Tip #23 to Get a Top ACT Math Score (page 2)
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
- 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 ?
- 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) ?
- 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 ?
- 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 ?
- D When a picture is described, draw it. Nobody can just visualize this and get an answer. Don't be a hero here; draw a diagram.
- H When a picture is described, draw it. Not even your math teacher, the one who walks around running his finger along the walls muttering math calculations to himself, could solve this one in his head. Draw a somewhat neat diagram, and it's easy! Plus, using a diagram avoids careless errors. Notice that the answer choices are far enough apart that a fairly neat diagram will show you which answer choice is correct!
- C First, label the info from the question into the diagram. Then ask yourself if the diagram seems accurate. Yes, it does, because DB does look like half of EB, and DC looks like a little less than DB, so the numbers work. Then if the geometry jumps out at you, by all means do it, and after our geometry Skills coming up, they probably will, but you can also "Use the Diagram!" Since EA looks longer than CD but shorter than EB, it must be between 6 and 14. That only leaves choices C and D. Pretty cool, huh? Now, is it C or D? Well, EA is only slightly longer than DC, not almost double, so I'd go with choice C, which is correct! Sometimes "Use the Diagram" is enough to get the right answer; sometimes it's just a plan B to narrow it down, when you can't decide how to get it with geometry Skills.
- G This is a great "Use the Diagram" question! First, label the info from the question into the diagram. To do this question the "math class way" would require using both the midpoint formula and the distance formula, which we certainly know how to do from Skill 17. But we can save a ton of time by just looking at the diagram and the answer choices. Connect point P to Q. Then sketch a point halfway between them, the midpoint of the segment. Then connect point M to that midpoint. Voilà! Now, how long does that segment look, based on the fact that MP is 4? It looks about the same, actually. Then look at the choices. Wait, none of them say 4. Do we panic? No, convert them into decimals. Aha! Choice G is about 4.
Since AB = 8 and AC = 8 + 8 = 16, AD must be between 8 and 16, so only choice D works.
Go to: Tip #24
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