Notes for the Final Exam

A-Block Review 6/11 7:45 - 9:10
B-Block Review 6/12 7:45 - 9:10

You are welcome to come to both review sessions if you have a study.  I will write you a pass.

The final is on Wednesday, June 13th from 12:00 to 1:30.  You can stay until 2:00.  You should get there a little before noon so you can get settled, return your book, etc.

For the final you need to bring:

•    pencil (please do not take your final in pen)
•    eraser (no sharing of anything!)
•    calculator (you may want to bring extra batteries just in case - no sharing!)
•    book

A-Block in room 613 (I will be with you 12:30 to 1:00)
B-Block in room 614 (I will be with you 1:00 to 1:30)

Where I will be the other times:
   room 615  12:00 to 12:30
   room 616  1:30 to 2:00

You can find me and ask questions at any time but it would be better if you wait until I am in your room or just next door.

Countdown to the Final Exam

Old final exams are available at the LHS Math Final Exam Archive.  When we review, you may ask about any question from any unit, any exam, any material used in class, anything except Mongols.

A-Block Schedule:

6/05  List of Topics, Solving, One Question per Chapter handout

6/06  Skills Multiple Choice material

6/07  Writing Equations practice, Extra Conics Questions

6/11  Bring your questions (you have 80 minutes to ask and get answers)

B-Block Schedule:

6/04  List of Topics, Solving, One Question per Chapter handout

6/07  Skills Multiple Choice material, Extra Conics Questions

6/08  Writing Equations practice

6/12  Bring your questions (you have 80 minutes to ask and get answers)

General Schedule:

6/05  Bio MCAS (D A G H E)

6/06  Bio MCAS (E C E F H A)

6/11  Special Review Day 1 (A C E G)

6/12  Special Review Day 2 (B D F H)

6/13  Social Studies Final 8:30am - 10:30 am

         Math Final 12pm - 2pm

6/14  Foreign Language Final 8:30am - 10:30 am

         Optional Review 12pm - 2pm

6/15  Science Final 8:30am - 10:30 am

         English Final 12pm - 2pm

6/18  Conflicts and Make-up Exams

6/19  See Teachers to get final grades

Counting and Probability

This unit starts with ways of counting possibilities.  It takes a few days to learn all of the counting techniques.  We then use that to determine the probablility of different outcomes.

5/09  Counting Day 1
          HW p.631/Activity  and  p.640-641/31-39 odd, 43, 47, 51,52, 55, 56, 61, 62

The activity is similar to the pizza possibility that we covered in class but this time, instead of figuring out how many pizza combinations are possible, you have committed to the two-topping pizza and want to figure out how many of those are possible.  It will also provide practice drawing possibility tree diagrams.

5/10  Counting with repeats - how to avoid double counting (Day 2)
         HW p.647-648/21-27 by 3's, 34-38, 40, 42

5/14  Counting Day 3
         HW finish worksheet of extra problems

5/15  Pascal's Triangle and revisiting the Binomial Theorem (Math MCAS A G H B)
         HW finish worksheet
5/16  Math MCAS  -  no class (C E F H D)
5/17  Counting Quiz, Intro to Probability worksheet
         HW finish worksheet plus p.633-635/24,34-37,40-43,45 and p.648/30-33
5/18  Experimental vs Theoretical Probability (B-Block, henceforth A-Block is one day later)
         HW finish worksheet

5/21  Inclusive vs Mutually Exclusive
         HW p.656-658/7-15 odd, 24-31, 41, 42, 47-49
5/22  Independent Events
         HW p.662-663/13-16, 21-26, 37 plus p.650-651 activity
5/24  Dependent Events
         HW p.668-670/9-31 odd, 39, 41, 55, 58

5/25  More Dependent Events

         HW finish worksheet

5/28  Memorial Day - no school
5/29 "Realistic" Applications
         HW finish worksheet

5/31  Review
6/01  Probability and Counting Test (B-Block)
6/04  Probability and Counting Test (A-Block)

6/05  Bio MCAS (D A G H E)
6/06  Bio MCAS (E C E F H A)

6/13  Math Final 12pm - 2pm

Conic Sections (or how to slice a cone)

Chapter 9 covers the study of conic sections, relations that are usually not functions.  This means more work to graph the relations with your calculator and more solutions when we get to word problems.  Be ready!  Conic sections are circles, ellipses, hyperbolas and parabolas.  Circles are a special case of ellipses so they will be done altogether.  Every case has an algebraic and a geometric definition.  We will study both.  (There are more ways of expressing conic sections - polar and parametric definitions - but we won't be getting to those this year.) We will spend two days on hyperbolas, a day focusing on the algebraic and a day focusing on the geometric definitions.  We won't get all of the vocabulary the first day so some of the homework needs to be revisited the second night. The geometric definition of parabolas will show us some important features of this quadratic relation that were hidden before.  Given that we spent a great deal of time with the algebraic definition of parabolas in a previous unit, the single night of parabola homework focuses on the similarities with the other conic sections.


4/23  Intro to Conic Sections
          HW finish handout
4/24  Circles and Ellipses (algebraic definition of ellipses)
          HW p.583-585/10-55 by 5's, 71, 73, 76, 77-81 odd, 95
4/25  Ellipses (geometric definitions)
          HW p.592-3/23,25,35-45 odd, 51-57 odd, 60, 62-64
4/26  Hyperbolas (algebraic definition)
          HW p.601-603/9-48 by 3's (ignore foci), 65


4/30  Hyperbolas (geometric definition)
          HW p.601-603/find foci for 9-48 by 3's, do 28, 29, 31, 35, 38, 49
5/01  Parabolas
          HW p.576-578/9-17 odd, 31, 33, 36, 42, 45, 49, 50, 53, 68
5/02  Non-linear Systems
          HW finish worksheet
5/03  Combined Conic Practice
          HW finish worksheet


5/07  Review
5/08  Ch 9 Test of Conic Sections

Exponential and Log Functions

Exponential and Log functions are inverses of each other.  That is the most important thing to remember about them together.  We have been studying functions where x is the base and the exponent can be positive, negative or fractional.  Now we will study functions where the base is a number and the exponent is the variable.

Note:  I am not following the order or the emphasis of the book so we will have handouts everyday but this material is covered in Chapter 6.

3/28  Intro to Exponential functions
         HW finish handout
3/29  Intro to Logarithmic functions
         HW finish handout
3/30  End of Term 3

4/02  Base e and solving for any variable in y = b^x
         HW finish handout
4/03  Exponential word problems
         HW finish handout
4/04  Properties of logs (and their proofs)
         HW p.382/18-69 by 3's, 72, 73
4/05  Skills quiz (A-Block), Properties of Logs (B-Block)
         HW (A-Block) p.368/38-46 even and p.398/62-70 even, 71

4/06  Good Friday - no school, lose B-Block class

4/09  Compound and Continuous Interest (A-Block), Skills quiz (B-Block)
         HW (A-Block) p.367-368/29-35 odd, 36, 52, 53
4/10  Log Application problems
         HW finish handout
4/11  Review (A-Block)
         HW finish handout (answer key online)
4/12  Test (A-Block),  Review (B-Block)
4/13  Test (B-Block)

April Vacation 4/14 - 4/22

Radical Functions

The rest of Ch 8 is about Radical functions, functions where the exponent on the x is a fraction.  As usual we will work through defining, simplifying and solving.

3/12  Definition, graph, transformations of Radical Functions
3/13  Test of Rational Functions
3/14  Functions and Inverses, Simplifying and Evaluating
        HW p.525-527/11, 15, 19, 23, 25, 29, 33, 37-51 odd, 52, 53, 59-65 odd, 66-72
3/15  Operations with Radical Functions
        HW p.533-535/15 - 75 by 5's, 78, 81, 84, 87, 90-92, 111-113

3/19  Radical "Tricks"
        HW finish handout
3/20  MCAS (no B-Block) Solving Radical Equations
        HW p.542-543/11-41 odd, 53, 55, 57, 63, 73-77 odd
3/21  MCAS (no A or B-block)
3/22  MCAS Solving Radical Equations - 2nd day for A (see 3/23), 1st for B (see 3/20)
3/23  Solving Radical Equations (2nd day for B-block)
        HW p.542-543/18-42 even, 48-60 even, 61, 62, 72-76 even

3/26  Review Radical Functions
3/27  Test of Radical Functions

The Rational Function Syllabus

We started studying rational functions before break. You should have a review sheet of polynomial properties that will help you, together with your understanding of how fractions work, to master rational functions.
2/27  Details and Vocab for Rational function graphs
         HW p.496-497/23-41 odd, 42, 43, 57-65
2/28  Simplifying, Multiplying and Dividing Rational functions
         HW p.502-503/9-43 odd, 44, 45
2/29  Adding and Subtracting Rational functions
         HW p.509-510/11-45 odd, 46, 47
3/01  Extra Practice, Direct and Inverse Variation
         HW p.486-487/15-39 by 3's, 41, 43-46
3/05  Solving Rational equations
         HW p.517-518/9-27 odd, 47, 48
3/06  Solving Rational inequalities
         HW p.518/29-45 odd, 49-57
3/07  Extra Practice
         HW finish worksheet
3/08  Half Day (C B H F)
         Since A-Block is not meeting today, the review sheet will be given out on 3/07
3/09  Review (B-Block)
         HW finish worksheet
The test will be on Tuesday 3/13.  We may start Radical functions on Monday.

Rational Functions

The next unit is on Rational Functions (functions that can be written as fractions with polynomial numerators and denominators). The first day was an introductory activity. The second day was a graphing activity. I will not give you homework until we have a more in-depth discussion graphing activity. The unit will really start in earnest after vacation.

Typo alerts

There are two typos that I have found that make a difference. The first one is in Example 2 of the Extra Practice Factoring and Dividing worksheet. That one I put the correction on the board (the third line of the example should have -6 not +6). The new correction is on the Finite Differences/Technique Review worksheet. Problem 5 has a table of numbers. The point (3, 15) should be (3, -15). Left unchanged you will have a great deal of difficulty practicing the finite differences technique.

Midterm Histogram

The histogram of midterm results is here. We set the average for the scale to 80%. This means half the students did better than 80%. It is normal that half the students are below the average but it is not good if they spread way out below the average. Theoretically, if half the students are between 80-100% then the other half should be between 60-80%. That is not the case with this test. The tail falls off at 42%. More than three quarters of the students got a score above 70% on the test but those that struggled really struggled a lot. My students that did poorly need to see me so we can rethink what they need to do to be successful. Do they have good techniques for studying (which is different than being diligent)? Are they trying to memorize procedures without really understanding them? A lack of understanding is exposed when questions are asked slightly differently than before and the student is unable to adjust to the change and answer the question. I want my students to be happy and successful in my class but the curriculum and the pace cannot change so let's work together for best results.

Polynomials (Ch 7)

We continue our study of functions that have positive integer exponents on the x variable - polynomials. The schedule below is ambitious and will probably change as the need for more practice and quizzes becomes more apparent.

1/23 Introduction to Polynomials
          HW finish worksheet of practice and exploration
1/24 Exploration of the impact of the degree on the shape
          HW finish worksheet of exploration questions plus p.429/17-27 odd, p.438/23-37 odd, 38
1/25 Manipulating polynomials (adding, subtracting, multiplying)
          HW p.430/39-49 odd, p.445,447/15-33 by 3's, 101, 102
1/26 Dividing Polynomials
          HW p.446/71-81 odd, 85, 89, 99, 100, 105-110

1/30 Patterns of special products and the binomial theorem
          HW finish worksheet, deduce special factoring patterns (check your work here)
1/31 Factoring Polynomials
          HW p.446-447/35-69 odd, 115
2/01 The Fundamental Theorem of Algebra
          HW Worksheet of Practice Problems
2/02 Prove Properties of factors and zeros
          HW Review of Techniques

2/06 Solving: what it is, what tools do we have?
          HW p.453-454/11-25 odd, 51-59 odd, 61-64
2/07 Putting all the ideas together
          HW General Results Worksheet
2/08 Real-world problems
          HW Worksheet of word problems
2/09 Review
          HW Fix a "bad" test

2/13 Singing Valentines (bad day for a test)
2/14 Test of Polynomial Functions

Finishing up Quadratices (and the term)

We still have to look at complex numbers, an integral part of our study of quadratics. We will finish up Chapter 5 and have a mid-year exam before the end of term 2. (Dates given are for A-Block, B-Block is one day later for the end of the week.) Remember that I am trying not to overwhelm you with homework but if you need extra practice, there are plenty more problems in our textbook.

1/04 Zeros and Solutions
         HW finish handout
1/05 Introduction to Complex Numbers
         HW p.320-321/19,23,29,35,41-44,45-63 odd,77,79

1/09 More with Complex Numbers
         HW p.320-321/65-75 odd, 81-95 odd, 96-100
1/10 Review Quadratics
         HW finish review packet
1/11 Quadratic Inequalities (will not be on quiz, will be on 1/20 for B-Block)
         HW 334-335/36-57 by 3's, 58-60, go back and solve 12,15,18,31,35 with a 2D graph, not a number line.
1/12 Quadratic Quiz
         HW start working on Mid-Year Review Packet

1/16 Martin Luther King Day, no school
1/17 Review Questions
1/18 Review Questions
1/19 Mid-Year Cumulative Exam
         HW Quadratic Optimization Problems
1/20 End of Term 2

Both sections will have their second quadratic quiz on 1/12. They will also both receive the mid-year review packet that day. Both sections will have two days in class before the exam to ask questions and work on the packet. Both sections will have the Mid-Year exam on 1/19. Quadratic Inequalities will be on very different dates for the two sections and will not be assessed on the second Quadratics Quiz.

Remember that the makeup for the first Quadratics Quiz must be completed by 1/13. Test corrections for the Matrix test are due by 1/20. Retakes for the second Quadratics Quiz are due by Tuesday, 1/24.

Answer Key for Quad Word Problems

You can download the answer key for the quadratic word problems here.

Quadratics

For the quadratic functions we will be using books with a more investigative focus.  After each investigation we will summarize the results and I will collect the "Check Your Understanding" to check your understanding.

Day 1  Investigation 2/all pp.332-334
              HW pp.346-357/A 7-10; C 17; R 28,29; Rv 43-45, 4
Day 2  Investigation 3/1-7 pp.336-337  HW see day 3
Day 3  Investigation 3/8-12 pp.337-339
               HW pp.348-358/A 11,12; C 18-23; R 30; E 37,38; Rv 48-50
Day 4  Investigation 4/1-5 pp.340-342  HW see day 5
Day 5  Completing the square and Investigation 4/6-9 pp.342-343
               HW pp.348-358/A 13-15; R 31, 33; E 39, 40; Rv 51, 52

On the 6th day we will add a few things that are not in the book (vertex form and quad regression).
On the 7th day we will review techniques for factoring and solving.
On the 8th day, there will be a quiz.  This will probably be the last day before vacation. The quiz should only take half the block, then we can play a game.

Since I am not issuing textbooks for this unit, I have uploaded the pdf of the unit into the conference.  You don't have to go online, you can just use that. Or download it from here. (Note: If there are contents links on the side, you may not be able to click on them - use actual page numbers at the top).

The reflection

Our analysis of 3D systems using rref led to several different results - more than we saw when using rref on 2D systems.  Of course, in 3D, more things can happen - as you saw from your brainstorming with your three "planes".  I would like you to write a reflection of the similarities and differences between systems of equations and their rref matrices in 2D and 3D.  This should come after your final analysis of the systems on the worksheet.  With 2D we knew which systems were consistent, inconsistent, and dependent from their rref matrices and what the system looked like when the lines were drawn.  Were you able to do the same with your 3D systems?

Matrices

Now we learn how to deal with lots of information at once. There are many applications of matrices that are not covered in our text so we will be exploring some of them via worksheet. Make sure you bring your calculator every day!

11/14  Intro to Matrices (dimensions, transpose, scalar mult., add/subtract...)
          HW p.222/24-28 even, 38-46 even
11/15  Matrix Multiplication
          HW p.230/18-24
11/16  Networks
          HW finish handout
11/17  Transformations using matrices
          HW finish handout
(Note: I will be out on 11/18 but the handout that day is self-explanatory.)

11/21  Intro to RREF
          HW p.257/19-37 odd
11/22  Practice by using the RREF tool on the computer
          HW finish handout
11/23-11/27 no class due to Thanksgiving break

11/28  Review of Matrices so far
11/29  Intro to Inverse Matrices
          HW finish handout
11/30  Solving Systems using matrices
          HW p.249/23-31 odd, 32, 33
12/01  3D Systems (and higher!) and their solution options (now with matrices)
          HW Reflection and p.257-258/34-36, 38-40

12/05  Review of Matrices
          HW finish handout
12/06  Extra Challenge Problems on Matrices

12/08  Ch 4 Matrix Test

The last day this week you will work through a packet reviewing exponential properties.

An introduction to the mathematics of 3D

We will be moving into chapter 4 which studies matrices - a technique that allows us to handle huge amounts of data. 3D makes a great bridge topic between systems of equations and matrices. Remember, this is only an introduction. You do not have to be an expert! That comes in two years. ;-)

Day 1: Representing 3D with points, equations of planes, graphs.
Day 2: Solving systems of equations in 3D - there are many possible outcomes. (Answer Key)

The homework both days is to finish the handouts.

Systems of Equations and Linear Programming

Note date changes due to storm/power outage!

Chapter 3 explores applications of systems of equations and systems of inequalities. You will do a lot of graphing. Get some graph paper and a ruler!

Day 1:  3.1  Solving Systems by Graphing
                  HW (due after Transformation Quiz) p.161-163/13-23 odd, 47-52, 79, 80
Day 2:  3.2  Solving Systems by Substitution and Elimination
                  HW p.161-162/137-42, 53 and p.169-171/21-35 odd,36-39,43-45,63,64

Day 3:  3.3  Linear Inequalities (and going over TI drawings!)
                  HW p.176-178/26-31, 41-51, 54, 73, 74
Day 4:  3.4  Systems of Linear Inequalities
                  HW p.183-186/9-45 by 3's, 46-48, 51, 68-70
Day 5:         Systems of Linear Word Problems
                  HW Finish Handout of problems
Day 6:  3.5  Linear Programming (Day 1)
                  HW Finish Handout of problems

***** 2 days without power *****
Day 7:  3.5  Linear Programming (Day 2)     (Answer Key)
                  HW Finish Handout of harder problems
Day 8:  3.5  Review
                  HW Finish Review Handout

Day X:  A-Block only - an activity
                  HW review for test
11/08  Ch 3 Test

We will spend time (before or after the test depending on the block) looking at 3D Systems of equations before moving on to Matrices, the topic of Chapter 4.

Transformations

We have been talking about what functions are and how we can combine them. Transformations are about manipulating functions - moving them around, changing their size, flipping them over. We are studying the topic in general but every time we study a particular kind of function in the future, we will again discuss how the transformations affect that function. This is section 2.7 in the text.

Because of the Friday Professional Developement Day, A-Block will have one more day on the topic (a moving-around activity!!). Thus, I have used a table.

Date	A-Block	B-Block
10/05	Transformation Exploration	no class
10/06	Summary of Transformation Exploration, Graphical Transformations	Transformation Exploration
10/11	Transformation Word Problems	Summary of Transformation Exploration, Graphical Transformations
10/12	Double Horizontal Transformations	no class
10/13	Kinesthetic Transformations HW in the book p.139-140/15-45 by 5's, 47-57 odd, 58, 60-65	Transformation Word Problems
10/14	no class	Double Horizontal Transformations
10/17	Drawing on the TI and Transformation Review	Drawing on the TI and Transformation Review HW in the book p.139-140/15-45 by 5's, 47-57 odd, 58, 60-65
10/18	Solving Systems by Graphing HW in the book p.161-163/13-23 odd, 47-52, 79, 80	Solving Systems by Graphing HW in the book p.161-163/13-23 odd, 47-52, 79, 80
10/19	Transformation Quiz	no class
10/20	Solving Systems by Substitution and Elimination	Transformation Quiz
10/21	no class	Solving Systems by Substitution and Elimination

More thinking about functions

For this week (9/26 to 9/30) we look more deeply into the functions we have been studying.

Day 1:  Go over the more abstract homework of last week
       HW Extra Practice with Function Operations
Day 2:  Discuss strategies for solving problems
       HW Extra Special Function Practice
Day 3:  "How Do You Know?" Worksheet

Thursday, September 29th is Rosh Hashanah so there is no school. I will also be out on Friday, September 30th.

On Monday, October 3rd we will review and on Tuesday, October 4th we will have a test of the material in Ch 2.