The activity at the beginning of the hour helped me visualize where the secant line was, and how to solve for it at the same time. For the first GIF that we had to make I didn't really have any problems with it, given that the function was already given to us in the form of f(x)=.5x^2. When it came to the second GIF that we had to make though, that was when I personally had trouble with trying to figure out how to make it so that the two points would move independently from one another and approaching each other. The process took Thomas B. and I a couple of minutes before we actually found out how to do it. We basically just changed each value into the variables a or b for the x values, and f(a) or f(b) for the y values. Then, we just had to make it so the functions had sliders with them so that the values would go up and down automatically. That's basically how we fixed that problem. My setup for the first two GIFs worked for my third one because all I had to do was to make a separate function of my own and leave the point-slope form function that only had a and b in them for the moving line that we can see in the third GIF. The analysis of secant lines help us to determine the tangent line of a function through the calculation of the slope of the secant line as a certain variable approaches 0.
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This week we worked more on limits, which still confuses me a bit. Overall I found that the notes that I take in this class so far has proved more useful than the notes that I ever wrote last year in Honors Pre-Calc. Maybe it's just because of how the two teachers teach, I don't know. But I digress.
In the beginning of the week we learned how to take the limits as x approaches infinity. I remember that these were pretty interesting last year so I wasn't really worried about this section. Though, I did start to have trouble when we started talking about end-behaviors. This concept was pretty hard to grasp last year for me and I was worried that I still wouldn't understand anything regarding it. After the notes on it though, I felt that I understood the concept way more than last year, and I'm thankful for that because it is a pretty big concept when it comes to limits. Then, we had a day where we talked about questions that we might have had on the homework linked with infinity limits and stuff. Now, an important day was next, quiz day. The quiz was over sections 2.1 and 2.2. So basically limits, and infinity limits. Overall I didn't think that the quiz was that hard but there was one question at the end that made me scratch my head, and proving limits algebraically was still a struggle for me I found out. The following days we would start to look at section 2.3, which is about Continuity. I don't ever remember learning about this last year So it was fairly new to me. Now granted, it wasn't really that hard of a concept to grasp so that was pretty neat. I guess the most confusing part of Continuity was the fact that: "A continuous function is one that is continuous at every point in the domain." It took my table and I a few tries before we understood what that meant. Now, what really blindsided me was the introduction of the "Salt-and-Pepper Functions." It blindsided me not because of how difficult it was to grasp, but because of how it made me think of it as harder than it should be. It really made me mad that that was the case. Next week we're going to have a chapter test on all this stuff so I hope that I will be ready by then, till then though time to study and do homework for practice. The second week of school has come and gone. Which means that, it's time to reflect on another week of school once again.
In general, this week for AP Calc was pretty chill and relaxed. Unless we're talking about the day before the assessment that is. But I'll get to that in a bit. The weekend before the start of this past school week was spent working on the Pre-Calc review packet that we got on the first week of school. It was supposed to be a refresher on a lot of the things that we should have learned in our Pre-Calc class last year. At first I found myself struggling to keep up with my friends at my table since it seemed like they were remembering how to do everything on the worksheet much more clearly than I do. This worried me a lot. But as I went through and completed the worksheet I found myself getting used to doing this type of math again, and now I feel more confident about my ability as a math student once again. Now, the packet was due on the test/assessment day. Which was Tuesday this time. Even thought I was feeling more confident, I didn't think that I was ready for an assessment already. But, it is an AP class so I just did my very best on it. I found that the problems that gave me the most difficulty in doing were the graph related problems. So basically the same stuff that I found difficult in the worksheet. But even through all this, I did manage to get a 28/29 on the assessment which made me really freaking happy. We started our AP-Calc adventure by learning about limits. Which most of the people in my class have already learned due to us taking 3 tris of Honors Pre-Calc, or regular Pre-Calc, last year. Even so, the lesson was very much appreciated because it helped me remember little things that I might have forgotten if not for Mr. Cresswell teaching it again. And of course, the start of a new lesson comes the homework for that section. It wasn't anything difficult really. It was mostly just identifying limits and proving them algebraically. It is the first week of the school year once again. The first few weeks have always been hard for me because I have a new set of classes for the year, and with these come new things to learn which also means: new challenges.
For AP Calculus in particular, it will probably take me a few more days in order to get back into the groove of things and start thinking mathematically once again. This was true for every one of my past math classes, so I expected it to hit me right around this time. If we're talking about a certain realization that I had for this first week of school, well I would say that I realized that I do indeed need to review a lot. This is mostly due to the fact that when we received the pre-calculus review packet, I found myself lost at a lot of the concepts that I know I should know. It's either that I just need to do certain problems over and over again until I finally remember how to do them or I actually have to re-learn the actual concepts, which I know I never find fun. I found that I still fully retained a lot of my algebraic solving ability, which I was very happy about since a lot of the first problems on the review packet were on algebraic manipulation. But, what I found myself having trouble with were problems involving sin, cosine, tangent, and dealing with graphs. By "dealing with graphs" I don't mean just graphing functions, I'm referring to interval notation, domain and range, and just graphical reasoning in general. I am definitely going to touch up on this topics through the weekend in order to get ready for the assessment that we're going to have. |
AuthorBryll Matthew Moreno |