A. P. Calculus - AB (alpha)

Remember -- Calculus lunch on Wednesday. Bring your calculators.

For Wednesday, January 17:
Here are five optimization problems to try. We can go over the different type of problems at lunch.
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For Wednesday, January 10:
Have a go at the following problems. I uploaded a PDF of the problems if you want to print them out. We will go over them on Wednesday during lunch.

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For Tuesday, January 9:
Do the following three problems:
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For Monday, January 8:
Page 234, problems 40, 53, 55 and the following two questions. Also, do the calculator problems that follow the questions.

1. An Australian rancher wants to build a rectangular enclosure to house his flock of emus. He only has $900 (Australian) to spend on the fence and he wants to get the largest area possible for his $900. Being the clever guy that he is, he plans to build the enclosure along a river to save the cost of fence on that side. The side of the fence that is parallel to the river will cost $5 per foot, whereas the sides perpendicular to the river only cost $3 per foot. What dimensions should he make his enclosure, mate?

2. Find the area of the largest rectangle that has two vertices on the x- axis and two vertices on the curve, y = 9 - x^2 (y equals nine minus x - squared).
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For Thursday, January 4:
Two problems, on page 234, problem 47 and problem 56. 56 is multiple choice, but I hope you are under no illusions that simply picking an answer is acceptable. I want to see how you set up the problem.
ALSO: (give answers rounded to 3 - decimal places.)
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If you want to print the problems:

For Tuesday, December 19:
Finish the problems that were assigned for today. We will also look at a different kind of optimization problem with the problem lying in the xy - coordinate plane.

For Monday, December 18:
Page 231, problems 16 (note the can in this problem has only one end, so the surface area is only πr^2 + 2πrh) and 30.
Page 262, problem 47.
Also the following problem:
Anna is in a rowboat 3 miles from a straight coast. She wants to go to George's house 2 miles down the coast. Anna can row at 4 mph and can jog at 6 mph. Where should she land on the coast in order to arrive at George's house in the shortest time possible.

For Friday, December 15:
Page 230, problems 2, 7, 13 and 15.
As it turns out, I don't have an optimization cheatsheet, but I will put one together. For now, remember:
1. Identify the entity to be optimized.
2. Make a function for the entity you are trying to optimize.
3. Relate the unknowns in your function using the limiting condition.
4. Substitute to eliminate all but one unknown.
5. Differentiate the function with respect to your remaining unknown.
6. Set the derivative equal to zero and solve for your one unknown. This will be your optimized value.
7. Re-read and answer the question.

For Tuesday, December 12:
Page 260, problems 3 and 4. Please be sure to read the directions above the problems. Also, 17, 18 and 32.

For Monday, December 11:
First, finish up any of the work from the past two days that you have not done, including the multiple choice problems I handed out in class.
Then, on page 221, problem 51, and on page 264, problem 70. For problem 70, do it as if you were doing it for the exam so that we can also talk about how to answer free response questions (FRQ's).

For Friday, December 8:
Finish up the work for Thursday, and page 199, problems 45 - 49. Page 261, problem 32.

For Thursday, December 7:
This assignment is for Thursday. If you have looked at it and want to talk about some of the questions, we can do so at lunch on Wednesday.
Page 219, problems 1, 3, 4, and 5 (don't bother with graphing). Also, problem 8, 13, 17, and 21 - 24.

For Tuesday, December 5:
Look for extremes at 3 places:
1. dy/dx = 0,
2. dy/dx does not exist,
3. endpoints.
On page 198, problems 1-10. Don't bother copying the graphs. Do problems 28 and 50.

For Monday, December 4:
Page 198, problems 19, 21, 23, 27 and 29. Find all maximums and minimums, see if you can identify whether they are maximums or minimums and whether they are absolute or local. (See definitions on page 191 and 193 if you are not clear what local/absolute mean.)

Honors Pre-Calculus -- Delta
For Wednesday, January 10:
On page 313 of the problem set 3.6 that I handed out, graph the functions in 45, 46, 47 and 48. There are some tricky aspects of these curves so you will have to plot some points or use the sign analysis that we were doing in class to confirm the behaviour of your curves. If you need to get a lttle help, I have posted the curves in the hall outside my office.

For Monday, January 8:
Finish the problems we were working on in class, which includes problem 21 and y = 1/x^2.
Also, graph the rational functions in problems 37 and 44.

For Thursday, January 4:
On the "Exercises 3.6" worksheet that I handed out in class, first, graph the functions in problems 25, 27, and 28 on page 313. Then, graph the function in problem 1 on page 312. Ignore any other directions on the worksheet itself. I only want you to graph the functions. Use separate axes for each curve. Identify any specific information you used to define your curve. Use words, but you may use "H.A." for horizontal asymptote and "V.A." for vertical asymptote. Remember all the requirements for an acceptable set of axes in the xy - coordinate plane.

For Wednesday, December 20:
On the 3.6 exercises, problems 15 - 24 and 33 - 44, identify all rational functions that have the x - axis as a horizontal asymptote as x ---> -∞ and as x ---> + ∞. You do not have to copy all of the functions, just list the problems that do have the horizontal asymptote.
ALSO, I will collect the packet that we have been working on. It must be complete and have your name on it.

For Tuesday, December 19:
From the packet of exercises that I handed out (3.6 Exercises), for problems 15 - 24, identify all vertical asymptotes. Don't forget to copy the correct problem.

For Monday, December 18:
No homework, but those who have not finished the in-class opportunities must have them to hand in Monday morning. We will begin working on Rational Functions of Monday.

For Friday, December 15:
Don't forget we will use the double period for a small in-class opportunity. It will not include end behaviour.

For Thursday, December 14:
See if you can understand and fill out the following table. The table describes the end behaviour of polynomials, depending on the character of the function's leading term. I have included a downloadable, printable version below the picture so that you can print it and do your work on the printed version. Keep in mind that n means the leading exponent and a sub n means the coefficient of the leading term of any polynomial.
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For Wednesday, December 13:
For problems 51, 52 and 53 on the "Section 2.4 Exercises" worksheet, find the possible rational zeroes and all actual rational zeroes. If you can, then find the irrational and imaginary zeroes if there are any.

For Monday, December 11:
Good work on Friday.
On the handout with the Section 2.4 exercises, problem 12 using synthetic substitution to do the division. Also, problems 13, 16, 21 and 24. Finally, for problems 33 and 34, determine what are the POSSIBLE rational zeroes.

For Friday, December 8:
For each of the following polynomial functions in 37 - 40, value the function at x = 1, x = 2, and x = -2, using synthetic substitution.
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ALSO Do the division by synthetic substitution in 23 and 24 below.

Honors Pre-Calculus -- Zeta
For Wednesday, January 17:
On the problem sheet that I handed out and previously misidentified, on page 313, graph the functions in 45, 46, 47 and 48. There are some tricky aspects of these curves so you will have to plot some points or use the sign analysis that we were doing in class to confirm the behaviour of your curves. If you need to get a little help, I have posted the curves in the hall outside my office.

For Wednesday, January 10:
On the section 6.1 problem set that I handed out, let's try graphing the functions in 20, 21, 22 and 24.

For Tuesday, January 9:
On page 313 of the rational functions problems packet, graph 29 - 32.

For Monday, January 8:
We will look at the work that was assigned for Thursday.

For Thursday, January 4:
On page 313, problem 5. I want you to graph it. Start by using what we know -- vertical asymptotes and intercepts. Then, make a table of values, plug in a few values and see if you can figure out what the horizontal asymptote is. Remember, the horizontal asymptote is the value the function approaches as x gets big in both a negative and positive direction. Read the section on Horizontal Asymptotes in the toolkit and see if you can understand how we analyze end behaviour of rational functions.
P.S. - Check out the directions for Wednesday about what you were supposed to read -- Vertical Asymptotes.

For Wednesday, January 3:
Read in the graphing toolkit, the section on Vertical Asymptotes and the section on Intercepts. Finish the worksheet that we were working on in class. We w9ll talk about it and I will collect and grade it.

For Wednesday, December 20:
We will begin to talk about rational functions. I need to get all in-class opportunities. Otherwise, no new homework.

For Monday, December 18:
We will do the in-class opportunity on Monday and Tuesday.

For Thursday, December 14:
No homework. Tomorrow, we will go back over end behaviour. We will do the in-class opportunity next Monday and Tuesday.

For Tuesday, December 12:
Think about and see if you can come up with a logical explanation for why we need only look at the leading term of a polynomial to figure out it's end behaviour.
Also, for the following two polynomial functions,
a. find the possible rational zeroes,
b. then find the actual rational zeroes,
c. then find any non-rational zeroes, and finally
d. write the function as a product of linear factors.
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For Monday, December 11:

For Thursday, December 7:
For the following three functions, use the rational zero theorem to find the possible rational zeros for each, and then find the actual zeros using synthetic substitution.
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A.P. Calculus--BC (aka Math Adventures)For Thursday, January 18:
Page 333 (half of the number that won't be mentioned), do problems 52, 54, 56, 58. ALSO, if you did not do the problems for last Thursday (Jan. 11, below), do them.

For Thursday, January 11:Bonjour, tout le monde!!!!Let's make sure we have this slope field stuff down. On page 332, let's do the matching 41 - 46 and on page 377, problems 37-42. You guys can compare answers on Thursday. I also put a few slope field AP practice problems in the packet that I left for the sub that you can do before starting on the practice test.

For Tuesday, January 9:
Read pages 326, starting after example 5. Ignore exploration 1 and read "Slope Fields" through example 7 (don't try to graph these). Then look at example 8 and see if you can understand the matches of the differential equations to the graphs.

For Monday, January 8:
Page 364, problems 47, 48, 51 and 53.

For Thursday, January 4:
Page 361, problems 4 - 10 even and 11 - 14.

For Tuesday, December 19:
Page 415, problem 4 free response. Practice as if it were a test problem and we will talk about it.

For Monday, December 18:
Let's do page 435, problems 20 and 21.

For Friday, December 15:Volumes. On page 411, problems 11, 12, 13, 23 and 24.

For Tuesday, December 12:
Jasper, do the parametric exercises on the worksheet I gave you today.
Others, (I am trying to put some problems up, but the machine is fighting me) do problems 46, 47, 42, 43, 48 and 49 below.

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For Monday, December 11:Jasper, keep working on those integration practice problems.
Everyone, finish the area between curves problems we were working on in class AND on page 399, do problems 1, 3, 4, 53 and 55.