last quiz on impossible integrals, newton's method, cylindrical shells, and l'Hopital's Rule (and whatever else we cover next week) will be on the scheduled final exam date on Monday, 6/8.
WEDNESDAY 5/27
Final exam!!
TUESDAY 5/26
SW compute impossible integrals and approximate roots of functions using Newton's method.
Impossible integrals are really just like computing final position by adding displacement from a known starting position. Notes are here.
Newton's method is an iterative method used to approximate the roots of a function. Notes are here.
TUESDAY 4/28
SW practice FRQ related to slope fields and solving DE's
MONDAY 3/23
objective: SW take evaluate and take derivatives of inverse trig functions
collected area & volume take home quizzes
pretest on calculus with inverse functions
Q&A on the 2011 (Form B) #3 & 4. We will have an in-class assessment similar to #3 that will be combined with your take-home grade the area and volume material.
notes, examples and practice on the section on inverse trig functions. We'll tackle this again tomorrow... it didn't go that well.
FRIDAY 3/20
objective: SW problem in an AP style.
students worked to complete the AP Calculus FRQs from 2011 (Form B) #3 & 4.
Go HERE to check out the solutions. Spend time comparing your solutions to the scoring guidelines. See me if you have questions.
distributed the area & volume test. It's due on Monday. Do your own work (no help from others, the internet, etc).
practice the natural log and exponential function work (pages 183-200). Your test on this material will be on Tuesday 3/31.
WEDNESDAY 3/18
objective: SW differentiate and integrate with "e"ase.
There will be a quizzeroo on the content of pages 189-194 tomorrow.
WEDNESDAY 3/11 (55 days until the AP Calc Exam)
objective: SW review working with exponential and logarithmic functions.
SW learn to differentiate expressions involving ln(x).
Students took a pretest on "Calculus with e and ln(x)". We reviewed the results to preview our upcoming study of this topic.
TUESDAY 3/10
objective: SW practice solving area and volume problems.
SW reflect upon their success in Calculus and think about making a change.
We decided:
Friday 3/20 will be the quiz area and volume.
prepare by doing the homework. Check your answers in room 216 and/or with others.
prepare also by looking in the Barron's book. See Chapter 7 (page 293) - examples 2, 5, 6, 7, 8 & 9 are AB content. At first glance, the following exercises seem appropriate: p319 #1-4, 6-12, 17, 18-26. The answer key is on page 329, and that page also starts the "answers explained" section. Get practicing!!
Wednesday 3/18 (after school) will be the definite integral retake. The format of this will be similar to the practice test / pretest that was distributed.
WEDNESDAY 3/4
objective: SW take a test on definite integration, including applications involving definite integration.
TUESDAY 3/3
objective: SW compute volumes of objects with known cross sections.
HW: p176 #1, 2, 4 and STUDY FOR YOUR DEFINITE INTEGRATION TEST!!
TUESDAY 2/24
objective: SW gain an understanding of how to compute solids of revolution.
what we did:
reviewed and discussed solutions to the pretest / practice test on definite integration. The quiz is when?
introduced solids of revolution. Weren't in class? Check out these Khan Academy videos (parts 1 - 4). We'll take formal notes tomorrow.
MONDAY 2/23
objective: SW complete a pretest on computing areas and volumes with definite integrals.
Recall: There will be a quiz on Friday 2/27 covering:
definite integration with u-substitution,
straight line motion,
average value of a function,
and the second fundamental theorem of Calculus.
WEDNESDAY 2/18 & FRIDAY 2/20
objective: SW compute the area between two curves.
FRIDAY 1/30
objective: SW analyze the accumulation function.
Wrapped up notes on the accumulation function, pages 148-149.
HW: pages 150-151.
Remember: quiz on u-substitution on the block next week. Practice. Maybe you should review your flashcards of trig derivatives and integrals. What do you think?
Finish page 126 (check them here, I did them already) & then do page 128.
Review page 125. We never got around to the HW quiz on p124-125. It's coming eventually.
Check out the Riemann sum notes from class above... I computed the estimates. Can you obtain these with your calculator? Can you explain why some estimates are better than others? Which is the best?
Oh yeah... study for the midterm. Midterm will consist of 30 multiple choice questions and 10 open ended questions. This document indicates what topics are covered.
FRIDAY 1/9/2015
objective:
SW use sigma notation to add up a sequence of numbers.
SW approximate he area under a curve with right rectangles.
do exercises on page 134 for Monday -- see notes on area under a curve for guidance.
discussed and sorted out what's what and what's coming up:
For Monday, 1/12: Quiz on optimization (1/2 block long) followed by notes on Riemann Sums. Make sure the HW on p134 is done before coming to class.
For Wednesday, 1/14: Make sure the HW on page 124-125 is done and that you can use the sigma notation formulas. You can expect a HW quiz covering he material on p124-125 and sigma notation. I'll teach notes on u-substitution.
your midterm will be on 1/22. Better get practicing!
WEDNESDAY 1/7/2015
objective:
SW integrate polynomials and trigonometric functions.
objective: SW review differentiation topics with AP style multiple choice questions.
Students work on the following exercises today:
2, 6, 15, 22, 27, 38, 42, 58, 62, 67, 71, 77, 84, 95, 100
Here are the solutions:
2A, 6D, 15A, 22A, 27E, 38B, 42A, 58B, 62A, 67A, 71E, 77E, 84B, 95D, 100D
MONDAY 12/22
objective: SW review differentiation topics with AP style multiple choice questions.
Review packet of questions distributed. Students work on the following exercises today:
1, 5, 14, 21, 26, 36, 41, 57, 61, 66, 70, 74, 83, 90, 99, 103
Here are the solutions:
1E, 5E, 14C, 21D, 26E, 36B, 41E, 57B, 61C, 66C, 70C, 74C, 83B, 90D, 99E, 103D
FRIDAY 12/19
objective: SW test on function analysis.
Wednesday 12/17
objective: sw practice for the function analysis test on Friday.
Students practice all of the HW problems for the section, except #11. I don't like that one.
HW assigned: All of the problems in the optimization section.
TUESDAY 12/9
objective: SW solve optimization problems. You thought we were taking a break because it's an early Tuesday? Ha.
What we did:
Delivered examples #1-4 on page 108. They're here.
HW assigned: #1-4 on page 111.
MONDAY 12/8
objective: SW complete a practice test for their upcoming quiz*.
What we did:
Norman was out sick. This practice test was distributed, and students spent the time working through the exercises. It covers the material from the sections on:
Take notes, examples, and practice - page 93-94. Note that we are analyzing functions to an extent not previously possible. To graph a function in pre-calc you only had an idea of what it might look like - you might plot intercepts or individual points. Now we can get learn a lot from the derivatives to obtain detailed, accurate graphs. Also note, "justify your answer" means state your answer and support it with evidence based upon the derivatives. See examples in notes.
Homework: work through the exercises on page 100-101.
TUESDAY 12/02
objective: SW take a quiz on SLM
The quiz took the entire period.
I distributed this paper -- it contains solutions to several examples on page 91 & 92. You should study the solutions and then complete the following homework assignment: p97-100 (don't do #5 on page 100).
FRIDAY 11/14
objectives:
SW analyze SLM of objects.
SW solve projectile motion problems.
what we did:
warmup: analyze a SLM problem (answers in notes below, last page)
take notes on projectile motion: page 77 examples 5 & 7. Here are the notes.
HW: p79-80 skip #5
WEDNESDAY 11/12/2014
objectives:
SW learn to evaluate erivatives with the TI-84.
SW graph piecewise functions with the assistance of the TI-84.
SW analyze he SLM of an object.
What we did:
Find f'(x) for f(x) = 3e^x - 2x^2 + 7
you can't, because you don't know how to differentiate the exponential function
we learned to use the nderiv() function on the TI-84 to evaluate the derivative at a point.
we learned about how the calculator works to estimate this result, and compared it to the actual value.
Explored using the TI-84 to graph the piecewise function on p58, Example 2a. Then practiced graphing other functions.
Your quiz on derivatives with tables is postponed until the day after I return your quiz on the rules of differentiation... whenever that is.
WEDNESDAY 10/15/2014
Students finish quiz -- shortened period due to PSAT delayed entry.
TUESDAY 10/14/2014
Students quiz on he rules of differentiation.
MONDAY 10/13/2014
objective: SW differentiate with trig functions :)
Today we developed definitions intuitively for the derivatives of sinx and cosx. We will examine more legitimate derivations for these derivatives at a later time. For now, memorize the rules in the boxes and use them.
Here are the answers to the previous homework assignment, p44-46 #1-37. Just a reminder, you can always go to Wolframalpha.com to find answers to your homework.
. FRIDAY 10/10/2014
objective: SW differentiate expressions, making use of the rules of differentiation.
Today we clarified how to approach functions that need differentiating. Since we just learned the chain rule, we're super ready to use the chain rule, but sometimes the chain rule doesn't apply, or it doesn't apply yet. We examined example 10 to exemplify this issue. In example 10, you might be inclined to bust out the chain rule... Baby = 2x-3 and Mom = x^4, or x^6, or... I don't know?!? Example 10 ONLY lends itself to using the product rule first. In this example, when you get around to taking the derivative of the second factor, then yes, the chain rule will be used. It just has to wait it's turn.
Here are the worked out solutions to the examples on page 43. You practiced some of these today in class. Check your work. Did I simplify more than you? Remember: if these exercises are on a multiple choice test, you'll need to manipulate your answer in order to be able to select one of the available choices. On top of differentiating, you need algebra strength and agility to work the mathematical gymnastics. Spend time trying to understand the simplifications as well.
Notes:
we will have a quiz on the rules of differentiation, not including the chain rule, next week on Tuesday, 10/14/14. This covers the material on pages 39-41 of your notes. This includes the application problems!
we will have a quiz on differentiation with table problems, which will include the chain rule, next week on Friday, 10/17/14. This covers all of the rules, but only for the table style problems. The quiz is designed to test your implementation of the rules, not your algebra.
the full quiz on differentiation will probably be on the block period, 10/22/14.
==
.Today in AP Calculus AB
FRIDAY 5/29
SW compute volumes of solids of rotations with cylindrical shells.
WEDNESDAY 5/27
Final exam!!
TUESDAY 5/26
SW compute impossible integrals and approximate roots of functions using Newton's method.
TUESDAY 4/28
SW practice FRQ related to slope fields and solving DE's
FRIDAY 4/24
objective: SW practice a strategy to hone their skills on FRQs.
Strategy: Try, check, reflect, repeat.
Here are links to the resources I mentioned in class:
WEDNESDAY 4/22
objective: review results from practice AP Exam (2003).
Here are the solutions to the multiple choice.
In time for Friday, grade your FRQs and work through them. See me with questions.
Let's move your slope fields, DEQ, and exponential growth quiz to next week. We'll talk on Friday.
MONDAY 4/13
Students took a test on inverse trig functions and inverse functions in Calculus.
FRIDAY 4/10
objectives: SW use slope fields to visualize the solution to differential equations.
WEDNESDAY 4/8
objective: SW solve separable differential equations.
SW use slope fields to sketch the solution to a differential equation.\
Here are the notes for the examples on separable equations including the problems I had on the board.
TUESDAY 4/7
objective: SW take a PRETEST on slope fields, solving separable differential equations, and exponential growth functions.
SW solve separable differential equations.
WEDNESDAY 4/1
objective: SW evaluate derivatives of inverse functions.
TUESDAY 3/31
objective: SW quiz on Ln and exp with Calculus
MONDAY 3/30
objective: SW review for tomorrow's quiz on Ln and exp
THURSDAY 3/26
objective: SW integrate expressions that involve inverse trig functions.
WEDNESDAY 3/25
objective: SW evaluate and differentiate inverse trig functions.
TUESDAY 3/24
objective: SW solve an AP FRQ dealing with area and volume.
SW evaluate and differentiate inverse trig functions.
MONDAY 3/23
objective: SW take evaluate and take derivatives of inverse trig functions
FRIDAY 3/20
objective: SW problem in an AP style.
WEDNESDAY 3/18
objective: SW differentiate and integrate with "e"ase.
TUESDAY 3/17 (early dismissal, 30 min period)
objective: SW differentiate and integrate expressions involving the natural log function
MONDAY 3/16 (50 days until the AP Exam)
objective: SW integrate, when appropriate, using natural logs.
WEDNESDAY 3/11 (55 days until the AP Calc Exam)
objective: SW review working with exponential and logarithmic functions.
SW learn to differentiate expressions involving ln(x).
TUESDAY 3/10
objective: SW practice solving area and volume problems.
SW reflect upon their success in Calculus and think about making a change.
We decided:
WEDNESDAY 3/4
objective: SW take a test on definite integration, including applications involving definite integration.
TUESDAY 3/3
objective: SW compute volumes of objects with known cross sections.
WEDNESDAY 2/25
objective: SW write definite integrals for solids of revolution.
TUESDAY 2/24
objective: SW gain an understanding of how to compute solids of revolution.
what we did:
MONDAY 2/23
objective: SW complete a pretest on computing areas and volumes with definite integrals.
Recall:
There will be a quiz on Friday 2/27 covering:
WEDNESDAY 2/18 & FRIDAY 2/20
objective: SW compute the area between two curves.
There will be a quiz on Friday 2/27 covering:
THE DAYS IN BETWEEN
FRIDAY 2/6
objective: SW perform definite integration with u-substitution (continued, review)
MONDAY 2/2
objective: SW understand and apply the Fundamental Theorem of Calculus.
FRIDAY 1/30
objective: SW analyze the accumulation function.
Wrapped up notes on the accumulation function, pages 148-149.
HW: pages 150-151.
Remember: quiz on u-substitution on the block next week. Practice. Maybe you should review your flashcards of trig derivatives and integrals. What do you think?
THURSDAY 1/29
objective: SW complete AP-style free response questions.
Get the work here.
WEDNESDAY 1/28
objective: SW evaluate definite integrals graphically.
FRIDAY 1/16
objective: SW perform u-substitution.
WEDNESDAY 1/14/2015
objective:
- SW quiz on sigma notation
- SW estimate area under a curve with Riemann Sums
- SW perform u-substitution for integration problems that require it.
what we did:HW:
FRIDAY 1/9/2015
objective:
what we did:
WEDNESDAY 1/7/2015
objective:
what we did:
HW:
TUESDAY 1/6/2015
objective: SW integrate polynomials by performing ANTIDIFFERENTIATION.
SW take a pretest on integration.
HW: p124 #1-12
MONDAY 1/5/2015
objective: SW review for the optimization quiz on Monday 1/12.
Handed out this sheet of review problems.
My solutions are here. Come on in - let's talk if you have questions.
TUESDAY 12/23
The AP Test is in 132 days
objective: SW review differentiation topics with AP style multiple choice questions.
Students work on the following exercises today:
2, 6, 15, 22, 27, 38, 42, 58, 62, 67, 71, 77, 84, 95, 100
Here are the solutions:
2A, 6D, 15A, 22A, 27E, 38B, 42A, 58B, 62A, 67A, 71E, 77E, 84B, 95D, 100D
MONDAY 12/22
objective: SW review differentiation topics with AP style multiple choice questions.
Review packet of questions distributed. Students work on the following exercises today:
1, 5, 14, 21, 26, 36, 41, 57, 61, 66, 70, 74, 83, 90, 99, 103
Here are the solutions:
1E, 5E, 14C, 21D, 26E, 36B, 41E, 57B, 61C, 66C, 70C, 74C, 83B, 90D, 99E, 103D
FRIDAY 12/19
objective: SW test on function analysis.
Wednesday 12/17
objective: sw practice for the function analysis test on Friday.
TUESDAY 12/16
objective: same as yesterday
what we did:
HW: do the function analysis problem, do the economic optimization homework, do the optimization hw, and practice for your test.
notes: you have a test on Friday!
MONDAY 12/15
objective: SW solve economic optimization problems (p115-119)
What we did:
HW: p117 #1-9 odd
Note: quiz Friday covers all content in pages 82-103.
FRIDAY 12/12
objective: SW perform an ABCD writing exercise.
SW practice optimization problems.
What we did:
Heads up:
WEDNESDAY 12/10
objective: SW solve (more) optimization problems.
What we did:
TUESDAY 12/9
objective: SW solve optimization problems. You thought we were taking a break because it's an early Tuesday? Ha.
What we did:
MONDAY 12/8
objective: SW complete a practice test for their upcoming quiz*.
What we did:
FRIDAY 12/5
objective: SW determine the absolute max and absolute min of a function on a given interval.
What we did:
WEDNESDAY 12/3
objective: SW analyze given functions using f' and f''.
What we did:
TUESDAY 12/02
objective: SW take a quiz on SLM
The quiz took the entire period.
I distributed this paper -- it contains solutions to several examples on page 91 & 92. You should study the solutions and then complete the following homework assignment: p97-100 (don't do #5 on page 100).
FRIDAY 11/14
objectives:
- SW analyze SLM of objects.
- SW solve projectile motion problems.
what we did:WEDNESDAY 11/12/2014
objectives:
What we did:
Homework due Friday: Take the time to study for your related rates test.
WEDNESDAY [[tel:11/5/2014|11/5/2014]]
objectives:
- SW demonstrate an understanding of how to assess the continuity and differentiability of a given piecewise function
- SW solve related rates problems.
Homework assigned: page 67 #1, 2, 3, page 68 #4, 5, 6a, 7.TUESDAY 10/28/2014
objective: SW assess the continuity (today) and differentiability (tomorrow) of given functions.
You have a quiz tomorrow on differentiation with trig.
Build the math muscle! Here are suggested practice problems from the textbook (page 158):
FRIDAY 10/24/2014 (Norman at workshop)
objective: SW review for a quiz by completing a practice quiz.
.
WEDNESDAY 10/22/2014 (block day)
objective: SW differentiate equations implicitly (continued).
.
TUESDAY 10/21/2014
objective: SW quiz on derivatives by tables
MONDAY 10/20/2014
objective: SW differentiate equations implicitly.
Here are examples 4 through 8 from page 52. Read them, work them into your notes, and then try the homework.
Homework assignment (changed) is p53-54, #1-13 odd. Find time to ask questions tomorrow.
Remember: quiz tomorrow on derivatives with tables.
FRIDAY 10/17/2014
objective: SW practice differentiating functions involving trig functions
THURSDAY 10/16/2014
objective: SW differentiate functions involving trig functions (continued)
Notes:
WEDNESDAY 10/15/2014
Students finish quiz -- shortened period due to PSAT delayed entry.
TUESDAY 10/14/2014
Students quiz on he rules of differentiation.
MONDAY 10/13/2014
objective: SW differentiate with trig functions :)
Today we developed definitions intuitively for the derivatives of sinx and cosx. We will examine more legitimate derivations for these derivatives at a later time. For now, memorize the rules in the boxes and use them.
Here are the worked out examples from page 49, #1-9.
Homework tonight: p50, #1-9.
Here are the answers to the previous homework assignment, p44-46 #1-37. Just a reminder, you can always go to Wolframalpha.com to find answers to your homework.
.
FRIDAY 10/10/2014
objective: SW differentiate expressions, making use of the rules of differentiation.
Today we clarified how to approach functions that need differentiating. Since we just learned the chain rule, we're super ready to use the chain rule, but sometimes the chain rule doesn't apply, or it doesn't apply yet. We examined example 10 to exemplify this issue. In example 10, you might be inclined to bust out the chain rule... Baby = 2x-3 and Mom = x^4, or x^6, or... I don't know?!? Example 10 ONLY lends itself to using the product rule first. In this example, when you get around to taking the derivative of the second factor, then yes, the chain rule will be used. It just has to wait it's turn.
Here are the worked out solutions to the examples on page 43. You practiced some of these today in class. Check your work. Did I simplify more than you? Remember: if these exercises are on a multiple choice test, you'll need to manipulate your answer in order to be able to select one of the available choices. On top of differentiating, you need algebra strength and agility to work the mathematical gymnastics. Spend time trying to understand the simplifications as well.
Notes:
HW: finish the exercises in this section, p44-46.
.
WEDNESDAY [[tel:10/8/2014|10/8/2014]] (block day)
objective: SW differentiate expressions using the chain rule.
'nuff said:
Homework: p44 #1-15.
.
TUESDAY [[tel:10/7/2014|10/7/2014]]
no info is available for this date or before this date.