Chapter 5 - The Definite Integral

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!)

Post Ch 4 Test, enter a version of the RAM program (or look up a fancier one online - for

           example riemann.zip at http://www.ticalc.org/pub/83plus/basic/math/calculus/ -

           and download it right into your calculator)

12/14  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
12/17  5.3  Rules for Definite Integrals
                  HW p.290-291/1-17
12/18  5.3  Derivatives of Definite Integrals
                  HW p.291-293/19-37 odd, 38, 39, 41, 45-51 odd

12/21  5.4  Fundamental Theorem of Calculus
                  HW p.302-303/3-48 by 3's
12/23  5.4  Fun Activity using Calculus

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

1/04  Review what we know so far
         HW p.315-317/1-4,6-9,12,13,35-38,46
1/06  More with the Fundamental Theorem of Calculus (5.4)
         HW p.302-305/10,11,16,17,19,20,29,31,35,43,46,58-61,73,75
1/07  Trapezoidal Rule (5.5)
         HW p.312-314/1-9 odd,10-12,20,39
1/08  Simpson's Rule and Review
         HW finish handout

1/11  Review Day 1
         HW p.316-319/15-30 by 5's,33,54,56,58-60
1/13  Review Day 2 - Extension Problems
         HW finish handout solutions
1/14  Half-day, no class  B A G F
1/15  Test of Ch 5, End of Term 2

1/18  Martin Luther King Day, no school

Here are the solutions for the Chapter 5 questions.

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 interesting.

11/11  Veterans' Day - no school
11/12  Interpreting the Derivative, Extrema (4.1) CW p.193-195/2, 3-9 odd, 32, 33, 51, 55
           HW finish CW plus p.194-195/12-30 by 3's, 36-42 by 3's, 45-49
11/13  Mean Value Theorem (4.2)
           HW p.202-204/1-11 odd, 15-36 by 3's, 40, 42, 43, 45, 57

11/16  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  Quiz of 4.1-4.3,  Optimization (4.4)
           HW p.226-232/1-21 odd, 31, 33, 35, 64
11/20  Business Applications (4.4)
           HW p.125/48 and p.228-232/23-27,37-41,46,47,49,58-63

11/23  More optimization problems (4.4)
           HW finish packet
11/25  Optimization Quiz   Half Day A C F H
11/26  Thanksgiving! Yummy!!

11/30  Parent Conferences
12/02  Related Rates Day 1 (4.6)
           HW p.251-252/1-19 odd
12/03  Related Rates Day 2 (4.6)
           HW p.252-254/20-23, 25-35 odd, 42-44
12/04  Linearization
           HW finish packet (answer key)

12/07  L'Hopital's Rule (8.2)
           HW finish handout plus p.450-452/3-45 by 3's, 69-71
12/09  Quiz of 4.5 & 4.6,  Recap uses of Derivatives, extension problems (answer key)
12/10  Review
12/11  Chapter 4 Test
           HW Enter a version of the RAM program (or look up a fancier one online - for 

           example riemann.zip at http://www.ticalc.org/pub/83plus/basic/math/calculus/ -

           and download it right into your calculator)

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!

Chapter 3 - Derivatives

Here is the proposed syllabus for Chapter 3. The dates may change but the ideas will remain the same.  It is a long chapter so we will have several quizzes along the way to the test at the end.

09/28  3.1  The Derivative (definition, notation, calculation, graph)
                  HW p.105-108/5-11 odd, 13-17, 22-27, 31-35 odd, 42, 44
09/30  3.2  Differentiability (also Back-to-School Night)
                  HW p.114-115/1-4, 11-16, 31-35 odd, 39, 48
10/01  Smoothness and Numerical Derivative
                  HW finish packet plus other listed problems in sections 3.2 and 3.4
10/02  3.3  Rules of Differentiation Day 1 (given rules)
                  HW p. 124/1 - 29 odd

10/05  3.3  Rules of Differentiation Day 2 (prove rules)
                  HW p. 124-125/24, 30-35, 37-43 odd, 47-51
10/07  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
10/08  Review derivative ideas so far
                   HW Concepts worksheet
10/09  Professional Development all day - no school

10/12  Columbus Day - no school
10/14  PSAT Day - altered schedule
10/15  Quiz on 3.1-3.4
                   HW Trig Derivative Exploration
10/16  3.5  Derivatives of Trig Functions
                   HW p.146-147/3-21 by 3's, 27-31, 37, 40-43, 50-52

10/19  3.6  Derivatives of Composed Functions (the Chain Rule)
                  HW p.153/1-39 odd
10/21  3.1-3.5 More Practice/Remediation
                  HW finish handout
10/22  3.6  More Chain Rule practice
                  HW p.154-156/53-56, 59-69 odd, 62, 78
10/23  3.7  Implicit Differentiation
                  HW p.162/1 - 41 odd

10/26  3.7  Implicit Differentiation and Parametric Curves
                  HW p.163-164/43, 46-49, 51, 55-57, 65 and p.153-154/41-50
10/28  Quiz of 3.5 - 3.7
                  HW Review of Exponential, Logarithmic and Inverse functions
10/29  3.8  Derivatives of Inverses
                  HW finish worksheet
10/30  3.8  Derivatives of Inverse Trig Functions
                  HW p.170-171/3-30 by 3's, 31, 37-40, 41, 43, 47

11/02  3.9  Derivatives of Exponential Functions
                  HW p.178-179/1-13 odd, 29, 30, 33, 34, 49-51 53, 59, 62
11/04  3.9  Derivatives of Logarithmic Functions
                  HW p.178-180/15-27 odd, 31, 32, 37-41 odd, 56, 60, 61
11/05  Short quiz of derivatives, Logarithmic Differentiation, start review problems
                  HW p.179-180/43-48, 54, 64  and  p.181-183/3-42 by 3's
11/06  More review (it's a big chapter) (partial answer key to worksheet)
                 HW p.183-184/45-66 by 3's, 70, 71, 73, 74, 77, 78, 80, 82

11/09  Ch. 3 Test
11/11  Veterans' Day - no school
11/12  Start Ch 4 - Applications of Derivatives

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.

Chapter 2 - Limits and Continuity

Since Calculus depends on making infinitely small adjustments to our calculation, we start our book work with a study of limits. Now we can add up an infinity of small things.

9/07  Labor Day - no School
9/09  2.1 Limits as x --> c   HW p.66/2, 4, 6, 9-39 odd, 47-51 odd
9/10  2.1 Sandwich Theorem HW finish worksheet
9/11  2.2 Limits involving Infinity  HW p.76/1-7 odd, 9-14, 19, 21-25 odd, 35-38

9/14  Rosh Hashanah - no school
9/16  2.2 More Limits Practice  HW p.76-77/27-33 odd, 41-43, 45-51 odd, 54, 55, 65, 68-71
9/17  Limits Quiz    Half Day [ C B A G ]
9/18  2.3 Continuity and the IVT  HW p.84-86/2-8 even,21,23,33,43-45,47,49,51,53,60

9/21  2.4 Rates of change, tangents and normals  HW pp.92-94/3,7-31 odd,41,45
9/23  Yom Kippur - no school
9/24  Review (answer key),  see pp 95-97 for more problems,  download Ch 2 Solutions
9/25  Ch 2 Test

Welcome!

Calculus is the study of change.  We will be working through how that applies to many functions and then taking that knowledge and applying it to real world problems.

This blog will be a source for the syllabus, homework, hints and links to useful sights.  Sometimes I post a unit 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.  Enjoy (and keep up with your homework!)!!!