Working with Formulas

Powers and Roots

Working with Formulas

Lesson by Mike McGarry

Magoosh Expert

Lesson by Mike McGarry

Magoosh Expert

Summary

ACT formula questions do not require outside knowledge because every needed formula and variable definition is provided. The key to success is recognizing the three common task types—plugging in values, solving for a variable, and using proportional reasoning—and applying a clear method for each.

Formula questions usually come from real-world contexts such as science or business, but the only information needed is the formula and the variable definitions given in the problem.
One common task is to substitute known values into a formula and solve for the unknown, as in a stopping-distance problem where plugging in values for speed and acceleration leads directly to the answer.
Another frequent task is solving algebraically for a specific variable, which may involve square roots, isolating terms, dividing by expressions, or rewriting equivalent forms correctly.
Fraction equations require extra care: reciprocal expressions cannot be simplified by taking the reciprocal of each part separately, so the correct method is to isolate the fraction, combine terms with a common denominator, and then take reciprocals only when appropriate.
Proportional reasoning questions ask how one quantity changes when others are doubled, tripled, or halved, and the easiest strategy is to start by setting all variables—and even fixed constants in the comparison setup—to 1, then adjust the changing values and solve.
When multiple quantities change at once, the same proportional reasoning method works, including formulas with exponents and denominators, such as gravitation and planetary motion examples.

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