Please note that my PowerGrade grade books uses a grade coding scheme to handle work that has not yet been completed. This can result in grades of 0.01 or grades ending in 0.01. Please see the Class Notes section in PowerGrade for an explanation. Also, please note that quarter grade averages in PowerSchool are almost meaningless until several homeworks, several quizzes, and at least one test are entered. Until then, a single minor assignment can cause a big jump up or down in the average.

Final exam project

You are to make a presentation to the class of 15-25 minutes. The presentation will consist of a demonstration of a method plus at least one problem for the class to do.

Grading will be based on the clarity of your presentation, your understanding of the topic, and your ability to answer questions from the class and the teacher. 10% of your grade will depend on your participation during other students’ presentations. You are expected to be here for all presentations. For every unexcused absence during the presentation period, your grade will be reduced by 20% if your project has not yet been presented, and 10% if your project has already been presented.

Your presentation grade will be based on these points:
(30%) Did you explain the problem itself to the class in a way that they can understand it, and which makes it clear that you understand it?
(30%) Was your presentation clear and free of major errors?
(20%) Did you give the class with an appropriate problem to work on? Did you give them enough time to do the problem? After they did the problem, were you able to demonstrate the answer clearly?
(20%) Were you able to answer questions from the class and from the teacher?

Hannah: Teach the class to solve a differential equation using an integrating factor. (A good source is MIT OCW 18.03, lecture 3. The MIT Open Course Ware series is available free on ITunes U.)

Sylvia: Teach the class to compute arc lengths of curves given in polar form.

Alex:Teach the class to solve equations of the form ay'' +by' +c =0 with initial conditions. Confine yourself to examples where the characteristic equation is factorable and has no repeated roots. (Source: MIT OCW 18.03, lecture 9.)

Alexei: Teach the class the method of logarithmic differentiation.

Maya: Use mathematical induction to prove the binomial theorem.

Important: AP exam instructions. Download and read.

AP Calculus test instructions-29apr16.pdf

Thu, 7 Apr

Review section 8,8. Do #5-15 odd, and #23. Then do problems 2, 5, and 6 on the 2010 BC Form B. (One part of problem 5 involves doing an improper integral, somthing we hadn't seen for a while.)

Below is an old exam that covers the parametric equation and vector material on the test. Ignore the last problem: We haven't done this yet. (It's also the only thing we haven't done yet.) You will also need to look over polar coordinates, which will be a significant part of the coming exam.

Section 12.7 #1-3712. odd by Thursday; by Tuesday, 9 Feb section 12.10 #9-16.

Homework due first class, Mon, 25 Jan

1) (Important!) Prove that the integral from 1 to infinity of 1/x^p converges for p>1 and diverges for p≤1. We will need this fact often when we start our work on series. You're going to need to divide the proof into 2 separate cases, one with p = 1 and one with p ≠ 1, because the anti-derivative of 1/x does not involve the x^(n+1)/(n+1) formula used for the antiderivatives of x^n for n ≠ –1. The proof for the 1/x case is actually already in your notes. Feel free to copy it. In all cases, be careful with your notation. Don't just use infinity as if it were a number.
2) Also, read section 7.7 and do #5-33 odd. PLEASE note the instruction just before problem 5: Only use L'Hôpital's rule when it is appropriate to do so. Otherwise, your answers will be wrong.

Tues, 26 Jan

p. 745 #13-31 odd; p 754 # 5,9, 15, 21

Mon, 25 Jan

Hwk: Read 12.2. Do # 3-21 odd. Quiz next class on L'Hôpital's rule and summing geometric series.If you need a review on geometric series beyond what we did in class, look at Khan Academy or grab an Algebra II book.

## Please note that my PowerGrade grade books uses a grade coding scheme to handle work that has not yet been completed. This can result in grades of 0.01 or grades ending in 0.01. Please see the Class Notes section in PowerGrade for an explanation. Also, please note that quarter grade averages in PowerSchool are almost meaningless until several homeworks, several quizzes, and at least one test are entered. Until then, a single minor assignment can cause a big jump up or down in the average.

Final exam projectYou are to make a presentation to the class of 15-25 minutes. The presentation will consist of a demonstration of a method plus at least one problem for the class to do.

Grading will be based on the clarity of your presentation, your understanding of the topic, and your ability to answer questions from the class and the teacher. 10% of your grade will depend on your participation during other students’ presentations. You are expected to be here for all presentations. For every unexcused absence during the presentation period, your grade will be reduced by 20% if your project has not yet been presented, and 10% if your project has already been presented.

Your presentation grade will be based on these points:

(30%) Did you explain the problem itself to the class in a way that they can understand it, and which makes it clear that you understand it?

(30%) Was your presentation clear and free of major errors?

(20%) Did you give the class with an appropriate problem to work on? Did you give them enough time to do the problem? After they did the problem, were you able to demonstrate the answer clearly?

(20%) Were you able to answer questions from the class and from the teacher?

Hannah: Teach the class to solve a differential equation using an integrating factor. (A good source is MIT OCW 18.03, lecture 3. The MIT Open Course Ware series is available free on ITunes U.)

Sylvia: Teach the class to compute arc lengths of curves given in polar form.

Alex:Teach the class to solve equations of the form ay'' +by' +c =0 with initial conditions. Confine yourself to examples where the characteristic equation is factorable and has no repeated roots. (Source: MIT OCW 18.03, lecture 9.)

Alexei: Teach the class the method of logarithmic differentiation.

Maya: Use mathematical induction to prove the binomial theorem.

## Important: AP exam instructions. Download and read.

## Thu, 7 Apr

Review section 8,8. Do #5-15 odd, and #23. Then do problems 2, 5, and 6 on the 2010 BCForm B.(One part of problem 5 involves doing an improper integral, somthing we hadn't seen for a while.)## Homework for Tues, 29 March

Do this old test.## Review sheet for 29 March test

Below is an old exam that covers the parametric equation and vector material on the test. Ignore the last problem: We haven't done this yet. (It's also the only thing we haven't done yet.) You will also need to look over polar coordinates, which will be a significant part of the coming exam.## Mon, 8 Feb

Section 12.7 #1-3712. odd by Thursday; by Tuesday, 9 Feb section 12.10 #9-16.## Homework due first class, Mon, 25 Jan

1)(Important!)Prove that the integral from 1 to infinity of 1/x^p converges for p>1 and diverges for p≤1. We will need this fact often when we start our work on series. You're going to need to divide the proof into 2 separate cases, one with p = 1 and one with p ≠ 1, because the anti-derivative of 1/x does not involve the x^(n+1)/(n+1) formula used for the antiderivatives of x^n for n ≠ –1. The proof for the 1/x case is actually already in your notes. Feel free to copy it. In all cases, be careful with your notation. Don't just use infinity as if it were a number.2) Also, read section 7.7 and do #5-33 odd. PLEASE note the instruction just before problem 5: Only use L'Hôpital's rule when it is appropriate to do so. Otherwise, your answers will be wrong.

## Tues, 26 Jan

p. 745 #13-31 odd; p 754 # 5,9, 15, 21## Mon, 25 Jan

Hwk: Read 12.2. Do # 3-21 odd. Quiz next class on L'Hôpital's rule and summing geometric series.If you need a review on geometric series beyond what we did in class, look at Khan Academy or grab an Algebra II book.