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.