Tip #23 to Get a Top ACT Math Score

When you are given a diagram on the ACT, ask yourself if it seems accurate. If it does, you can use it, sometimes just to see what to do next, and other times to get a correct answer without even doing much math. For example, if you are given the length of some part of the diagram, you can often use that to estimate an unknown. You've done this before. Imagine you're on a road trip. You look at the map and say, "We have to go from here to here on this squiggly highway." The map key says that each inch is 100 miles, so you use your thumb to represent an inch and you estimate the length of the squiggly line highway. We call this "Use the Diagram."

If the diagram is clearly not drawn to scale (not accurate), resketch it somewhat accurately and then "Use the Diagram." It turns out that often the whole question is hinged on its being out of scale, and when you put it into scale, the answer becomes obvious.

Also, while we're in art class, here's another great strategy. If a question describes a diagram, but none is shown, draw one. Sometimes this gives the answer immediately, and sometimes it shows you what to do next, but either way it always helps!

At first all this might feel weird. For a year in geometry class you were taught not to estimate with a diagram. Plus, on the ACT, estimating makes the question so much easier that it feels "cheap," like you are cheating. It's not! It's actually what they want you to do. Remember the test is supposed to test your cleverness, not just what you learned in math class. This strategy brings out your innate cleverness.

Let's look at this question:

Solution: Sketch the diagram to scale, following the instructions in the question:

Correct answer: E

Example Problems

Easy

1. If points A, B, C, and D are different points on a line; AB = BC = 8; and D is between B and C; which of the following could be the measure of segment AD ?
   1. 3
   2. 5
   3. 8
   4. 10
   5. 16

Medium

2. What is the y intercept of the line in the standard (x, y) coordinate plane that goes through the points (–4, 5) and (4, 1) ?
   6. –1
   7. 1
   8. 3
   10. 5
   11. 7

Hard

3. In the figure below, A, B, and C are collinear, and angles A, C, and EBD are right angles. If EB = 14, DB = 7, and DC = 6, to the nearest whole number, what is the measure of EA ?



1. 3
2. 5
3. 7
4. 10
5. 16
4. A room has the shape and dimensions in meters given below. A support beam is located halfway between point P and point Q. Which of the following is the distance of the beam from point M ?



6. 3
7. 
8. 
10. 
11. 9