Link to regentsprep.org reciprocal trig functions, solving trig equations, etc.

Link to reciprocal trig functions
http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

Link to important angles:
http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigANGLES.htm

Link to inverse trig graphs:
http://www.regentsprep.org/Regents/math/algtrig/ATT8/indexATT8.htm

Link to solving trig equations:
http://www.regentsprep.org/Regents/math/algtrig/ATT10/indexATT10.htm

Link to trig identities:
http://www.regentsprep.org/Regents/math/algtrig/ATT14/indexATT14.htm

Aims week of 12/13:

Aim 65: How can we graph the tangent function?
hw: pg 721 9-12, 17-19, 31

Aim 66: More on graphing tangent function.
hw: none

Aim 67: More on graphing trig functions.
hw: none

Aim 68: review
hw: study for test

Aim 69: Test: chap 9
hw: none

Aim 70: Exploring trig functions
hw: none

Aim 71: Exploring Geometry through Origami
hw: none

Have a nice break!

Aims week of 12/8:

Aim 60: How can we model using the sine wave function?
hw: pg 714 17-22

Aim 61: How can we graph the cosine function?
hw: pg 721 2,4,6,14,16,30

Aim 62: How can we connect the graphs of the sine and cosine curves?
hw: pg 722 33-36

Aim 63: How can we connect the graphs of the sine and cosine curves?
hw: finish worksheet

Aim 64: Practice with sine and cosine waves
hw: none

Aims week of 12/1:

Aim 55: What is the sine function?
hw: pg 706 1, 2-12 even

Aim 56: How do we graph the sine function?
hw: pg 713 1-3, 11-16

Aim 57: What is the period of the sine function?
hw: pg 715 29, 30-38 even

Aim 58: Review
hw: study for test

Aim 59: Test on unit circle, degree - radian - (x,y), sine function
hw: none

Aims week of 11/24:

Aim 53: What is a bi-conditional statement?
hw: pg 90 2-16 even

Aim 54: Review: what have we learned about conditional statements, converses, counter-examples, law of detachment, law of syllogism, and bi-conditional statements?
hw: study for test

Aim 55: test
hw: none

Happy Thanksgiving!

Aims week of 12/1:

Aim 55: What is the sine function?
hw: pg 706 1, 2-12 even, pg 708 40-43

Aim 56: How do we graph the sine function?
hw: pg 713 1-3,11-16

Aim 57:

Aim 58:

Aim 59: Test Unit Circle, Radian measure, Sine functions.
hw: none

Aims week of 11/24/08

Aim 53: What is the relationship between height and distance traveled in a unit circle?
hw: pg 700 2-18 even

Aim 54: continuation of relationship between height and distance traveled.
hw: none

Aim 54: continuation of relationship between height and distance traveled.
hw: none

Happy Thanksgiving! gobble, gobble.

Links to regentsprep.org graphing trig functions

link to unit circle graphs:
http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcirclegraphs.htm

graphing trig functions:
http://www.regentsprep.org/Regents/math/algtrig/ATT7/indexATT7.htm

Aims week of 11/17:

Aim 49: Review right triangle trigonometry and unit circle
hw: worksheet #'s 10-18

Aim 50: What is a periodic function?
hw: pg 693 2,4,6,7,10,16

Aim 51: per 1 - What is regression analysis? per 8 - more on unit circle
hw: review pg's 914-916 pg 916 2,4,6 (calc required)

Thursday - no class, parent teacher conference

Aim 52: How can we convert radians to degrees and degrees to radians?
hw: none

Links to regentsprep.org Trig functions

link to review sine, cosine, & tangent functions:
http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigreview.htm

link to trig functions:
http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

link to important angles:
http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigANGLES.htm

link to radian measure and arc length:
http://www.regentsprep.org/Regents/math/algtrig/ATM1/arclengthlesson.htm

link to unit circle:
http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcircle.htm

Aims week of 11/9:

Aim 45: Review benchmark assessment and set SMART goal.
hw: none

Note: Tuesday is Veteran's Day: No School

Aim 46: What do polynomials with complex roots look like?
hw: pg 585 1-9, 15-18

Aim 47: Wrap up - graphing polynomial functions
hw: study for test

Aim 48: Test - Graphing polynomial functions
hw: none

Links to regentsprep.org Polynomials

Solving polynomial equations of higher degrees:
http://www.regentsprep.org/Regents/math/algtrig/ATE13/HighPolyLesson.htm

Examining graphs of polynomials of higher degrees:
http://www.regentsprep.org/Regents/math/algtrig/ATE13/HighPolyGraphLesson.htm

Aims week of 11/3:

Aim 41: How can we explore polynomial functions?
hw: 553 2-16 even

Note: Tuesday is Election Day: No School

Aim 42: What does the graph of a polynomial function tell us?
hw: 553 22-25

Aim 43: How can we find the equation of a polynomial function, given its graph?
hw: pg 565 2,4,17-22

Aim 44: Benchmark Goal Setting Assessment
hw: none

Aims week of 10/27:

Aim 36: Chapter 7 wrap-up
hw: pg 635 1-13

Aim 37: Chapter wrap-up and review
hw: study for test

Aim 38: Chapter 7 test
hw: none

Aim 39: How can we find roots of polynomial functions?
hw: none

Aim 40: Logic puzzles
hw: none

Aims week of 10/20:

Aim 31: What are properties of logs?
hw: pg 611 49-50, 55-58

Aim 32: How can we solve problems using properties of logs?
hw: pg 616 12-30 even, 38-46 even

Aim 33: What does the graph of the log function look like?
hw: pg 617 60-69, 75-80

Aim 34: What does the graph of the log function look like?
hw: pg 627 1-13

Aim 35: What is the natural log function?
hw: none

Aims week of 10/14:

Monday - Columbus Day - no school

Aim 27: How can we prepare for the PSAT?
hw: none

Aim 28: What are the properties of logs?
hw: pg 610 16-27, 29-40

Aim 29: How can we solve problems using logs?
hw: study for test

Aim 30: Test - Exponential Functions & Logs

Aims week of 10/6:

Aim 23: How do we undo a function?
hw: pg 631 1-7

Aim 24: How do we undo an exponential function?
hw: pg 635 4,5,10

Aim 25: How can we calculate a logarithmic function?
hw: study for test

Thursday - no school

Aim 26: How can we calculate logs in other than base 10?
hw: none

Links to regentsprep.org Logarithms

link to log expressions:
http://www.regentsprep.org/Regents/math/algtrig/ATE9/logs.htm

link to log equations:
http://www.regentsprep.org/Regents/math/algtrig/ATE9/logsEQ.htm

Aims week of 9/29:

Aim 20: How do banks calculate interest?
hw: none

note: No school T and W

Aim 21: How do we calculate an exponential regression?
hw: pg 605 1-4,6,8,10

Aim 22: How can we apply exponential functions?
hw: none

Links to regentsprep.org Exponents Functions

Link to exponential functions:
http://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htm

Link to applications of exponential functions:
http://www.regentsprep.org/Regents/math/algtrig/ATP8b/ExamplesexponentialFunction.htm

Link to exponential expressions:
http://www.regentsprep.org/Regents/math/algtrig/ATE8/exponentialExpression.htm

Link to solving exponential equations:
http://www.regentsprep.org/Regents/math/algtrig/ATE8/exponentialEquations.htm

Link to logarithmic functions:
http://www.regentsprep.org/Regents/math/algtrig/ATP8b/logFunction.htm

Aims week of 9/22:

Aim 15: How can we solve practical applications using sequences?
hw: pg 888 1-3 write rules for each sequence, 10-12

Aim 16: What is an exponential function?
hw: pg 596 2-8 even, 9,11,20,22

Aim 17: How do we measure half life?
hw: pg 597 24, 26

Aim 18: Review for test
hw: study for test

Aim 19: Test on Sequences: arithmetic & geometric
hw: none

Links to regentsprep.org sequences

link to arithmetic sequences:
http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

link to geometric sequences:
http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm

Aims week of 9/15:

Aim 10: What is a geometric sequence?
hw: pg 858 68-71, pg 863 2-8 even

Aim 11: How do we write the rule for a geometric sequence?
hw: pg 863 12-18 even, pg 865 1-6

Aim 12: More on multipliers & applications
hw: tba

Aim 13: Practice with sequences
hw: tba

Aim 14: Test - Sequences
hw: none

Aims week of 9/8:

Aim 5: What is a sequence? (note this is in ch 12)
hw: pg 851 1-8

Aim 6: How can we write a rule for sequences?
hw: pg 851 14-30 even

Aim 7: How can we graph sequences?
hw: pg 856-7 2-8 even, 32, 38, 40

Aim 8: What is an arithmetic sequence?
hw: pg 857 21-29, 42, 52

Aim 9: What have we learned so far - Examination
hw: none

Links to regentsprep.org Sequences

Sequences:
http://www.regentsprep.org/Regents/math/algtrig/ATP1a/Sequences.htm

Practice with Sequences:
http://www.regentsprep.org/Regents/math/algtrig/ATP1a/SequencePrac.htm

Links to regentsprep.org Exponents Review

Positive, Negative, and Zero exponents:
http://www.regentsprep.org/Regents/math/algtrig/ATO1/posnegzles.htm

Rational / Fractional exponents:
http://www.regentsprep.org/Regents/math/algtrig/ATO1/FractionalExp.htm

Evaluating Rational / Fractional exponents
http://www.regentsprep.org/Regents/math/algtrig/ATO1/FractExpressions.htm

Aims week of 9/2:

Aim 1: Intro to course
hw: Set up notebook

Aim 2: Review exponents (reference regentsprep.org outlines in separate post)
hw: pg 542 2-24 even

Aim 3: How do we evaluate rational exponents?
hw: pg 547 14-30 even

Aim 4:

10 Habits of Successful Math Students

1. Arrive before the bell rings and ASK QUESTIONS.

2. Complete the Do Now immediately and ASK QUESTIONS.

3. Copy all notes and examples from the board and overhead projector. Add explanations and suggestions given verbally.

4. Complete all homework assignments.

5. Don’t miss class!

6. If an absence can’t be avoided get notes and complete the assignment or test ASAP (before the next class if possible.)

7. Review assignments and tests as soon as they are returned and ASK QUESTIONS.

8. Get help! Before, during, or after school.

9. Have a graphing calculator available and know how to use it to its full capability.

10. STUDY! STUDY! STUDY!!!

Responsibilities

Responsibilities of Students

1. Report to class on time, immediately take out binder, and review the answers to homework, or begin the Do Now.

2. Take notes and participate in all class activities including group assignments.

3. Treat my fellow students, the teacher, and others with respect at all times.

4. Observe all school rules, including those that prohibit wearing hats in class, wearing headphones or using entertainment devices in class, eating or drinking in class, using offensive language, or cheating. Poor classroom behavior will result in one or more of the following: -student-teacher conference—grade reduction—phone call home—parent teacher conference—meeting with administration.

5. Complete all homework on time, and make up all assignments when absent.

6. Utilize available tutoring services when I need extra assistance.

Responsibilities of Parent/Guardian

1. Provide a quiet place for my child to study.

2. Question my child on a regular basis about what he/she learned that day.

3. Monitor my child’s attendance in tutoring if appropriate for him/her to attend tutoring sessions.

4. Contact my child’s teacher and/or guidance counselor (718-796-8516) or (SGordon22@schools.nyc.gov) if I have any questions on my child’s progress.

Responsibilities of Teacher

1. Prepare and conduct a meaningful lesson each day.

2. Collect student work on a regular basis including examinations, projects, and homework.

3. Return student work in a timely manner and provide meaningful constructive feedback on work submitted.

4. Listen to my students, treat them with respect, and maintain an impartial and positive attitude towards them.

5. Contact parents when necessary to alert them of their children’s progress.

6. Be responsive to student’s request for assistance.

Class Rules

Entering class.

Please enter class quickly and quietly by the front door. Take your assigned seat and get out your materials to work. Copy the Aim and the Do-Now for that day's lesson into your notebook. Work on the Do-Now until the teacher calls for your attention.

Participating in class.

Class participation is an important part of your learning and of your grade. Please raise your hand if you have a question or wish to participate in a discussion. There is no calling out of answers or other comments in the classroom at any time.

Notebook.

Students are expected to write down the aim of each lesson, to take notes during class, to complete in-class assignments, to keep handouts, and to hold on to returned tests and homework. It is imperative that students have an organized system for keeping all these materials together. Whether a student chooses to use a binder with appropriate sections or a combination of binder and notebook, the entire collection is referred to as the math notebook. The math notebook is subject to inspection during the course and may form part of the class work contribution to the grade. The entire math notebook is available to students for use on an "open notebook" test.

Lateness.

If you arrive late to class, enter quietly by the front door. Sign the late log with your name and the time. Take your seat without any fuss or conversation, and prepare to join the work in progress. Repeated lateness will result in detention.

Homework.

Homework will be assigned each night. It forms an important part of your learning experience and of your grade. It should be written neatly on clean paper or the original handout, clearly labeled with your name, date, and the assignment. Homework is due the next time class meets, unless you have been told otherwise. If homework involves working problems, all work should be shown and the final answer clearly marked. If homework involves writing, it is expected that the writing will be done in full sentences and follow all the rules of good composition, including spelling and grammar. And finally, homework must be written legibly — if I can not read it, I can not give credit for it.

Absence.

A student who is absent should bring a note from home to explain the absence. Students are responsible for making up work that they have missed, and for meeting deadlines for projects, tests, and other tasks.

Respect.

All members of the class are expected to show respect for each other, teacher and students alike. We respect each other by taking care of the property and environment of the classroom, by listening when it is someone else's turn to speak, and by accepting the fact that we will all make mistakes. Mistakes are an important part of how we learn, and are not an opportunity to make fun of someone else. We are here to help each other. Disrupting the class is disrespectful to others and will not be tolerated.

Web Site.

To help students and parents keep up with general course information, I will be maintaining a web blog that can be accessed at http://rkamath-msgordon.blogspot.com/

Grades.

Grades are determined by a combination of three factors:
70% tests and quizzes
15% class work (includes participation, behavior, notebook, and preparation for class)
15% homework


More information about the general rules and expectations for success at RKA can be found in the Student Planner.


PLEASE KEEP THESE GUIDELINES IN YOUR MATH NOTEBOOK / BINDER.

Grading Policy

Grades are determined by a combination of three factors:

70% tests and quizzes: point totals will be marked on all examinations. The marking period grade will reflect a weighted average of all examinations.

15% class work: consists of specific assigned tasks during class time, which are graded. There is also a component that recognizes class participation. This course relies on activities, group efforts, and whole class discussion as important parts of the learning experience. Points will be assigned to different components of class work on a rotating basis. For example, some days will consist of a notebook check or a collection of the Do Now. A log will be kept of students going to the board to put up prior homework problems or work on current work problems. Your marking period class work grade consists of the percentage reflecting your total class points over the total number of possible points.

15% homework: will be assigned daily and collected. Homework is marked based on effort and work shown. Completed homework assignments are expected to be written neatly on clean paper or the original handout, clearly labeled with name, date, and the assignment. Homework is due the next time class meets, unless directed otherwise. Your marking period homework grade consists of the percentage reflecting your completed assignments over the total number of assignments.

Final Exam - Wednesday June 4th

Exam Topics: Click on underlined topic to go to regentsprep.org outline

Algebra II – Math B 2nd Semester:

1. Operations
Radicals
Negative and Fractional Exponents
Complex Numbers: evaluating, simplifying, graphing

2. Variables and Expressions
Factoring Polynomials - Review and More

3. Equations and Inequalities
Absolute Value Equations
Absolute Value Inequalities
Quadratic Equations, Discriminant, Quadratic Formula
Sum and Product of Roots of a Quadratic Equation
Quadratic Inequalities
Direct Variation
Exponential Expressions and Equations
Radical Equations

4. Patterns, Functions, and Relations
Relations and Functions: definition, function notation, domain and range
Composition of Functions
Inverse Functions: definition, graphical representation

Aims week of 5/19:

Aim 69: How do we evaluate fractional exponents?
hw: pg 544 11, 12, 13

Aim 70: more on fractional exponents.
hw: finish worksheet

Aim 71: continuation fractional exponents & evaluating radicals
hw: pg 547 2-28 even

Aims week of 5/12:

Aim 64: Review sheet exponential powers
hw: none

Aim 65: Review exponential powers:
hw: pg 542 2-24 even

Aim 66: What is a parent graph?
hw: pg 542 1-23 even

Aim 67: More on parent graphs & exponents.
hw: study for quiz

Aim 68: Quiz on exponents.
hw: none

Links to regentsprep.org Polynomials

link to exponents review:
http://www.regentsprep.org/Regents/math/algtrig/ATO1/posnegzles.htm

link to fractional exponents:
http://www.regentsprep.org/Regents/math/algtrig/ATO1/FractionalExp.htm

link to evaluating fractional exponents:
http://www.regentsprep.org/Regents/math/algtrig/ATO1/FractExpressions.htm


link to polynomials of higher degree:
http://www.regentsprep.org/Regents/math/algtrig/ATE13/HighPolyLesson.htm


link to graphing polynomials of higher degree:
http://www.regentsprep.org/Regents/math/algtrig/ATE13/HighPolyGraphLesson.htm

Aims week of 5/4:

Aim 58: How do we graph complex numbers?
hw: pg 520 13, 33

Aim 59: How do we find the absolute value of complex numbers?
hw: pg 537 19-23 pg 538 19-24

Aim 60: Wrap up complex numbers
hw: problems on review sheet

Aim 61: Review: finding roots of quadratics
hw: study for test

Aim 62: test - complex numbers
hw: none

Aims week of 4/28:

Aim 53: What are complex numbers?
hw: pg 520 8-12, 24, 28

Aim 54: What can we conclude about the cyclic nature of i?
hw: pg 520 1-7,35,36

Aim 55: How do we add and subtract complex numbers?
hw: 520 14-23

Aim 56: How can we find the product of complex numbers and review of radicals?
hw: Complete problems on radical handout.

Aim 57: What have we learned so far about complex numbers?
hw: none

Aims week of 4/14:

Aim 48: Review for test: topics include all prior quadratic topics from previous test along with finding inverses of functions graphically and algebraically, using the quadratic formula to find x intercepts, evaluating the solution set using the discriminant. Test encompasses all sections of Chapter 5 excluding 5-6 and 5-7.
hw: study for test

Aim 49: Chapter 5 test
hw: none

Aim 50: What can we conclude about the sum and product of roots?
hw:

Aim 51: How do we graph quadratic inequalities?
hw:

Aim 52: Brainteasers
hw: none

Links to regentsprep.org Imaginary Numbers

Definition imaginary numbers :
http://www.regentsprep.org/Regents/math/algtrig/ATO6/ImagineLes.htm

Cyclic nature of powers of i:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/powerlesson.htm

Simplifying square roots with negative numbers:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/SquareRootLes.htm

Adding and subtracting complex numbers:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm

Multiplyling and dividing compex numbers:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/multlesson.htm

Absolute value of complex numbers:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/absvlecomlesson.htm

Representing complex numbers graphically:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/cgraphlesson.htm

Solving quadratic equations with complex roots:
http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadcomlesson.htm

Aims week of 4/7:

Aim 43: What is the inverse of a function?
hw: pg 508 2,4,6,8,10,12

Aim 44: What is a square root function?
hw: pg 509 16, 18,20,30,32

Aim 45: How can we solve using the quadratic formula?
hw: pg 531 2,4,6,8

Aim 46: What does the discriminant tell us about a quadratic?
hw: pg 532 28,30,32,34,37,42

Aim 47: How do we find the x and y intercepts of a quadratic?
hw: none

Link to regentsprep.org Inverse Functions

link to regentsprep.org Inverse Functions
http://www.regentsprep.org/Regents/math/algtrig/ATP8/inverselesson.htm

link to graphically represent an inverse function on regentsprep.org
http://www.regentsprep.org/Regents/math/algtrig/ATP8/applesson.htm

link to quadratic formula:
http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadformula.htm

link to discriminant
http://www.regentsprep.org/Regents/math/algtrig/ATE3/discriminant.htm

link to summary:
http://www.regentsprep.org/Regents/math/algtrig/ATE3/QuadLesson.htm

Links on quadratics

Link to jmap.org : regents review questions

http://www.jmap.org/JMAP/RegentsExamsandQuestions/3-AdobePDFs/WorksheetsByTopic/QUADRATICS/RR_QUADRATIC_FUNCTIONS.pdf

Math Competition - Problem # 6

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

THREE WEEK PROBLEM #6

TWENTY FOUR

Create the number 24 by using only a 1, 3, 4 and 6.

The only operations symbols you may use are those

for addition, subtraction, multiplication and division.

You may use parentheses.

In how many different ways can you get 24?

You must show your all your working.

********************************************

Due Date: Friday, April 18, 2008

**********************************************************

Remember:

* Your entry must clearly show your name, school name, mathematics class code, teacher’s

name and date of submission

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive a

certificate for participating.

**************************************************************************************

MPSC THREE WEEK PROBLEM #6, 2007-8 Tom Frossinakis (AUSSIE) March 30, 2008

Aims week of 3/31:

Aim 38: How can we find the vertex of a parabola?
hw: pg 501 1-4, 8, 12, 18

Aim 39: How can we model using parabolas?
hw: pg 502 22,24,30,32,36, 37

Aim 40: How can find x intercepts; review factoring
hw: pg 511 2-12 even

Aim 41: more on parabolas
hw: study for test

Aim 42: Chapter Test on Quadratics
Given an equation ---> sketch a graph
Given a graph ---> write an equation
Given an equation ---> find the vertex (max / min)
Factor
Solve word problems (find vertex (h,k))
hw: none

Quadratic Equations

Try it yourself:

http://hotmath.com/util/hm_flash_movie.html?movie=/
learning_activities/interactivities/translating_scaling.swf&
return_to=undefined&title=Transforming%20Functions

Graphing Form and Standard Form As you have worked with quadratic functions, equations, and expressions you have regularly seen two forms. One is known as graphing (or vertex) form, the other is known as standard form.

A quadratic equation in GRAPHING or VERTEX FORM looks like:

Y = a(x–h)² + k.

- the vertex is (h,k) and the axis of symmetry is the line x=h.
- the parabola opens up when a is positive and opens down when a is negative.
- if |a| > 1, the graph will be narrower than the graph of y = x²

- if |a| <1, the graph will be wider than the graph of y = x^ 2

For example, the equation Y = 3(x–1)² – 5 is in graphing form where a = 3, h = 1, and k = –5.

The following quadratic equation represents the same parabola as y = 3(x – 1)² – 5, but it is written in what is generally called standard form. For y = 3x² – 6x – 2, a = 3, b = –6, and c = –2.

A quadratic equation in STANDARD FORM is written as y = ax² + bx + c.

The vertex of a parabola locates its position on the axes. The vertex serves as LOCATOR POINT for a parabola. The other shapes we will be investigating in this course also have locator points. These points have different names but the same purpose for each different type of graph.

Aims week of 3/24:

Aim 33: What are identity and inverse matrices?
hw: pg 427 2,4,6

Aim 34: How can you use inverse matrices to solve matrix equations?
hw: pg 427 14,16,18,37,40

Aim 35: continuation solving matrix equations.
hw: none

Aim 36: Investigation into quadratic functions
hw: pg 490 22,24,26,33

Aim 37: What are the standard and graphing form of a quadratic equation?
hw: none

Aims week of 3/17:

Aim 29: How do we use matrices for a geometric transformation?
hw: pg 413 2,8,10,11,16, 18

Aim 30: What is a square matrix and it's determinant?
hw: pg 430 - 431 2-18 even

Aim 31: Review linear systems & matrices
hw: study for test

Aim 32: Chapter 3 test

Friday - No School!

Matrix Defintions

Introduction to Matrices:
Matrices are simply tables of numbers, but the rise of modern computing has made them increasingly important in science, economics, computer science, and mathematics. Matrices have their own notation and form, and their own unique arithmetic which you’ll need to become familiar with before proceeding further. Once you understand the mechanics, the computations are straightforward, and your calculator can even do them for you! Matrices have many applications, and we’ll see how they tie together with systems of equations later in this unit.

A MATRIX is a rectangular array of numbers or algebraic expressions enclosed in square brackets. (Some math texts use parentheses instead.) Usually, a matrix is denoted by a capital letter. The plural of matrix is matrices. Each matrix has ROWS and COLUMNS. In mathematics we are very precise: rows are horizontal, and columns are vertical. If matrix M has 2 rows and 3 columns, we say the dimensions of M are 2 3, or M is a 2 by 3 matrix. m2,1 is the ENTRY in the second row and first column of matrix M; in general, mr, c is the entry in the rth row and cth column.

Two matrices can be added only if they have the same dimensions.

We can multiply matrices of any size as long as they "fit " right. You get the entries of the product matrix by finding "sums of products " of rows of the first matrix with columns of the second. Here is a more formal description:

To get the r,c entry of the product matrix, multiply the corresponding entries in the r^th row of the first matrix and the c^th column of the second matrix and add the products.

Aims week of 3/10:

Aim 24: Review - Solving Linear Systems
hw: finish worksheet

Aim 25: What is a matrix (matrice)?
hw: pg 392 2,3,6,10,14,16,18,20

Aim 26: How do we add and subtract matrices?
hw: pg 399 2,4,6,32,34,36

Aim 27: How do we multiply and divide matrices?
hw: pg 406 2,4,8,14,21,26,28

Aim 28: More on Matrix operations
hw: none

Math Competition - 3 Week Problem #5

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

THREE WEEK PROBLEM #5

TRAIN IN TUNNEL

How long will it take a two-mile long train

traveling at 12 miles per hour to travel completely

through a mile-long tunnel?

You must show your reasoning.

********************************************

Due Date: Friday, March 28, 2008

**********************************************************

Remember:

* Your entry must clearly show your name, school name, mathematics class code, teacher’s

name and date of submission

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive a

certificate for participating.

**************************************************************************************

MPSC THREE WEEK PROBLEM #5, 2007-8 Tom Frossinakis (AUSSIE) March 4, 2008

Math Competition - Semester Problem

MATHEMATICS PROBLEM SOLVING COMPETITION

SEMESTER 2, 2007-8

SEMESTER PROBLEM #2

FORTY

Using four different whole numbers and any number of mathematical operations, write expressions for all the whole numbers from 0 to 40.

The same set of the four different numbers must be

used for each of the numbers from 0 to 40.

Examples: 24 + 8 + 5+ 3 = 40; 24 –5 + 8/2 = 23

All working must be clearly shown.

*****************************************

Due Date: Friday, May 30, 2008 (or sooner)

*******************************************************

Remember:

* Your entry must clearly show your name, school’s name, mathematics class code,

teacher’s name and date of submission.

* All steps must be clearly shown.

* The most accurate and best presented entry will win the prize.

* Your mathematics teacher will give you credit for your entry and you will also receive

a certificate for participating.

**************************************************************

MPSC SEMESTER PROBLEM #2, 2007-8 (FORTY) Tom Frossinakis (AUSSIE) March 4, 2008

Aims week of 3/3:

Aim 19: More on Absolute Value
hw: pg 368 35 , finish worksheet

Aim 20: How do we graph 2 dimensional absolute value functions?
hw: pg 372 13, 15, 18, 20

Aim 21: Review Chap 2
hw: pg 387 1-4,6,8,10 Due Friday

Aim 22: Test: What have learned in Chapter 2?
hw: none

Aim 23: What are linear systems?
hw: none

Link to regentsprep.org direct variation

Link to regentsprep.org direct variation
http://www.regentsprep.org/Regents/math/algtrig/
ATE7/Direct%20Variation.htm

Link to absolute value equations:
http://www.regentsprep.org/Regents/math/algtrig/
ATE1/abslesson.htm

Link to absolute value inequalities:
http://www.regentsprep.org/Regents/math/algtrig/
ATE2/absinequal.htm

Aims week of 2/25:

Aim 14: Review Linear equations and slope
hw: pg 350 2,4,8,18,27,40

Aim 15: What is direct variation?
hw: pg 354 2,4,9,12,29

Aim 16: How do we graph 1 variable equations and inequalities?
hw: pg 367 16,18,20,22,24,26,30,32 (will collect on Monday)

Aim 17: What is absolute value?
hw: none

Aim 18: How do we graph absolute value inequalities?
hw: none

Note: per 8 did not meet on Thursday due to parent teacher conferences or Friday due to the multicultural show.

Aims week of 2/11:

Aim 9: How do we evaluate a composite function?
hw: pg 317 4,6,14,16

Aim 10: How do we analyze graphs using graphing calculators?
hw: pg 340 6-16 even

Aim 11: How can we shift a graph - horizontally and vertically?
hw: pg 343 1,2,4,9,11,12

Aim 12: How can we shift a graph (con't)?
hw: pg 323 2,4,8,31,32,35

Aim 13: Test Functions - what have we learned so far?

Aims week of 2/4

Aim 4: How do we investigate a function?
hw: pg 311 2,4,6,11

Aim 5: What is function notation?
hw: pg 311 18-30 even

Aim 6: How can we determine the domain and range graphically?
hw: pg 319 64-69

Aim 7: Review
hw: study for test

Aim 8: Test - What have we learned so far.

Regentsprep.org links to Function, Domain, & Range

http://www.regentsprep.org/Regents/math/algtrig/ATP5/LFunction.htm - Definition of a relation and a function.

http://www.regentsprep.org/Regents/math/algtrig/ATP5/EvaluatingFunctions.htm - Functional notation and evaluation.

http://www.regentsprep.org/Regents/math/algtrig/ATP5/DomainRange.htm - Graphing domain and range of a function.

http://www.regentsprep.org/Regents/math/algtrig/ATP5/OntoFunctions.htm - One to one and onto functions.

Aims week of 1/30

Aim 1: How do we collect and organize data?
hw: pg 296 1,2,3,7,8

Aim 2: How do we describe a linear equation?
hw: pg 299 2-10 even

Aim 3: How do we find a line of best fit?
hw: none

Spring 2008 Semester Opening Comments

The nice thing about the beginning of 2nd semester is that everyone gets a fresh start. YOU have the primary responsibility for what gets done and how much you will learn. If you want maximum results from this course, keep the following in mind:

* Your primary responsibility is to think about mathematics!

* Thinking requires that you be active in your learning.

* You will need to read the book and do your homework every night to practice thinking.

Spring 2008 Grading Policy

Grades are determined by a combination of three factors:

70% tests and quizzes: point totals will be marked on all examinations. The marking period grade will reflect a weighted average of all examinations. A final exam will be given at the end of the semester, reflecting work covered throughout the semester.

15% class work: consists of specific assigned tasks during class time, which are graded. There is also a component that recognizes class participation. This course relies on activities, group efforts, and whole class discussion as important parts of the learning experience. Points will be assigned to different components of class work on a rotating basis. For example, some days will consist of a notebook check or a collection of the Do Now. A log will be kept of students going to the board to put up prior homework problems or work on current work problems.

15% homework: will be assigned daily and collected. Homework is marked based on effort and work shown. Completed homework assignments are expected to be written neatly on clean paper or the original handout, clearly labeled with name, date, and the assignment. Homework is due the next time class meets, unless directed otherwise. Your marking period homework grade consists of the percentage reflecting your completed assignments over the total number of assignments.

Class Rules

Class Rules

Entering class.
Please enter class quickly and quietly by the front door. Take your assigned seat and get out your materials to work. Copy the Aim and the Do-Now for that day's lesson into your notebook. Work on the Do-Now until the teacher calls for your attention.

Participating in class.
Class participation is an important part of your learning and of your grade. Please raise your hand if you have a question or wish to participate in a discussion. There is no calling out of answers or other comments in the classroom at any time.

Notebook.
Students are expected to write down the aim of each lesson, to take notes during class, to complete in-class assignments, to keep handouts, and to hold on to returned tests and homework. It is imperative that students have an organized system for keeping all these materials together. Whether a student chooses to use a binder with appropriate sections or a combination of binder and notebook, the entire collection is referred to as the math notebook.

Lateness.
If you arrive late to class, enter quietly by the front door. Sign the late log with your name and the time. Take your seat without any fuss or conversation, and prepare to join the work in progress. Repeated lateness will result in detention.

Homework.
Homework will be assigned each night. It forms an important part of your learning experience and of your grade. It should be written neatly on clean paper or the original handout, clearly labeled with your name, date, and the assignment. Homework is due the next time class meets, unless you have been told otherwise. And finally, homework must be written legibly — if I can not read it, I can not give credit for it.

Absence.
A student who is absent should bring a note from home to explain the absence. Students are responsible for making up work that they have missed, and for meeting deadlines for projects, tests, and other tasks.

Respect.
All members of the class are expected to show respect for each other, teacher and students alike. We respect each other by taking care of the property and environment of the classroom, by listening when it is someone else's turn to speak, and by accepting the fact that we will all make mistakes. Mistakes are an important part of how we learn, and are not an opportunity to make fun of someone else. We are here to help each other. Disrupting the class is disrespectful to others and will not be tolerated.

Web Site.

To help students and parents keep up with general course information, I will be maintaining a web blog that can be accessed at http://rkamath-msgordon.blogspot.com/

More information about the general rules and expectations for success at RKA can be found in the Student Planner.

PLEASE KEEP THESE GUIDELINES IN YOUR MATH NOTEBOOK / BINDER.

Aims week of 1/7:

All lessons this week will be geared towards reviewing for the final. Homework will be on worksheets.

Link to review sheet from regentsprep.org: http://www.regentsprep.org/Regents/math/geometry/FormulaSheetGeometry.pdf

Aims week of 1/2:

Note: Final Exam for 1st Semester will encompass all material covered: PH chapters 7-12, please reference prior postings for more detail.

Aim 71: Circle catchup - area of sectors, radian measure, and arc length
hw: assigned problems on worksheet

Aim 72: What are the coordinates of a point on a unit circle?
hw: assigned problems on worksheet.

Aim 73: How can we prove relationships in circles?
hw: none