Tip #19 to Get a Top ACT Math Score

Example Problems

Easy

1. 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

2. 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?
   6. More than 4
   7. Between 3 and 4
   8. Between 2 and 3
   10. Between 1 and 2
   11. Less than 1
3. Parallelogram MNOP, with dimensions in centimeters, is shown in the diagram below. What is the area of the parallelogram, in square centimeters?



1. 300
2. 480
3. 544
4. 600
5. 680
4. A square is circumscribed about a circle of 9-inch radius, as shown below. What is the area of the square in square inches?



6. 81
7. 144
8. 81π
10. 308
11. 324
5. In the figure below, each pair of intersecting line segments meets at a right angle. What is the perimeter of the figure?



1. 70
2. 35
3. 34
4. 17
5. Cannot be determined from the given information

Answers

1. 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.
2. 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



3. 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.

4. 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.

5. 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