Home of the For many students, mental math can be one of the most frustrating parts of the MCAT. The bad news is that you will undoubtedly need to do some math on test day. The good news is that you don’t need to be a world-class mathematician to get the right answers! Here are some tips for approaching mental math on test day.
Come prepared
As part of your MCAT preparation, you should brush up on these core math competencies:
- Arithmetic (addition, subtraction, multiplication, division)
- Scientific notation
- Logarithms
- Geometry and trigonometry
- Basic algebra
Need more detailed resources and practice with MCAT Math? Check out our High Speed Math Mastery Course! You can also try to find practice problems and explanations through web searches, but they may go into too little or too much detail for what you need for the MCAT.
Don’t panic!
Trust your preparation, and remember that no single question is going to determine whether you go on to become a successful doctor! It may be worth flagging and skipping a question if you’re not sure how to solve it, and you can return after finishing the rest of the section to try to solve it.
Decide how much math to do
Just because the answer choices are numerical does NOT mean you necessarily need to do any math. Some of these questions may be “getting at” some non-arithmetic logic. For example, consider a question like this:
Suppose you have 100mL of a buffer solution made from 50mL 0.5M acetic acid (pKa = 4.8) and 50mL of 0.5M sodium acetate. Which of the following is closed to the final pH after adding 1mL of 0.1M HNO3?
- 1.0
- 4.5
- 5.5
- 9.0
Addition of a strong acid to a buffer solution will tend to decrease its pH, which rules out answer choices C and D. However, given that the buffer is at its equivalence point [with equal parts base and acid] to start, and that the amount of acid added (.0001 mol) is so small compared to the amount of buffer agents (.025 mol), we can safely rule out A. Voila – no complicated math required!
Rely on responsible rounding
In many cases, you can simplify the mental math you need to do by applying some responsible rounding. What is “responsible” rounding? It depends on the question. You just want to make sure that you don’t round enough to affect the answer, so the answer choices will dictate how much rounding you can do.
For example, if the answer choices are orders of magnitude different, then rounding a decimal to the nearest whole number to simplify a piece of multiplication is very likely safe. But, if the answer choices are (a) 20, (b) 25, (c) 30, and (d) 40, then rounding an operand to the nearest multiple of 10 may very well lead you astray!
As a general rule of thumb, try to not round numbers by more than 10%, and definitely not by more than 15%, when solving problems. If you have to, round a numerator and denominator in the same direction (e.g. making both the numerator and denominator larger numbers) to balance the effects of rounding!
Need help with remembering the MCAT Equations? Check out our article on How to Memorize Equations for the MCAT.
Do some bounding
Sometimes, the answer choices are far enough apart such that you may not need a precise calculation. You just need a reasonably tight range in which the result must fall. This strategy can be especially useful for computing things like pH. For example:
What is the pH of a solution with [H+] = 3.7 x 10-5 M?
- 3.8
- 4.4
- 5.2
- 12.5
We know that pH = -log[H+]. I don’t know anyone who can compute log(3.7 x 10-5) in their head (I certainly can’t!). Luckily, we don’t have to! If we think about it… 1 x 10-5 < 3.7 x 10-5 < 1 x 10-4, which means that the answer must be between -log(1 x 10-5) = 5 and -log(1 x 10-4) = 4. What’s the only answer choice in that range?
Break the math into chunks
If you find that you do need to do some actual computation, don’t try to do it all at once. Instead, break it into manageable chunks. For example, suppose you need to multiply 18 * 74. Instead of trying to do all that at once, instead break the problem down. If we think back to our algebra I class, how do we multiply polynomials, e.g. (x + 2)(x + 3)? We FOIL (first, outer, inner, last)!
(x + 2)(x + 3) = (x * x) + (x * 3) + (2 * x) + (2 * 3) = x2 + 5x + 6
The same applies to “regular” arithmetic!
18 * 74 = (10 + 8) * (70 + 4) = (10 * 70) + (10 * 4) + (8 * 70) + (8 * 4) = 700 + 40 + 560 + 32 = 1332
Personally, I find it much easier to do four easy multiplications followed by an addition than one hard multiplication. You also have your whiteboard on test day, so feel free to write this out!
Choose a representation you find easiest
Just because an expression is written a certain way doesn’t necessarily mean you have to evaluate it that way. For example, sometimes you may find scientific notation easier to deal with, but other times, you may want to use regular decimal. They’re equivalent, so pick your favorite!
The same also applies to order of operations (although the new order you pick must be valid 🙂). For example, a lot of students have trouble multiplying by fractions. For example, suppose you need to compute 7/5 * 60. This expression is simpler than it looks to evaluate!
You can think of multiplying by a fraction as equivalent to multiplying by the top number and dividing by the bottom number. You can do the multiplication and division in either order, since (a * b) / c = (a / c) * b! For me, 7/5 * 60 is easiest to evaluate as (60 / 5) * 7 = 12 * 7 = 84. These numbers are much friendlier to work with than(60 * 7) / 5 = 420 / 5 = 84.
Don’t get discouraged!
Mental math is hard for everyone, but it’s just like any other skill. It gets easier with practice, so don’t give up! If you’re looking for a more comprehensive review experience, you may also consider MCAT Self Prep’s High Speed Math Mastery Course or getting more personalized help through one-on-one Tutoring. Good luck studying!
Warm Regards,
Alex
Alex scored a 528 after self-prepping for his exam as a non-traditional student working at Google. After spending years helping students overcome challenges on many standardized exams, he’s ready to help you with any MCAT challenges you face! You can learn more and sign up to work with him one-on-one here.
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