Matrices

The study of matrices involves the most recent applications of mathematics that we study. While understanding the techniques required to manually manipulate the data, we will spend a lot of time using the calculator and the computer.  We will be moving through matrices quickly with a lot of applications.  It is chapter 7 in the Demana book and chapter 14 in the Brown book.

Here is the list of Skill Objectives.

4/26   Algebra 2 Review day
          HW B p.521-522/9,11-13,16;  p.526-528/5-11 odd, 12, 15, 16, 18
                  D p.540-542/33-39 odd, 43, 45, 48, 52

4/29   Matrix Multiplication, Augmented Matrices, etc.

          HW Extra Problems on Matrix Multiplication (link to online Row Operations site)

4/30   Applications of matrices to linear systems

          HW handout includes 6 problems and these Demana problems:

                  p.554/67-70, 73, 74, 76, 78, 79, and p.563/13, 15, 21
5/01   Transformations Day 1 HW p.1-4 of handout

5/03   Transformations Day 2 HW p.5-7 of handout

5/06   Communication Matrices WW B p.540-542/3,5,7,9-13  (AP Chem Exam)

5/07   Markov Chains (probability with matrices)

          HW finish handout plus Brown p.547-550/5, 9-11, 14-17

5/08   3D Matrix Apps HW do all of handout

5/10   Determinants with vectors HW handout problems 1-7 (AP Stats)

5/13   MCAS (No G-Block) Determinants in 3D HW handout problems 8-14
5/14   MCAS (No E-Block) Determinants in 3D HW handout problems 8-14

5/15   Determinant summary, Review HW handout  (AP US History Exam)
5/17   Matrix Test (Practice Test, Solutions)

Finish (and understand) all packets by then and you should be fine. Look over your Matrix Skills sheet to be sure.

Vectors

Here is the syllabus for the topics. In Demana it is the beginning of Chapter 6.  In Brown it is Chapter 12.  The skills you should know for manipulating and using vectors are listed here.  Make sure you know how to do all of them before the test!

4/01   Intro to Vectors

             Demana p.464-465/3-27 by 3's and 29-39 odd and Brown p.423,425/5-7, 17-20

4/02   Angles between vectors, The Dot Product

             Brown p.444-445/1-19 odd, 23, 27-29

4/03   Vector Proofs (D: 6.1 and B: 12.1, 12.2)

             finish worksheet plus Brown p.425-426/21-23 and p.429-431/11,12,15,18,27-29,33,34

4/05   Equations of Lines, Vectors in 3D

             finish worksheet plus B p.436-437/17,18,23 and D p.466/63,64

             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).

4/08   More 3D: Equations of Planes, vectors perpendicular to planes (B: 12.5)

             Worksheet problems 1-10 plus B p.452/42-45 and p.455/15,21,28-31,33,34

             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!)

4/09   Spheres, vectors & planes, Angles between planes (B: 12.5, 12.6)

             B p.450-451/11,13,17,27,31-36,41,42 and p.456-458/21,25,27,34,35,37-39

4/10   The Cross Product

             Vector Cross Product worksheet

4/12   Projections, Distance from a point to a plane

             Work on worksheet and do "Points, Lines and Planes in 3D" problems 11-14

4/13-4/21   April Vacation

4/22   Review Day 1 (download a practice test, download solutions)

• We went through finding the distance from a point to a line in 2D and a point to a plane in 3D. The question arose about finding the distance from a point to a line in 3D. Look again at the homework problems in the Brown book: p.457-458/34-39.
• For projection practice, do Demana p.473/25-28 and 58a.
• If you did not do so, finish the 3D points, lines and planes worksheet (problems 11-14).
• Other than that, go back and make sure you have done and understood all of the previous homework in light of the objective skills of the unit. 

4/23  Extension problems

4/24  Vector Unit Test

Polar Practice Test

Here is a practice test.  I don't have an answer key yet but it is good to try the problems.

Find more old tests with answers here.

The schedule seems to have realligned...

SNOW DAY UPDATE (see below)

Since things seems to have realligned, here is the rest of the polar coordinate schedule, now with dates. The test is scheduled for the day after the first night of Passover.  I know this will be a problem for some of you so please see me early to make arrangements if you cannot take the test that day.

3/15     Cylindrical & Spherical Coordinates  

            HW Worksheet

3/18        cis, Products of Complex Numbers

              HW B p.406-407/10, 12, 15, 17, 24-31 and D p.512/63 (derive Quotient Rule)
3/19       SNOW DAY  
3/20 (E)  Powers and Roots of Complex Numbers (De Moivre's Theorem)
              HW B p.410-411/4,5,9-14 and p.413/5,6,8,11-13
3/21 (G)  Powers and Roots of Complex Numbers (De Moivre's Theorem)
              HW B p.410-411/4,5,9-14 and p.413/5,6,8,11-13

3/22 (E)   Extra Practice HW finish worksheet

3/25 (G)  Extra Practice HW finish worksheet

3/25 (E)   Review
3/26 (G)   Review
3/26 (E)   Polar Test
3/27 (E)   Extra Complex Problems3/28 (G)   Polar Test

Important Dates

3/21  MCAS Day 1 (Hr G H A)

3/22  MCAS Day 2 (D E F B C)

3/25  MCAS Day 3 and 1st night of Passover

3/26  2nd night of Passover

3/28  End of Term 3

3/29  Good Friday - no school

Parametric Addendum

Given that it was tough giving Parametric equations enough time in class, I am changing the first assignment on parametrics to section 12.3 of the Brown book.  Do the following problems on pages 437-439/23-29, 39, 40.  This is our new Day 3.

Polar Coordinates

This is a quick but interesting unit on another way of describing the location of points in space.  It is a somewhat surprising application of trig that can also be used to work with complex numbers.  The schedule is plagued by holidays and MCAS but we will work around it as best we can. Polar coordinates are covered in the Demana book in sections 6.4-6.6 and in the Brown book in Chapter 11.  I am using Day1 notation rather than dates because the E-Block and G-Block sections will be off (due to the half day - but not if there is a snow day on the 7th!).

Day 1    Intro to Polar  CW Brown p.400-402/1-11 odd
            HW Demana p.492-493/5,6,23-30,52-54,61,63
Day 2    Converting equations and graphs (polar <=> rectangular)
            HW D p.500-502/5,7-13,17,21,23,45,49,53,55
Day 3    Parametric Equations 
            HW B p.437-439/23-29, 39, 40
Day 4    Parametric Equations some more
            HW Worksheet
Day 5    Cylindrical & Spherical Coordinates  
            HW Worksheet
Day 6    cis, Products of Complex Numbers
            HW B p.406-407/10, 12, 15, 17, 24-31 and D p.512/63 (derive Quotient Rule)
Day 7    Powers and Roots of Complex Numbers (De Moivre's Theorem) 
            HW B p.410-411/4,5,9-14 and p.413/5,6,8,11-13
Day 8    Extra Practice 
            HW finish worksheet
Day 9    Review
Day 10  Polar Test (could be 3/25 for E-Block, 3/26 for G-Block, neither date is optimal - see below)

Important Dates

3/07  Professional Development Half-Day C B H F

3/19  MCAS Day 1 (Hr G H B)

3/21  MCAS Day 2 (Hr G H A)

3/22  MCAS Day 3 (D E F B C)

3/25  1st night of Passover

3/26  2nd night of Passover

3/28  End of Term 3

3/29  Good Friday - no school

Sum and Difference Links

There are several resources to view proofs of the angle addition and angle subtraction identities.  Look them over and make sure you understand them.  You will be required to prove some of the basic identities on your test and the proofs of these identities require diagrams which may not occur to you during a test situation if you haven’t thought about them before.

Demana Precalculus 5.3 page 421 (a distance formula based proof)

Brown Advanced Math 10.1 p.369 (a law of cosines based proof)

Mr. Richardson’s PowerPoint presentation

            download here

Another website with very elegant triangle proofs:

            http://www.cut-the-knot.org/triangle/SinCosFormula.shtml  and

            http://www.cut-the-knot.org/triangle/SinCosFormula2.shtml (beautiful!)