How To Do MCAT Math Without A Calculator
- Feb 25, 2021
- MCAT Blog
Is there math on the MCAT? Yup. Can you use a calculator on the MCAT? Nope. This scares a lot of students, but let’s think about it another way – although calculations may look tough initially, MCAT math is always subordinate to science. The MCAT is not at all about math for the sake of math. You’ll be more than ready to tackle MCAT math problems on test day by doing practice and keeping these tips and tricks in mind. When you’re done, test your new skills with a free MCAT practice test.
MCAT Math Tips
First and foremost, you should be comfortable with working around units. Units are important because they help us keep track of what we’re using a number to qualify. Doing algebra with units is a way to check your work and to verify that you’re using the correct form of an equation. When taking the MCAT, you’ll likely have to pull at least a few equations from memory when answering a question, and it’s very normal to second-guess whether you’re putting the right variables in the right places, especially if the equation isn’t particularly intuitive.
But what if we were dealing with different units of distance? For instance, what if there was a mismatch in scale, like if the question gave us information in meters, but all the answers were in millimeters? From the point of view of unit checking, as a way to make sure we’re putting the right variables in the right place of the equation, all we have to do is make sure the same TYPE of units end up in the same place on either side of the equation, without worrying so much about what those units are. In this case, as long as we see some unit for distance in the same place on both sides of the equation, we know that we’ve set up the problem correctly. However, when the time comes to match our units to the correct answer choices, we need to make sure that the specific units line up.
This is where unit conversion comes in. To convert between units, we can utilize the concept of dimensional analysis. You might have seen this concept already, in the context of, say, stoichiometry, but it applies much more broadly to conversion between units in general. So, if we’re given an equivalence relationship between two units, like 1 foot equals 0.3 meters, we can write that as a fraction in the form of 1 foot divided by 0.3 meters or as 0.3 meters divided by 1 foot. Because 1 foot and 0.3 meters are equal, those fractions both equal 1, meaning that we can multiply any other value by that fraction without changing its magnitude. While doing so, we’re simultaneously doing algebra with the units, which results in them being changed.
Remember that equations are tools, and we need to pick the right tool for the job. This means that the equation (or perhaps equations) should BOTH contain variables related to the information presented in the question stem AND yield a calculated result that corresponds to the answer choices.
And here’s another possibility: what if the passage gives us a new equation related to frequency, perhaps in the setting of an experimental passage? Well, not to worry. The beautiful thing about passages is that no matter how involved or intimidating they seem, they must be accessible based on core MCAT content knowledge. Now, “accessible” doesn’t mean “easy”—the information you need might be buried in a blizzard of confusing terminology and acronyms—but the information does have to be there. This means that the key to handling novel equations is to leverage passage information to understand the point of the equation, and how it fits into the broader ideas discussed in the passage. Work through each variable in the equation one-by-one, making sure that you account for every variable. Even if you’ve never seen a certain symbol before, again, it must be defined somewhere.
Calculation Errors to Look Out For:
● Negative numbers
Possibly the most classic example of a “silly math mistake” is obtaining an answer with the wrong sign – negative instead of positive, for instance. The best way to avoid this is to be very careful when subtracting a negative number. Subtracting a negative number is identical to adding the absolute value of that number; for instance, if I take 9 and subtract negative 6, this is the same as taking 9 plus 6 to equal 15.
This probably isn’t new to you, but it’s incredibly easy to forget to write down one of the negative signs, or simply to see “9,” “6,” and “minus” and think “3,” especially when plugging values into an equation that involves subtraction.
Likewise, care is needed when multiplying by negative numbers. In other words, if a minus sign is in the mix, it’s worth slowing down to make sure that everything lines up.
● Dividing by a number less than 1
Another common source of mistakes is dividing by a number that is less than 1. Dividing any positive value by such a number must always result in a larger, or more positive, answer, while dividing any negative value by a number less than one will always yield a more negative answer. This can be a bit challenging to conceptualize; while 10 divided by 5 is quite obviously taking a group of 10 and dividing it into 5 smaller groups of 2, dividing 10 by 0.1 is a bit more abstract.
● Failure to properly distribute when moving a term to the other side of the equation
Algebra errors are also quite common when manipulating equations. Most of these involve improper distribution when moving terms between the sides of an equation. As an example, take the kinematics equation vf2 = vi2 +2ad. Imagine that the only information we have is that acceleration is equal to -0.5m/s2, and that we’re trying to solve for displacement. First, we can plug in -0.5 for a, and multiply by 2 to give us vf 2= vi2 – d. Then, we subtract vi2 from both sides, yielding vf 2 – vi2 = d. Next up, we just need to divide both sides by negative 1 to get d isolated on the right side, but what is vf 2 – vi2 divided by negative 1? The most common mistake students make here is to only apply the negative sign to one of the terms on the left.
There’s no reason to freak out just because there is math on the MCAT. With some small additions to your MCAT prep, you can easily solve MCAT math problems without a calculator. Our MCAT Online Course and MCAT Live Online students have the option to attend supplemental office hours for more help with MCAT math. Blueprint MCAT free account students can register to attend free MCAT webinars!
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