Friday, June 6, 2014

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

Monday, May 19, 2014


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 (documentold answer key)  (Practice Test, Answer Key)
         HW finish handout (Extra Credit B p.250-251/21,22)
6/06  Conics Test   

Thursday, April 17, 2014


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 TestSolutions)

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

Tuesday, March 25, 2014

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

Friday, March 7, 2014

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)
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

Sunday, February 23, 2014

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:

Sunday, February 2, 2014

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

Friday, January 3, 2014

Right Triangle Trig and Sinusoids

Trigonometry is our longest unit spanning more than two months and three tests. We start in the Demana book but will move into our second book, the Brown book, as we progress.  We begin with Right Triangle Trig, mostly review from last year.

12/20  Right Triangle Trig Review
           no HW but if you struggled with today's activity, read section 4.2 in the Demana book

12/21 - 1/02 Christmas Break!

Circular functions (4.3) are a big part of understanding trigonometry conceptually. We will spend a few days making sure you understand.  Problems 67-76 on January 6th are the problems you should really push yourself to understand - don't just give up and wait for me to go over them.

01/03  Snow Day

01/06  4.3 Circular Functions
           HW Demana p.347-349/2,3,7,27-35 odd, 41-53 odd, 60-64, 67-76
01/07  More Practice CW Brown p.272/3-10,  13, 14 and worksheet
           HW Brown p.272-274/17-27 odd, 29-32, 33-41 odd
01/08  Finding all solutions with circular trig HW finish handout
01/09  Professional Developement - Half Day (B A G F)
01/10  Quiz of 4.1-4.3
           HW Graphing Trig Functions handout

1/13  4.4 Sinusoids
         HW Demana p.357-358/13-41 odd, 42, 49, 50, 53, 73, 75
1/14  CW p.360/91-97   HW p.357-359/51, 52, 54-57, 59-69 odd, 70-80 even
1/15  Trig Evaluation Practice and Extra Problems
         HW finish problems 1-12 of Extra Problems worksheet
1/17  Discuss Extra Problems Worksheet (and End of Term 2)
         HW finish Extra Problems worksheet (13-21)

1/20  Martin Luther King Day - no school
1/21  Solving with Sinusoids  CW problems 1-5 (answer key)
         HW problems 6 - 9
1/22  Continue Solving with Sinusoids
         HW finish rest of handout, problems 10 - 17
1/24  Quiz of 4.1-4.4  (I will be out taking a course - day 1)

1/27  4.5 Graphs of the other Trig functions and 4.7 Inverse Trig functions
         HW p.366-368/13-16,18-39 by 3's,43,60,63,64 and p.385/37-40
1/28  Extra Sinusoid and Inverse Trig Problems
         HW in Brown: p.290-291/11-14, 27-29, p.306-307/30,31,33,36, p.314-316/15,17,18,21,25,26
1/31  Test of Ch 4   (I will be out taking a course - day 2)
         HW Trig Area and Identity intro