volumes the calculus way

Hello everyone! I hope you all had a lovely Spring Break. It still feels like winter here, but since it’s April we can just pretend like it’s Spring! As my seniors are gearing up for AP tests at the beginning of May I will be including videos of some of the final chapters that they’ve been studying this past month. The topic today is how to find the volume of a solid by using cross-sections. Both AB and BC Calculus students study this topic so I will include one video for both classes. I’ve shown the most frequent shapes that Calculus books use for the cross-sections (square, equilateral triangle, circle etc.) Hopefully this will help some of you as you begin reviewing everything this month for the AP exams!!

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short and sweet!

Hello everyone! I’m super busy this week tutoring my students for their finals (which mostly take place next week). Yesterday I had 13 hours of students, yikes!! I’m going to try to blog everyday this week but am going to keep my posts pretty short in the essence of my time crunch :)

 

Here’s a video on how and why it’s good for my BC Calculus students to know the cylindrical shell method for finding volumes of revolution (in addition to their preferred methods of disks and washers)…

 

 

And here’s a video explaining how to look at a graph of a derivative and answer questions about the original function. I ALWAYS get a ton of questions on how to do this! My AB Calculus students have been doing this very recently…

is it xmas yet?

One more week and then Winter Break! All of my students have their finals in January so this week is filled with lots of chapter tests and quizzes. I know it’s a busy time for all of you…and not just in math!

 

My AB Calculus students have been studying the relationship between position, velocity and acceleration. They have been working on word problems involving all three which can definitely be confusing. Hopefully this example will help you sort through similar problems. I’m planning on doing another video on this same subject next time too. It’s just too much to cover in only one video!

 

 

My BC Calculus students recently learned integration by parts. This is a method that helps you take a very difficult integral and rewrite it as a much easier one instead. I’ve shown two very frequent types of integration by parts…the tabular method where you keep taking the derivative of “u” until you get 0 and a wrap-around problem where you eventually get the same integral that you started with (which doesn’t seem like something that would be very helpful, but it is!)

 

 

Have a great week! Just keep looking forward to winter break, and I know you can make it!!

splitting the middle term : how kids can see a connection in precalc and calculus

If students will hear me out, I usually show them how to factor quadratics that have a leading coefficient by splitting the middle term (instead of using other tricks). I’ve noticed that it introduces them to the idea that a GCF doesn’t only have to be a monomial but that it can be a binomial quantity, which in turn helps them with more difficult factoring in Precalculus and also with simplifying derivatives in Calculus!

 

This was just an extra post today in addition to my daily posts for you students! See you tomorrow!

rough monday

Oh wow, it was hard hearing that alarm go off this morning after a relaxing Thanksgiving break! I so much just wanted to rollover and go back to sleep! I did make it here today though, and if we all push through it’s only a quick, busy 3 weeks until Winter break :)

 

I’m anticipating that my BC Calculus students will be working on solving differential equations by separation of variables this coming week. I’ve included two examples in my video. If the timing works out properly, I’m planning to do a few word problems using separation of variables next week.

 

 

And right before Thanksgiving my AB Calculus students were working on related rates which is where they will be picking back up again today. I’ve worked through one of the very commonly seen “ladder” problems.

 

See you tomorrow for Precalculus!