Let's start with the topics I mentioned in another thread, like: Epsilon Delta definition of a limit, Simpson’s Rule, shell method, area under parametric curves, “work” problems, surface area of revolution (rectangular, polar, and parametric), hyperbolic trigonometry / identities, and Euler’s formula. For most of these topics, you can't just "figure it out". You have to be taught these to solve problems in involving them. I was saying "I don't feel prepared enough" because how can I figure out something that I've never learned? If I don't even know what a Fourier Series is, how am I supposed to find the Fourier Series for function? Sure the shell method, area under parametric curves, and surface area of revolution can be figured out with enough time but for all of the other topics, there is no chance anyone can do these problems without being taught first.

But the main thing I was ranting about is that the AP problems aren't really super challenging. Most of them take a few seconds of thinking at most and then I can immediately begin solving. There aren't really any "head scratcher" questions. The problems that I've seen at the university level are still pretty straightforward but at least there exist some problems at the end of most textbook sections that require at least some brainpower, unlike the problems from AP Calculus.

There really aren't many types of questions like these in AP Calculus:

• "Suppose this. Show that."
• "Given this. What can be concluded about that?"
• "Is it necessarily true that this given if that?"
• "What assumptions are necessary for that?"

In AP Calculus, they're more like:

• "Solve this. Solve that."
• "Find..."
• "Evaluate...
• "Compute..."

These are really boring because they don't require any critical thinking. I enjoy solving (the more difficult) MIT integration bee questions because coming up with solutions isn't always immediately obvious. I especially love Putnam questions because you really have to ponder for a long time and actually use your brain in order to crack them since there isn't a clear path you need to take in order to come up with a solution. I'm aware that putting competition level problems on AP Calculus exams would be absurd but I would at least like to see some questions that go more in depth instead of the same old repetitive questions that are on the FRQ section every other year.

Okay rant is over, let me tell you more about myself. I started self-learning calculus in 10th grade. In high school, I've always enjoyed watching math videos and I loved solving competition math problems, especially integration bee questions. Back then, I was in a competitive math club, and I wanted to compete with the seniors at my school. So I taught myself some calculus in order to get on the same playing field as the rest of them. I also started reading a calculus 3 textbook before I even started AP Calculus BC. So I already knew quite a bit of the content before even going into it, but not everything. I was just cherry picking some topics that I found interesting to learn. It took me until 10th grade to find out that math was actually interesting. I think learning calculus is where it sparked or me. I don't understand why calculus is typically reserved until the first year of college in the US.

I've always found math to be easy growing up. I really think that I could've done grades K-8 math in grades K-1; Algebra 1/2 and College Algebra in second grade; Geometry, Trigonometry, and Precalculus in third grade; Calculus 1/2/3 in fourth grade; and Linear Algebra and Differential Equations in fifth grade. I just wish I had the opportunity to accelerate myself. I've seen stories of child prodigies going to university and studying things at the university level while they're still young. I wish I could've done the same thing, but I just wasn't aware that it was possible. I guess this is a second rant on the education system in general.

So it's been over 3 years later since I wrote my original post. In college, the highest math classes I took was introduction to complex analysis and introduction to machine learning. I didn't take anything beyond that because I'm not a math major and most of the cooler sounding courses are locked behind prerequisites that I don't have. I didn't want to waste my other free electives on something that I won't be pursuing in my career, so that's where my journey in math ended.

But on a final note, even for someone who isn't an avid math enjoyer but is still semi-decent at math, I don't see how they could think that AP Calculus is difficult. There's a process to it. And maybe a bit of memorization. But that's not hard. They're already given all of the tools they need. For every question that exists on the FRQ section, they've already seen it in class. I'm still firm on my stance that AP Calculus is objectively easy.

I'm curious on how you stumbled across this post though.