Cracking the AP Calculus AB & BC Exams, 2014 Edition by The Princeton ReviewAfter working through the entirety of The Princeton Review: Cracking the AP Calculus AB & BC Exams, I found the explanations to be thoroughly clear and informative. Additionally, considering how many mathematics books Ive worked on, Ive never seen the details in the solutions to be so clear as I have with this one. I am very pleased with the overall knowledge that Ive accrued from it.
The topics I had struggled with the most in the past were Solids of Revolutions and Series. The Princeton Review: Cracking the AP Calculus AB & BC Exams has finally made the former abundantly clear so that I was able to overcome it, and now I can find solids of revolutions through washer and cylindrical shells methods with confidence. The latter, I found the treatment of series to be quite lazy. Thats Chapter 35. How can the author omit divergence and p-series tests? Inexcusable. The chapter should have been broken down into two chapters with more examples: the first dealing with easier types of series and the second, harder ones. But the treatment of Taylor and Maclaurin series was not bad at all. Also, the author was lazy in the volume of solids with known cross-sections; he just merely copied the questions for examples 9 and 10 but failed to explain why we had to multiply by 2 with y. That wasnt clear enough.
In the solutions, especially for the BC Section II questions, the author will say, Obviously, we dont need to.. and then move on. Uh...explain the obvious, will you? Speaking of laziness, how about the Section II questions in BC examinations? Why did the author have to repeat the questions already asked in AB examinations? What a waste of questions. Worse than that, the solutions for the same questions were given: the first one was correctly done and the other one had an incorrect final solution. I am a little disappointed in looking at the specific type of several questions from the AB/BC examinations because the logic is: I should have been prepared by the book to encounter these questions yet they werent covered anywhere in the past chapters.
Now, I want to compare The Princeton Review: Cracking the AP Calculus AB & BC Exams with the other two AP Calculus Study Guide books: Petersons and Be Prepared for the AP Calculus Exam. I havent worked on the Barrons yet, but I have a feeling that one will be the superior guide of any.
Suppose I was in the shoes of a tyro who has fallen so behind in Calculus or has a horrible teacher. The Princeton Review: Cracking the AP Calculus AB & BC Exams is my highest recommendation because it really covers the basics in the most painless way. In fact, anyone taking Calculus I, II, or III should get this too; its so much easier to understand. I know there will be people complaining that The Princeton Review: Cracking the AP Calculus AB & BC Exams is just too easy and covers the basics. Then, they should refer to The Humongous Book of Calculus Problems which was written by the same author of Petersons. Both books have more or less the same problems, but the details in Humongous are more extensive, and the problems are a lot more difficult. Nevertheless, get the Petersons for the sample tests. Finally, Be Prepared for the AP Calculus Exam is reserved for those who are very familiar with the very technical details and want to cover all bases as possible.
All in all, The Princeton Review: Cracking the AP Calculus AB & BC Exams is an outstanding study guide for Calculus regardless if one is taking the AP exam or not. Really, be sure to know all of the concepts (I dont care if you are taking AB or BC. This is Calculus at its finest.)
As for the Editions, (9th, 10th, 11th, 12th, 13th, 14th, whatever), they are the same with only one difference: a new cover with the changed edition number. Really, there should have been few more topics included (such as logistics and accumulation) in the book. After you finish the book, you should move up to the next level of AP Calculus study guide books to further indurate your foundation, and never forget to go to the AP website to work on the samples of free-response questions.
Pg. 14: Example 1, Condition 2: The right hand limit is... There should have been a +, not -, at the top corner of 2 at the bottom of the lim portion.
Pg. 217: Problem 7. All we have to do is evaluate... There should be a square sign for the parenthesis in the integrand.
Pg. 251: Continuation of Example 1. Finally, take the limit as a tends to 4:.. The final solution is a mess. It should be = 2pi + 4 at the end.
Pg. 254: Number 7. No square root in the denominator. Take it off.
Pg. 278: The harmonic series, for example, looks like this: All plus, not minus, signs!
Pg. 282: Example 5. Determine whether the series 1 - ? + 1/3 - 1/4 +... Fix that!
Pg. 287: In the gray box, although I am a stickler, it should have been a -, not +, before the ellipsis for sinx and cosx.
Pg. 416: Number 2. We take the derivative of the numerator and the denominator It should be pi, not 0, in the bottom of the lim portion throughout. Then, plug the pi in to get -1, not 1.
Pg. 593: Continuation of Part c of Number 5. The points of inflections are (plus/minus sqrt(1/3), -1/9), not (plus/minus sqrt(1/3), -sqrt(1/9))
Pg. 594: Part c of Number 6. During the Step 1, the top part of the integral sign should be 4pi, not 4x. Follow that throughout the next line.
Pg. 665: Number 18. It should have been f(-4), not f(4). That was annoying.
Pg. 672: Number 34. By the graph of.. It should be y = e^(-x^2/4).
Pg. 786: Part b of Problem 3. You just solved it earlier with the correct solution! It should be -48pi on the left side to get the solution of dr/dt = -1/16 ft/sec. (two people working on the tests, mm?)
I havent looked at every detailed solution for the chapters because when I got the answer right, I moved on.
***3/29/14*** I reviewed one problem from Section II of AB Exam concerning about the methane accumulation, part c where it asks What is the average rate of methane accumulation in the cave over the time interval 0 =< t =< 24 hours? The solution is wrong. It should be [20 + int of r(t)dt from 0 to 8 + int of (r(t) - 1.5)dt from 8 to 24] / (24 - 0) = 1.099 liters per hour.
2014 AP Calculus AB Free response question 2
Calculus AB 2014 Scoring Guidelines
For this solid, each cross section perpendicular to the. Let a be the leftmost. Find the slope of the line tangent to. Because the function is differentiable,. Note that v A 2 is taken directly from the table, and v B 2 is found to by substituting. The twice-differentiable functions f and g are defined for all real numbers x. Values of f,.
The College Board. Visit the College Board on the Web: hopelutheran-clehts.comeboard .org. GO ON TO THE NEXT PAGE. CALCULUS AB. SECTION II, Part A.
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C Email questions or comments: thinkcalculus at gmail. Grimes assured me that they will not be working after am tomorrow. We will continue to meet in C We will see if this is the case. Show all work or receive zero credit. Read it. Sign it.
Google Translate. Skip to main content Skip to main menu. HW 30 Grade your break assignment and correct the mistakes in different color pen. HW 29 AP problem from the lesson. HW 23 Read p. HW 22 Finish the classwork problems.