TASC Math Exam—Isolating a Variable

By Stuart Donnelly

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.