Welcome to the first assignment for AP BC Calculus students at Athens High School! Athens students in my BC class of 2005-6 please sign the guestbook at the end of this page and introduce yourself after you have completely read the page and mastered the skills required to take BC Calculus.

During the summer I would like you to make sure you have the skills necessary to succeed in Calculus. Among those skills are:

  1. graphing calculator usage,
  2. algebra skills,
  3. trig skills and
  4. analysis of functions and their graphs.

To help you improve those skills over the summer, I would like you to be able to contact me via the Internet warblock@yahoo.com and use the Internet for mathematical purposes. The AP Test in calculus requires that you have these graphing calculator skills: Visit this site for more details: AP BC Calculus site for students
Work through the following problems and e-mail me if you have any questions.

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Graph the following functions:
y=x
y=x2		 y=x3
y =sin x
y= cos x
y=tan x		 y= sec x
y = csc x
y= log x
y=ln x		 y=2x
y=ex
y=arctan x
y=1/x		 y=|x|
y=1/x 2
(During the course of the year you will be expected to produce these graphs without a calculator, but to practice your skills, use one of the AP approved calculators.
    When you graph, see the difference in the trig graphs using degrees and radians,
  1. try creating windows that cover one period, two periods, three periods etc for the trig functions.
  2. As you look at the graph, determine whether the functions are increasing, decreasing, concave up or concave down.
  3. State the domain and range of the functions.
  4. Find the roots (zero’s) of each function.
  5. Discuss the asymptotic behavior, and symmetry of each graph.
  6. Graph some of these graphs simultaneously and find their points of intersection.
  7. Finally, find the points of intersection of x2 and 2x. Find 2 without a calculator and approximate the third to 3 decimal places of accuracy.
If any of these directions are confusing to you e- mail me at warblock@yahoo.com or ask Dr. Math or Mr. Calculus.
Graph y= (1 + 1/x)^x and zoom in at x= 0 many times and see what value the calculator gives you for x= .001, .0000001,.0000000000000001 Also see what values are given for x large such as, x=100, x=10000000, x=100000000000000. See if you can get our calculator to make a table or list of the x and y values you used.
You must be able to solve an equation such as this one from a former AP Test:
  • 78=80-10cos(pi*t/12) accurate to 3 decimal places between 0 and 24.
    Visit my website for additional problems and resources. Warren Block's Homepage
    Use a calculator in degree and radian mode to tell if the following identities are true or false, choose any number you like for x, a and b, for trig functions try 30 degrees or pi/6, pi/4 etc.

    sin ^2 x + cos ^2 x = 1
    | a + b| = |a| + |b|    		 sin 2x = 2 sin x cos x
    ( a + b2 = a2 + b2
    1/a + 1/b= 1/(a + b)
    (x2 - a2)/(x - a) = x + a    		ln a +ln b=ln ab
    x1/2 + y1/2=(x+y)1/2

    • For the false statements can you find some numbers that will make them true? In other words, are they sometimes true and sometimes false. Are there any that are always true? Why? .
    Visit last year's student webpages for advice about the class you are about to take and to see the answers to the 2003, 2004,2005 BC Free Response questions
  • Class of 2003 Webpages placement exam
  • Class of 2004 Webpages placement exam
  • class of 2005 webpages and interactive problems
    Finally, have some fun, try playing these games or finding some other mathematically oriented games on the Internet and if you like them, e-mail me the address so that I can post them, and play them myself.
    1. chaos game
    2. Shack’s Math and Logic Puzzles.
    3. SAMEGAME Play the samegame and figure out the scoring pattern. Find a formula for figuring out the score of clearing 20 at one time.

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