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Shut Up, Thomas!!!!!

A. P. Calculus - AB (alpha)

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

For Thursday, May 10.
We will talk about the Intermediate Value Theorem, the Mean Value Theorem and the average value of a function. We need practice on our calculators, so please try at least one of the problems in the Calculator use section of the Review Packet. I would recommend you try the three problems on the first page, nos. 31, 32 and 33.

For Wednesday, May 9.
No Calculus lunch.

For Monday, May 7.
In the "Riemann Sums" section of the review packet, do problem 6 on page 618.

For Friday, May 4.
On the AP Review packet, do problems 1 and 2 on page 210 in Section 2, "Extremes, First Derivative Test, Second Derivative Test Points of Inflection."

For Thursday, April 26.
I am not going to be assigning homework during the review period. Each day, as we address a different topic, I will provide you with a packet of representative AP problems. We will not get to all of them during the class session. You can do them on your own to firm up your understanding of the material. Here is our review schedule as it now stands:
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For Monday, April 23:
Enjoy your weekend!!!!!

For Thursday, April 19:
Page 331, problems 25-28, 29, 31, 33 (Draw your own little grids -- they do not have to be on graph paper), and for 35 - 46, just do the matching. For the matching problems, you do not have to copy the slope field onto your papers.

For Tuesday, April 16:
Watch the video that I am putting up about slope fields. It is called Slope Fields Introduction. It is here Slope Fields .
Have a good weekend!!!!

For Friday, April 13:
Page 331, problems 8 - 10 and 14 - 16. Also page 361, 1 - 3.

For Monday, April 8:
Tuesday in-class opportunity covering applications of the integral. That means, average value of a function, total accumulation as the area under a rate curve, areas between curves in the xy - coordinate plane, volumes (those weird ones with a specified cross section) and volumes of rotation around both the x and the y axes.
Homework, try these, page 434, problems 2, 12, 21a. Do 53 and 55 (page 437). You may use the calculators to calculate these integrals. The important part is how do you set up the integrals. Also, try 21c, which involves rotating around the line y = 4. I have added a video (( Rotation around other than the axes )) about how to find volumes of revolution about lines other than the x or y axis. OK, take note -- I put the video up. It is called "Rotation around other than the x or y axes"). I get through setting up the integral and then my computer ran out of juice. I don't get through the full integration. However, it is a simple polynomial integrand, so that is not the challenging part. The video does demonstrate how to set up the integral, which is what we have not gone over in class, so it is worth watching.

For Friday, April 5:
Page 411, problems 29b and 32. Page 435, problems 21b and 22a.

For Wednesday, April 4:
Page 435, problems 20, 24 and 25.

I put up two videos that run back over finding volumes of rotation of areas between two curves. There are two videos because I stopped to get some work from Sebastian, but apparently one can't stop and then resume the video shoot. They are titled "Rotation of Areas Between Curves" 1 and 2. Roation of Area Between Curves

For Thursday, March 22:
Page 411, problems 3, 4, 12, 13 and 14.
Here is a re-cap of how to calculate a volume of rotation **Volume of rotation**

For Tuesday, March 20:
OK, remember. The integral of the cross-section is the volume of our solid.
Let's try page 410, problems 1c, 1d, 2a and 2b.
ALSO, I tried something to help you with this. This link is a quick review of volumes through integration. Volumes by Integration Let me know if you can access this thing, if you can play it and if it helps at all.
TOMORROW'S MINI IN-CLASS WILL AGAIN BE ABOUT DERIVATIVES.








Honors Pre-Calculus -- Delta
For Wednesday, May 9.
In exercises 7.4 (inverse trig functions) do problems 34 - 38. You will have to think a little about how to tackle 37 and 38. You can do it.

For Monday, May 7.
On the Inverse Trig packet, Exercises 7.4, do problems 13 - 25 odd, and try problem 29.

For Friday, May 4.
The domain of the inverse tangent function is the same as with the inverse sine function -π/2 ≤ y ≤ π/2. With that in mind, do problems 4 a, b, 6 a, b, c and 7 a, b in the 7.4 exercises in the packet we were looking at in class today.

For Thursday, April 26.
On PAGE 568 of the packet, exercises 7.5, 11 through 16. Remember, we are finding the general solution to these problems.

For Thursday, April 26.
On page 568 of the handout I gave out today (exercises 7.5), do problems 1 - 9 odd. Remember, for each function value there are two angles between 0 and 2π that have that function value, with the exception of sine and cosine equal to 1 and - 1. Also, for each solution, we must add k2π, where k is any integer, to capture all the angles from - ∞ to + ∞ that are solutions.

For Monday, April 23:
Let's do a few more identities, since everyone did such good work on Friday. On the identities worksheet, (Section 7.1 Exercises) problems 70, 71, 73, 75, 84 and 88.

For Thursday, April 19:
From the identities worksheet (Section 7.1 Exercises) 29, 30, 34, 35, 36, 37 and 38

For Wednesday, April 18:
Complete the trig identity puzzle.

For Friday, April 13:
No homework. I figure everyone needs a bit of a rest.

For Thursday, April 12:

For Monday, April 8:
Everyone has to start the in-class opportunity by Monday.

For Wednesday, March 21:
On the same worksheet used for Monday, graph 9, 11, 15, 18, 20 and 25.

For Monday, March 19:
On the attached document, do problems 1, 2, 5, 6 and 41. For 41, just see if you can figure out the amplitude (a) and the period. Do not be concerned with the phase shift.


For Friday, March 16:
Finish the graphing sine and cosine worksheet.

For Thursday, March 15:
For problems 1 - 6 below, convert each angle to radians if given in degrees, and to degrees if given in radians (do not worry about the reference angle). For 1 - 6, you do not need to copy the given problem angle.
Then, do problems 9 - 14 and 21 - 26. Please copy the original problem onto your paper for these problems






Honors Pre-Calculus -- Zeta
For Wednesday, May 9.
Using the Law of Cosines, at least for the first calculation, in Exercises 6.5 (same packet as Law of Sines), problems 1, 6, 9 and 10.

For Tuesday, May 8.
In the law of sines worksheet, exercises 6.4, problems 36 (Radio antanna), 38 (Length of a guy wire), and 40 (calculating an angle).

For Monday, May 7.
In the law of sines packet, exercises 6.4, problems 19, 21, 23 and 25. Solve the triangles. If there is more than one triangle, find both. If there are no triangles with the given measures, explain.

For Thursday, April 26.
Evaluate the following inverse trig expressions:
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For Monday, April 23:
We have our minor in-class opportunity coming up on simplifying trig expressions, verifying identities and solving trig equations.

For Wednesday, April 18:
On the trig equations worksheet (section 7.5) problems 21, 22, 24, 35 and 48. For 48, note that they only ask for the solutions between 0 and 2π.

For Tuesday, April 17:
In the packet, 7.5 exercises, problems 4, 7, 8, 13, 14 and 16.
Have a terrific weekend!!!!

For Wednesday, April 11:
On the trig identities worksheet, let's do 30, 35, 45, 47, and 51.

For Tuesday, April 10:
On the trig identities worksheet, problems 52, 53, 55, 57 and 59.


For Monday, April 8:
On the trig identities worksheet (7.1 exercises), let's do numbers 27, 29, 34, 36, 37, 38, 39, 46 and 48.

For Wednesday, April 4:
Do the following problems (9 - 20). Remember, the first rule of simplifying trig expressions is:
1. Go back to the basic functions -- sine and cosine, and sometimes tangent.
Rule number 3 is:
3. Look for Pythagorean Identities.
You remember the three Pythagorean Identities, right:
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and from those, the following are also true:

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For Wednesday, March 21:
In-class opportunity on everything to do with trig functions in the unit circle. This includes:


For Tuesday, March 20:
Find equations for and graph the following:
1. The tide was 4.5 feet deep at noon and rising. At it's highest, it is 12 feet deep and at its lowest it is 2 feet deep. It takes 12 hours to go from high to low to high tide again. Plot a graph of the depth of the water as a function of time, with t = 0 being noon.
2. You are riding a ferris wheel that has a diameter of 80 feet. Where you get on you are at 7 feet above the ground. The ferris wheel keeps loading people until you are at 67 feet (and still climbing). Then it starts the ride and you time it to make a full circle in 84 seconds. Plot your height above ground as a function of time, with t = 0 being when the ride started running steadily.


For Monday, March 19:
No homework for Monday.









A.P. Calculus--BC (aka Math Adventures)
For Friday, April 13:

For Monday, April 8:
Clue, problems 13. For Clue problems 12, the suspect problem is the inverse tangent, and the treasure problem is integration using shells, neither of which we are familiar with. I will walk you through them. I don't think shells matter for the test, but you might want to know the derivative of the inverse tangent.

For Friday, April 5:
Do Clue problems 12. 12 location is integration with shells, which we have never talked about, so don't bother unless you want to.

For Thursday, April 5:
In CLUE, problems 9 and 10. We will do some length of curve problems in class.

For Thursday, March 22:
Pages 7 and 8 on the Parametrics worksheet.

For Tuesday, March 20:
Let's get through page 6 on the parametrics worksheet. You may need to look up a couple of formulations for arc length or areas of polar curves. We will look at the Clue problems 8 as well.