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What are good supplemental problem books for calculus?

  1. Feb 25, 2007 #1
    im in ap calculus ab right now, and i think i can say that my teacher intentionally makes the course harder than other ap calc ab classes in other schools. The problems she puts on tests and take home assignments are really hard, and are way different and more difficult than the textbook problems. On several occasions, ive asked my friends from other schools taking or have taken calc ab/bc to help me on take home problems, and many times they were "this is way harder than what my teacher gives."

    so,i guess i just got stick with a crazy teacher. However, i know exactly what i can do to ace the class. Im not good at the problems because they are hard, and i just need to practice doing more problems. The thing is, i need to practice problems that are as hard or even harder than my teacher's problems. Ive purchased this book called "schaum's 3000 problems solved in calculus" but that book was way too easy and ineffective for boosting my problem solving skill. I need a supplmental book with really hard problems. It's kind of like my SAT and SAT 2 prep; i bought the books with generally harder questions than the actual test, which were usually barrons.

    So, to sum it all up, can you guys reccomend me a supplemental problem book with some good, hard problems?

    btw, she did give some hints at times. She told the class many of the test problems and take home problems are taken directly from an ap calculus test prep book. However, she wont tell us the name. She assured us its not a barrons or princeton review or etc. Shje tells us its an obscure brand in california, and they can only be purchased in bulk.
  2. jcsd
  3. Feb 25, 2007 #2
    Well if you want AP-like problems you could buy one of the AP test review books, that would have problems much like those you will see on the AP test. As to your teacher, I would consider a good thing to have a teacher who gives hard problems, because if you think the problems she gives you now are hard, once you become used to them you will likely find the AP test that much easier.
  4. Feb 25, 2007 #3
    she says thats her strategy, and she is focused on preparing students for the ap test, and it will probably pay off on the test day. However, i only pulled a B last semester and im trying to keep my GPA high and finish strong. And i know if i want an A, i will have to practice more with hard problems.
  5. Feb 26, 2007 #4
    I am curious. Give us one of those nasty problems. I wonder how unreasonable your teacher is.
  6. Feb 26, 2007 #5
    Blessing in disguise. Anytime I have a prof who teaches above the level they are supposed to, I always benefit from being pushed. Anyway, if you want some good hard problems:


    Not all of them are calculus related though...
  7. Feb 26, 2007 #6


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    I cannot agree more from my experience. Well designed higher level problems are merely beneficial.
  8. Feb 26, 2007 #7
    lets see
    i cant really show you the really bad ones, since they all involve pictures
    here are some

    this is one from my chapter 4 (applications of derivatives, max and min crap)
    7. [10 points] Roadway plastics manufacturers plastic dome shaped road bumps (used for lane separation) of radius 2 inches. These bumps are in the shape of a cap of a sphere (a slice taken off the top of a sphere). The volume of a road bump of radius 2 inches and height h inches can be calculated:
    the volume is pi/2(h^3/3 + 4h) cubic inches. The wear resistant plastic used costs 30/pi cents per cubic inch. Currently the bumps are 1 inch high, so they cost 65 cents each. The department of safety wants to order new bumps that are higher, and they are willing to pay 68 cents each.

    a. 6 points approxximately how high will the new higher road bumps be? use tangent line approximation and show the equation used to determine your analysis

    linear approximation________

    b. 4 points kwill your estimate be an overestimate or an underestimate? sketch a graph to support your explanation

    on question, i got 1 out of 10 points

    herees another
    10 points let f be a function that is even and continuous on a closed interval [-3, 3]. The function and its derivatives have the following properties

    where x = 0
    f(x) = 1
    f'(x) is undefined
    f''(x) is undefined

    where 0<x<1
    f(x) is positive
    f'(x) os negative
    f''(x) is positive

    where x = 1
    f(x) = f'(x) = f''(x) = 0

    where 1<x<2
    f(x), f'(x), f"(x) are all negative

    where x = 2
    f(x) = -1
    f'(x) and f"(x) are both undefined

    where is in the interval (2,3]
    f(x) is negative
    f'(x) is positive
    f"(x) is negative

    a. 2 points find the x coorinate of each point at which f attains an absolute maximum. justify your answer

    b.2 points find the x coorinate of each point at which f attains an absolute minimum. justify your answer

    c. 2 pointsfind the x coordinate of each point of inflection on f.

    d. 4 points sketch a graph with the given characteristics of f

    on this question, i got 6/10, and i got full points on d.

    she puts alot of LONG problems which are mostly conceptual rather than problem solving, but she also has really nasty problem solving type probl;ems. here are some from our latest take home assignment (we are doing chapter 6 which is antiderivatives/differetial equations) (book work is always optional and is no credit; the only hoemwork grade are the take home assignments)

    a conical tank with radius 4 th and height 10 ft that was initiall full of water is being drained at a rate of root h/6. Find a formul for the depth and the amount of water in the tank at any time t. Recall that the volume of a right circular cone with radius r and height h is V = 1/3 * pi * r^2 *h

    you have to take into account that now after the problems are done, they dont seem as hard anymore (obviously) after going more in depth into the material.
    The thing is, my teacher gives these type of problems before really doing in depth into the material, which makes everyone struggle and do poorly.

    And she never really gives us any practice that reflects what's on her tests, so everyone ends up doing bad on the tests as well.

    So, what i want is, is a supplemtnal problem book with those types of problems so when i do the problems in her class, i can tackle them and get an edge over everyone else.
    I do appreciate the fact she makes hard problems, and i full confidence itll pay off in may. BUT, i still care about my gpa, and the fact that it's this hard gives me a lower letter grade than most of my other classes and lowers my gpa.
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