<p>@chilldude thank you so much for clarifying. </p>
<p>Can anybody help me figure out #9 here? <a href=“http://online.math.uh.edu/apcalculus/exams/AP_AB_version1_1.htm[/url]”>http://online.math.uh.edu/apcalculus/exams/AP_AB_version1_1.htm</a> It’s a question from the official 2006 AB administration. I got A, but the right answer is B. I can’t find my mistake. I know the slope of the normal line is 1/(4radical2). Or at least that is what I got.</p>
<p>Thank you in advance</p>
<p>Normal lines are found with the opposite reciprocal slope. So the slope should be -1/(4radical2).</p>
<p>Oops! How could I forget negative reciprocal. Wow… Thank you so much.</p>
<p>Sorry if you think I am spamming this thread, but I want to post questions here or else people might not see them. Would somebody please help me with this problem: </p>
<p>A rough approximation for ln(5) is 1.609. Use this approximation and differentials to approximate ln(128/25).
a) 1.633
b) 1.621
c) 1.632
d) 1.585
e) 1.597</p>
<p>It’s another question from the 2006 administration (<a href=“http://online.math.uh.edu/apcalculus/exams/AP_AB2_version1_1.htm[/url]”>http://online.math.uh.edu/apcalculus/exams/AP_AB2_version1_1.htm</a>) that I thought everybody would like to see.</p>
<p>My calculator gives me 1.633, which is the correct answer, but how do you get that answer using differentials?</p>
<p>About double angles: IMO one of the most important and useful ones to know is sin(2x) = 2sinxcosx. This makes both differentiation and integration much easier for trig functions.</p>
<p>d/dx sin(2x) = 2cos(2x), and it’s quicker than product rule for d/dx sinxcosx.
int cosxsinx = int .5sin(2x) = -.5cos(2x). Quicker than integration by parts.</p>
<p>@risubu I’m suspecting it has to do with the fact that 128/25 is really close to 125/25. Which is ln 5.
Then you use linear approximation to find an approximate value at 128/25 by taking the derivative of ln (which is 1/x) and plugging in 5. Slope of 1/5, use point slope form to create a linear approximation.</p>
<p>y - 1.609 = 0.2(x - 5)
Plug in 128/25 and solve for y, getting 1.633</p>
<p>Also, yes, definitely know the sin 2x identity.</p>
<p>^@chilldude thank you replying. It works the way you did it. It also works when I put ln(128/25). I get exactly 1.633. </p>
<p>But shouldn’t I be using the formula f(x+h)=f(x)+f’(x)h?
where h is the change in x?</p>
<p>@Flamewire yes sin(2x)=2sinxcosx is very useful and easy to remember.</p>
<p>@risubu: That’s essentially what I’m doing, actually. I didn’t remember the exact formula, but the way I did it is just a longer way of doing the approximation.</p>
<p>To use that formula, plug in:
f(5 + h) = 1.609 + f’(x)h
f’(x) = 1/x
f’(5) = 1/5
h = 128/25 - 5 = 0.12
f(5.12) = 1.609 + 0.2(0.12)
= 1.633</p>
<p>@chilldude Ah, thank you very much. That helps A LOT. ;)</p>
<p>@chilldude, thank you for clarifying 
so how are you guys studying? i’m trying to go through barrons and pr. not all of the problems but like a good idea of the topics.</p>
<p>I’ve finished PR. Now I’m taking practice tests and reviewing concepts I missed and doing practice problems for questions I missed.</p>
<p>I’m considering skipping Pre-Calculus and taking it over the summer and going straight into AP Calculus, would this be suicidal, and would I totally flunk the class as well?
How are is the class, and how many of you are freaking out about the AP test?</p>
<p>@squirelly If you know trig then AP Calc is doable. However, it will definitely be much, much harder - pre-calc is an Honors class at my school for a reason.
If you were to skip pre-calc, you need to do extra studying over the summer so that you will have a strong foundation for AP Calc.</p>
<p>Classes vary; AB at my school has all crappy teachers and my BC teacher is really good (but it’s all seniors in that class so people never want to do anything… hah)</p>
<p>Pre-calc at my school is basically just trig; there’s not much you’d be missing if you did well in Algebra II. I’d say go for AP Calculus AB if you can, but some schools make you take Pre-calc first.</p>
<p>My class is doing AP Exam questions and recycling everything right now…I only have AP Calculus twice a week though, so I only have three more classes until the exam (yikes!). I feel pretty prepared; I think this exam will be the easiest of the ones I am taking this year.</p>
<p>Our high school is an IB school, but has offered AP Calculus AB and BC for years. Last week, however, they decided to pull AP Calculus from the curriculum next year, and are going to offer the class during a 4 week summer school session instead. Though my daughter gets As in math, I have a hard time imagining anyone being successful with this class being jammed into a short summer session, much less preparing students to earn a 4 or more on the AP exam. I would appreciate any thoughts or feedback if anyone has experienced this. Thank you.</p>
<p>^@TxJr2013Doing either of those classes in a short 4 week interval sounds like a complete nightmare! Could she still take a calculus course during the school year through IB perhaps?</p>
<p>For the FRQ, does anybody know the format of the answer booklet? Will we have blank pages to write our calculations, or lined paper that is provided for normal FRQ essays (Bio and such).</p>
<p>I can say that calculus during summer can be hard as hell. I completed a semester of AB in two weeks and it says a nightmare. </p>
<p>Sent from my GT-N7100 using Tapatalk 2</p>
<p>@squirelly </p>
<p>Bro you’ll do just fine if you did well in your other math classes. I took the same route despite some of my teachers even telling me it’s not something I should do. Well, third quarter just ended and I had a 99 average with five tests. First semester I had a A- and I did better than 99% of people on the midterm. I also took Pre-Calc over the summer at a college level and got an A average (95) there. So if you think you should be in Calc AB, go for it. Also, most of the stuff I learned in Pre-Calc I never used in AP Calc. </p>
<p>Kind of nervous about this test though. I really want to get a 5 on this.</p>
<p>Calc is going to be the first ap test I take next week. I have a strong desire to get a 5</p>
<p>Me too. I’ve been studying and I feel like it’s not cutting it for me.</p>