Tip #19 to Get a Top ACT Math Score

For the ACT you need to have certain formulas memorized. You need to know these:

Perimeter Area Volume

And the perimeter of any shape is the addition of the lengths of the sides. When they want you to use a more uncommon perimeter, area, or volume formula, they'll give it to you in the question.

Let's take a look at this question:

Solution: Since the square has area 625, we can determine the length of a side of the square. Set up the area formula. Plug in what we know and solve for the variable. This is a great ACT strategy! So (s)(s) = s² = 625. Take the square root of both sides to get s = 25. Since one side measures 25, the perimeter is (4)(25) = 100. Make sure to finish the question. Don't be tempted by choice A. Ask yourself, "Self, did I finish the question?" With practice you can avoid this number one most common ACT careless error.

Correct answer: C

Example Problems

Easy

A square lot, with 75-foot sides, is completely fenced. What is the approximate length, in feet, of the fence?
1. 70
2. 75
3. 150
4. 225
5. 300

Medium

If 10,000 cubic yards of water is to be funneled into a rectangular tank with a floor that measures 75 yards by 110 yards, about how many yards deep will the water be?
1. More than 4
2. Between 3 and 4
3. Between 2 and 3
1. Between 1 and 2
2. Less than 1
Parallelogram MNOP, with dimensions in centimeters, is shown in the diagram below. What is the area of the parallelogram, in square centimeters?

Perimeter Area Volume

A square is circumscribed about a circle of 9-inch radius, as shown below. What is the area of the square in square inches?

Perimeter Area Volume

81
144
81π

In the figure below, each pair of intersecting line segments meets at a right angle. What is the perimeter of the figure?

Perimeter Area Volume

70
35
34
17
Cannot be determined from the given information

Answers

E To find perimeter, just add up the sides. To avoid a careless error and to make it clear what to do next, sketch a diagram. Since all sides of a square are equal, perimeter = 4(side) = 4(75) = 300.
J The volume of a rectangular solid, i.e., a box, equals (length)(width)(height). Just fill the info that we know into the formula, and solve for the variable that we are missing. This is a great word problem strategy. It solves 90% of all formula-related word problems. Just "fill in what we are given and solve for whatever is still a variable." So

D The area of a parallelogram = (base)(height). So

The key here is to memorize the parallelogram formula and to remember that 15 is the height, not 17. Height is always at a right angle, like when the nurse at school is measuring your height and says, "Stand up straight, no slouching." Also, remember to add the two parts of the base, 8 + 32 = 40.

K The word "circumscribed" throws some kids. Lot's of kids say, "I don't know that word, I'll just guess and move on." But in this book you'll learn all that you need for the ACT. When they throw a tough word at you that we have not discussed in this book, they'll define it in the question or you won't even need it. Here we don't need the word; you can cross it out. It's totally implicit in the diagram.

"Circumscribed" just means "drawn around." So the square is drawn around the circle, which is obvious from the diagram anyway! So, don't get intimidated. Stay confident and focused. So the area of the square = (length)(width). And for a square, length and width are equal. You can see in the figure that the circle has a radius of 9 and a diameter of 18, and you can see that the diameter is the same as the length of a side of the square, so its area = (18)(18) = 324.

C The ACT loves these. The key here is to realize that all the vertical lengths of the steps add up to 7, and all the horizontal lengths of the steps add up to 10. Now that you know this trick, it's easy! So perimeter = 34.

Go to: Tip #20

« prev page
1
2
next page »

View Full Article