On the ACT math section, questions are either self-contained or belong to an item set. But do not worry — even if you are unfamiliar with the term “item set,” these question types are not as daunting as they may seem. In fact, both ACT math question types are approached similarly.
Self-contained ACT math questions stand alone or bear no relation to the questions that come before and after them. The opposite of this type is the item set, or a series of questions centered around one or more data sources.
How to Approach ACT Math Item Sets
With item sets, you are first given information in the form of text, a graph or other visual, or some combination of these. This information is followed by two to five questions, or items, that are all based on the same data source or sources.
You will know that you are dealing with an item set if you come across a box with a message like this one: “Use the following information to answer questions X-Y.” Item sets tend to appear in the middle of ACT math, and there may be up to two item sets on an ACT exam.
Thankfully, item sets are always logically independent, meaning that they do not build on one another. In other words, you can get the first question wrong and still get the following ones right, or vice versa.
According to the ACT, “Knowledge of basic formulas and computational skills are assumed as background for the problems, but recall of complex formulas and extensive computation is not required.”
Like all other ACT math questions, item sets are multiple-choice. Because the ACT math test contains 60 questions to be answered in 60 minutes, students should spend no more than one minute on any one item, regardless of the question type.
However, there is a slight difference in approach. With item sets, more time should be spent examining the data initially. Spending these extra seconds at the beginning to truly understand the data source or sources will allow you to move through the accompanying questions more quickly.
Consider this example of questions 32-34 on page 28 of this free ACT 2020-2021 practice m ath test. The item set contains both text and a diagram. Question 32 asks about the area of the park, so you need to know the area formula for a trapezoid: A=(a + b)/2 x h. When you plug in 28 for a, 40 for b and 16 for h, you get 544 square inches, which is choice G.
Question 33 asks about the perimeter of the park, so you must know to add together the lengths of all four sides. However, one side value is unknown. To solve for it, you can use the Pythagorean theorem (a2 + b2 = c2) — which is a squared plus b squared equals c squared — recognizing there is a right triangle inside the trapezoid.
Notice that you already have the height, 16 inches, and that you can figure out the base by subtracting 28 from 40 to yield 12. When you solve for c in 122 + 162 = c2, you get 20 as the remaining side length of the trapezoid. Next, you add all the side lengths together — 20 + 28 + 16 + 40 — to yield a perimeter of 104 inches.
You may be tempted to quickly select answer choice C, but recall that the question asks for the perimeter in feet and that the introductory text states: “In Mikea’s scale drawing, 1 inch represents 1.5 feet.” Therefore, the final step is to multiply 104 by 1.5, yielding 156 feet , which is choice E.
Question 34 may be the easiest of the three, as it just asks for a ratio: “The length of the south side of the park is what percent of the length of the north side?” Start by noting that 40 inches divided by 28 inches equals approximately 1.4285. However, to turn this value into a percentage, you must multiply it by 100, leaving you with roughly 142.9%, or choice H.
An important point to bear in mind with item sets is that you may be given more data than you will need to answer the questions. With the above example, for instance, the radius of the merry-go-round was not useful.
How to Prepare for ACT Math Item Sets
The importance of studying for ACT math using official past exam questions cannot be overemphasized. However, there are also ways to prepare for the test in everyday life using nontest prep materials.
For example, students can increase their comfort with math-based visuals by examining graphs and charts that appear in newspapers and magazines. With any visual, students should allow themselves 10-20 seconds to study it and get the gist of it. After all, given the scant time allotment of the ACT, getting the gist of a visual is all students can reasonably aim for.
Before your exam day, practice paraphrasing the main idea of a visual in no more than a sentence. You can then take this exercise a step further by imagining test questions that could accompany a visual or even creating a few questions that closely model ACT style.
Item sets do not differ much from other ACT math questions. Prepare for them by slightly adapting your strategies and knowing what to expect.
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