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Topic: Are my students going to ready next fall?
Replies: 1   Last Post: Jun 28, 1998 11:27 AM

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warren block

Posts: 10
Registered: 12/6/04
Are my students going to ready next fall?
Posted: Jun 7, 1998 8:30 PM
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Below is a letter I intend to give to my all my potential enrollees in
next year's AB and BC calculus classes. What other common mathematical
misconceptions and common errors, or fundamental knowledge should be
included. Do you know of any other college placement tests available on
the web? Please respond to the listserve or to me personally at the
address at the bottom. Thanks

June 8, 1998
Dear Incoming Calculus Students,

During the summer I would like you to make sure you have the
skills necessary to succeed in Calculus. Among those skills are
graphing calculator usage, algebra skills, trig skills and 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@hotmail.com or Warren.Block@moa.net) and use the Internet for
mathematical purposes. All of the following information will be
available at my website soon, so visit
http://edcen.ehhs.cmich.edu/~warblock/
If you do not have the Internet at home, use the Troy Public
Library, Oakland University, or OCC. If you have a modem at home, but no
Internet access, you can use Juno for free e-mail access. It does not
give you Internet access, but it does let you communicate with others.
If you do not have an e-mail address, visit me before leaving school and
we can set you up with one at one of the following websites.
l. http://www.hotmail.com (slow but great features)
2. http://www.juno.com/ (free, which is great if you don't have
the Internet access at home)
3.
http://edit.my.yahoo.com/config/form?.form=main_mail&.src=ym&.done=http%3a//edit.my.yahoo.com/config/mail%3f.intl=
(similar to hotmail but I
haven't tried it yet.)

The AP Test in calculus requires that you have these skills:
1. produce the graph of a function within an arbitrary viewing
window,
2. find the zeros of a function,
3. compute the derivative of a function numerically, and
4. compute definite integrals numerically.
If you do not believe me visit this site for more details:
http://www.collegeboard.org/ap/math/html/exam002.html
While we will learn how to do 3 and 4 during the year you should come
prepared to do the following:
1. Graph the following functions: y=x, y=x^2 y= x^3, y= sin x, y = cos
x, y= tan x, y= sec x, y=csc x, y =ln x , y= log10 x, y = 2^x, y = e^x,
y=arctan x, y = 1/x, y= |x| and 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 recommended calculators, a
new list will be coming out soon with the new casio's and TI-89, etc.
For the current list, check this site.
http://www.collegeboard.org/ap/math/html/exam003.html When you
graph, see the difference in the trig graphs using degrees and radians,
try creating windows that cover one period, two periods, three periods
etc for the trig functions. As you look at the graph, determine whether
the functions are increasing, decreasing, concave up or concave down.
State the domain and range of the functions. Find the roots (zero's) of
each function. Discuss the asymptotic behavior, and symmetry of each
graph. Graph some of these graphs simultaneously and find their points
of intersection. (If any of these directions are confusing to you e-
mail me at warblock@hotmail.com or ask Dr. Math at:
http://forum.swarthmore.edu/dr.math/tocs/about.math.high.html or Mr
Calculus at
http://www.geocities.com/Athens/Acropolis/6432/

2. 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.
3. You should be able to write the equation of a line given 2 points
(in slope intercept form y=mx+b and Taylor's form y=m(x-x1) + y1). Find
the slope and equation of the line going through the following points:
a. (0,0) (3,4)
b. (1,-2) (-1,2)
c. (2,3) (-8,-7)
d. (x,c) (x^2,c^2)
e. (x,x+h) (f(x), f(x+h)
f. (1 hour, 10 miles) (2 hours, 50 miles) What does the slope
represent?
For more information on slope visit this page:
http://math.rice.edu/~lanius/Algebra/stress.html

4. 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
ln(ab)=ln a + ln b
| a + b| = |a| + |b|
sin 2x = 2 sin x cos x
( a + b)^2 = a^2 + b^2
1/a + 1/b= 1/(a + b)
(x^2 - a^2)/(x - a) = x + a
For the false statements can you find some numbers that will make them
true? In other words, are they sometimes true and sometimes false. Is
there some way to change them to make them always true? Are
there any that are always true? Why? E-mail me your answers. Later on in
the summer, the answers will be posted.

5. Visit Michigan State University's website to take their sample
exam at: http://deptwww.msu.edu/mtdemo/
6. 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.
http://math.bu.edu/DYSYS/applets/chaos-game.html
http://www.intergalact.com/threedoor/threedoor.html


Warren Block
Troy Athens High School homepage: http://www.troy.k12.mi.us/athens/
4333 John R
Troy, Mi 48098
810-5241200
Warren.Block@moa.net
homepage: http://edcen.ehhs.cmich.edu/~warblock/


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