AP Calculus

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Last Week's Work

Hope you're not too bogged down with the work (Well if you are waiting until the last minute: Shame on You!)

I received this email from one of you and I thought maybe some of you silent ones might have similar questions:
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> Hey Mr. Lemay,
> Just wonder how to do the following problems:
> 16-22 even, 36, 38, 39, 60,61, 63, and 67.
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My reply:

Dear STu Dent:

For 16 - 22:

I've given you the 4 function definitions. What these questions are asking you to do is to find the values of the these "composite functions"

For example if f(x) = 2x-1 and g(x) = the points {(1, 2), (2, 3), (3, 4)}

find (f+g)(2)

This means find f(2) = 2(2)-1 or 3 and g(2) = 3 and add the two numbers together.

OK?

36, 38, and 39 are just exponent properties. A good review/explanation can be found here:

http://www.purplemath.com/modules/exponent.htm

For 60 and 61. Points of intersection can be found by setting the two functions equal and solving for x and then back substituting for y.

Here is good explanation for 60 (a non-linear system)

http://www.purplemath.com/modules/syseqgen3.htm

For 61, try a graphing calculator only I want an exact answer, not a trace answer. Think about the work Mrs. B did you you around the Unit Circle and trig functions (When are Sin x and Cos x the same?)


For 63: Is 0/# = 0? Do we care about when x^3 = 0? Can we just worry about where x^4-1 = 0?

For 67: Take a look at this page: http://www.purplemath.com/modules/ineqrtnl.htm

Hope this helps. Give a yell if you need more help. I'll have you show me what you've tried.

Mr. L.

One of my Summer Precalc students asked:

So I am really taking this course so that I can hopefully do well in calculus next semester. You said that the unit circle is really important but I am having a hard time memorizing it. I am having a hard time with the sine and cosine and figuring out the angle in radians in any quadrant other than the first one. Do you have any segestions (sic) on how I could memorize them easier?

Here is how I replied and if you, as a future Oxbow AP calculus student are also having a difficult time with that part of the summer review, I suggest you do this also:

Part (a) Memorize the sine and cosine of 30^o (π/6), 60^o (π/3) and 45^o (π/4) (see what purplemath.copm recommends on this (the bottom of the page http://www.purplemath.com/modules/specang.htm)

Part B (b) Know how to draw the reference triangle and find the reference angle

Then apply part a to part b remembering ASTC for the + and -

If you need tangent, secant, cosecant or cotangent, just remember the basic identities.

This is how I do these kind of problems.

Here is the work that the AP Calculus class of 2011 needs to complete over the summer.

AP Calculus Summer 2010 Review Packet in PDF format. You need Adobe Acrobat Reader (link).

Students planning to take AP Calculus at Oxbow during the 2010 - 2011 School year must come to class the first day of class with this packet completed. I am available for questions this summer if you have any. Feel free to email me. 

From CB:

Friends - There was another change in the course description which affects how multiple choice questions will be scored. From the course description: "Multiple-choice scores are based on the number of questions answered correctly. Points are not deducted for incorrect answers, and no points are awarded for unanswered questions. Because points are not deducted for incorrect answers, students are encouraged to answer all multiple-choice questions. On any questions students do not know the answer to, students should eliminate as many choices as they can, and then select the best answer among the remaining choices." This same change was announced today for AP Statistics - in the course description for that course. John F. Mahoney Moderator AP Calculus EDG Benjamin Banneker Academic HS Washington, DC

There is a revision in the AP Calculus Course description (Acorn Book) http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/2178.htmllogin "Beginning with the May 2011 exams, the format of the free-response sections of the AP Calculus exams is being modified so that Part A (graphing calculator required) consists of two problems and Part B (no calculator allowed) consists of four problems. There is no change in the multiple choice problems." 30 minutes will be allowed for Part A and 60 minutes will be allowed for Part B. Students will be allowed to continue to work on the Part A problems (without a calculator) during those 60 minutes. John F. Mahoney Moderator, AP Calculus EDG Benjamin Banneker Academic HS Washington, DC 20001

Here is the URL.

http://connect.ctdlc.org/r20216246/

When you're asked to install Adobe Connect, do so. It is a quick browser based download.

I'll be there from 7-9:30 Saturday evening.


Remember that this is an academic college level resource and is not for fooling around.

Here are some old notes that may help. link

Any page references refer to an old precalculus text I used to use. You can ignore them.