Math & Science ACT Workuot

A = 16π

A ≈ 50.3

This matches up nicely with (H). If you don’t have a calculator, or you’re not especially handy with it, no

problem. Use ballparking. You know that π is roughly equivalent to 3, so your answer will need to be

close to 16 × 3 or 48. Only (H) is close enough.

Coordinate Geometry

Let’s try a Coordinate Geometry problem. ACT likes to make a big deal about the distinction between

Plane and Coordinate Geometry, but as we’ll see, your approach won’t really differ at all.

23. In the standard (x,y) coordinate plane, point G lies at (−3,−4), and point H lies at (2,5). What is the length of GH in
    coordinate units?

A. 7

B. 4

C.

D.

E.

Here’s How to Crack It

Your first impulse here will probably be to whip out the distance formula and complete this problem in

lightning-fast time. The only problem is that the distance formula looks like this:

Yikes. If you’ve got this formula stored away in the RAM of your brain, great. Unfortunately, for most of

us, this is a really easy formula to forget, or worse, to remember incorrectly. What you’ll find about ACT

Geometry is that for 90% of the problems, you’re best off just dealing with the basics. For weird shapes

in Plane Geometry, this will mean carving things up into recognizable shapes and working from there. On

Coordinate Geometry, you will find that simple formulas and the Basic Approach can get you plenty of

points.

Let’s use the Basic Approach. First and foremost, this is a Geometry problem, and they haven’t given you

a figure. Draw your own. It should look something like this: