The Official SAT Question of the Day

Thursday, December 16, 2010

Week 18

Algebra II will work on uniting their linear and quadratic worlds by exploring linear-quadratic systems both graphically and algebraically.

Class Notes and Work:

Class Notes Completed:

Homework due January 7, 2011:

Algebra II Midterm Topics:

Precalculus is getting an initial introduction to exponential functions, with emphasis on the properties of their graph.

Holiday Homework:

Midterm Study Guide:

Thursday, December 9, 2010

Week 17

Algebra II will apply quadratics in context and continue to hone their description of parabolic functions and their ability to solve quadratic equations. We will focus on applications involving area and projectiles and maybe even a little bit of quadratics in the business sector.

Lecture Notes:

Lecture Notes with Solutions:

Application of Quadratic Equations
Vocabulary of Quadratics


Homework: (due December 21st)

Precalculus will wrap-up rational functions (exam Wednesday!) and will introduce the fundamentals of logarithmic and exponential functions. We will revisit inverse functions, exponent rules, and transformation of functions before the break hits. These two functions will be new and everyone will need to dig in to understand both the basics as well as nuances of these two functions.


Saturday School for 12.11.10

Monday, November 29, 2010

Week 16

Precalculus is heading into a fast and furious review of rational functions! Please preview and review both the reference sheets as well as the powerpoint presentation below.


Rational Functions Reference Sheet:



Algebra II will continue to deepen their interaction with quadratics and expand their problem-solving repertoire. We will add both the quadratic formula and graphing to our solving skill-set. The little picture below is the summary of the entire week, graphically speaking. If you can understand this little picture then you've got it!

Reference Sheets:

Proof of Quadratic Formula:


Overview of Solving Quadratics
Quadratic Formula




Tuesday, November 23, 2010

Week 15

I hope everyone had a relaxing long weekend off and are back ready to work!

Don't forget bonus is due before we leave on holiday break! Try any of the problems and remember to cite any resources you used to solve the problems.

This Wednesday is World Aids Day and we will spend about 25 minutes on Wednesday looking at the data on HIV worldwide. Here is the link to the video that will inform our conversation:
HIV Worldwide Video

At this point in Algebra II our exploration of quadratics, students should be comfortable graphing and interpreting quadratic equations in multiple forms (standard, vertex, and intercept) as well as the process of completing the square. During week 15 we will complete our look at factoring and begin to solve quadratics by factoring and completing the square. Their are videos below that review previous topics as well as preview the upcoming factoring techniques we will cover in the coming week.

The homework for this week has already been given, but is included below as well. In addition, I have posted both the factoring decision tree as well as a cheat sheet that was compiled by Paul Dawkins for you use as reference sheets.

Factoring Powerpoint:

Solving by factoring and completing the square powerpoint:

Reference Sheets:






Algebra II Videos:
Factoring Overview
Solving by Factoring
Completing the Square

Precalculus will be examined Wednesday of this week over polynomials. Thursday we will begin a brief unit on rational functions, with particular attention to their graphs. Please find the homework for the week below as well as a reference sheet on polynomials.

Rational Functions Powerpoint:

Rational Functions Reference sheet:

Due Wednesday, December 1st:

Due Friday, December 10th:

Tuesday, November 16, 2010

Week 14

Algebra II is continuing with quadratics focusing on differing factoring methods and always connecting the consequences of algebraic manipulations on the graphical representation of a parabola. I have included the factoring help sheet that I handed out a week ago! Please use this to help you make decisions about how to factor a particular polynomial.

Reference Sheet:

Factoring Powerpoint:

Video Clips:
Review of Factoring
Factoring Complicated Expressions

1. LTF Area of Bounded Regions due November 23rd (hard copy only)
2. Thumbnail below is homework due December 3rd.


Precalculus will continue with polynomial expressions and focus on polynomial regression and modeling. This will rely heavily on the use of technology and interpreting outputs from technology. A keystroke guide to regression is represented as a thumbnail immediately below:


(LTF Document)


Tuesday, November 9, 2010

Quarter 2 (week 13)

We have officially moved into Quarter 2 and all of you (students) have a clean slate. It is important to remember what that means for you! Your grades from first quarter do not carry over to second quarter and that whatever you earn from this point forward will only average into your second quarter grade. Whether you have high or low first quarter marks, second quarter is a whole new world.

This week we will not have class on Wednesday for parent-teacher conferences and Thursday I will be away presenting at Amistad-Elm City High School. Thursday will be a day for independent practice and should be seen as an opportunity for much needed practice.

Algebra II started with some introductory descriptions of quadratic functions last week and are moving onto how to manipulate functions algebraically and how algebraic moments appear graphically. We will progress through the guided notes embedded below and as we explore them together I will post screenshots of our progress!
For Day 1 and 2 notes filled-in click
Reference sheets:


Precalculus will be continuing and finalizing their review of polynomial functions. We will look at college textbooks and their treatment of the topic as well as curve-fitting using polynomial regression. It is a short week so it will be a quick look.


Tuesday, November 2, 2010

Week 12

Precalculus continues their mastery of polynomials, with specific attention to roots and zeros of poly's. Here is a pic of a quartic polynomial, one of the polynmials will be looking at this week. If you have a chance, please pre-read the slides for polynomials. It will help you understand the material SO much more the coming week. You should start with 3.5 and finish with 3.8


Reference Sheets:



In Algebra II we will have an exam on Tuesday involving both the raw mathematics around solving systems of linear equations as well as traditional applications of systems. This exam, like those previous, will require you to understand systems numerically, graphically, and algebraically.

We will be starting our next polynomial function, quadratics, on Wednesday. Here is a pic of the graph of a quadratic called a parabola. Please find the short powerpoint on the graphs of quadratics, a reference sheet (we will complete it on Wednesday and I'll post the completed version then), as well as the homework! If you want to preview the upcoming material on quadratics the link below takes you to an excellent online text that describes them in detail!


Graphic Organizer Reference Sheet:


Thursday, October 28, 2010

Week 11

Greetings Scholars. As you may or may not know, the quarter ends next Friday and that means report cards are just around the corner. Please continue to work hard till the end and inch your grade up a couple crucial points over the next 5 days.

Precalculus will be reviewing polynomials with an emphasis on wedding algebra with technology. Please bring your graphing calculators with you and be prepared to use them alongside algebraic methods. I have included the powerpoints for the week below as well as the homework. The homework is due in two weeks (November 12th). Please don't get behind :)

Powerpoints (Start with 3.1):

Here is a so that you can preview and progress through the homework at your own pace!


Algebra II will be be applying systems of equations in both real-world scenarios as well as interesting mathematical ones. Each day as we work through word problems together, I will post our class examples below. I will post the classwork as thumbnails and the screenshots from the smartboard as embedded pdf files.

Guess and Check:




*Special thanks to the University of Houston math department and the Arlington Algebra Project for the great materials they have designed.

Friday, October 22, 2010

Week 10

The coming week has an old favorite coming back to Algebra II: Systems of Equations. We are going to quickly review the methods that can be used to solve systems of equations and move forward to conquering the typical SAT and college placement exam questions that deal with systems. Please find the notes and homework for Algebra II below. The first two embedded documents are especially crucial conceptually--please review them carefully.

3 Cases for Solutions of Systems of Questions:

3 Methods for Solving Systems of Equations



Likewise, Precalculus is returning for the front end of the week to a familiar topic. We are going to address, directly and for the last time, exponent rules and nth roots. Please find the notes and homework below. Friday, we will start our review of polynomials via graphical investigations.

Laws of Exponents:



Friday, October 15, 2010

Week 9

The quarter is winding down and another test is coming next week. This is likely the final test of the first marking period for both classes so please study, practice, seek help, and put your best foot forward in the coming week.

For Algebra II the exam will be on linear functions, primarily, and with some review topics from exponents and functions. The homework for this week leans on the problem-solving aspect of the exam and is based on problem sets from the book.

Algebra II CP Homework:
pp. 29-30 4-8, 14-50 evens (total of 21 problems)
pp. 37-39 8-30 (total of 22 problems)
p. 61 1-3, 7-8, 9-19, 23-25, 32-34 (total of 22 problems)
pp. 71-73 2-58 evens (total of 28 problems)
pp. 86-87 4-62 evens (total of 29 problems)

Algebra II H Homework
p. 51 all
pp. 61-62 18-34 evens, 35-37, 46-53
pp. 72-73 16-56 evens
pp. 78-79 4-60 all
pp. 260-262 2-72 evens

In class we are continuing with the meaning of linear functions, revisiting consecutive integers, modeling with linear functions, and just plain more solving word problems:

Meaning of Linear Functions Do Nows

Consecutive Integers

Modeling with Linear Functions

More Linear Word Problems

Lines of Best Fit

The precalculus exam will focus on the basics of matrices, including the following: basic operations, determinants, and inverses. In addition, students will apply these basic operations in solving systems of equations.

Precalculus Homework:
pp. 71-72 #11-45
pp. 76-77 #8-27
pp. 83-84 #15-54

Wednesday, October 6, 2010

Week 8

Exciting times in both classes this coming week as we move toward application of problems in context. Algebra II will be doing "traditional" math application problems that involve lines, specifically distance vs. time graphs, as well as some non-traditional interpretation of linear functions. Precalculus will be applying matrices to solve linear systems of varying size with an emphasis on use of technology for systems that contain 4 or more variables.


TI Matrix info sheet:


Algebra II:
Class Examples of Word Problems:

Focus on Consecutive Integer Word Problems:

Meaning and Linear Functions:

Video links for word problem types:
Mixture Problems
Investment Problems


Monday, September 27, 2010

Week 7

As of Thursday of week 6 both classes have transitioned to new topics. I'll post answers to the exams as soon as I have created an answer file for them. Please put your emotions behind you and try to embrace the next set of topics with renewed fervor.

A special shout-out to the high performers from the junior class. Here are the top four scorers.
Daniel Manning
Roy Ramnarain
Elizabeth Walsh
Marylin Joyce

Algebra II is going to spend three weeks on linear equations beginning with 7 days of pure skills review followed by 7 days of applying linear equations. It is crucial that we focus on mastering the basic skills relating to lines, because they will serve as a basis or at least reference point for all that follows. Please find video links, our class notes (for the first seven days), and the homework below.
Video Links:
Slope-Intercept Form
Point-Slope Form
Standard Form
Parallel and Perpendicular Lines
Class Notes:

Online Practice with Parallel and Perpendicular Lines:
Parallel Lines
Perpendicular Lines


Precalculus will also be turning to linear equations, but in the context of systems. We will review the basic mechanics around solving systems of equations both algebraically and graphically, but will quickly move onto matrices.

Video Links:
Systems of Linear Equations in Two Variables
Systems of Linear Equations in Three Variables
Class Notes:


Wednesday, September 22, 2010

Week 6

Exam this week! Algebra II courses will have their exam on Tuesday, September 28 and Precalculus will have their exam on Wednesday, September 29th!. Please review all of the notes and problem sets you have accrued.

Algebra II:
Here are a set of videos that review some of the basic concepts on the upcoming exam. Let me know if they help! In addition, please find a copy of the entire set of notes we completed together in class here*:

Please find the homework embedded below!

Click on the topics below to reach the video:
Domain and Range
Function Notation
Composition of Functions

Algebra II Homework:

I have also included some review videos for precalculus and your homework for the week is located below.

Click on the topics below to reach the video:
Parent Functions Overview
Transformations part 1
Transformations Part 2
Transformations part 3
Piecewise Functions

Precalculus Homework:

*These notes are from the University of Houston, which has a proactive math department that provides students with great mathematical tools and supports!

Thursday, September 16, 2010

Week 5

Greetings all. You all recently received a report about your grades and how you are doing thus far in your classes. If you have any questions at all please e-mail me below or at my school address!

Precalculus will be doing a rather sizable packet as homework; it has been taken directly from a college algebra course. I will sight the source of the document after it is turned-in and provide a link to answers for it.

There will be no new powerpoints, but we will look at piecewise functions again so here is that presentation one more time:

Algebra II will be fine tuning their ability to interpret and apply function notation alongside of a more intense focus on interpretation of graphs with an emphasis on domain and range.


Thursday, September 9, 2010

Week 4

Believe it or not, we have already been in school for a month!

This Wednesday there will not be class, becuase of the college-prep day; take the practice SAT seriously and get a legitimate sense of where you are.

Algebra II has two powerpoints this week covering inverse functions and an overview of the set functions we will be covering throughout the year.

Algebra II Classwork (with Answers):

Algebra II Homework:

Pre-Calculus will continue to work on transformations and becoming increasingly more comfortable intepreting a variety of functions, specifically piecewise functions. Our baseline model will deal primarily with funections defined by "position, velocity, and acceleration."

Friday, September 3, 2010

Week 3

This post will change over the next couple of days, so please continue to check for updates until about Tuesday evening. This is going to be a quick week and will require hard work over the short time we have together.

Pre-Calc Powerpoint:

Pre-Calc Homework:

Algebra 2 Powerpoint:

Algebra 2 Classwork with Answers:

Algebra 2 Homework:

Friday, August 27, 2010

Week 2

Please find the powerpoint presentations for Algebra II and PreCalc here as well as they homework due this coming Friday.

I will likely update this post throughout the week. So stay tuned.


Homework Part 1:

Answers to Homework Part 1:

Homework with Answers Part 2

Algebra II:


Classwork with Answers:

Tuesday, August 24, 2010

Week 1

Hopefully everyone turned in their summer packet and did reasonably well on their opening exam. Congratulations.

Please feel free to ask any questions about any of the posts you find on the blog either by using the comment feature at the end of the post or by e-mailing me directly. I am going to attempt to keep Scholars as up to date as I possibly can and trust that you will all use it as a resource.

Please find the Powerpoint presentations for week 1 as well as the homework due Friday below.

Algebra II:




Monday, August 23, 2010

Setting your Math Education in Context

8th grade Algebra I allows students the possibility of being a competitive student both with their U.S. and global peers; however, even many U.S. students who are fortunate to have Algebra I in the eighth grade still find themselves losing to their international peer group. We can hopefully stop that.

I have embedded the powerpoint presentation (edited and adopted from Achieve) from Algebra II Honors that we went through with the hope that you will return to it when you start to feel like class is too difficult. Remember, that your math education isn't only about a particular math class or how competitive it will make you globally, it also has a financial impact on your future earnings.

Flip through the powerpoint and let me know what you think.

Tuesday, August 10, 2010

Summer is over and that IS a good thing!

Students often bemoan their six week summer at BCCS, but it turns out that it is, really, all for the better. The August 2, 2010, issue of Time magazine has a lead article on how summer break is actually hurting academic performance of students. Instead of repeating the entire article, I have included a video Time cited as well as a graphic representation of summer academic loss below. Enjoy and be thankful that your summer is so short!

If you don't have the time to watch the video here is the bar graph of summer loss showing the disproportionate effect of summer on high income verses middle to low income students.

What should we do instead? What about a school year that looks more like this? What do you think?

See everybody in a couple of weeks.

Saturday, June 26, 2010

When will I ever use this?

A question that occurs daily in math classrooms across the country is, "When will I ever uses this?" There are so many retorts both nuanced and cliched that the scholars on Mayhew hear from me, and yet I still worry that I never fully point the way to all the actual career paths that are available to them. I found a great website that answers not only when and where math is used, but WHO uses mathematics.

Click: When Will I Use Math?

An even more telling set of information is the ranking of "Best and Worst Jobs 2010" recently posted on the Wall Street Journal's online website. Of the top 20 jobs listed 13 out of the 20 require a great deal of math. You can also find salary information next to the entries listed. If your doing math your getting paid . . . well.

Click: BEST JOBS of 2010

Here is a snapshot of the #1 job for 2010

Pros: Great work environment, few tight deadlines, low stress.
Cons: Moderate unemployment (expected to rapidly improve).

How do you get that job?
Besides skill at math, becoming an Actuary requires passing several exams and taking courses from the Casualty Actuarial Society (CAS) or the Society of Actuaries. However, many companies will employ prospective Actuaries while they are still training for the exams.

Starting salary $49,000
Midlevel salary $85,000
Top level salary $161,000

Wednesday, June 23, 2010

Easiest "hard" problem on the final

No matter what math class a student was in all students were required to do this problem. It requires knowledge strictly from your typical Algebra I class, but it requires a thoughtful, reasoned response in order to correctly answer the question. It proved, somewhat unexpectedly, to be a difficult one today.

Here it is for anyone to try. I welcome any questions or comments on this question.

Write an equation for line l.

Friday, June 18, 2010

Reference Sheet

Please find the link to the reference sheet that will be available for the final this coming Wednesday below. Please take a few minutes to familiarize yourself with it.

Click on Algebra Cheat Sheet

Thursday, June 17, 2010

Summer Packets

Greetings scholars.
Please find the 2010 Summer Packet embedded here for you to print and complete.
Remember that this packet is due the first day back and is worth two homework grades. You will be tested on it your first day back. If you have any questions, please email me.
Have a great summer.