Honors Advanced Math

Final work

2008-05-30T14:09:00.002-04:00

The schedule for the rest of the school year is as follows:

6/02 Sequences and Series Test (review answer key posted in First Class)
6/03 MCAS (Hr G H E) no class
6/04 MCAS (E F A D) no class
6/05 Review Day 1 (Functions, Polynomials, and Limits)
6/06 Review Day 2 (Trigonometry)

6/09 Review Day 3 (Vectors, Parametrics, Polar, and Conics)
6/10 Review Day 4 (Exponential and Log Functions, Matrices)
6/11 English Final 8am Science Final 11am
6/12 ForLang 1 Final 8am Math Final 11am in room 710
6/13 SocStds Final 8am ForLang 2 Final 11am

6/16 Last Day of School (BC students get Calculus books)
6/17 Get your grades

Sequences and Series

2008-05-19T16:24:00.002-04:00

We are going to study our last topic of the year: Sequences and Series (Ch 13 in the Brown book). Below is the syllabus. I expect to give you time to start all of the homework problems in class and some of them may become assigned classwork.

5/19 Explicit Definitions; Geometric, Arithmetic Sequences
          HW pp.477-479/18-33 by 3's, 34, 37, 39, 43-45, 48-50, 53,56

5/20 Recursive Definitions of Sequences
          CW pp.481/1,2,11,12,13-17 odd
          HW pp.481-485/19,20,22,23,26,27,29,32-34

5/23 Finite and Infinite Series; Sigma Notation
          CW pp.508-510/9,11,25,27,39
          HW pp.489-492/10-13,17,19,27,29,35,39,41,44

5/27 Limits of Infinite Sequences and Series
          HW pp.496-498/3-33 by 3's, 34-36

5/29 Sums of Infinite Series
          HW pp.502-505/9-21 odd, 29,31,33,37,38,41-43

5/30 Extra Problems

6/02 Sequences and Series Test

Review Answer Key

2008-05-15T18:22:00.002-04:00

The answer key, such as it is, has been uploaded in the FirstClass conference in both Word and pdf formats. I can't promise I didn't make mistakes but that kind of discussion is what the conference is for. ;-)

Conic Sections (Cutting Cones and Quadratic Relations)

2008-04-28T21:53:00.016-04:00

Note: This is a final revised syllabus (it won't be revised again).

Quadratic Relations usually are not functions, but they are symmetric and interesting. Of course they can be challenging because they can be transformed just like functions (translations, dilations, rotations) and there is a lot of vocabulary.

Here is the proposed syllabus:
4/28 Intro to Quadratic Relations   HW finish Circle Worksheet
4/29 Algebraic and Geometric Ellipses
        HW D p.622-623/3-30 by 3's, 42 (omit eccentricity)
5/01 Rotated Ellipses and Parametric Ellipses HW Rotation Worksheet
5/02 Algebraic Hyperbolas
        HW D p.632-633/3-36 by 3's, 51 (omit eccentricity)

5/05 Geometric Hyperbolas HW D p.633-634/48-50, 52-55, 61
5/06 Parabolas HW D p.611-612/3-51 by 3's, 55, 58
5/08 Conics through Parametrics HW Parametrics     Half Day C B G F
5/09 More on Quadratic Relations HW finish worksheet plus
        Brown read pp.242-244, do p.245/18,20,22,23,24

5/12 Focus/Directrix Defn and Eccentricity HW D p.641/13-19 odd, 33-36
5/13 3D Quadric Surfaces
        HW p.818-819/1-7,12-14,17,19-29 odd (identify only),56,59-63
5/15 Review
5/16 Conics Test

Other Important May Dates:
5/17 Junior Prom
5/21 Math MCAS (Sophomores)
5/22 Math MCAS (Sophomores)
5/23 US History MCAS (Juniors)
5/26 Memorial Day

Finishing up matrices

2008-04-14T21:36:00.000-04:00

We finished up the matrix unit with some homework from the Brown book. Markov chains came before the test, Communication matrices came after.

4/14 Transition matrices and Markov Chains.
HW finish handout and do p.547-550/5, 9-11, 14-17

4/17 Matrix Test

4/18 Communication Matrices
CW (before vacation) p.540-542/3, 5, 7, and 9–13

The homework for the rest of the Matrix unit

2008-04-08T14:24:00.002-04:00

The Transformations and Determinants parts of this unit are mostly handout based. Here is the homework:

4/03 Transformations of the plane pages 1-4
4/04 Transformations of the plane pages 5-7

4/07 Transformation Matrices in 3D problems 1-6
4/08 Determinants problems 1-8
4/10 Determinants problems 9-20
4/11 Determinant summary all problems

Matrices - more than you imagined!

2008-03-31T09:14:00.001-04:00

Matrices is a relatively new branch of mathematics - only about 150 years old! It is used for a tremendous variety of applications, many of which we will explore. Here is the syllabus. Much of the homework will be worksheets so the details will be posted later.

3/25 post-vector-test HW Read Brown sections 14-1 and 14-2 and do
           B p.521-522/9,11-13,16 and p.526-528/5-11 odd,12,15,16,18
3/27 Identity and Inverse
           HW finish worksheet plus D p.565/33-35,37,45-48
3/28 Linear Systems and Row Operations
           CW Three variable linear systems worksheet
           HW D p.577-578/5-8,17,23,29,31-36,47-57 odd
           (do the row ops by hand for 5-36, use the calculator for the rest)

3/31 Inverses from Row Operations
           HW Computer Lab
4/01 Applications
           HW Worksheet (6 problems plus D p.578/59-62,65,66,68.70.71
                                     and D p.585/13,15,21)
4/03 Transformations Day 1
4/04 Transformations Day 2

4/07 3D Matrix Applications
4/08 Determinants with vectors
4/10 Determinants in 3D
4/11 Determinant wrap-up

4/14 Markov Chains (Probability with matrices)
4/15 Review
4/17 Matrix Test
4/18 Communication Matrices

4/19 - 4/27 April Vacation

Post-Test Matrix Review

2008-03-24T17:59:00.001-04:00

Here is the Matrix Review assignment. Come in Thursday knowing how to add and multiply matrices.

Read Brown sections 14-1 and 14-2 and do
B p.521-522/9,11-13,16 and p.526-528/5-11 odd,12,15,16,18

Polar Coordinates

2008-03-13T14:55:00.001-04:00

Polar coordinates are another way of locating points in space. You can do really cool things with them, especially when we look at complex numbers again. Make sure you finish the classwork at home if it doesn't get done in class. Make sure you use the correct book.

3/11 Intro to Polar Coordinates (D 6.4 and 6.5, B 11-1)
           CW D p.515-516/3,5,7,15,21,29,51,55
           HW B p. 400-402/1-21 odd, 39

3/13 Converting Equations and Graphs
           CW D p.524/57, 58, 61, 63
           HW D p.523/5,7-13,16,45,49,65-67

3/14 Extra Practice and 3D (Spherical and Cylindrical Coords)
           CW/HW Worksheet of problems

3/17 cis, Product of Complex Numbers (D 6.6, B 11-2 to 11-4)
           HW B p.406-407/10, 12, 15, 17, 24-31

3/18 Powers and Roots
           HW B p.410-411/4,5,9-14 and p.413/5,6,8,11-13

3/20 Extra Complex Roots Problems
           HW finish worksheet

3/21 Good Friday - no school

3/24 Review of Polar

3/25 Polar Test (MCAS schedule, class at 1:30 - 2:25)
           HW on Matrices review - posted later

Revising the schedule (and pointing out a typo)

2008-03-03T17:57:00.002-05:00

Ceding to the pleading, I am moving the test to Friday (part 1 = 45 minutes of testing) and Monday (part 2 = 10 minutes of testing). This means we will start something new tomorrow. Finish the worksheet from today for homework. (Typo Note: In problem 4, Matt starts at (35, 50)).

Helpful calculator hints: For the Ferris wheel problems, put your calculator in Parametric mode, with Simultaneous (rather than Sequential). Also, in the Y= window, change the line type to the -0 so you can see where the rider is at each time t.

Finishing up Vectors

2008-02-26T11:09:00.002-05:00

We are starting to really use vectors to find other things, like the equations and angles between planes and the volume of parallelepipeds. We end by concentrating on the coordinate equations - the study of parametrics. Keep up and don't let the Science Fair take over your life!

2/26 Spheres, Vectors and Planes (12-6)
           HW   p.450-452/10, 12, 13, 15, 21, 43-45
           and p.455-457/1, 19, 29, 35, 37

2/28 Area and Volume from the Cross Product
           HW p.464/11-16, 20-22

2/29 Parametrics
           CW B p.437/24, 34, 38, 39 (finish for HW)
           HW D p.507-508/3-24 by 3's, 34, 40

3/03 Parametrics in 3D and Review

3/04 Vector Test

More with 3D

2008-02-25T14:03:00.002-05:00

We talked about equations of planes and vectors perpendicular to the planes. The homework is from two sections of Brown. 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!)

HW p.451/25-28, 32, 38 and p.467/1-4, 7-9, 13, 15, 16

Moving in 3D

2008-02-14T17:29:00.004-05:00

We started a worksheet today that contained notes about vectors in 3D and had a series of questions. Finish the questions for homework. 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).

Vector Proofs and Vector Equations of Lines

2008-02-11T17:20:00.001-05:00

2/12 More practice with vector proofs and a new way to write the equations of lines
HW finish worksheet of problems plus Brown p.436-437/17, 18, 23

Vectors (Where are we going?)

2008-02-07T11:09:00.001-05:00

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.

2/07 Intro to Vectors
           D p.488/3-27 by 3's, 29-39 odd
           B p.423, 425/5-7, 17-20

2/08 Angle between vectors and the Dot Product
           B p.444-445/1-19 odd, 23, 27-29

2/11 Vector Proofs   CW D p.489-490/55-58
           B p.425-6/21-23 and p.429-432/3-18 by 3's (not 6), 27-29, 33, 34

2/12 More Vector Proofs, Vector Equations of Lines

2/14 Vectors in 3D

2/15 Physical Vectors in 3D (Exciting Activity!!!)

Sum, Difference, Double and Half Angle Formulas

2008-01-29T12:51:00.002-05:00

We are proving (and practicing) with several important identities this week, all of them involving modifying the angles. You must be able to generate a proof of them on your own, as well as using them to answer/simplify problems.

1/28 5.3 Sum and Difference Formulas
                  HW p.444/1-29 odd, 31-34, tan(A + B), tan(A - B)

1/29 5.3 More proofs of cos(A + B) and cos(A - B)
                  HW p.444-445/33-43 odd, 44,47,49,52,55,60,63-65,67

1/31 5.4 Double Angle Formulas
                  HW p.452/5-35 odd

2/01 5.4 Half Angle Formulas
                  HW p.451-452/39-47 odd, 51-53

2/04 Review

2/05 Test of 5.1 - 5.4

Fundamental Trig Identities

2008-01-22T09:39:00.001-05:00

We return to the Demana book for our work with Trig Identities. Section 5.1 focusses on the Fundamental Identities - the ones you just have to know. These include (but are not limited to) the cofunction, reciprocal, and Pythagorean identities.

1/18 p.430/1-29 odd, 31-34
1/22 p.430-431/35, 38, 41-45 odd, 59, 61, 67, 69-72

Core Set of Problems, etc.

2008-01-13T18:15:00.000-05:00

Here are the Core Set of problems that you have to know how to do:
p.349/27, 28
p.354/22, 24
p.358/36-39

Here are two you should know how to do:
p.342/17
p.349/23
There is also an interesting suggested problem on the conference from James Zhang that relates the two together.

There will be something like:
p.343/19, 20; p.353/15, 16
p.357/29-32

Another extra credit problem, due Friday 1/18 is p.349/29.

Mixed Applications (and the Goat)

2008-01-08T11:24:00.001-05:00

We will be working on using our knowledge of Geometry as well as the trigonometric area formula, the Law of Sines, and the Law of Cosines to solve problems. Some of the problems are difficult. From the homework listed below, traditionally, at least one problem from 36-43 has been on the next test so you must know how to solve these problems. We will be working on them in class too.

(Remember, we are using the Brown book.)
1/08 HW p.355-358/11, 14, 18, 21, 23, 29, 39, 40
1/10 HW p.356-358/20, 24, 25, 32, 36-38
1/11 HW p.357-358/33-35, 41-43

Also, for extra credit, you may do the infamous Goat Problem.
It is p.344/34 of the Brown book. It is due on Monday, 1/14.

Law of Sines and Cosines

2008-01-04T16:14:00.001-05:00

After working on a worksheet where the area formula for triangles evolved from trig applications (and some identities were derived), the homework moves to using trig for some geometric applications. The next week of homework is from the Brown book. We start with the Law of Sines, continue with the Law of Cosines and then mix it up with Mixed Applications.

1/04 read p.345, do p.347-349/1-27 odd
1/07 p.352-354/1-17 odd, 22

Return and Review

2008-01-03T20:44:00.001-05:00

Welcome back from vacation. Today we reviewed the fundamentals of trig functions. This served as a refresher and a way to quickly set you up for any test corrections you need to make. We also talked about inverses and started a packet that reminded you that reciprocals and inverses are not the same.

HW: finish the packet

Finish up Ch 4 before Vacation!

2007-12-13T10:00:00.001-05:00

We will finish up Chapter 4 before vacation. Here is the plan:

12/07 Worksheet of Extra Problems for 4.1-4.4 HW finish it
12/10 Quiz of 4.1-4.4   HW Relationships of Trig Functions
12/11 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
12/13 4.7 Inverses - Graphs and Restrictions
             HW p.402-403/1-11 odd, 17, 19, 33-35, 49, 51, 54, 57
12/14 4.7 Composing Inverses
             HW p.402-403/23-31 odd, 37-47 odd, 55, 59; p.414/42, 43
12/17 Solving with Sinusoids HW finish it
12/18 Wrap-up
12/20 Ch. 4 Test
12/21 Combined and Composite Trig Functions Worksheet

12/22 to 1/1 Vacation
1/2 Parent Conferences
1/3 We are back!

Sinusoids!

2007-12-04T09:54:00.001-05:00

Section 4.4 will be covered in two sections: Sinusoids(graphs of transformed sine functions) and Modeling (using trig functions to model real world problems).

12/4 HW p.376-377/5,6-21 by 3's,22,25,28,30,33-36
12/6 CW p.379/71-74; HW p.377-378/41-57 odd,60,61,64,67

The rest of the week with right triangle and circular functions

2007-11-26T18:14:00.001-05:00

I will be out on Friday (11/30) so plan accordingly (eg. copy the pages in your book to bring with you or be ready to work in groups).

11/27 CW p.366-367/61-70
             HW Finish the CW problems plus p.344/48,49 & p.346/Explor1
                    plus, in the Brown book, p.265-267/14, 17, 24, 25

11/28 Professional Development - no school

11/29 Solving Trig Equations HW finish worksheet plus
                   Brown book: p.272-274/17-27 odd, 29-32, 33-41 odd

11/30 CW/HW Demana p.410-414/1, 3, 8, 15, 16, 25, 37-40 and
                                         p. 365-367/49-53, 55, 57-60, 72
                   Brown p.337-338/29ab, 30ab, 31-34, 39, 41, 42

Circular Functions

2007-11-26T14:53:00.000-05:00

We are going to spend two days on section 4.3 but I am only going to post the first night of homework right now.

p.365/1-13 odd, 17-20, 22, 23, 27, 29, 33-47 odd