Philip Martin

# "Illustrative figures are NOT necessarily drawn to scale..."

Hopefully, students have been taught or intuitively know that reading the directions prior to any ACT test is a waste of time. There is nothing there that can change test-to-test that will affect the outcome of a student's ACT score.

There is one interesting line, however, that is intended not to be *true*, but to cover the ACT in case of a mistake, which is this:

"Illustrative figures are NOT necessarily drawn to scale"

What the ACT is trying to say is this: "Just because a line segment *looks* like it's 5 units long when compared to another line segment in the same question that is 10 units long, that doesn't mean that the segment is 5 units long. Similarly, just because an angle *looks* like it measures 45 degrees, that doesn't mean it is 45 degrees! It could be 90, or 140, so you better do the math!"

However, this is false. Every math problem on the ACT test that involves diagrams *IS INDEED DRAWN TO SCALE.* Why? Well, because the ACT uses math software to draw its diagrams. I myself use similar software. These softwares *do not allow* a user to draw diagrams and figures that are mathematically inconsistent.

That's great and all, but how is this helpful? The reason it is helpful is that it can help students skip a minute's worth of math, or possibly more, and get a question correct (or at least, if they can't figure out the math, make a guess out of two or three options compared to the usual 5).

Take a look at this problem to the left from a recently administered ACT Math test. Mathematically speaking, a student's fastest way to solve this problem would be to use the Law of Sines (which is NOT what I would call ACT Math that you *Have to Know*) or some clever thinking. I have, to this point, never solved this problem, but I just did for the first time to prepare for this post. How did I do it? Well, I took advantage of the fact that *this figure is drawn to scale*.

Taking a piece of paper (OK, a UPS receipt, but a student will have a bubble sheet to do this with!), I put it up to the line on the bottom of the triangle that has a length of 240 (see image below!). I marked that, like a ruler on my paper, then based on that, made easy marks of length 120 (half the size) and 180. Then, I took that same length of 240, put it up against the length of the side of the triangle that I need to know, and made a new mark with a star.

As you can see, the star, which again is the length asked for in the question, looks like it's somewhere between 180 and 240. Maybe 200? What I know fore sure is this: The answer is greater than 180 and less than 240. Guess what? Only one answer falls within this range, which is answer choice B (which comes out to something like 196).

This same strategy can be used with angles or any other question that utilizes the length of certain line segments. Though this isn't a replacement for math knowledge, as it becomes practiced, it becomes more instinctual. Usually questions this late in an ACT test (notice that it is number 59) take students the longest to answer. This strategy reduced the solve time for me to less than a minute to be certain.

I teach this strategy (as well as the other three ACT Math mini-strategies) in my live classes and pre-recorded class, The ACT System. Check out more at philipmartinact.com!