**by Andrew Dombrowski**

“Which equations do I have to know for the MCAT?” This is one of the most common questions students ask when starting to prepare for the MCAT, and for good reason—the ability to quickly and accurately use equations is a huge part of success on the Chemical and Physical Foundations section, and the need to study efficiently also means that you should not invest time into learning equations that won’t show up on Test Day. There are many resources available to help answer this question: Next Step’s Strategy and Practice books contain an equation sheet, and abundant equation sheets are also available online. **However, a point that is often overlooked is that how you study equations for the MCAT is just as important as which equations you study.**

Consciously or unconsciously, many of us have built up the habit from science classes of solving physics or chemistry problems in more or less the following way: (1) read the problem; (2) write down an equation that contains the relevant variables; (3) manipulate the equation to get an expression for the variable you need; (4) plug in the values you’re given in the problem; (5) get a quantitative answer. This isn’t *wrong*, but it’s not always the best fit for the MCAT, for a couple of reasons:

First, there’s no partial credit on the MCAT, unlike in many science courses, where you can get some credit for writing down the equations and making a reasonable attempt.

Second, the MCAT tends to ask questions that are difficult in a different way from questions that you’d be likely to answer on a classroom physics test. In a classroom setting, you may get questions where it’s easy to see what you have to do, but the actual solution is technically challenging. In contrast, the MCAT tends to prefer questions where the hardest part is recognizing what you have to do, but the actual solution involves relatively few steps. This is a consequence of the MCAT being a multiple-choice exam that packs 59 questions into 95 minutes in each of the science sections.

With that in mind, let’s review some tips for getting the most out of the equations that you study:

#### Talk it out

Equations are just compressed sentences about how the world works, so as you study, expand them to make sure you understand what they’re telling you. Ask yourself questions, too! *F = ma *means that force equals mass times acceleration. So, what does that mean? Why “mass” and not “weight”? Why “acceleration” and not “velocity”? Working your way through questions like this will help you solidify your understanding on a conceptual level. To be sure, though, this is easier for some concepts more than others; electricity and magnetism are notoriously difficult to visualize on a gut level, but it’s always at least worth making an attempt and to work with analogies that might help (for example, electrical current is often compared to fluids).

#### Focus On Relationships

Partly due to time constraints, the MCAT often contains questions where instead of plugging numerical values into an equation, you’re asked to reason proportionally about what happens if you double, triple, or halve a certain variable. Another possibility would be asking you to recognize what graph corresponds to the relationship between two variables. The way to succeed on these questions is to practice translating equations into relationships. For instance, the electrical force between two point charges is *F* =*k*(*q*_{1}*q*_{2}*/r*^{2}). This tells you that the force will increase linearly with the magnitude of each charge, but will decrease exponentially as you increase the separation between them. Alternately, you could also say that the force will increase exponentially as you bring the point charges closer together.

#### Study Units

When you study an equation, do a few rounds of dimensional analysis where you practice to see how the units work out to be the same on each side of the equation. To take a simple example, when studying *v* = *λf*, note that *v *has units of (m/s), *λ *has units of (m), and *f *has units of (1/m [or m-1]), meaning that you get (m/s) on each side of the equation. Studying the units is useful for two reasons: first, it helps you improve your understanding of the underlying concepts, and second, it enables you to leverage information from the answer choices on Test Day. For an example of how that works, let’s imagine that you see a question where the answer choices are all in watts (W). If you recognize that watts are a unit of power, such that 1 W = 1 J/s, you can then recognize that you either have to find some value in joules and divide it by seconds, or employ the equation *P = IV *and multiply current by voltage. Based on this information, you can then scan the question stem or passage for the information that you need.

With these tips, you can be sure of getting the most out of the equations that you study! The effort you put into studying equations actively will pay off on Test Day by allowing you answer questions in the Chemical and Physical Foundations section accurately and quickly. Good luck!