# AP Statistics vs. AP Calculus: Which Is Harder?

Here’s how hard AP Statistics is compared to AP Calculus and the other way around:

For most students, AP calculus is harder when it covers integration and related topics.

If a calculus class only covers differentiation, then it is often easier for students than AP statistics.

It mostly boils down to how much of the math can be solved systematically vs how much requires broader thinking.

Contents:

## What Is Covered in AP Statistics? (3 Topics)

Let’s do statistics first.

If we’re going to compare AP statistics to AP calculus, the best way to do it is to look at the topics covered.

I’ll explain the gist of each topic in each class, and that will help me explain which is harder and why.

### #1 Probability

Statistics is actually the study of probability.

You use probability to reason out all of the other things covered by statistics (combined with additional math tools).

So, this is the starting point, and for some students, it’s the hardest part of the whole thing.

Probability is not always intuitive, and that can trip up some students.

It’s also extremely important to math and STEM in general.

### #2 Statistical Reasoning

Basically, this is where you learn to decide if the things you’re doing with your statistics are really useful.

Here’s a quick example.

Did you know that 100% of people who have heart disease drink water on a daily basis?

If you think that this means that drinking water causes heart disease, then you might need to study more about statistical reasoning.

### #3 Data Analysis

This is really the heart of the course.

Data analysis is a bit of an umbrella term.

Within this topic, you’ll learn about methods for collecting data.

You’ll learn how to analyze that data.

You’ll cover biases, standard models of comparison, standard deviations, goodness of fit, confidence intervals, chi-square tests, and more.

All of the stuff you read about in studies (or news articles about studies) relates back to these fundamental concepts of data analysis.

This section is more or less the reason that we use statistics in STEM.

## What’s in AP Calculus? (6 Topics)

That’s a good overview of statistics.

Now, we can get into calculus.

The best way to understand AP calculus is to understand how calculus is usually taught at universities.

In college, calculus is usually split into three different classes (each a semester long).

In Calc I, you learn differentiation and related concepts, all in two dimensions.

In Calc II, you learn integration and related concepts in two dimensions.

In Calc III, you cover differentiation and integration in more dimensions.

The AP curriculum for calculus is split into two classes: AB and BC.

Schools actually get to choose how they teach the classes.

Some combine AB and BC into a single class, which makes it a lot like college.

The first semester is differentiation, and the second is integration.

Other schools have a year for AB and a year for BC.

If students pass the AB exam, they get credit for Calc I.

If they pass BC, they get credit for Calc I and II.

While AP curricula do dabble with Calc III, there is not currently an AP exam that can get a student credit for Calc III.

With all of that out of the way, let’s talk about what specific topics are covered in AP calculus.

### #1 Limits

Calculus starts with limits.

This is where you first learn how to use infinity in math.

It’s kind of cool, a little weird, but ultimately not too hard.

It turns out that all of calculus is derived from the concept of limits.

Thankfully, you don’t have to derive all of calculus in the AP class.

You just have to learn the essentials of limits (and the topics that follow).

### #2 Differentiation

Differentiation is a specific math technique that allows you to manipulate a formula in order to learn more about it.

This is the first time you really start to feel like you’re doing calculus, and it’s a lot of fun for a lot of students—largely because differentiation is a very accessible topic.

Virtually anyone can learn it.

### #3 Applications of Differentiation

The applications are when things get a little more challenging, but students still have a high success rate at this point.

Applications are where you’ll get into rates of change, related rates, points of interest, and drawing graphs.

By the time you’re done with this part, you actually have a high-level understanding of differentiation and this aspect of calculus.

This is also where the AB curriculum ends.

### #4 Integration

Integration is the opposite of differentiation (kind of like how addition and subtraction are opposites).

It’s also considerably harder.

In AP calculus, you’ll learn the standard methods of integration (substitution, parts, etc.).

You’ll also learn that there are a lot of integrals that can’t be solved with standard methods, and you’ll start to learn how to deal with those situations.

### #5 Applications of Integration

Applications of integration include the concept of infinite sums, definite integrals, and figuring out the area under a curve.

You’ll learn why these techniques are useful and how to apply them to word problems.

For some students, this is harder than learning to calculate integrals, but for a lot of students, it isn’t.

Often, by the time you learn how to solve integrals, you’re already thinking about math in a way that makes the applications easy to understand.

### #6 Series

Series are a bit different.

For the most part, series are not solved using formulas.

Instead, they’re more like logic puzzles.

For a certain type of student, this is the best part of calculus.

For the average student, series can be intimidating and challenging.

Once a student can solve series, then the applications are actually usually a lot easier.

Series are ultimately a way of solving integrals that can’t be solved using the standard methods.

## Is AP Statistics or AP Calculus Harder?

At a glance, you might assume that AP calculus is harder.

It clearly covers a lot more ground, and from me to you, the concepts that come later in calculus are definitely more challenging than what you’ll do in AP statistics.

Yet, the answer isn’t actually that simple.

It really depends on which AP curriculum is being compared.

I mentioned earlier that calculus comes in AB and BC formats.

The AB format only covers the first half of the concepts I listed (ending with applications of differentiation).

And, I would argue that for most students, this content is easier than statistics.

On the other hand, the concepts in BC calculus mostly focus on integration and applications.

This is a lot more challenging (we’ll get into why in the next section), and I think most students would agree that BC calculus is harder than statistics.

Also, keep in mind that I’m only comparing the AP curricula.

There are advanced statistical methods and applications that are quite a bit harder than anything covered in AP calculus, but mercifully, they’re not covered in AP statistics either.

## Why Is AP Calculus Harder Than AP Statistics?

Let’s really get into this.

Why did I rate the courses the way I did?

For starters, AB calculus and AP statistics cover roughly the same amount of material.

BC calculus covers everything in AB calculus plus all of the extra stuff.

In terms of sheer quantity, BC Calculus is definitely a harder class.

But, from a conceptual perspective, I think the ranking holds even if the courses were split so that they all cover the same amount of material, and there’s a pretty simple reason for it.

Everything in AB calculus follows what I like to call formulaic math.

Even though you’re learning new concepts, there are strict rules to those concepts, and as long as you follow the rules, you’ll get to the right answer every time.

It’s like following mathematical recipes.

With statistics, there are a lot of things that follow recipes, but some of the concepts aren’t entirely formulaic.

Figuring out how to source data and check for biases isn’t something that you can punch into a calculator.

They’re higher-level concepts, and you have to understand them deeply to pass the AP exam.

The same goes for some aspects of probability.

Probability can get so confusing that world-class experts disagree on solutions.

Obviously, the AP exam doesn’t cover problems that are quite so hard, but there’s a challenging element to the very concept of probability that is tough for people at every level.

As scary as that might sound, AP statistics is still presented in a way that is accessible to most students.

There are some aspects that require you to think deeply, and you can’t just follow a formula, but most students still succeed.

Calculus BC is another animal.

This course focuses on integrals, series, summations, and applications of those concepts.

There are a few cases where you can follow a formula and get to the right answer, but the vast majority of integrals and sums that exist in math can’t be solved by formulas.

Integration is really where calculus becomes an advanced math that separates the math lovers from everyone else.

Solving these problems is often more like solving a puzzle than following mathematical recipes.

Again, I don’t want to oversell the challenges.

The AP course is designed around expectations for students, and a significant number of problems on the exam are formulaic.

But, this is a course that is an introduction to the mathematical wilderness—where you often have to create new solutions for each problem.

Now, some people are going to argue against this idea.

They’ll say that BC calculus is actually easier because students score higher on the test, on average.

That’s true (at least the part about the scores), but it’s not because the concepts are inherently easier.

It’s because BC calculus tends to weed out a lot of students, and only the very best math students at a given school are going to take this exam.

This, ironically enough, is something you would think about in AP statistics.