5 × 10^{0} Strategies for Success on Quantitative Questions
by Andrew Dombrowski
Calculationbased questions are one of the largest and most common sources of anxiety for students on the Chemical and Physical Foundations section, both due to time pressure and the fact that the MCAT puts you in the novel and somewhat uncomfortable position of having to answer these questions without a calculator. However, the good news is that there are some simple, concrete steps you can take, both during your studying process and on Test Day, to maximize your likelihood of success on these questions.
While Studying for the MCAT
1. Make scientific notation your best friend
Practice, practice, practice with converting values given in other magnitudes and units into scientific notation, manipulating them, and then converting the results from scientific notation back into whatever units you have to use for a given question.
What does this look like in practice? Consider the following question: if a 45g kidney stone was broken up by extracorporeal shock wave lithotripsy into 900 smaller pieces, which were then excreted normally, what was the average mass of each smaller piece in milligrams, assuming an even breakdown? Let’s convert our numbers into scientific notation: 45 g = 4.5 × 10^{1} g, 900 = 9.0 × 10^{2}, and 1 mg = 1 × 10^{3} g.
We can break down our calculation into two steps: first, figure out how much each piece weighs in grams; and second, convert that to mg. These calculations are shown below:
Note, of course, that this is not the only way to solve this problem. On one hand, you could have set up an extended dimensional analysis conversion, combining these two steps into one. On the other hand, you could have immediately recognized that 5 × 10^{2 }g = 0.05 g = 50 mg, leveraging familiarity with the conversion between grams and milligrams that you may have built up in chemistry labs. The point is not that there is a single right way to solve problems like this; instead, the point is that you must practice until you can do problems like this in your sleep, regardless of exactly how you prefer to set them up.
2. Study units
When learning a new concept in physics or chemistry, be sure to focus on the units. Understand which units go where in every equation that you learn. This can help you in two ways. First, it builds good mental habits. Noticing units in a passage or in a question stem on Test Day will guide you to the important parts of a passage and help you identify what you need to do to answer a question as efficiently as possible. Second, it allows you to get the most out of the information an MCAT question gives you. Quantitative problems will have answers that include units, and your calculations must give you an output that matches. This will help you determine how to tackle a problem and assess whether your solution is plausible.
3. Analyze your mistakes rigorously
When you find that you’ve made a math mistake on a practice test, don’t just write it off as a silly mistake. Treat it just as seriously as you would a mistake indicating that you need to review waves (for example), because points are points. Figure out how you can minimize the likelihood of such a mistake recurring. For example, if you got a question wrong by erroneously stating that (3.0 × 10^{2} m/s)^{2} = 3.0 × 10^{4} m^{2}/s^{2}, you might notice that this mistake involved failing to square both 3.0 and 10^{2}. A simple way of resolving this might be to try to write exponents in larger handwriting so that you have a visual reminder that the exponent applies to everything in parentheses – so you might write out (3.0 × 10^{2} m/s)^{2} instead of (3.0 × 10^{2} m/s)^{2}.
This may sound silly, but if it helps you get a question right in an appropriate amount of time, it could make a real contribution to your score. However, every student experiences their own set of challenges when it comes to calculations, so it’s important that you work to figure out where your challenges are and which strategies you can put in place to address them.
On your MCAT Test Day
1. Write out your work.
Seriously. This may seem like it involves spending extra time on a section where you may already be in a rush, but it’s a good investment, because it prevents you from going around and around in circles and it allows you to check your work.
2. Manage your time.
This is easy to say but hard to do. Imagine you’re working through a problem that involves the equation E = hc/λ, you work through your calculation, and it doesn’t correspond to any of the answer choices. You check your work, at first you can’t see where the problem is, but then you try changing something slightly – and it still doesn’t correspond to an answer choice. What do you do?
At this point, you’ve likely used up all the time you have to spend on this problem. Mark it so that you can check your work again if you have time, and move on. Your goal in any given section is to answer all of the questions correctly that you can. Let’s say you invest five minutes in this problem, meticulously check your work, and get the right answer – but by doing so, you now have to rush through the last four questions in the section, and you miss two questions that you could have gotten if you’d had time to think about them. Your score on the original calculation problem was effectively 1, because you got it right, but doing so caused you to miss two other questions. This hypothetical scenario underscores the importance of time discipline: knowing when to cut your losses is part of maximizing your score.
Effective practice during your MCAT prep can make you more readily prepared to face the same type of problem on your MCAT Test Day. We hope this helps make the difficult quantitative questions a little bit easier.
Good luck!
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