What is Ap calculus: Definition and 117 Discussions

Advanced Placement Calculus (also known as AP Calculus, AP Calc, or simply AB / BC) is a set of two distinct Advanced Placement calculus courses and exams offered by the American nonprofit organization College Board. AP Calculus AB covers basic introductions to limits, derivatives, and integrals. AP Calculus BC covers all AP Calculus AB topics plus additional topics (including more advanced integration techniques such as integration by parts, Taylor series, parametric equations, vector calculus, polar coordinate functions, and curve interpolations).

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  1. karush

    MHB 217 AP Calculus Exam continous function with k

    217 $f(x)=\begin{cases} \dfrac{(2x+1)(x-2)}{x-2}, &\text{for } x\ne 2 \\[3pt] k, &\text{for } x=2 \\ \end{cases}$$(A)\,0\quad(B)\,1\quad(C)\,2\quad(D)\,3\quad(E)\,5\quad$
  2. karush

    MHB 215 AP Calculus Exam Problem Power Rule

    If $y=(x^3-cos x)^5$, then $y'=$(A) $\quad 5(x^3-\cos x)^4$(B) $\quad 5(3x^2+\sin x)^4$(C) $\quad 5(3x^2+\sin x)^4$(D) $\quad 5(x^3+\sin x)^4(6x+\cos x)$(E) $\quad 5(x^3+\cos x)^4(3x+\sin x)$ ok I am sure this could be worded better. but I think many students take these tests and are not used...
  3. karush

    MHB 214 AP Calculus Exam velocity

    $\tiny{207 \quad DOY}$ A particle moves along the x-axis. The velocity of the particle at time t is $6t - t^2$. What is the total distance traveled by the particle from time $t = 0$ to $t = 3$ ? $(A)\,3 \quad (B)\,6 \quad (C)\,9 \quad (D)\,18\quad (E) \, 27$ ok think this is correct...
  4. karush

    MHB 1.1.4 AP Calculus Exam Problem int sec x tan x dx

    $\tiny{213(DOY)}$ $\displaystyle\int \sec x \tan x \: dx =$ (A) $\sec x + C$ (B) $\tan x + C$ (C) $\dfrac{\sec^2 x}{2}+ C$ (D) $\dfrac {tan^2 x}{2}+C $ (E) $\dfrac{\sec^2 x \tan^2 x }{2}+ C$
  5. karush

    MHB 2.2.212 AP Calculus Exam problem find increasing interval

    212 Let f be the function given by $f(x)=300x-x^3$ On which of the following intervals is the function f increasing (A) $\quad (-\infty,-10]\cup [10,\infty)$ (B) $\quad [-10,10]$ (C) $\quad [0,10]$ only (D) $\quad [0,10\sqrt{3}]$ only (E) $\quad [0,\infty]$ Steps ok this was a little...
  6. karush

    MHB 2.2.211 AP Calculus Exam practice problem

    211(DOY) If If $y=x \sin x,$ then $\dfrac{dy}{dx}=$ (A) $\sin x + \cos x$ (B) $\sin x + x \cos x$ (C) $\sin x + \cos x$ (D) $x(\sin x + \cos x)$ (E) $x(\sin x - \cos x)$ Solution ok this is a relatively simple problem but was wondering if $y'$ should be used in combination with...
  7. karush

    MHB 210 AP Calculus Exam problem tangent line to curve

    Find the slope of the tangent line to the graph of $$f(x)=-x^2+4\sqrt{x}$$ at $x=4$ (A) $8-$ (B) $-10$ (C) $-9$ (D) $-5$ (E) $-7$
  8. karush

    MHB 2.1.207 AP calculus practice exam problem Lim with tan(4X)/6x

    $\displaystyle\lim_{{x}\to{0}}\left(\frac{\tan 4x}{6x}\right)=$ (A) $\dfrac{1}{3}$ (B) $\dfrac{2}{3}$ (C) 0 (D) $-\dfrac{2}{3}$ (E) DNE solution direct substitution of 0 results in undeterminant so use LH'R so then after taking d/dx of numerator and denominator and factor out constant we...
  9. karush

    MHB 2.2.206 AP Calculus Practice question derivative of a composite sine

    206 (day of year number) If $f(x)=\sin{(\ln{(2x)})}$, then $f'(x)=$ (A) $\dfrac{\sin{(\ln{(2x)}}}{2x}$ (B) $\dfrac{\cos{(\ln{(2x)}}}{x}$ (C) $\dfrac{\cos{(\ln{(2x)}}}{2x}$ (D) $\cos{\left(\dfrac{1}{2x}\right)}$ Ok W|A returned (B) $\dfrac{\cos{(\ln{(2x)}}}{x}$ but I didn't understand why...
  10. karush

    MHB 1.1.205 AP calculus exam practice question

    given that $\left[ f(x)=x-2, \quad g(x)=\dfrac{x}{x^2+1}\right]$ find $f(g(-2))$ (A) $\dfrac{-11}{5}$ (B) $\dfrac{-4}{17}$ (C) $-3$ (D) $\dfrac{14}{85}$ (E) $\dfrac{-12}{5}$ _____________________________________________________________________________ Solution find $g(-2)$...
  11. karush

    MHB 4.2.204 AP calculus practice question

    If $\displaystyle f(x)=\int_1^{x^3}\dfrac{1}{1+\ln t}\, dt$ for $x\ge 1$ then $f'(2)=$ (A) $\dfrac{1}{1+\ln 2}$ (B) $\dfrac{12}{1+\ln 2}$ (C) $\dfrac{1}{1+\ln 8}$ (D) $\dfrac{12}{1+\ln 8}$ ok I am little be baffled by this one due the $x^3$ in the limits since from homework you just take...
  12. karush

    MHB 1.4.203 AP calculus practice question on Limits

    I am posting some AP calculus practice questions on MeWe so thot I would pass them thru here first The solution is mine... any typos or suggestions... $\textbf{Find the Limit of}$ $\displaystyle\lim_{x\to \pi} \dfrac{\cos{x}+\sin{x}+1}{x^2-\pi^2}$ (A) $-\dfrac{1}{2\pi}$ (B) $\dfrac{1}{\pi}$...
  13. N

    Maximum Velocity for different accelerations

    Homework Statement Force of jet= A(r(t))4/3 A: constant determined by the fighter model in the class being considered and the drag force on the plane r(t): the rate of fuel consumption as a function of time Consider 3 possible situations for r(t): 1. when the rate is constant for the...
  14. N

    Finding velocity with constant, incre., decrea, varying acce

    Homework Statement Force of jet= A(r(t))4/3 A: constant determined by the fighter model in the class being considered and the drag force on the plane r(t): the rate of fuel consumption as a function of time Consider 3 possible situations for r(t): 1. when the rate is constant for the...
  15. C

    AP Calculus BC: Differentiability and continuity

    Homework Statement The function h is differentiable, and for all values of x, h(x)=h(2-x) Which of the following statements must be true? 1. Integral (from 0 to 2) h(x) dx >0 2. h'(1)=0 3.h'(0)=h'(2)=1 A. 1 only B.2 only C. 3 only D. 2 &3 only E. 1,2 &3 Homework Equations None that I am...
  16. karush

    MHB 10) AP Calculus linear functions

    $\textbf{10)} \\ f(x)\text{ is continuous at all } \textit{x} \\ \displaystyle f(0)=2, \, f'(0)=-3,\, f''(0)=0 $ $\text{let} \textbf{ g } \text{be a function whose derivative is given by}\\ \displaystyle g'(x)=e^{-2 x} (3f(x))+2f'(x) \text{ for all x}\\$ $\text{a) write an equation of the...
  17. N

    High School Calculus Velocity question

    Homework Statement If you throw a ball straight down from a building that is 443 meters tall with a velocity of 22 m/s how long would it take to reach the ground, and what would be its speed at impact? Homework Equations Since the ball is being thrown down with a velocity of 22 m/s I plug that...
  18. nomadreid

    Find k in AP Calculus BC problem

    Homework Statement Given path (x,y) described by dx/dt = 1/(t+1), dy/dt = k*exp(kt), constant k > 0. At t = 2 the tangent is parallel to y = 4x + 3. Find k. The given solution: approx. 0.495 . Homework Equations (dy/dt)/(dx/dt) = dy/dx = slope of tangent of path The Attempt at a Solution...
  19. E

    Studying Comparing AP Calculus to College Calculus

    Hello everyone, I was just wondering what AP Calculus is compared to a regular college class and if they are comparable. For example does AP Calculus teach computational skills over conceptual over vise-versa? Or how does the AP Calculus curriculum compare to a regular college calculus class...
  20. E

    Is it possible to self-teach Calculus BC in 3 months?

    Hello I am self teaching myself AP Calculus BC and the exam is on May 5. I was wondering if there were any good online resources for me to use online and I have a textbook which is James Stewarts Calculus 5th Edition. Do you think this is possible to self teach myself Calculus BC in 3 months...
  21. I

    Schools How Rigorous are High School Calculus classes?

    Hello everyone, I'm a high school student and wondering about the rigor of the AP Calculus classes that U.S. high school students often take. When I say rigor here, I'm talking about mathematical rigor as is commonly talked about with regard to math classes, and also whether or not the class is...
  22. Astro826

    I really with my course selection for next year

    Hi guys, I really need help with deciding my courses for next year. Currently, I'm a sophomore in high school rising to a junior next year, and today, we began doing course selections for next year. Now, before I continue, I didn't just start thinking about my courses for next year today. I've...
  23. Calaver

    How should I claim mathematics credit for self study?

    Hello everyone, I am currently a sophomore in high school (year 10 by the US system), with two years before I graduate to university. Last year, I began to learn calculus and physics on my own because they interested me. There is more to this story, but basically I seem to be at a crossroads now...
  24. J

    Self-study AP Physics C after taking IB Physics SL & Calc?

    I am a current High School senior intending on majoring in Physics in college. Last year I took IB Physics SL and got a 4 on the test but kept my head above water on all the unit tests. I'm currently taking AP Calculus BC and am doing very well. I have exhausted all other science classes in my...
  25. M

    Other AP textbooks for Physics and Calculus

    Hi, I'm studying on my own for AP exams a year from now and need some advice on which books to get. I'm taking AP calculus (AB or BC, haven't decided yet), AP Physics 1, AP Physics 2, AP Physics C: Electricity and Magnetism, and AP Physics C: Mechanics. I already have a Calculus book by Ron...
  26. MRrelativity

    AP Calculus teacher not very good

    Hello forum, I'm a high school senior, who is taking a AP Calculus course, I enjoy math a lot and I'm attending Missouri S&T next fall to pursue a degree in physics. My problem is my AP Calculus teacher is not a very good teacher, I've even talked to others in my class about this and most of...
  27. S

    MHB AP Calculus AB Free Response Question

    I needed help on this AB Calculus Free Response Question: A particle moves along the x-axis do that its velocity $v$ at time $t \ge 0$ is given by $v(t) = \sin( t^2)$ for the interval $0 \le t \le \sqrt{5\pi}$. The position of the particle at time $t$ is $x(t)$ and its position at time $t = 0$...
  28. icecubebeast

    AP Calculus AB vs AP Calculus BC Exams?

    Hello, I was wondering if I should take the AP Calculus AB exam first or just take the AP Calculus BC exam. I am currently learning AP Calculus BC and my friends say that you have to take both in order to get college credit for both (I'm skeptical of this). Since AP Calculus BC covers the same...
  29. J

    Find Volumes of Rotated Solids in AP Calc

    Homework Statement 1. R is the shaded region in the 1st quadrant bounded by the graph of y=4ln(3-x), the horizontal line y=6, and the vertical line x=2 Find the volume of the solid when revolved about the horizontal line y=8 2. Let R be the region in the 1st quadrant enclosed by the graphs of...
  30. N

    Do I Need to Take Calculus II at MIT if I Get a 5 on AP Calculus BC?

    If I get a 5 on AP Calculus BC, do I still have to take Calculus II at MIT? Or I don't have to take it?
  31. B

    AP calculus AB, 2 related problems

    Homework Statement First problem: Data in the form of a table is given for all integers x in [-2,3], f(x), g(x), f'(x), and g'(x) Given that h(x) = g(2/x), find h'(2/3) Second problem: Given g(x) = ∫2-3xx2 f(t) dt, and h(x) = g(x2), find the derivative of h'(x)? Lower bound on the integral...
  32. D

    Reviewing AP Calculus 1999 exam instantaneous rate problem

    The graph of the function f, consisting of three line segments, is given below(#5) "[URL Number 5, collegeboard website[/URL] a)compute g(4) and g(-2) I have no idea how they got to that solution. I have been looking at it for a long time and still do not understand! Please help!
  33. G

    Derivative of a Quadratic Function: Understanding the Use of cis(x)

    Homework Statement Hi, My teacher marked me wrong when I was asked to find the derivative of -x^2 - 2x + 8 it was a review for the AP test were we just review everything and I put 2cis(pi)x - 2 she marked it wrong and put a question mark over cis(pi)... What's up with this...
  34. P

    Preparing for the AP Calculus AB/BC Exam

    Homework Statement Anybody know any good websites or notes for review for the AP Cal AB or BC exam? I know sparknotes have some good notes as well as course notes. - Thanks
  35. G

    AP Calculus AB Solutions 1969-1978 willing to trade

    I'm in need of the solutions/scoring guidelines to the AP Calculus AB Free Response Questions 1969-1978... I have the questions I just need the solutions/scoring guidelines only If anybody would like to share this document that would be wonderful it would really help me out in studying for this...
  36. G

    AP Calculus AB Scoring Guidelines Prior to 1998?

    Homework Statement Do they even exist? I can't find them anywhere! I know they must exist... does anybody know where to find them... these are the scoring guidelines for the AP Calculus AB exam that they put out for the free response questions... I can't find any prior to 1998 and the...
  37. N

    Schools My high school doesn't have AP Calculus

    To kick off my first post here I will begin with a desperate plea for help and guidance: My high school is unfortunately not one of the best by any means. It is gigantic and has over 3000 students in it, meaning that most of the focus is spent on teaching students who don't give a damn about...
  38. Char. Limit

    What's Next After AP Calculus BC?

    I am a high school senior seriously interested in mathematics (and physics, and chemistry, but that's beside the point). I am wondering what would be the best path for me to learn involving mathematics now that the AP Calculus test is over (I don't want to have to wait until September to...
  39. E

    AP Calculus BC Test: Tips, Revision & Important Topics

    Hello! I am writing the AP CALCULUS BC test on 5 May, 2010.All the best to all people who are writing their AP tests. Does anybody have any tips/ suggestions for revision or some ideas about really important/expected topics? Thank you. Elixer
  40. jacksonpeeble

    College Board AP Calculus Exams

    I've recently started thinking about which exam I want to take for AP Calculus, and I'm wondering from those of you who have taken it or know details - is the AB or BC exam recommended? I've taken all of the AB and BC material, but I'm not sure if I can handle that quantity of material or want...
  41. Char. Limit

    Ace Your AP Calculus Midterm: Tips & Tricks!

    Hello, I have an AP Calculus midterm tomorrow and was wondering if anyone had any tips or tricks to help me succeed. The course material covers finding derivatives of any single-variable function, applying them in optimization and related rates, integral approximation, finding the integral by...
  42. F

    Studying What Are the Best Resources for Self-Studying AP Calculus BC?

    I am self-studying ap calculus bc. I need someone to recommand me a good prep book. I will also get a tutor. If possible also give me a link with good worksheets and solutions. please give me the link of the picture of the prep book you recommand I hear PR and Barron are pretty bad.
  43. L

    Continuous Function Problems AP Calculus

    Homework Statement Let f be the function given by f(x)= (x-1)(x²-4)/ (x²-a). For What Positive Values of a is f continuous for all real numbers x? Homework Equations The Attempt at a Solution What I tried doing was separating the (x²-4) into (x+2)(x-2) then moving along from...
  44. I

    Finding an Advanced Math Topic for AP Calculus AB Project

    This is a bit different kind of help that I need compared to most other threads in this forum. I was not sure of where exactly to post this. But, since it is pretty much homework, and it's for my AP Calculus AB course, I thought this would be an appropriate place to put this thread. If not...
  45. S

    AP Calculus AB & Macroeconomics Book Recommendations

    I'm taking the AP class on calculus AB, and I want to order a book. Anyone would recommend one? I think the Princeton Review is the best one, but the Kaplan's and Barron's seems good too, so any opinion would help. Also I'm taking AP macroeconomics. I know this is not a a topic that people...
  46. M

    AP physics b and ap calculus ab

    does anyone know where i can find ap cal and/or phyics multiple choice sections of past tests?? i really need them to study. please help
  47. S

    Testing AP Calculus AB Exam: Advice Needed

    Anybody taken the ap calculus ab exam? I'm taking the class right now, just curious to what you think about the exam. I expect it to be rather easy. ap calculus seems oversimplified. advice?
  48. L

    AP Calculus Questions: Everything You Need to Know for Success

    Here are some questions I have concerning AP Calculus that I have compiled while doing my homework assignments. Please help me answer them. Thank you very much! Questions: -Do you never need to worry about the chain rule when integrating? I'll add on to these questions when I have more.
  49. C

    AP calculus, implicit derivatives

    Homework Statement 1. Given the curve x² - xy + y² = 9 (a) Write a general expression for the slope of the curve (b) find the coordinates of the points on the curve where the tangents are vertical (c) at the point (0,3) find the rate of change in the slope of the curve with respect to x...
  50. D

    Help with old AP Calculus problems?

    I have been working for over 6 hours trying to break these problems down (my first calc problems!), but I cannot get any major breakthroughs. I have made minor strides in each but have hit a wall. If any of you can offer explanations, work, anything, I would be eternally grateful! #1 Let h(x)...
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