AP Calculus BC 2011 Thread

<p>BAD -2
lmao</p>

<p>For the BC only questions, it’s usually parametric/vector/polar for the calculator part, and series, something with Euler’s method (which I ALWAYS screw up), and occasionally L’hopital/indefinite integrals for the noncalculator part. It’s 2 calculator & 4 noncalculator this year though.</p>

<p>I feel decent actually. But I had the whole day to cram.</p>

<p>Can anyone please help me with part b of this question?</p>

<p>[Page</a> Not Found](<a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board)</p>

<p>I don’t understand where 0.2+0.2+1.4 comes from?</p>

<p>Broken link sorry, <a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;
Question 1</p>

<p>its the area underneath the curve</p>

<p>They used the graph to find the area under the curve. The first 0.2 is the area under the first triangle, etc. Don’t you hate how they don’t explain anything? :/</p>

<p>What, why are there 4 non-calculator parts?</p>

<p>How often do parametric/polars appear on the MC?</p>

<p>I know! The lack of explanation is unbelievably annoying.
I’m still a little confused; the line on the graph is v(x), so shouldn’t the area underneath it be its integral, or the position?</p>

<p>can anyone explain how to do number six on the linked FRQs above? I know how to do series but not well enough to understand what cb did there. That question has had me stumped =/</p>

<p>Do we need to know how to do long polynomial division to simplify integral? I don’t know Lagrange or Alternating Series Errors Bounds, can I still get a 4? On a calculator FRQ when you’re asked to find a area of something and you need to find the limits of integration through intersection. When plugging the limits of integration that you got into your calculator definite integral function, how many decimals places should you keep for your limits of integration?</p>

<p>How important is it to know how to represent a repeating decimal as a geometric series?</p>

<p>Also is consistently wrong good for subsequent steps on the FRQ?</p>

<p>how do you integrate (x^2)-1/x from 1 to e</p>

<p>feeling pretty good about this test just because my teacher is really good and we have spent the last month everyday reviewing/practicing exams and he explains everything well. good luck to all tomorrow</p>

<p>@Abrayo: Idk that’s what my teacher said.</p>

<p>@Califragil: It’s similar to position, but not quite. If they took the integral of v(t) dt, it would be position. But they took the integral of the absolute value of v(t) dt, which is the total distance traveled. It’s like walking forward 10 ft and walking back 10 ft. When you get back to where you started, your position is 0, but the distance you traveled is 20 ft.</p>

<p>@ College 112:
I think you split up the integral (x^2)-1/x into int(x^2/x = x) - int(1-x)
You can then integrate to get x^2/2 - ln x, and evaluate at 1 and e.</p>

<p>Agh…I’m scared. I have somewhat of a grasp on series, but I don’t have the formula for calculating the Lagrange error memorized. Also, I’m not very comfortable with polar derivatives/integrals and problems involving advanced trig integrals…what would you guys recommend that I focus on?</p>

<p>Does anyone know what year the Lagrange Error thing appeared in the Free-Response?
I haven’t seen one. Ever.
But I’m going from oldest to newest.</p>

<p>I’m going for polar > advanced trig stuff.</p>

<p>f(x) = x^2 - 1/x</p>

<p>If you want to find nInt(x^2 - 1/x, x, 1, e) then acquire the antiderivative
F(x) = x^3/3 - ln|x| + C</p>

<p>And evaluate from 1 to e via
F(B) - F(A) =
F(e) - F(1) =
[e^3/3 - ln(e)] - [1^3/3 - ln(1)] =
e^3/3 -1 -1/3 - 0 =
(e^3 -4)/3 = 5.36185</p>

<p>There are basically only three things you need to know about polar coordinates (pretend # is theta):

  1. y = rsin#
  2. x = rcos#</p>

<p>Knowing this, you can find derivatives using product rule (so you don’t have to memorize all these formulas below):
dy/d# = r’sin# + rcos#
dx/d# = r’cos# - rsin#</p>

<p>And just put dy/d# over dx/d# to get dy/dx:
dy/dx = (r’sin# + rcos#)/(r’cos# - rsin#)</p>

<ol>
<li>Area under a polar curve = 1/2 int r^2 d#
I think the AP test usually asks simple questions about this because they know it confuses people.
So you’ll probably be given r = somethingwith#. Set r = 0 and solve for #. You should get 2 values. Those are your limits of integration.
And then just plug in the limits and r into the formula for the area under a polar curve.</li>
</ol>

<p>What about the length of a curve?
It’s just sqrt[(dx/d#)^2-(dy/d#)^2] right?
Or is that for something else?</p>

<p>edit:
How can you tell points of inflection on a f(x) graph or an f’(x) graph?
What’s the difference?
Or absolute minimum/maximums?
I know that on an f(x) graph, the relative min/max are given by it crossing the x-axis (and going from neg to pos or pos to neg)?</p>

<p><a href=“Supporting Students from Day One to Exam Day – AP Central | College Board”>Supporting Students from Day One to Exam Day – AP Central | College Board;

<h1>6.b) What is going on here . . . I don’t understand any of the three points they want.</h1>

<p>They essentially just want the area of triangle T. So you would find the base and the height and plug it into the formula (1/2)<em>b</em>h.</p>