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.