Secret MCAT Math Shortcuts

Session 311

Today, we will be working on test strategies and talking about secret MCAT Math shortcuts because ultimately, you don’t get a calculator on the MCAT and you will not be needing it. So we are going to teach you the shortcuts.

We are joined by Nicole from Blueprint MCAT. If you would like to follow along on YouTube, go to premed.tv.

Listen to this podcast episode with the player above, or keep reading for the highlights and takeaway points.

[02:43] MCAT Math

For those students who are intimidated by MCAT Math, Nicole knows how that feels. MCAT Math was something that she struggled on at first. ChemPhys is generally the most math-heavy section of the MCAT and it was her worst section score for a while. She had to learn to approach MCAT Math differently.

“MCAT Math is a whole different ball game and it requires a whole different mindset than just your average math.” Click To Tweet

It is really a skill that you have to build. Regardless of whether or not you feel like you are “good at math,” every single person listening to this podcast is capable of learning how to approach the math on every single most difficult MCAT Math problem they could possibly be given. It is an approach that you can learn.

[04:02] Approach to a Hard Math Problem

What a hard math problem looks and how to approach it would depend on your strengths and weaknesses.

One thing the MCAT often asks you to do is to combine equations. You might need to bring in two different concepts and apply them to one scenario. MCAT loves to test your ability to synthesize information. It gets into that critical reasoning that the MCAT is very interested in evaluating.

Another thing you might have to do is manipulate decimals, manipulate fractions and work with logarithms. All of these items are fair game and are some of the things that can be more challenging for students.

“Luckily, there are a lot of strategies and shortcuts that we can use.”Click To Tweet

Nicole will share and dive into some of her personal favorites today.

[05:10] Introduction to a Concept of Math Hashtags

Nicols wants to introduce a concept she talked about with her class which a lot of instructors at Blueprint love to talk about.

There are teams with hashtags: #TeamNoMath, #TeamLessMath and #TeamEasierMath. Her most favorite team to be a part of is #TeamNoMath.

“Nothing makes me happier than when I get a math question and I can actually get to the correct answer without using math at all.”Click To Tweet

Simplify what you do by getting through the math problem without even doing any math.

The next team is #TeamLessMath where you will try to find a shortcut to make it easier for you. If you cannot get to #TeamNoMath and you cannot quite get to #TeamLessMath, at least make it to #TeamEasierMath.

The next step is to find a shortcut. If you can’t find a shortcut and actually have to do all the math because there are plenty of instances where you do need to do that as well, you will see how you can use things like rounding and estimation to make your life easier.

#TeamNoMath

If you’re studying for the MCAT right now, one equation you might be very familiar with is the Henderson-Hasselbalch which people call the H-H equation.

Henderson-Hasselbalch describes how we make buffers and some of the relationships between pH pKa and the ratio of acid to base that is present in a given solution.

This equation includes a logarithm, which a lot of students are not fans of, and it can be really difficult. What you can do is go through and just straight up solve this equation.

An Example

For example, you are in the bloodstream, the pH of the bloodstream is 7.4. Molecule Dr. Gray has a pKa of 6.4. Then you would be asked how much of the acidic form of Dr. Gray is present versus how much of the basic form of Dr. Gray is present in the blood given that pKa 6.4. and our pH is 7.4.

You can go through and do the math. However, you can also answer that question based on a conceptual understanding of how pH and pKa are related.

The “No Math Solution”

First of all, you have to understand what it means when pH equals pKa. If your pH is equal to pKa, that means you have equal parts protonated and deprotonated forms of the molecule. Your acidic and basic forms are in equal concentration at that time when pH is equal to pKa by definition.

pKa is where a molecule likes to be. You are comfy, you are balanced as a molecule if the pH of your environment is at the pKa which is specific to molecules. You can then think that your pH in your environment, in the example given, is higher than your ideal pKa.

If you have high pH, you are more basic than you are acidic. And if you are more basic, that means you have less protons in solution. Compared to your balanced state, there are less protons available which means there is going to be a higher concentration of the deprotonated form of molecule. That means that you are going to have a higher level of base than acids.

“A lot of times the final answer that is asked of you in these questions is either the ratio of base to acid or acid to base.”Click To Tweet

Based on knowing which is larger and depending on what fraction you are asked for, you can determine if that fraction is greater or less than one. Sometimes just determining that, is enough to get to your answer choices.

From there, your next step would be to determine what is greater or less than one and by how much. pH and pKa are both log scales that are based on powers of 10. You have to be able to do these in your head. It’s not going to be a crazy logarithm, but even numbers of 10.

Conceptual Understanding

This is a big conversation. Once you get proficient with this conceptual understanding of what is pKa and what it means to be protonated, or to be deprotonated, you don’t need the logarithm because you have the conceptual understanding.

There are certain equations where you can just straight up and avoid the math every single time.

Another way to avoid math is if you had a question that was asking about body temperature. Obviously, you have a reaction taking place in the body and that is not going to end up being 500 Kelvin.

“The MCAT is only going to present you scenarios that make sense essentially, according to real life.” Click To Tweet

You can eliminate answers right off the bat. Even if we can’t get the #TeamNoMath, we can also do less math by looking at our answers and see if any of these just don’t make any sense given the situation.

[12:20] Shortcuts to Equations

Here is an example question where a shortcut can be applied. “If the average bone mineral density is 3.88 grams per centimeter cubed, which of the following is a reasonable estimation of the specific gravity of fats in the body?”

The first thing Nicole always looks at whenever she sees any math question is the magnitude of the answers.

This will allow you to start getting into #TeamLessMath. You put in minimal effort to get the maximum number of correct questions. Do the absolute minimum possible to get the correct answer.

“You don't get points for showing work on the MCAT… you got a shortcut, then you are saving time and time is points on the MCAT.” Click To Tweet

Looking at the sample equation, the first thing you notice is you have two answers that are greater than one and two answers that are less than one. This is a good benchmark.

Looking at the spread of your answer choices is also important. By looking at the answer choices, you can tell if they are pretty far away from each other or if you can round your numbers.

For example, we are given the average bone mineral density that is 3.88 grams per centimeter cubed. Nicole would immediately be rounding that to 4 because you want to make numbers easier for each other.

How aggressive we are at round is another important thing to keep in mind.

[15:27] Units in MCAT Math Equations

Units play into equations and math on the MCAT. Every equation is going to have some units associated with the vast majority of numbers that you are working with.

If you are keeping track of your units, you need to make sure things cancel out. If you have not been writing out units, you need to start because they help you double-check that your answers make logical sense.

If you are supposed to have the unit of joules and you end up with joules times meters, something goes wrong. You might have misremembered an equation.

Look at your answer choices. Before you blindly dive into a calculation, always check your answer choices, at least give them a quick glance. You may even get yourself down to only having three options instead of having four options.

“Every single answer that you can eliminate on the MCAT…’ Time’ is points.’ ‘Process of elimination’ is also points.”Click To Tweet

Do anything that you can to double-check that you are not misremembering the equation and if it is not something that was given to you in a passage. Also, make sure that your answer options are all in the correct unit.