## What Kinds of Math Are Required for 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)
- Algebra
- Trigonometry
- Statistics and probability
- Logarithms
- Scientific notation
- Coordinate geometry
- Exponents

There is no calculus or other advanced math on the MCAT.

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 good number sense, which is the ability to think flexibly and critically about numbers and estimation.

Let’s take a look at how to approach some of the most important math rules and equations you’ll need for the MCAT.

### 1. 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.

**How much can you round on the MCAT? **When rounding a number, it will always be safe to round up or down by 10% of the number you’re rounding.

For 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 — which is **much** easier than 165.62 and 625.

**Related: Factors to Consider Before Signing up for Your MCAT Test Date**

### 2. Scientific Notation

When dealing with numbers that have many digits or working with numbers that are either very large or very small, scientific notation will save you a lot of headaches. It helps simplify calculations, comparisons, and representation 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 10^{4}).

Now, we can multiply the whole numbers and the exponents separately:

- 8 x 1.5 = 12
- Adding our exponential terms together, we get 10-
^{2} - The answer is quickly solved to be 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: 4.562 x 10^{4} is the same number as 4562 x 10^{1}.

On the flip side, when moving the decimal to the left and making the coefficient smaller, the exponent becomes larger: 782 x 10^{1} is the same number as 7.82 x 1^{3}.

**Read Next: High-Yield MCAT Topics and How to Study**

### 3. Multiplication

Multiplication on the MCAT is typically simple, though checking your answer on paper is usually a good idea to ensure you didn’t make a silly mistake! 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.

You may need to multiply two-digit numbers without rounding, which can be a bit tricky if you’re out of practice.

Here is an MCAT multiplication trick that helps make it 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.

32 x 10 + 32 x 7 = 320 + 32 x 7

If you get stuck at 32 x 7, our strategy keeps working by turning this problem into:

32 x 10 + 30 x 7 + 2 x 7 = 320 + 210 + 14

The answer to this longer (but simpler) equation is 544.

With a bit of practice, you’ll be able to multiply any two-digit number with ease!

### 4. Division

Division is just as common as multiplication on **test day**. Thankfully, long division will not show up on your MCAT, as that would take too much time.

One option to simplify division problems is to use rounding. For instance, if you’re asked to divide 2209 N by 743 m/s^{2}, you can round that to 2100 N / 700 m/s^{2}. This is equivalent to the fraction 21 N / 7 m/s^{2}, which is obviously equivalent to 3 N / 1 m/s^{2} or 3 kg. Based on this, you know the answer will be close to 3 kg.

Another MCAT division strategy involves thinking through how many times the denominator “goes into” the numerator. For instance, if you’re asked to solve 141 / 30, here’s how to go about it:

- Ask ‘how many times does 30 go into 141?”
- We can see that it goes in once (30), twice (60), three times (90), and four times (120) but not five times.
- From here, we 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.

### 5. Dividing Exponents

Division of numbers in exponent form just involves fairly simple subtraction. From our previous discussion on rounding, 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 10
^{2} 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 10^{2}). 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, and when multiplying, add them together.
- This gives us our final answer of 4 x 10
^{-3} moles.

**Related: MCAT Score Conversion Calculator**

### 6. Trigonometry

The MCAT wants you to be able to show a comprehensive grasp of the fundamental trigonometric principles, including:

- 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 this is SOH CAH TOA. The inverse functions are:

- sin-1(θ) = hypotenuse/opposite
- cos-1(θ) = hypotenuse/adjacent/
- tan-1(θ) = adjacent/hypotenuse

### 7. Logarithms

A logarithm is a mathematical function that represents the exponent to which a specified base must be raised to produce a given number. 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, on occasion, the natural log (ln). The general form of the equation is log_{10}(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.