Ok well this blog is the first one in a few weeks, and it’s going to be covering a lot. You already know my memory sucks, so bear with me.
First, there was the week before Spring Break. I have to check the website to see what even happened then. Okay, evidently, we learned about L’Hopital’s rule and then began review for the AP test.
I thought that L’Hopital’s rule was a pretty simple concept, but the activity that we did to introduce it was honestly very confusing. I thought it was difficult to grasp when I didn’t really know what was supposed to be going on or especially why I was doing what I was doing.
After this, we worked on AP review and then had spring break.
For spring break I went to Texas, but this is a calculus blog, so you don’t really care. I also started to study for my AP tests (including calc) which was frightening. I should really study a lot more calculus.
This past week I was only in class one time between travelling and all the lovely testing I had to do, and when I was in class, we just had a presentation about insurance and stuff.
Basically, what we’re doing now is AP test review. I am extremely scared for the AP test and have low motivation for studying, mostly because I have two other tests that are easier to study for. Hopefully we do a lot more review coming up because I seriously need it.
This week we did an activity about finding the volume of a solid created by some equations using known cross-sections. We did an arts and crafts activity to help us learn about this and visualize the problems. I found this activity pretty helpful, I guess.
Basically, to find the volume of the solid, you have to know the equations and the shape of the cross sections. These cross-sections can be any shape, and the volume depends on what shape they are. To find the volume, you just have to take the integral of the area of the cross-section, generalized using the equations. This means that you can use any shape of cross section as long as you know how to find the area.
To find the area, you need to plug in the distance between equations and such into the area formula for the shape of the cross section. Usually the base of the cross sections, or the diameter if they are a circular, will be one equation minus the other.
After having done this activity, it is pretty easy to visualize what a solid created with known cross-section would look like; it was helpful in that way. Even if you can’t visualize the solid, that is okay as long as you can find the area of the cross sections.
I think this activity was helpful in helping me to understand what was being asked and what the solids were/what they looked like. Now I feel that I can confidently do most known cross sections problems.
So it's finally the last tri!! I can't believe that this school year is only two thirds of the way done… oh boy. That's horrifying.
This was another crazy week in which I didn't really actually go to class much. Actually, out of all my classes, I went to Calc the most- that is I went three whole times. First I got sick and missed a day and a half for that, then I missed another day and a half for BPA States. Life is crazy. So is calculus.
Now that exams are over, we're back to learning about solids of revolution. We reviewed disks and washers on Monday, which was a little rough after having forgotten about them over the past week. The, we took a quiz over the stuff we learned before exams- disks and washers- on Tuesday, which I missed. Then, we learned a new method called the shell method. And took a quiz over this later in the week, which I also missed.
I didn't think that the shell method was hard. If anything, I was just overwhelmed by being absent so much. The shell method is used to find the volume of a solid when you can only use rectangles parallel to the axis of revolution. In some cases, it is actually easier than washers at least because you don't have to worry about subtracting out the middle part. It gets a little dicey when multiple equations are involved or the axis of revolution is not one of the actual axes. Really, once we practiced problems with different axes, I realized these were easy too.
Other than that, I just don’t really know what's happening anymore. Oh well, I think next week we finish the solids unit and,actually, all of the calculus learning- then it's review for AP. Ew.
I can never remember what happened in the past week.
Did we start chapter 6 last week? I think so. Actually, yes, we did.
Ahh, that means this week we continued chapter 6, took a quiz over last week and then I missed Friday so hopefully not much else.
We actually started the week with a random exploration thing from section 3.9 because apparently we were moving too fast. It had something to do with ex and why it’s derivative is ex. It was actually pretty interesting since now we really got to see the why behind something starting from a really basic point.
Then we took a 6.1-6.2 quiz, which I thought was pretty easy. The hardest part was remembering how to do the different types of problems- as usual.
We spent Wednesday and Thursday learning section 6.4 which was about… something. Oh yeah it was about “separable differentials”. That was an interesting time. It really wasn’t so hard, but a few of the problems, get pretty confusing. It also required a lot of random algebra manipulations which was probably the hardest part for me: just getting things to the point where I could take the antiderivative. As usual, though, it gets easier with practice.
I spent Friday at Ohio State and then feeling miserable because college is too dang expensive. The end.
After three days of being sick last week (in which I missed the chapter 5 test), I came back this week just in time to start chapter 6. Chapter 6 so far has been mostly annoying, not really hard.
For reasons that I’m sure make sense, we started off with section 6.2. This section was about u substitution with definite and indefinite integrals. It took us three days to get through the section, but it wasn’t bad at all. Mostly, doing the same thing over and over and over again was just really tedious, especially once you got the hang of it. There were some difficult problems in which they did their best to trip us up, but they only succeeded a few times (at which point I just waited until someone could help).
Next, we moved on to section 6.1 (yes, I know, out of order). 6.1 was all about slope fields. This section was a little trickier. Actually drawing the slope fields isn’t hard and can actually be very satisfying, but going in reverse was harder. I mostly struggled with looking at a slope field and figuring out which equation it went with. Once you do a bunch, however, they usually start to repeat themselves, so it gets easier. On Friday, we also did a lab (?)/ exploration (?) where we had to reason through going from the graph of the slope field to the equation. This was pretty helpful, and I think it really helped me to see the relationships between slope fields and their equations. At least now I can reason through them a little better.
So, that was this week. I also had to take the chapter 5 test, which, as I mentioned, I missed from last week; this was a little confusing but overall went okay (I hope).
Learning about the fundamental theorem of calculus was not as bad as it sounds. I think that learning about it in different ways was helpful in actually understanding what was going on.
First, we looked at the theorem inductively by watching a video of the changing area of a sin function and answering questions along with it. This was helpful because it made you think about what was happening and reason through it. It was also helpful to see how it worked visually.
After this, we learned about the theorem deductively through proofs. This was helpful too since we actually could see how and why the theorem worked. After seeing this proof, the whole thing seemed a lot simpler.
While doing my homework, I relied more on the deductive explanation to do the problems. This was more helpful since this showed definitively how to do the problems and helped me to reason through them better. Thinking about the deductive explanation meant that I didn't have to try and visualize everything and it's derivative and anti derivative at the same time, which would have been basically impossible. I could simply see the problem and know that my answer should be the same as the original or the anti derivative or whatever else.
I'm not really sure why the fundamental theorem of calculus is so important or fundamental to calculus. It's probably because it shows the relationship between functions, their areas, and their derivatives which allows you to find almost anything relating to a function and shows the importance of things like derivatives. I'm sure that this will be very important throughout the rest of calculus.
Out of the last 10 possible school days, we have actually had school 5 times. As you can imagine, this really throws off everyone's schedule. It's great, but also really confusing. This week we had snow days on Tuesday and Wednesday, meaning we only learned math for 3 days.
I'm pretty sure those 3 days were all also spent on one section- section 5.3. I don't know why the book people decided to put literally 3 or 4 sections worth of stuff in one section, but they did. Section 5.3 included such topics as integral properties, averages of function, and calculating integrated/areas. Also the fundamental theorem of calculus (I think).
None of this was hard, or time-consuming for a change. Actually, the homework was easy and went really fast. The hardest part for me was definitely the notation. Funky integral notation and trying to remember what everything means are annoying. Honestly, I think notation is so hard because you can’t just work your way through it, you have to just remember how it works. Once I got used to it, the notation was fine, but at first it was really confusing. The fundamental theorem was also pretty dang confusing, but it wasn’t on the homework so it was alright.
So, yeah, AP Calculus. I don’t know what else to talk about here. Next week we have a quiz over the first part of chapter 5. That’s it. Yep, math.
Seriously, these snow days are throwing everything off, but I am definitely not complaining.
Welcome back from winter break… ew.
Let me tell you that it is difficult to come back from a week and a half break and jump right back into review of stuff that you learned probably over a month ago.
In this shortened week (it was still too long) we spent two days working a Chapter 4 review assignment and two days taking the test. Needless to say, I had a great time.
I totally forgot how to do 90% of the material, and I struggle bussed my way through the review. I mean really struggle bussed. It was rough. And it took forever. I honestly spent two full class periods working on it as well as at least two or three hours at home. At one point, I spent 45 minutes on one problem only to find out that I could’ve done it in two. Thanks. Still, thank God for reviews because otherwise I would’ve failed the test (although that is still a possibility).
While attempting to do the review assignment, my main problem was that, well, I had forgotten everything. Half of the stuff I didn’t even know was a part of chapter 4. Surprisingly, I was actually relieved when I reached the optimization and related rates section of my review, because I actually remembered this stuff (kind of).
With a lot of time and a lot of effort, I was able to get through the assignment. I think I did pretty well on the test, I think.
I guess the lesson learned here is that reviewing after a break from learning and doing math is difficult, and that Cresswell should seriously shorten his chapter 4 review assignment.
Merry Christmas and Happy Related Rates!
Last week was all about optimization, but this week was all about related rates. Both suck, I’ll say that. Well, they’re difficult, anyways. A real fun time for sure. I didn’t think related rates were as bad as optimization, though- for the most part.
What’s hard about related rates is that they’re about, well, rates which are something that I am not really used to working with. Trying to find how fast something is moving or changing is not something I’ve really done before, or at least in a while.
The most challenging part is setting up the problem, figuring out where things went and what I’m even supposed to be solving for. It definitely took a lot of practice and thinking to figure out what equation to use and how to use it. Luckily, it did get a lot easier with practice- imagine that. I was able to reason through how to solve most of the problems- most.
The last couple problems on the book assignment, however, I did not get. I made drawings and tried to find an equation, but I could not. Unfortunately, I missed most of the CCC, so I couldn't get help from classmates either. I think these problems were more difficult because I didn’t really understand the concepts they covered or what they were even asking for.
Next week is only three days long, and I know it involves a quiz over related rates- yikes!- but then it’s winter break, so I’ll live.
This week, I attended AP Calculus a whopping two days. Then I got to get my wisdom teeth out (:D) and miss the last 60% of the week. Good. Times. But that’s not what I’m here to talk about. This blog is about AP Calc, and I’m here to tell you all about it.
During the part of the week I actually attended class, we finished section 4.2, which we actually started two weeks ago (?), so that was a little confusing. Luckily, the part of the section we had left was not as hard as the first part. We then learned section 4.3, or started to at least. I missed the last part of it, but I think I did the homework alright. Hopefully I didn’t miss much.
OKay, okay, I know I missed a quiz on Friday, but I’m fine. Yup, no stress.
I did think the stuff we were learning was pretty confusing. I mean, most of section 4.2 happened long, long ago, but going over it I was lost. The time gap didn’t help, I’m sure. I understood the basic principles of everything we went over, but actually implementing them was difficult, and long, mostly long.
4.3 wasn’t so bad, I don’t think. I think there were just so many terms and “tests” and rules and things that it got confusing. Once again, it’s just long and therefore easy to mess up somewhere along the way. Also it’s time consuming, and I was struggling to focus especially being in intense facial pain. O r maybe it was just becuase I no longer have wisdom teeth (hahaha). But anyways…
I’m hoping I didn’t miss anything earth-shattering while I was busy suffering at home. Ah, I love missing school (only half-kidding).
AP Calc student. I write these blogs.