Need help with Area Under a Curve?

Numerical integration tutorial!

http://archives.math.utk.edu/visual.calculus/4/approx.1/index.htm

This one is great! http://www.teacherschoice.com.au/Maths_Library/Calculus/area_under_a_curve.htm

Can you match the graph of a function with its derivative?

Can you match the graph of f with the graph of f ' ? Test your knowledge using this link: http://www.univie.ac.at/future.media/moe/tests/diff1/ablerkennen.html

Watch Instructional Videos on Brightstorm

Use the link below to reference great math instructional videos!

http://www.brightstorm.com/d/math

Can you distinguish the graph of f from f ' and f ''?

Given three graphs, do you know which one represents f, f ' and f ''? Test your skills here: http://archives.math.utk.edu/visual.calculus/3/graphing.3/index.html

Practice Problems

Try this link for practice using the first derivative: http://archives.math.utk.edu/visual.calculus/3/graphing.5/index.html


Check out this site for more information on the second derivative: http://ltcconline.net/greenl/courses/105/CurveSketching/SECTST.HTM

For more practice recognizing increasing/decreasing, maximum/minimum, concave up/concave down, and points of inflection click here: http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/Graphing.html

Agenda: January 11 - 22 (REVISED)

January 11: Section 3.5 (pgs. 198 – 208)
Essential Question: How can I describe asymptotes in terms of limits involving infinity?

Objectives:
· Determine finite and infinite limits at infinity.
· Learn rules for finding horizontal asymptotes.

Assignment: Page 205-208 #1-8 all, 17-33 odd, 55, 59, 71 (Due Jan. 12)
Take Home Quiz on Sec 3.1 – 3.4 Due January 12

January 12, 14-15: Section 3.6 (pgs. 209 – 217)
Essential Question:
· What does the first and second derivative tell us about the behavior of a function?
· What can the second derivative tell us about the shape of a curve?
· How can you use derivatives and your calculator to sketch a graph?

Objectives:
· Analyze and sketch the graph of a function using “Pic Said.” (“PI”=pts of inflection, “C”=critical #s, “S”=symmetry, “A”=asymptotes, “I”=intercepts, & “D”=domain)

Assignment: Page215-217 #1-5 all, 7, 15, 19, 21, 25, 29, 31 (Due Jan. (13) 15)
Assignment: Page 215-217 #33, 39, 47-52 all, 67 (Due Jan. (14) 19)

January 19-21: Section 3.7 (pgs. 218 – 228)
Essential Question: How can calculus be used to solve real life applications where we want to maximize or minimize an outcome?

Objectives:
· Solve applied real-life minimum and maximum problems.
· Students will orally present to the class assigned max/min problems.

Assignment: Page 223-228 #1, 2, 3, 6, 9, 11 (Due Jan. 20)
Assignment: Page 223-228 #13, 19-29 odd (Due Jan. 21 )
Max/Min Problem Presentations--January 22
Take Home Quiz on Sections 3.6 - 3.7 Due January 22


January 22: Ch. 3 Review (pgs. 242-244)--Due January 25
Review for Chapter 3 Test (Sections 3.1-3.7)
In class discussion of the following problems: Page 242 #1, 2, 5, 8, 9, 11, 15, 17, 19, 21a-b, 23, 24, 25, 27, 33, 35, 37, 41, 43, 49, 51, 57, 71, 75, 79,

Chapter 3 TEST January 26

Need a Review?

http://www.curriki.org/xwiki/bin/view/Coll_NROCMath/APCalculusABIUnit4ApplicationoftheDerivative?bc=;Coll_NROCMath.APCalculusABI
Check out the link above for a review on the following topics:
*Lesson 27--Related Rates
*Lesson 28--Relative Extrema & the First Derivative Test
*Lesson 29--Concavity & the Second Derivative Test

November 16-24

Monday – Tuesday (11/16 – 17)
*Work on related rates problems as assigned 11/9 – 11/13

Wednesday (11/18)—Early Release (No class)

Thursday (11/19)
*Pop Quiz (sec 2.6)
*Begin chapter 2 review in preparation for the chapter 2 test (11/24)
*Chapter 2 review: page 158 #1, 4, 5 – 35 odd, 39, 41 – 53 odd, 59, 60, 61, 63, 65, 91, 99, 101, 102, 110


Friday (11/20)
*Related rates and chapter 2 review continued


Monday (11/23)
*Related rates quiz
*Continue working on chapter 2 review

Tuesday (11/24)
*Chapter 2 Test
*Receive Thanksgiving AP Packet!

November 9 - 13, 2009

Monday, 11/9--Wrap Up 2.5
*Clean up and finish up section 2.5 assignments
*Gray implicit differentiation worksheet due Wednesday (11/11)
*Sec 2.5 Quiz Tuesday

Tuesday, 11/10--Sec 2.6 Related Rates
*Sec 2.5 Quiz
*Essential Question: How can calculus be used to solve real life applications where we want to maximize or minimize an outcome?
*Objective: Apply the definition of the derivative to problem situations involving related rates of change.
*Assignment #1: pages 154 - 157 #1-7 odd, 13, 15, 19, 21
*Begin work on sec 2.6 related rates homework worksheet (Due Thursday)

Wednesday, 11/11--Sec 2.6 cont'd
*Gray implicit differentiation worksheet due today!!!
*Assignment #2: pages 154 - 157 #17, 23, 25, 27, 31, 33, 35

Thursday, 11/12--Sec 2.6 cont'd
*Related rates homework worksheet due today
*Sec 2.6 worksheet

Friday, 11/13--Sec 2.6 cont'd
*Related rates concept check quiz
*Related rates classwork worksheet (due Tuesday)
*Assignment #3: pages 154 - 157 # 43, 45, 47, 54
*Study for sec 2.4, 2.5, 2.6 test (Tuesday)

Monday will be test review day; Wednesday (11/18) is early release (no class)

Note: All section 2.6 assignments are due on the day of the test.

Guess What I Just Found???

Another great resource! Check it out for yourself: http://www-math.mit.edu/~djk/calculus_beginners/index.html

Let me know what you think!

November 2 - 6

Monday, 11/2--Mini Test 2.1-2.4
*All assignments for section 2.4 are due today
*Non-calculator test!!!
*Homework--put final touches on the 1985 AP Practice Exam MC section you received Wednesday 10/28 (submit on 11/3)

Tuesday, 11/3--Sec 2.5 Intro--Implicit Differentiation
*Submit Practice AP MC Exam (1985)
Section 2.5 Essential Question: How can you take a derivative if y is in the problem more than once? What does it mean that the relationship between x and y is implied rather than explicitly stated?
Section 2.5 Objectives: Differentiate implicitly defined functions
*Notetaking Guide & Examples
*Assignment: page 146-148 #1-19 odd

Wednesday, 11/4--Sec 2.5 cont'd
*Assignment: page 146-148 #4, 6, 10, 18, 20, 25, 27, 29, 31

Thursday, 11/5--Sec 2.5 Cont'd
*Assignment: page 146-148 #45-50 all; 57, 58;

Friday, 11/6--Sec 2.5 Wrap Up
*Assignment: worksheet 2.5

Study for quiz on 2.5 (Monday 11/9)

October 26 - 30, 2009

Monday, 10/26--(I have Jury Duty!)
*Complete worksheet 2.4
*Assignment: page 137-140 #41-59 odd, 67, 83, 85

Tuesday, 10/27--No Class (GHSGT Checkpoint Test)

Wednesday, 10/28--AP Exam Practice Questions
*Please bring the worksheet received on 10/16 with the Free Response Questions
*Complete the worksheet with sample multiple choice items

Thursday & Friday, 10/29-30--Wrap Up & Clean Up Sect 2.4
*Begin preparing for a Mid-Chapter test--Sections 2.1-2.4 (Monday)

Monday, 11/2--Mini Test 2.1-2.4
*All assignments for section 2.4 are due today
*Non-calculator test!!!
Be able to:
1. Find the derivative using the limit process
2. Find the slope of a line at a point
3. Find the derivative of a function using the rules for derivatives
4. Determine the points at which the graph has horizontal tangents
5. Apply derivatives to position, velocity, and acceleration problems
6. Use the product rule and quotient rules to differentiate functions
7. Find higher-order derivatives
8. Find the derivative of composition functions using the chain rule

Tuesday, 11/3--Sec 2.5 Intro--Implicit Differentiation
*Notetaking Guide & Examples
*Assignment: page 146-148 #1-19 odd

Video: More Chain Rule!!

Video: Sec 2.4 Chain Rule

Online Calculus Tutorial

Click the link below. Select the folder of the topic you would like to view so the lessons will appear.

http://www.curriki.org/xwiki/bin/view/Coll_NROCMath/APCalculusABI?bc=

October 19 - 23, 2009

Monday, 10/19--Sec 2.3 part 3
*Q&A on previously assigned section 2.3 problems (see 10/15)
*Higher Order Derivatives--notes and examples
*Assignment (due Wednesday 10/21): page 126 #93-101 odd, 103, 109, 111, 112, 115, 116, 117, 119, 120

Tuesday, 10/20--Sec 2.3 Wrap Up/Recap
*Q&A on section 2.3 concepts
*Worksheet 2.3
*Prepare for section 2.2-2.3 quiz for Wednesday

Wednesday, 10/21--Quiz Sec 2.2-2.3
*Q& A--acceleration
*Quiz (20 minutes)

Thursday, 10/22--Section 2.4 The chain rule
*Section 2.4 Intro (notetaking guide)
*Assignment: page 137-140 #7-21 odd

Friday, 10/23--Sec 2.4 part 2
*Submit all assignments for section 2.3 on page 126
*Examples for the general power rule
*Assignment: page 137-140 #23-35 odd

October 12 - 16, 2009

Monday, 10/12--Prepare for Mini Test on 2.1-2.2
*HW Review /Q&A
*Complete the notetaking guide for section 2.2 (page 4)
*Recap--sample problems from 2.1-2.2
*Sec 2.3 Part 1--Notetaking Guide (the product rule)
*Homework--study for 2.1-2.2 Mini Test; complete the average velocity and instantaneous velocity worksheet for Thursday; try to complete page 126 #1-5 odd, 13, 31, 35

Tuesday, 10/13--Sect 2.1-2.2 Mini Test
*Mini Test Administration (25 minutes)
*Section 2.3 part 1-- the product rule (notes and examples)
*Complete page 126 #1-5 odd, 13, 31, 35

Wednesday, 10/14--Early Release/PSAT Administration

Thursday, 10/15--Sect 2.3 part 2
*Sec 2.3--The Quotient Rule & Trig Derivatives (more notes and examples)
*"How Do We Measure Speed" worksheet due today
*Assignment--page 126 - 129 #7, 9, 15-33 odd (omit #11, 17, 31)
*Assignment: page 126 - 129 #39-53 odd, 63, 73, 81
*Due Wednesday 10/21: page 126 #93-101 odd, 103, 109, 111, 112, 115, 116, 117, 119, 120

Friday, 10/16--AP Exam Practice Questions
*Select MC and Free Response AP Questions on material we have covered thus far

Section 2.3: Product and Quotient Rules and Higher-Order Derivatives

Essential Questions:
1. How do you find the derivative of an expression involving a product or quotient of two differentiable functions?
2. Can you differentiate all six trigonometric functions?
3. How do you find a higher-order derivative of a function? How do you notate these derivatives?

Objectives:
1. Use the product and quotient rules to calculate derivatives.
2. Apply derivatives rules to higher-order derivatives

Guess What Guys!!

I typed "derivative rules practice" in my Google toolbar and this is what popped up as the first result! This is great!!!

http://www.the-mathroom.ca/freebs/cald6/cald6.htm

Need Extra Help?

Check out this link for extra help and practice!

http://online.math.uh.edu/Math1431/