This week was all about all about gifs and derivatives. We used desmos to create graphs that relate to the derivative unit in class. I honestly started out really confused trying to make the graphs. I understood the concept and why we were doing it in order to learn about secant and tangent lines in relation to slope. However, I was very unsure how to actually create the graphs. I was able to figure out the first one in class, with help, but on the on the second one I was totally lost. I eventually figured out how to do it by evaluating each formula and how it related to the graph as a whole. I'm glad I figured it out on my own so I can understand the concept better. The first graph depicts the slope of the tangent line as it gets closer to the point (2,2) on the graph f(x)=.5x^2. The second is relatively the same but instead of a stationary point, it uses points f(a) and f(b). On the third i switched f(x) to equal the sec(x) mostly because I thought it would look cool (it does). It is also interesting to watch the points as they jump to different infinities.
The rest of the week we spent time doing lessons on derivatives. They make a lot of sense to me now that I understand how they are supposed to work. Last year I remember discussing them and doing related problems but I never knew why or what they were for. It is nice being able to connect everything and know the background of the formula.
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This week we had our first chapter test over limits and I thought I did fairly well. I was confident in many of my answers accept the salt and pepper function which I wasn't able to answer but that is alright. I understand the basis of how they work I just could not find the exact equations that would make the statement true. I do enjoy those problems though. I like that satisfying feeling of figuring out a problem such as these. This type of math is why I enjoy it. Sometimes it can be like solving one giant puzzle and once you finally figure it out you are filled with relief and a sense of pride. The salt and pepper functions are a little bit like that which makes them enjoyable. I also am really enjoying the mental math exercises we do every day. Those are also really fun and kind of like a game. I like thinking out things in my head like that. I like it so much that sometimes when I’m bored from running long distances I’ll start doing my times table and see how far I can get while still keeping track of all the numbers to pass time. I’m such a nerd. 'This week we wrapped up what we learned from pre-calc with a test. I was honestly a little worried about it at first but it turned out to be pretty easy. A lot of the topics were right off the packet and I had known most things from last year anyway. It was just a little hard remembering a lot from summer. The rest of the week we concentrated on limits. Taking the third trimester of pre-calc really helped with this because I remember being really confused when I first learned it. Now that I have had a basis of limits it is easier this year when we will expand on the topic. We did a limits packet on Wednesday which was actually pretty confusing at first because I wasn't really used to that kind of wording and then again I forgot a lot over the summer. The packet was one of those things where you're not sure if you're doing it wrong or if it's just that easy. Sometimes work is really easy and I just over think things. Regardless, the lesson on Friday made me feel better with limits. Seeing examples helps me understand things better and it allows me to make connections to actual problems that are expected. I have finished my first week of AP Calc and being in the class makes me pretty excited for the rest of the year. I have had the same type of structure in my math classes for years and it feels nice switching it up. I know it hasn’t been that long but I already like the class. This past week we did not get into anything too new. We were given a packet of everything we should know from last year in pre-calc which was actually a little hard because I had trouble remembering everything. Again, I am so used to a different style of problems so that added to it being a little tougher. Although tougher, I really like looking at problems I have done before in different ways in order to learn more and understand math better. I think a really good thing to come out of this year is going to be really understanding why and how to do something instead of doing it only by looking at a few steps. A big part of that means not relying on notes as much like I have in previous years. I have always had a love for math and I am excited to grow in my knowledge and have some fun doing it. |
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Haley FoxJust a high schooler trying to learn and blog. Archives
March 2017
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