Review and Final

We will review for four days before the special end-of-year schedule.  Make sure you look over the list of Proofs and Theorems you need to know.  The Final Exam Archive of the math department has a bunch of old finals (with answers!) for additional practice.  (Note: topics change a bit from year to year so don't freak out if there is a question on something we didn't cover.)  Also, all test corrections and grade mistakes must be taken care of by Thursday, June 13th.

6/07  Review Day 1 (Basic Functions, Polynomials and Limits) [answer key]
6/10  Review Day 2 (Trigonometry)  [answer key]
6/11  Review Day 3 (Vector and Parametric Equations)  [answer key]
6/12  Review Day 4 (6/13 for G-Block)  (Conics, Polar, Exponential and Log)  [answer key]

6/17  Long Block Review: Practice with 2010 Final  [answer key]
6/19  Optional Drop-in time 12:00 to 2:00 in room 816 for last questions

6/20  Math Final Exam 8:30 - 10:30 am

         E-Block room:  167       G-Block room:  164

         Remember to bring pencils, eraser, calculator (and maybe extra batteries?), a stomach full of
         healthy breakfast and a brain refreshed by a good night's sleep.  And your books.

6/24  Come see me to get your grades

Conics

We don't have much time so this last unit is done very quickly with little in the way of extensions.  You will need to be able to complete the square (see p.41 of Demana if you forget how)!  Conic Sections are covered in Ch 8 of the Demana book and Ch 6 of the Brown book.

5/24  Circles and Ellipses (see p.15 of Demana for some circle review)

         HW B p.249/9 and D p.599-600/3-36 by 3's, 46, 53 (omit eccentricity) 

5/27  Memorial Day

5/28  Parabolas (algebra, geometric, focus-directrix)

         HW D p.587-590/3-42 by 3's, 49-55 odd, 59, 61, 74-76

5/29  Hyperbolas (algebra, geometric, focus-directrix)

         HW D p.609-610/3-36 by 3's, 51,52,54,55,59,61

5/31  Parametric Definitions for all conics

         HW finish handout

6/03  Review (old answer key)

         HW finish handout (Extra Credit B p.250-251/21,22)
6/04  MCAS (Bio) B A G H D

6/05  Conics Test  

Sequence, Series and the end of the Year

A quick unit on Sequences and Series. All the homework is in the Brown book (Ch 13).

5/20   Explicit & Recursive; Geometric, Arithmatic, Harmonic Sequences

          HW pp.477-479/18-33 by 3's, 34, 37, 39, 43-45, 48-50, 53, 56

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

5/21  Finite and Infinite Series; Sigma Notation

          HW pp.508-510/9, 11, 25, 27, 39

          HW pp.489-492/10-13, 17, 19, 27, 29, 35, 39, 41, 44

5/22  Limits and Sums of Infinite Sequences and Series, Practice (answer key)

          HW pp.496-498/3-33 by 3's, 34-36

          HW pp.502-505/9-21 odd, 29,31,33,37,38,41-43

5/24  Sequence and Series Quiz

         Circles and Ellipses (see p.15 of Demana for some circle review)

         HW B p.249/9 and D p.599-600/3-36 by 3's, 46, 53 (omit eccentricity) 

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