ACT Math Tip: Speed and Preparation are Key!

Though on the surface they may appear to be very similar, the SAT and the ACT are very different. While both tests require similar skills, the ACT requires those skills to be performed much faster than the SAT. The average amount of time allotted per math question on the SAT is 75 seconds. On the ACT that time gets cut down to 60 seconds! That might not seem like too much of a difference, but it certainly adds up.

In light of this, it is crucial that students entering the ACT are familiar with as many question types as possible. While the SAT allows us that extra time to break down an unfamiliar question and figure it out, the ACT is designed to test a student’s ability to shoot from the hip. In short, it is essential that ACT students are familiar not just with the skills they need to solve certain questions, but also with the ways in which those skills will be tested.

Let’s look at a great example of a question that rewards good preparation.

1.  At a certain time of day, a 100 meter tall tower casts a 200 meter long shadow.  If, at the same time, another tower casts a 150 meter long shadow, how tall is the second tower?

Yikes! As you can see, this problem doesn't give us too much to go off of. Let’s draw it out and see if it becomes a little clearer.

Let’s take a look at what I did here. I placed the two towers next to each other and drew two overlapping triangles using the towers and their shadows. Here’s the tricky part; I knew that the two triangles would have all of the same angles, which makes them similar. Knowing this, I know that the ratio between the 100 meter tower and its 200 meter base is the same as that between the smaller tower (of height X) and its 150 meter base.

I can set this up as the equality below:

Now, while the actual math behind the problem was not particularly difficult, we did need to make that logical leap at the problem’s outset to realize that the towers formed two similar triangles. Sure, we could have reasoned that because the sun is in the same location relative to both towers, the angles formed by the cast shadows will be congruent, but, for students unfamiliar with the problem type this could waste valuable time.

There is no substitute for preparation. ArborBridge’s customized ACT curriculum focuses on exposes students not only to the skills that they need to know to ace the test, but also to the types of situations in which they will have to use them.