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How to Make Sense of Tricky Variables on the ACT Math Test

A “variable” in math is a placeholder for an unknown. In ACT Science, this takes on a slightly different meaning and is used to describe the factors in an experiment.  Independent variables are factors that are controlled by the scientists. Did the scientists increase the heat in the experiment? Did they add or remove pressure? If the scientists have control over the variable, it is independent. Dependent variables are factors that the scientists observe changing. This is what the look for and how they record data — but they don’t control it.

You will also need to know direct variation and indirect variation. Direct variation occurs when two variables change in the same way over time. If Column A increases and Column B increases at the same time, we can say that the two columns vary directly.  If when Column A increases, Column B decreases, there is an indirect variation between the two elements. In the real world, think of a pizza and the number of slices eaten. The weight of the pizza is inversely proportional to the number of slices eaten. That means that as more and more slices are eaten, the pizza weights less and less. In ACT Math, you may see direct and indirect variation in expression such as “y varies directly as x” or “y is directly proportional to x.” That means you can use the equation y = kx, where k is the constant of variation.

To understand the variables, look at the presented figures. Ask yourself: what does the figure tell me? What are the units of measurement? What changes, and when? Try a practice question!

av_img1

Which of the following graphs best illustrates the relationship between the volume of 30% acrylamide and the volume of water in the recipes listed in the table?

(A) av_img2

(B) av_img3

(C) av_img4

(D)av_img5

(E) av_img6

The correct answer is (C). Table 2 shows that as the volume of 30% acrylamide increases (from 11.6 ml to 66.6 ml), the volume of water always decreases (from 76.3 to 21.3 ml).

Remember, in order to answer ACT Science questions correctly, you will need to pinpoint the relationships between the variables. Don’t try to memorize. Always go back to the data to find the correct answer. All of the information you need to get the questions correct are found the in passages, we just have to know where to look!

 

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