Honors Advanced Math 09-10

Parametric, Cylindrical and Spherical

2010-04-29T16:23:00.002-04:00

4/29 Parametric Equations HW Worksheet
4/30 Cylindrical & Spherical Coordinates HW Worksheet

Polar Coordinates

2010-04-26T17:32:00.002-04:00

This is a quick but interesting chapter on another way of describing the location of points in space. Sections 6.4-6.5 in Demana, chapter 11 in Brown.

4/26-7 Intro to Polar CW Brown p.400-402/1-21 odd, 39
            HW Demana p.515-516/3,5,7,15,21,29,51,55
4/28     Converting equations and graphs (polar <-> rectangular)
            CW D p.524/57,58,61,63    HW D p.523/5,7-13,16,45,49,65-67
4/29     Parametrics 2D & 3D
4/30     Spherical and Cylindrical Coordinates

5/03-4 Polar Coordinates and Complex Numbers (cis)
5/05     Complex Powers and Roots
5/06     Review
5/07     Extra Practice (day of AP US History test)

5/10-1 Start Conic Sections (5/11 is the day of the AP Chemistry test)
5/12     Polar Test

5/13     Half-Day (C A G F)

Review Answer Key

2010-04-12T17:12:00.002-04:00

The answer key for the review portion of the handout is available to download here. For a summary of determinants, download this.

The matrix of dates unto vacation

2010-03-31T09:01:00.001-04:00

The rest of the schedule for matrices covers two days when I will be out.

3/31 Applications of matrices to linear systems
        HW handout includes 6 problems and these Demana problems:
              p.578/59-62,65,66,68,70,71 and p.585/13,15,21
4/01 Transformations Day 1 HW p.1-4 of handout
4/02 Good Friday - no school

4/05 Transformations Day 2 HW p.5-7 of handout
4/07 3D Matrix Apps HW do all of handout (I will be out.)
4/08 Determinants with vectors HW handout problems 1-7
4/09 Determinants in 3D HW handout problems 8-12

4/12 Determinant summary, Review HW handout
4/14 Markov Chains (probability with matrices)
        HW finish handout plus B p.547-550/5,9-11,14-17
4/15 Matrix Test (I will be out, Mr. Verner will be in.)
4/16 Communication Matrices CW B p.540-542/3,5,7,9-13

4/17 - 4/25 April Vacation

Matrices

2010-03-26T13:41:00.002-04:00

We will be moving through matrices quickly. It is chapter 7 in Demana and ch 14 in Brown. Both are useful.

The first two days will involve reviewing everything you learned about matrices in Algebra 2 and extending your thinking about that learning. Then we go into the new and cool stuff that you can do.

3/26 Alg 2 Review day
          HW B p.521-522/9,11-13,16; p.526-528/5-11 odd,12,15,16,18
               D p.565-566/33-39 odd, 43, 45, 48, 55

3/29 More Matrix Multiplication, Augmented Matrices, etc.
         HW handouts

The end of vectors

2010-03-19T09:00:00.001-04:00

The last bit of vectors involves a worksheet of extension and review problems. We will work on these in class but you should also be working on them at home. The problems are not trivial and anything like them may be on the upcoming test. The handout was begun on Friday, March 19th. Keep going. Bring any questions to class.

3/22 F-block 11:50
3/23 H-Block 12:30 (Day 1 of MCAS)
3/24 F-Block 1:35, no H-Block (Day 2 of MCAS)
3/25 Vector Test F-Block 1:30, H-Block 12:30 (Day 3 of MCAS)
3/26 Matrix review (back to regular schedule)

The beginning of vectors

2010-03-06T13:08:00.008-05:00

We are starting to look at vectors, line segments with direction. We will be using both books (Ch 6 in Demana, Ch 12 in Brown) so be careful when writing down the assignments. (Note: The dates reference F-Block. H-Block started this on Friday 3/05 and will have their Trig Identities Test on 3/09. I hope all went will with the National French Exam!)

3/08 Intro to Vectors (D: 6.1 and B: 12.1)
        HW D p.488/3-27 by 3's, 29-39 odd and B p.423, 425/5-7, 17-20
3/10 Angle between vectors and the Dot Product (B: 12.4)
        HW B p.444-445/1-19 odd, 23, 27-29
3/11 Vector Proofs   CW Worksheet (D: 6.1 and B: 12.1, 12.2)
        HW B p.425-6/21-23 and
                  p.429-432/11, 12, 15, 18, 27-29, 33, 34
3/12 Vector Equations of Lines, Vectors in 3D
        HW finish worksheet of problems plus
               B p.436-437/17, 18, 23 and D p.490/57, 58
               If you still feel that you need extra practice
               to feel comfortable with the material, section 12.5
               in the Brown book is the place to go (clear explanations,
               good diagrams, comprehensive problems).

3/15 Equations of Planes, Vectors Perpendicular to Planes (B:12.5)
        HW B p.451/10, 12, 12, 15, 21, 25-28, 32, 38
              We talked about equations of planes & vectors perpendicular
               to the planes. Read the corresponding explanations in the
               book. They are very clear, have lots of examples and better
               pictures than anything I can draw. (This reading should
               be considered part of the homework!)
3/17 Vectors and Planes, Angles between Planes (B: 12.5, 12.6)
        HW B p.452/43-45 and p.455-457/9-21 odd, 28-31, 33
3/18 The Cross Product
        HW p.456-458/21,25,27,34,35,37-39 plus
        Vector Cross Product worksheet
3/19 Projections, Uses of the Cross Product, Extensions
        HW Work on worksheet

Moving along with identities

2010-02-22T09:50:00.002-05:00

Identities are important for solving problems as they allow for key simplifying substitutions. You have to know the basic ones (cofunction, reciprocal, Pythagorean, etc.). You have to be able to prove (or disprove) others.

2/11 read Demana section 5.1, do p.430/1-29 odd

2/22 5.1 Review Basic Identities CW p.430/31-38
                 HW p.430-431/39-59 odd
2/24 5.2 Proving Trig Identities CW p.431/67, 69-72
                 HW p.437-8/7-35 odd
2/25 5.2 More Practice Proving Identities CW p.438/34,36,44
                HW p.438/37-47 odd,48,59,61
2/26 5.3 Sum & Difference Formulas
                 HW p.444/1-29 odd, 31-34, tan(A + B), tan(A - B)

3/01 5.3 More Proofs of cos(A + B), Double Angle Formulas
                HW p.444-445/33-43 odd, 44,47,49,52,55,60,63-65,67
3/03 5.4 Half Angle Formulas CW Brown p.384-385/37,45,46,51
                HW p.451-452/5-47 odd
3/04 Review (Half Day C B H F)
3/05 Test of Trig Identities

Dealing with the snow day

2010-02-10T11:13:00.001-05:00

Since we, obviously, cannot have a test on a snow day, the test will be rescheduled for the 11th. A solution key for the extension problems is downloadable here

The schedule up to February Break

2010-02-05T12:59:00.000-05:00

2/05 Post-Quiz HW Brown p.338/41 and p.357-358/25-28,31,32,36,41
2/08 Review and Extension Problems
2/10 Geometric and Inverse Trig Test
HW read Demana section 5.1; do p.430/1-29 odd
2/11 Basic Trig Identities CW p.430/31-38 HW p.430-431/39-55 odd
2/12 Finish Basic Trig Identities CW p.431/57, 59, 67, 69-72

2/13 - 2/21 February Break!

Mixed Application Problems

2010-02-04T16:41:00.001-05:00

Here are some problems that will help you study for your quiz:
(All Brown book)

p.337-338/31-33, 37
p.356-358/11, 14, 18, 21, 24, 25, 29, 34

Note: for problem 29 it refers you to formulas that you have yet to prove. Try to figure out the length of the median/angle bisector/altitude using what you know about geometry and trigonometry rather than trying to understand and memorize formulas. Remember, if you have the length of three parts to the triangle (some combo of sides and angles, or all sides), you can "solve" the triangle (eg. find the rest of the sides and angles using the Law of Cosines and the Law of Sines) and then apply what you know about medians (cut the opposite side in half), angle bisectors (cut the angle in half) and altitudes (make a right angle).

Important Laws

2010-02-01T14:09:00.002-05:00

We are starting the week with the Law of Sines and the Law of Cosines.

Day 1: Law of Sines HW Brown p.347-349/1-27 odd
Day 2: Law of Cosines HW Brown p.352-354/1-17 odd, 22

We will also be going over the last quiz on Wednesday.

Moving the quiz, finishing the chapter

2010-01-20T11:44:00.032-05:00

I am moving the quiz to Friday for both sections and it will cover 4.1-4.5. Here is the new syllabus:

01/19 F-Block doesn't meet        H-Block 4.5
01/20 F-Block 4.5, go over HW    H-Block go over HW, 4.7 day 1
01/21 F-Block 4.7 day 1 ;            H-Block Extra Problems
01/22 F-Block quiz                      H-Block quiz

01/25 F-Block 4.7 day 2                H-Block doesn't meet
01/26 F-Block doesn't meet    H-Block 4.7 day 2
01/27 4.7 day 3
01/28 Intro to using trig for area (move to Brown book)
01/29 practice

4.5 Graphs of the other Trig Functions
     HW p.385-386/1-4,5-11 odd,27-29,32-34,38,40,42,51,52,54
4.7 Inverses - Graphs and Restrictions
     HW p.402-403/1-11 odd, 17, 19, 33-35, 49, 51, 54, 57
4.7 Composing Inverses
     HW finish handout about inverses and periodic functions
4.7 Extra Practice
     HW p.402-403/23-31 odd, 37-47 odd, 55, 59; & p.414/42, 43
Brown 9.2 problems: p.342-344/1-19 odd, 20-22, 35, 36 (34 is a bonus!)

Moving the retest

2010-01-08T13:37:00.001-05:00

Given the advocacy (ok, it was really whining but I am being nice about it) the retest will move to Wednesday, after all of the AP History drama is done. The rest of the schedule moves up a day.

More with Trig Functions and Sinusoids

2010-01-05T22:41:00.004-05:00

We are continuing our study of trigonometric functions, bringing in the periodic nature of the functions (sinusoids and their applications) and looking at the other trig functions that we have been ignoring a bit. The last week listed is just a plan at this point.

12/17 Solving Trig Equations
          HW worksheet & Brown p.272-274/17-27 odd, 29-32, 33-41 odd
12/18 More solving Trig Equations with x-y-r proofs
          HW finish handout
12/21 Mapping Trig Values worksheet
          HW finish for after vacation
12/23 Quiz of 4.1-4.3

12/24 - 1/4 Christmas Vacation

01/04 Parent Conferences (no classes)
01/05 H-Block: Sinusoids HW p.376-7/5,6-21 odd,22,25,28,30,33-36
01/06 Exp & Log Second Review (ask your questions! get answers!)
01/07 F-Block: Sinusoids HW p.376-7/5,6-21 odd,22,25,28,30,33-36
          H-Block: Extra 4.1-4.4 problems
01/08 Exponential & Logarithm Retest

01/11 F-Block: Extra 4.1-4.4 problems
01/12 H-Block: CW p.379/71-74 HW p.377-378/41-57 odd,60,61,64,67
01/13 F-Block: CW p.379/71-74 HW p.377-378/41-57 odd,60,61,64,67
          H-Block: Solving with Sinusoids
01/14 F-Block: Solving with Sinusoids (half-day B A G F)
01/15 continue on Solving with Sinusoids

01/18 Martin Luther King Day (no school)
01/19 H-Block something extra that is as yet unplanned
01/20 Quiz Sinusoid Quiz; 4.5 Graphs of the other trig functions
01/21 4.7 Graphs and Restrictions of Inverse Trig Functions
01/22 4.7 Composing Inverse Trig Functions; End of Term 2

Starting Trig

2009-12-10T11:42:00.001-05:00

Regardless of whether remediation is needed for the exponential and log unit (given the groaning about the test), we will be starting trigonometry. If, after I have looked over the tests, we need to backtrack, that will happen after we have done the following:

12/10 Angles in degrees & radians, on the circle, special right triangles
           HW Demana p.343/3-39 by 3's
                 Brown p.265-267/3,6,9,16,17,23-25
12/11 6 Trig functions, Angular & linear momentum
           HW Demana p.344/40-42,48,50,51 and
                              p.352-354/13,17,19-24,51-56,62-66

12/14 Circular Functions and the Unit Circle
           HW Demana p.365/1-9 odd,17-20,27,29,33-49 odd,53
12/16 More Practice: CW p.366-367/61-70 (bring the book or pages)
           HW finish CW plus p.366/55-60

Review answer key

2009-12-08T22:39:00.001-05:00

You can download the answer key for the exp and log review here.

More with Exp and Log

2009-11-30T11:47:00.002-05:00

11/23 3.3 Log Functions (inverse of Exp Functions)
                  HW p.291-293/1-17 odd, 19-22, 27-51 by 3's, 55,58,67
11/25 3.4 Properties of Logs
                  CW/HW Worksheet of problems using log properties
11/26 Thanksgiving!

11/30 3.4 Extra Problems on Log Properties
                  HW finish handout
12/02 3.5 More Log Properties & Applications
                  HW listed on handout
12/03 3.5 Continue with Application Problems
                  HW listed on handout
12/04 3.5   Using semi-log paper
                  HW finish handout

The test on this chapter may be on Wednesday, 12/09.

Starting Exponential and Log Functions

2009-11-19T08:55:00.002-05:00

This is this week in Exponential functions (Ch 3).

11/16 Intro to the difference between polynomials and exponentials
           HW p.270/1-19 odd, 25-30, 31-35 odd
11/18 Rational Quiz
11/19 Characteristics of Exp and Logistic Functions, base e
           HW p.271-272/22,23,39,40,45-49 odd,51-55,57,58,61-64
11/20 Exp and Logistic Modeling
           HW Demana: p.279-280/1-17 odd, 19-22, 29-39 odd, 40
                 Brown: p.183-185/7-21 odd, 24

Last bit of Chapter 2

2009-11-12T10:36:00.004-05:00

We are spending an extra day on section 2.7 for better mastery. Here is a pile of homework.

11/12 p.237-238/43,45,47,54,57,59 and p.585/15,21,22,33,35
11/13 p.246/3-24 by 3's,29,41 and p.586/37-42 and Brown p.35/31-40

Rational Functions

2009-11-07T22:57:00.003-05:00

Rational functions are the ultimate study of polynomials. You need the zeros of the numerator polynomial to find the zeros of the rational function. You need the zeros of the denominator polynomial to find the discontinuities. You need to divide the numerator polynomial by the denominator polynomial to find the polynomial asymptotes for the end behavior. And we have already done lots of graphs from clues with asymptotes!

11/06 2.7 Rational Function review
                  HW look over "end behavior model" worksheet again,
                   do "more problems with rational functions" and
                   p.236/9,12,15,21-24,27-36 by 3's, 37-41 odd
                  (do not be alarmed! 7 of the them are matching graphs)

11/09 2.7 More with rational functions and power functions
11/11 Veterans' Day - no school
11/12 Solutions and Inequalities
11/13 Quiz of 2.2, 2.7, 2.8

Answer Key for Complex Recap

2009-10-29T13:15:00.003-04:00

Here is the answer key for tonight's worksheet.

Moving on to Complex Numbers

2009-10-28T23:00:00.003-04:00

Sorry this is a bit behind the date.

10/22 Pop Quiz and the Euclidean Algorithm HW finish worksheet

10/23 2.5 Complex Numbers (notation, conjugates, operations)
                   HW (due Wed, 10/28) p.218-221/ Quick Review 8, 10 and
                    Exercises/6-8,14-16,23,24,26,27,31,32,33-39 odd, 41-44,
                                    45-53 odd, 59, 60, 62, 64
10/26 2.5 Complex Numbers (the complex plane, magnitude)
                   HW finish handout of book problems p.219/55, 57, 61, 63
10/28 2.6 Complex Zeros (Fundamental Thrm and Linear Factorization)
                   HW p.225-227/3-39 by 3's,46,51,53,57 plus worksheet of
                   problems p.222/Exploration and p.226/41-45, 50
10/29 Extra Problems
10/30 Quiz of anything from the chapter so far

11/02   More problems from throughout the chapter
11/04   Either still more problems or start 2.7
11/05 Test of 2.1-2.6

More with Polynomials

2009-10-13T16:13:00.004-04:00

Chapter 2 starts with an in-depth look at polynomials. We will be spending two days per section to make sure that we have really explored the topic.

10/15 2.3 Polynomial modeling
                  HW p.196-197/3-30 by 3's,38,41,45,46,51,54-56
10/16 2.3 Creating polynomial functions
                  CW/HW Worksheet plus HW p.198/65-75 odd

10/19 2.4 Zeros of polynomials (and many theorems
                  HW Demana p.208-212/3-36 by 3's, 49-55 odd, 74
                        Brown p.61/9-21 odd, 16, 25 (Factor Thrm for 16 & 25)
10/21 2.4 Finish up theorems with Rational Roots Theorem
                 HW GCF/LCM Worksheet
10/22         Word Problems to put it all together

The start of Chapter 2

2009-10-09T13:26:00.003-04:00

We are starting chapter 2 with modeling problems (word problems!). They all focus on polynomials so that you have a context for our more theoretical study of the material. Due to Columbus Day and a professional development day, one homework assignment will cover almost a week of real time.

10/09 Power functions and polynomial functions
HW Demana p.76/45 and p.170-174/35,37,49,51,54,55,
57,68-71 plus Brown p.42-43/38,44
Note: The problems in red will be done in class for H-Block.

If you need more practice with quadratic functions, look at Demana p.170/19-34.