The road to Christmas break

First, here are the solutions for the Chapter 5 questions.

Secondly, here is the proposed syllabus up to Christmas Break.
12/17  5.3  Rules for Definite Integrals  HW p.290-291/1-17
12/21  5.3  Derivatives of Definite Integrals
                      HW p.291-293/19-37 odd,38,39,41,45-51 odd
12/22  5.4  Fundamental Theorem of Calculus  HW p.29
12/23  5.4  Fun Activity using Calculus

12/24 - 1/3 Christmas Break (Rest and Enjoy!)

Starting Ch 5 - The other half of Calculus

We have explored how to find the slope of any curve and many applications of knowing that rate of change. That was the first half of the Big Ideas of Calculus. Chapter 5 starts us on the path to the other Big Idea of Calculus - Integrals (definition to come soon!)

12/15 5.1 Estimating with Finite Sums (RAM) HW p.270/4-9,15,18,23-25,29,31-40
12/16 5.2 Riemann Sums -> Definite Integrals HW p.282-283/3-39 by 3's, 47-56

L'Hopital's Rule recap

The examples took all the time so let me recap when and how to use L'Hopital's Rule:

1.  Try to evaluate the limit. If the form is indeterminate, you may use L'Hopital's Rule

2.  Make sure the limit is written as a fraction (it must be in the 0/0 or infinity/infinity
     form).  You may have to rewrite the limit using logs or h = 1/x.

3.  Apply L'Hopital's Rule. Did you get a limit? Something undefined? You are done.

4.  Did you get another indeterminate form?  Apply L'Hopital's Rule again.

Remember that factoring, simplifying, applying other known limits and other limit techniques are always available.  Just because we are learning a new technique does not mean it is always the technique that can and should be used!

Ch 4 Answers

I am again posting the answer key for the textbook homework problems here. Remember: really try before going to the answer key. And do all of your homework!

All of Chapter 4 - Applications of the Derivative

Chapter 4 is about using derivatives to solve problems. Some are fun, some may be difficult, many will seem artificial but all of them are good for you. You may notice that there are no quizzes posted though this is a month long chapter. They could happen at any time. Curve sketching, optimization and related rates make excellent one question quiz topics. Be ready.

11/10   Interpreting the Derivative
11/11   Veterans' Day - no school
11/12   Extrema (4.1) CW p.193-195/2, 3-9 odd, 32, 33, 51, 55
         HW p.184-185/12-30 by 3's, 36-42 by 3's, 45-49, 51

11/16  Mean Value Theorem (4.2)
         HW p.202-204/1-11 odd, 15-36 by 3's, 40, 42, 43, 45, 57
11/17  Extrema and Inflection Points (4.3)
         HW p.215-216/1-25 odd, 33-39 odd
11/18  Curve Sketching (4.3)
         HW p.216-218/41, 42, 45-54, 63
11/19  Optimization (4.4)
         HW finish packet of problems

11/23  Business Applications (4.4)
         HW p.125/48 and p.228-232/23-27,37-41,46,47,49,58-63
11/24  Half Day A C F H
         More optimization problems (4.4)
         HW finish packet
11/25  Thanksgiving! Yummy!!

11/30  Related Rates Day 1 (4.6)
         HW p.251-252/1-19 odd
12/01  Related Rates Day 2 (4.6)
         HW p.252-254/20-23, 25-35 odd, 42-44
12/02  Linearization
         HW finish packet
12/03  L'Hopital's Rule (8.2)
         HW finish handout plus p.450-452/3-45 by 3's, 69-71

12/07  Recap uses of Derivatives, extension problems (answer key)
12/08  Review
12/09  More Review
12/10  Program to enter, study together (I am out)

12/14  Chapter 4 Test

Finishing up Chapter 3 - Derivatives

We are about done with the chapter. Here is the syllabus to the end:

11/04  Short quiz of derivatives, start review problems HW p.181-183/3-66 by 3's
11/05  More review HW p.183-184/70, 71, 73, 74, 77, 78, 80, 82
11/09  Ch. 3 Test

11/10  Start Ch 4 - Applications of Derivatives
11/11  Veterans' Day - no school
11/12  Essentially the end of the term

Derivatives of "the rest" of the functions

After our review discussion of inverses, exponential and logarithmic functions, we are ready to move on to finding their derivatives.

10/27 Derivatives of Inverses
            HW finish worksheet
10/28 Derivatives of Inverse Trig Functions
            HW p.170-171/3-30 by 3's, 31, 37-40, 41, 43, 47
10/29 Derivatives of Exponential Functions
            HW p.178-179/1-13 odd, 29, 30, 33, 34, 49-51 53, 59, 62

11/02 Derivatives of Logarithmic Functions
            HW p.178-180/15-27 odd, 31, 32, 37-41 odd, 56, 60, 61
11/03 Logarithmic Differentiation
            HW p.179/43-48, 54, 64

More derivative rules

The topics in the next few sections require a bit of practice so we will be spending more than one day on each.

10/12  3.5  Derivatives of Trig Functions
                       HW start p.146-147/3-21 by 3's, 27-31, 37, 40-43, 50-52
10/13  3.5  More practice with Derivatives of Trig Functions
                       HW finish p.146-147/3-21 by 3's, 27-31, 37, 40-43, 50-52
10/14  3.6  Derivatives of Composed Functions (the Chain Rule)
                       HW p.153/3-48 by 3's
10/15  3.6  More Chain Rule practice
                       HW p.154-156/353-56, 59-69 odd, 62, 78

10/19  3.7  Implicit Differentiation
                       HW p.162/1 - 41 odd
10/20  3.7  Implicit Differentiation and Parametric Curves
                       HW p.163-164/43, 46-49, 51, 55-57, 66
10/21          Extra Practice on All
10/22          Start reviewing Exp and Log Functions

10/26           Quiz of 3.5 - 3.7

Check you answers - chapter 3

You can download the chapter three solution manual to check you answers. I remind you that it is better to really try before resorting to the answers. It is too easy to give up quickly and check but the activity of really thinking and trying impresses the procedure on your mind better than reading the answer ever can.

Ch 3 - Derivatives (a BIG chapter for a BIG idea)

Here is the proposed syllabus for the first four sections of Chapter 3. The dates may change but the ideas will remain the same. Assignments will be added later.

09/25  3.1  The Derivative (definition, notation, calculation, graph)
                      HW p.105-108/5-11 odd, 13-17, 22-27, 31-35 odd, 42, 44

09/28  3.2  Differentiability (also Back-to-School Night)
                      HW p.114-115/1-4, 11-16, 31-35 odd, 39, 48

09/29  Smoothness and Numerical Derivative
                HW finish packet plus other listed problems in sections 3.2 and 3.4

09/30  3.3  Rules of Differentiation Day 1
                      HW p. 124/1 - 29 odd

10/01  3.3  Rules of Differentiation Day 2
                      HW p. 124-125/24, 30-35, 37-43 odd, 47-51

10/05  3.4  Velocity and other Rates of Change
                      HW p.135-138/3,8,10,11,13,21,25,27,31,35,46,47,49,50

10/06  Review derivative ideas so far
                      HW Concepts worksheet

10/07  Quiz on 3.1-3.4   HW Trig Derivative Exploration

10/08  Professional Development all day - no school

Finishing the chapter

This is the proposed syllabus. It may change but plan on this.

9/21 Go over pre-test, etc. Rates of change, tangents and normals
           HW pp.92-94/3,7-31 odd,41,45
9/22 Review
           see pp 95-97 for problems
           download Ch 2 Solutions
9/23 Ch 2 Test (the real test)

Continuity and Questions

We raced through continuity so I expect some more questions but try to get through the homework so you know exactly what your questions are. Friday is a Chapter 2 pre-test to see what you need more of and so you know what test questions in this class can look like.

9/15 Continuity and the IVT HW p.84-86/2-8 even,21,23,33,43-45,47,49,51,53,60
9/16 Half Day - no class [C B A G]
9/17 Pre-Test
9/21 Go over everything (limits worksheet, hw questions, pre-test, maybe new stuff)

Limits and Sandwich practice

We will be looking at limits on Friday and Monday - Monday will have the worksheet we didn't quite get to before the end of class on Friday. There will be plenty of time to ask questions.

9/10 p.76/1-7 odd, 9-14, 19, 21-25 odd, 35-38
9/14 p.76-77/27-33 odd, 41-43, 45-51 odd, 54, 55, 65, 68-71

First Assignments

We started the year with a few worksheets to get you thinking about slopes and areas - eventually to have the more "calculus-y" names of derivatives and integrals. Since Calculus depends on making infinitely small adjustments to your calculation, we start our book work with a study of limits. Now we can add up an infinity of small things.

9/07 2.1 Limits HW p.66/2, 4, 6, 9-31 odd, 33-36
9/08 2.1 Sandwich Theorem HW finish worksheet
9/09 Rosh Hashanah - no school
9/10 2.2 Limits involving Infinity

Welcome

This blog will be a source for the syllabus, homework, hints, and links to useful sights. Sometimes I post a syllabus ahead of time and then things change so check back often. If you have any questions, please don't hesitate to email me or visit during my free blocks. Remember, this is an AP class so it covers a college curriculum. It can be tough and you shouldn't be trying to struggle through it without help.