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 Friday, June 13th.

6/09  Review Day 1 (Basic Functions, Polynomials and Limits) [answer key]

6/10  Review Day 2 (Trigonometry)  [answer key]

6/11  Review Day 3 (6/12 for G-Block)  (Vector and Parametric Equations)  [answer key]

6/13  Review Day 4 (Conics, Polar, Exponential and Log)  [answer key]

6/16  Long Block Review: Practice with 2010 Final  [answer key]

6/18  Math Final Exam 8:30 - 10:30 am

         E-Block room:  167       G-Block room:  169 

         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.  These you
         will return after the test to our classroom in the math building.  I will be in room 816 from
         11:00 until 12:00 on Wednesday and Thursday.  Bring them by one of these two days.

6/23  Make-up final in the morning, all blocks for 25 minutes each
6/24  Come see me to get your grades

Conics

This is our last unit.  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.

5/20  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) 

5/21  Parabolas (algebra, geometric, focus-directrix)

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

5/23  Hyperbolas (algebra, geometric)

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

5/26  Memorial Day

5/27  Eccentricity and Focus-Directrix for all conics
         HW B p.249/1-3   and p.250-251/1-3,21,22  and  D p.600/46, 53 (find the eccentricity)

5/28  Parametric Definitions for all conics

         HW finish handout

5/30  Polar Definitions for all conics
         HW D p.626-628/3-42 by 3's, 55, 56, 58, 59

6/02  E-Block Extra Questions (3D)  MCAS (Bio) B E F D A
6/03  Rotating Conic Sections          MCAS (Bio) D A G H E
         HW finish handout, including Brown: read pp.242-244 and do p.245/18, 20, 22, 23, 24
6/04  Review (document, old answer key)  (Practice Test, Answer Key)

         HW finish handout (Extra Credit B p.250-251/21,22)

6/06  Conics Test   

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.

4/28   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

5/02   Transformations Day 1 HW p.1-4 of handout

5/05   Transformations Day 2 HW p.5-7 of handout  (AP Chem Exam in am)

5/06   Communication Matrices WW B p.540-542/3,5,7,9-13

5/07   Markov Chains (probability with matrices)

          HW finish handout plus Brown p.547-550/5, 9-11, 14-17
5/08   Half Day (C A G F)

5/09   3D Matrix Apps HW do all of handout (AP Stats at noon)

5/12   Determinants with vectors HW handout problems 1-7

5/13   MCAS (A G H B) Determinants in 3D HW handout problems 8-14

5/14   MCAS (C E F H D) Determinants in 3D HW handout problems 8-14  (AP US History Exam)

5/16   Determinant summary, Review HW (handout, answer key)

5/19   Matrix Test (Practice Test, Solutions)

Finish (and understand) all packets by the 19th and you should be fine. Look over your Matrix Skills sheet to be sure.

Vectors and Parametrics

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!

3/26      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

3/28      Angles between vectors, The Dot Product (End of Term 3)

             Brown p.444-445/1-19 odd, 23, 28, 29 and p.429-431/11,12,15,18, 31, 32

3/31      Vector Proofs (D: 6.1 and B: 12.1, 12.2)  (some example solutions)

             finish worksheet plus Brown p.425-426/21-23 and p.429-431/27-29,33,34, 37, 38

4/01      Equations of Lines, Vectors in 3D

             finish worksheet plus B p.436-437/17 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).

4/02      Parametric Equations
             HW B p.437-439/24-29, 39, 40 and p.451/27, 28
4/04      More Parametric Equations
             HW Worksheet

4/07   More 3D: Equations of Planes, vectors perpendicular to planes (B: 12.5)

             Worksheet problems 1-10 plus B p.452/43-45 and p.455/15,28-31,33

             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!)

4/08   Spheres, vectors & planes, Angles between planes (B: 12.5, 12.6)

             B p.450-452/11,13,17,31-36,41,42 and p.456-458/21,25,27,34,35,37-39

4/09   The Cross Product

             Vector Cross Product worksheet B p.466/2,3 p.467/9,13,15bd

4/11   Projections, Distance from a point to a plane

             Do p.457-458/37-39 if skipped before and "Points, Lines and Planes in 3D" problems 11-14

4/14   Start Review Problems (this is the first night of Passover)  (answer key)
4/15   Finish Extension Problems  (download a practice test, download solutions)

4/16  Vector Unit Test  (tell me early if this date is a problem because of Passover)

• For projection practice, do Demana p.473/25-28 and 58a.

• 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. 

4/18-4/27   April Vacation

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 and MCAS).

Day 1    Intro to Polar  CW Brown p.400-402/1-11 odd  (this is 3/07, before the Trig Identities Test)
            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    Cylindrical & Spherical Coordinates (helpful website)

            HW Worksheet and Answer Key (check your graphs on your calculator)
Day 3a  More practice with Cylindrical & Spherical Coordinates (only E-Block)

            HW Worksheet (answer key)

Day 4    cis, Products of Complex Numbers

            HW B p.406-407/11, 12, 15-17, 23, 24, 29, 30, 32 and D p.512/63 (derive Quotient Rule)
Day 5    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 6    Extra Practice 

            HW finish worksheet (answer key)

3/24     Review (answer key)
3/25     Polar Test (Practice Test, Answer Key)

Important Dates

3/13  Professional Development Half-Day C B H F

3/18  MCAS Day 1 (Hr G H A)

3/19  MCAS Day 2 (E F H D)

3/21  MCAS Day 3 (D E F B C)

3/28  End of Term 3

Trig Identities

Lots of Proofs this unit! We start with simplifying practice and then jump in.

Note: We will be using the Demana book for most, but not all, of the assignments.

2/24   Trig Identity basics

          HW D p.410-411/3-60 by 3's, 69-73 odd

2/25   Simplifying for a solution

          HW D p.411-412/52-62, 75-82, 85

2/26   Proving Trig Identities

          HW D p.418/11-51 odd (45, 47 are tough, don't stress), 71, 80

2/28   Sum and Difference Formulas

          HW D p.425-427/3,5,7,13,17,21,27,29,31-35,37,43,45,47,48,52,55,73

3/03   Double Angle, Half Angle and Power Reducing Formulas

          CW B p.374/39-41, p.385/45, 47

          HW D p.432/3-30 by 3's, 39-45 odd, 53

3/04   Review and Extension Problems  CW Worksheet (answer key)

          HW B p.384-385/37, 51, 53 and p.390-391/23, 26-28

3/05   Review Packet (answer key) (Practice Test and Answer Key)
3/07   Start Polar Coordinates

3/10  Trig Identities Test

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!)

Geometric Trig

Post-test homework was to do the area and identity worksheet. We continue with the more geometric applications of trigonometry. For this unit we will use primarily the Brown book.

2/03  9.2  Area Formula and applications

                HW p.342-344/1-19 odd, 20-22, 35, 36

                (p.344/34 is a bonus problem - turn it in for extra credit)

2/04  9.3  Law of Sines

                HW p.347-349/1-27 odd

2/05  9.4  Law of Cosines (Snow Day, E-Block read Brown p.350-352, give the HW a try)

                HW p.352-354/1-17 odd, 22

2/07  9.1 - 9.4  Mixed Trig Problems  (I will be out taking a course - day 3, last day)

                HW p.337/31-33, 37;  p.349/28;  p.354/23 and p.356-358/11,14,18,21,24,25

2/10  9.4  Mixed Trig Problems

                HW p.357-358/29-37

2/11  9.4  Mixed Trig Problems

                HW p.358/38, 39, 40, 42

2/12  Review and Extension Problems (Worksheet and answer key) (Practice Test and Answer Key)
2/13  Half-Day due to snow, no G-Block, see links to extension worksheet above

2/14  Test of Geometric Trig

The Geometric Trig test will have questions that require a full understanding of the trig area formula, the Law of Sines, and the Law of Cosines. There will be two problems (chosen by me) from the "C" problems on page 358 (not 41 or 43). I have not assigned every problem in the unit but notice that after you finish these problems you should be able to find the area, the sides, the angles, the length of the median/angle bisector/altitude, and the radii of the inscribed and circumscribed circles for any triangle - among other things.

2/15-2/23  February Break