Not all equations that you'll deal with on the TASC Math exam will be in single variables. There are common formulas that you may need to rearrange to find a certain variable or combination of variables.

The following examples illustrate how to isolate a particular variable given an equation or formula.

Example 1:


In this example, the formula is how force is calculated: Force equals mass times acceleration. As indicated, you're solving for mass, m.

F = ma

To isolate m, notice that it's being multiplied by a. This means you must divide by a on both sides.


Example 2:


This formula is used to calculate the volume of a cone given its height and radius. As indicated, you're solving for the radius, r.


First, multiply by 3 to "get rid of" the fraction.


Don't be scared of pi; it's just a number that can be divided.


Lastly, take the square root of both sides to isolate r.


Example 3:


Because you're looking for xy, you need to simplify both sides and get any terms with xy onto the same side.


Distribute 4x.


Notice that xy is on one side, and all that's left is to divide by 2.


This means that the solution to this problem is 4 – 10x.

About This Article

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About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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