The MCAT covers a wide variety of subjects, including biochemistry, physics, sociology, and organic chemistry. You’re required to take most of these MCAT subjects as undergraduate courses. However, the MCAT requires some math, which you may not have studied extensively.
Many students overlook just how much math is on the MCAT — about 10%-20% of the exam will require some mathematical calculation without a calculator. Some pre-meds get worried because they had a difficult time in previous math classes.
Don’t be overwhelmed. We’re here to help. In this comprehensive guide, we’ll cover everything you need to know about MCAT math, from rounding to manipulating equations. Then you’ll be better prepared for the MCAT, increasing your chances of medical school acceptance.
Download our free MCAT Equations Sheet to get access to every Chem-Phys equation you'll need to know for the MCAT. Memorize the Arrhen
Types of Math on the MCAT
The key math topics and calculations found on the MCAT include:
- Basic arithmetic (addition, subtraction, multiplication, division, fractions, proportions, square root estimations, ratios, and percentages)
- Scientific notation
- Exponents
- Logarithms
- Trigonometry
- Algebra
- Statistics and probability
- Interpreting graphs
- Coordinate geometry
There is no advanced calculus, differential equations, or linear algebra on the MCAT. Advanced math concepts are kept to a minimum or completely avoided.
MCAT math topics are designed to test reasoning abilities that are important for your success in medical school and as a physician. Top scorers develop a strong number sense, which is the ability to think flexibly and critically about numbers and estimation.
Common Math Rules & Equations to Master
Don’t be overwhelmed by how much you’ll need to memorize without a calculator; the MCAT is designed to not need a calculator, only using math concepts that a doctor should know the basics of.
Let’s take a look at how to approach some of the most important math rules and equations you’ll need for the MCAT.
Rounding
Rounding is your best friend. It shows up in virtually every type of MCAT math question.
The exam is not testing how precisely you can calculate values using complex numbers. Instead, rounding to friendly numbers (often whole numbers) is the way to go and is expected by the test makers. You can see this clearly in AAMC answer choices, as they are often approximations.
When rounding a number on the MCAT, it’s typically safe to round up or down by 10% of the number you’re rounding.
Example: A passage describes Metformin, a medication to treat Type II diabetes, that has a molar mass of 165.62 g mol-1. You’re asked to find how many moles of the medication a patient will ingest if they take 625 milligrams twice daily.
Using our rounding rule, we know that 165.62 can be rounded up or down by 16.562. A good number sense tells us that rounding down to 150 is an easy number to work with. 625 can be rounded up or down by 62.5, so we choose to round down to 600.
This means you’re now working with the numbers 150 and 600 — much easier than 165.62 and 625.
Addition and Subtraction Shortcut
When adding 7, 8, or 9 to a number, try to think of it as adding 10, and then subtracting the difference. For example, instead of 74 + 8, try 74 + 10 – 2. This also works for subtraction; instead of subtracting 7, 8, or 9 from a number, subtract 10 and add the difference. 346 - 127 should be taken in two steps: 346 - 120 = 226, and then 226 - 10 + 3 = 219.
Multiplication
Multiplication on the MCAT is typically simple, but checking your answer on paper is still a good idea. There’s no shame if your times tables through 12 are rusty. Set aside a little time to work through them until they’re automatic.
MCAT multiplication trick to make multiplying two-digit numbers without rounding more manageable: Multiplying 32 x 17 might seem calculator-level, but it’s not! Mental math experts suggest turning this type of problem into a two-step math problem: 32 x 10 + 32 x 7. After all, multiplication is just fancy addition. After you get 32 x 10 = 320, you may get stuck at 32 x 7. Our strategy keeps working by turning this problem into 30 x 7 + 2 x 7 = 210 + 14. The answer to this longer (but simpler) equation is 544.
Division
Division is just as common as multiplication on test day. Thankfully, long division will not show up on your MCAT. To simplify division problems, you can use rounding. Say you’re asked to divide 2209 N by 743 m/s2. You can round that to 2100 N / 700 m/s2, equivalent to the fraction 21 N / 7 m/s2, which should be easier for you to mentally calculate to 3 N / 1 m/s2 or 3 kg. Remember this is rounding, but you now know the answer will be close to 3 kg.
MCAT division strategy: Think through how many times the denominator “goes into” the numerator. For instance, if you’re asked to solve 141 / 30, ask yourself how many times 30 goes into 141? Once (30), twice (60), three times (90), four times (120) — yes — but not five times. From here, try ½ of 30, and we see that 120 + 15 = 135. We should probably stop here and say the answer is roughly 4.5, but we could keep going and determine whether ¼ of 30 would get us closer to 141.
Exponents
Exponents refer to the superscript number indicating how many times to multiply the primary number by itself. You may be expected to divide exponents on the MCAT.
Division of numbers in exponent form just involves fairly simple subtraction.
Let’s try to divide 600 mg / 150 g mol-1. First, we’ll need to fix our units using orders of magnitude: 600 mg is the same as 6 x 102 mg, but we need it in grams. The conversion factor here is 1 x 10-3, giving us 6 x 10-1 g.
We end up with (6 x 10-1) / (1.5 x 102). Note the manipulation of 150 so that it is smaller than the numerator coefficient. Now, we figure out how many times 1.5 goes into 6. We can see that it goes in 4 times evenly, but what do we do with the exponents?
When dividing exponents, subtract them.
When multiplying exponents, add them together.
This gives us our final answer of 4 x 10-3 moles.
Logarithms
A logarithm is a mathematical function that represents the exponent to which a specified base must be raised to produce a given number. Logarithms are to exponents as addition is to subtraction.
The logarithm base 10, often denoted as “log base 10” or simply “log,” calculates the exponent to which the base 10 must be raised to yield a specific number.
Logarithms on the MCAT are always log base 10 or occasionally the natural log (ln), meaning log base e, Euler’s number.
The general form of a logarithmic equation is log10(x) = y, where x is the number for which the logarithm is being calculated, and y is the exponent to which 10 must be raised to produce x.
Mastery of logarithms is essential for answering questions about acid-base chemistry as well as other physics and chemistry topics. They are particularly useful for simplifying calculations involving very large or very small numbers.
Certain log (and natural log) properties are useful to memorize:
- When taking the log of a number that is > 1, the answer will be positive.
- When taking the log of 1, the answer is 0.
- When taking the log of a number < 1, the answer will be negative.
- You can’t take the log of a number < 0.
Logarithm shortcut: You may be asked to find the log base ten of a number that isn’t a multiple of 10. Consider log(7). One simple trick is to realize that the log of any number between 1 and 10 is going to equal between 0 and 1 — since log(1) = 0 and log(10) = 1. For simplicity’s sake, let’s estimate log(7) to be 0.5. This can help us evaluate the log of longer expressions.
Now consider log(7 x 105). If we estimated log(7) to be 0.5, then we know log(7 x 105) will be roughly equal to 0.5 + log(105). And since the log of any exponent of 10 is simply the exponent itself, we can estimate the answer to be 0.5 + 5 or 5.5.
Scientific Notation
When dealing with numbers that are very large or very small, scientific notation saves a lot of time and headache. It simplifies calculations, comparisons, and representations of numerical data.
For instance, if you’re asked to multiply 0.000008 by 15,000, start by changing these numbers to something easier to work with. Try (8.0 x 10-6) x (1.500 x 104). Now, we can multiply the whole numbers and the exponents separately: 8 x 1.5 = 12; 10-6 x 104 = 10-2. Then the answer can be quickly solved: 12 x 10-2, or 1.2 x 10-1.
Sometimes, you will need to manipulate the order of magnitude of a number that is in scientific notation. The rule is that when you move a decimal place to the right (making the coefficient larger), the exponent becomes smaller. For example, 4.562 x 104 is the same as 4562 x 101.
On the flip side, moving the decimal to the left and making the coefficient smaller makes the exponent larger: 782 x 101 is the same number as 7.82 x 103.
Trigonometry
The MCAT wants you to be able to show a comprehensive grasp of the fundamental trigonometric principles, including the following:
- Defining basic trigonometric functions such as sine, cosine, and tangent, as well as their inverses (sin⁻¹, cos⁻¹, tan⁻¹).
- Identifying the sine and cosine values at key angles: 0°, 90°, and 180°.
- Understanding the relationships between the lengths of the sides of right triangles that involve angles of 30°, 45°, and 60°.
We can only use these trigonometric functions with right triangles. The functions are the ratios of the triangle side lengths:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
A common mnemonic to remember these functions is SOH CAH TOA.
The inverse functions are:
- sin-1(θ) = hypotenuse / opposite
- cos-1(θ) = hypotenuse / adjacent
- tan-1(θ) = adjacent / hypotenuse
What You’re Provided With on Test Day
All you’re provided on test day is a laminated booklet that acts as scratch paper, along with a wet-erase pen.
You’ll need to find the correct answer to each math-related question by using only scratch paper. You will not be able to use a calculator for the MCAT.
Many students feel terror wash over them when they realize there’s no calculator allowed for the MCAT. But the absence of a calculator is good news in disguise — it means the level of calculations has to be relatively simple.
The AAMC calls their special scratch paper the MCAT Test Day Noteboard Booklet. It’s a laminated booklet that comes with a wet-erase pen and plenty of space to write out your calculations.
In order to use the Noteboard Booklet efficiently, there are two things you need to do before your test day:
- Relearn basic math concepts you haven’t used for years. During your MCAT prep, you may need to relearn math concepts you haven’t seen since high school. This includes basic trigonometry, logarithms, exponents, scientific notation, and fundamental algebra.
- Use practice questions that require you to use scratch paper. Do lots of realistic practice questions that require manual calculations with scratch paper during your study time. These practice questions prevent you from over-relying on mental math during test day.
Related Read: MCAT Test and Score Release Dates
Expert Problem-Solving Strategies for MCAT Math
Questions that require numerical problem-solving typically appear in the Chemical and Physical Foundations of Biological Systems Section (Chem/Phys for short). But you may find scattered math problems in the other three MCAT sections, too.
Being able to quickly identify the correct equations, numbers, and mathematical setup is crucial. Below are the best tips and strategies to set you up for MCAT math success.
Practice, Practice, Practice
The most important strategy is the most obvious: practice! You should complete practice problems multiple days a week during your MCAT prep.
Review your practice test results and use of scratch paper to improve the speed of your calculations.
Use Mental Math Tricks
Mental math tricks can help you develop good, consistent number sense. Dedicate time to practicing mental math during your study week.
Start with simple arithmetic operations such as addition, subtraction, multiplication, and division, and gradually increase the complexity of the problems as you become more comfortable.
Memorize MCAT Physics & Chemistry Equations
There are a lot of formulas and equations you need to know for the MCAT. Practice writing down these formulas and equations from memory. An equation will often have to be manipulated algebraically to solve for a particular variable.
The best equation strategy is to complete all of the algebraic manipulations of an equation before trying to plug in numbers. This will allow you to cancel out terms that may appear on both sides of the equation.
Example: If asked for the final velocity of an object during free fall, we can use kinetic and potential energy equations, 1/2mv2 and mgh, respectively.
A quick setup of the two equations gives us mgh = 1/2mv2.
We know we’re solving for v, but before we start to rearrange the relationship, notice the mass terms cancel out, leaving us with gh = 1/2v2.
Next, we move the ½ and exponential terms to give v = √2gh. Only now should you plug in the relevant numbers and do the math.
Download our comprehensive guide to every Chem/Phys equation on the MCAT you need to know.
Create an Effective Study Plan
Follow a foolproof study plan with ample time to hone your math skills and boost your percentile score.
Depending on how much time you have until test day, your lifestyle, and your target score, we recommend a 3- or 6-month study schedule. However, a 1-month study plan is feasible if necessary.
Studying for the MCAT can involve finding little pockets of time during work breaks, downtime during social events, or audio studying during your commute.
Learn more about crafting the perfect MCAT study plan with this free webinar.
FAQs
The math on the MCAT is relatively simple, but that doesn’t mean it’s easy.
Although MCAT math is at a high school level, the short time you have to solve problems can make even simple math difficult.
If you follow our tips above, you should easily answer MCAT questions with math, even without a calculator.
Best strategies include practicing (a lot), rounding by up to 10% of the original numbers to make them easier to work with, using scientific notation, and memorizing formulas, basic trigonometry, and logarithmic equations.
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Dr. Ken Tao
Ken is the Director of MCAT and Research at MedSchoolCoach. He is an alumnus of UC Berkeley and Harvard University, boasts degrees in Bioengineering, Molecular and Cell Biology, and a Ph.D. in Neuroscience. Ken previously worked with undergraduate students at Princeton Review where he was the only tutor certified in all subjects. Ken was one of the highest rated MCAT tutors ever and a teacher trainer. He founded Magoosh's MCAT division and has written content for dozen's of MCAT books and guides.
