. Do you see how the figure below is a trapezoid within a parallelogram? The ACT will shade either the triangle or the trapezoid and ask you to find the area of the unshaded region. Or, they will put a parallelogram inside a trapezoid. You will need to know the formulae for parallelograms, trapezoids, and triangles, most of which are provided on the test. In future posts, I’ll give you practice with all these different combinations.
4. The Basic Trig Question
For Sin, Cos, and Tan, all you need to know is SOH-CAH-TOA.
5. The Basic Circle Question: Diameter, Circumference, and Area
You’ve got to be able to find a circle’s area and circumference. These operations form the basis of a large chunk of the questions. Yeah, okay … it’s corny, but the following graphic will help you remember these crucial equations. If you still don’t remember these equations, just write each a dozen times or so. Okay?
6. The Circle Equation
There’s not much to the circle question. You don’t use the formula; you read it. You just take out the coordinates of the center and the radius. That’s it.
(a,b) are the coordinates of the center
r is the radius
7. The Midpoint Formula
Sometimes, the ACT will just give you two endpoints and ask you to use the formula below to find the midpoint. Mostly, though, the ACT gives you one endpoint and the midpoint, and asks you to calculate the other endpoint.
Stay tuned … we will be going over all these question types and many more in future posts!