Honors Advanced Algebra
Grades:10-11
Mr. Kuehl

Course Purpose: Advanced Algebra is a course in which students will review and expand upon their knowledge of Algebra and prepare themselves for higher-level math and science.

Course Goal: That the students display their God-given talents in advanced algebra by applying mathematics to various real-world and mathematical situations in service to Him.

Course Outcomes:  The student will. . .
·   review, expand, and apply their understanding of linear, quadratic, polynomial, absolute value, piecewise, rational, radical, exponential, and logarithmic functions, particularly by simplifying, solving, and performing regression and interpolation techniques to fit data to these model functions
·   add, subtract, multiply, divide, and compose two functions and find the resulting domain and range
·   calculate and prove the inverse of a function and its domain and range
·   recognize the algebraic patterns of the functions listed above in tables, equations, and graphs
·   identify the effect of transformations from the parent function of a graph and equation
·   collect real world data, display it graphically, analyze its trends, and logically choose and calculate an equation of best fit
·   be able to make a transition from one form of an algebraic relationship to another provided one form from which to begin (Ex.  From Table of Values to Equation to Graph to Worded Description)
·   apply the rules of exponents to simplify expressions involving exponents
·   make use of the rectangular and imaginary planes to graph relationships and Algebraic concepts
·   identify and graph each type of conic section and their important features given its equation
·   find the rate of change of an equation using the definition of a slope/derivative and explain its meaning
·   analyze arithmetic and geometric series and sequences and determine their mathematical pattern, equation, and sum
·   use mathematical induction to prove mathematical theorems
·   expand binomials using the binomial theorem
·   solve a system of linear, non-linear, and conic equations and equalities by elimination, substitution, graphing, matrices (A^-1B and row operations), and determinants
·   add, subtract, multiply, scalar multiply, find the inverse and the determinant of, and arrange data in matrices
·   graph parametric equations, and convert between parametric and rectangular equations
·   apply solving systems of inequalities to do linear programming
·   calculate the probability of an event incorporating the fundamental counting principle, permutations, combinations, independent, dependent, and conditional events, and simulation
·   calculate the measures of center and spread for a set of univariate data
·   graph data using scatterplots, stem and leaf plots, boxplots, and histograms
·   determine whether data follows a binomial or normal distribution, and use the features of these distributions to predict results 

Course Outline: Text: Algebra 2 (Holt, Rinehart, and Winston, 2003)

Semester One:
                Unit 1: Data and Linear Representations (Chapter 1, pp. 2 – 83)
                Unit 2: Numbers and Functions (Chapter 2, pp. 84 – 153)
                Unit 3: Systems of Linear Equations & Inequalities (Chapter 3, pp. 154 – 213)
                Unit 4: Matrices (Chapter 4, pp. 214 – 271)
                Unit 5: Quadratic Functions (Chapter 5, pp. 272 – 351)
                Unit 6: Polynomial Functions (Chapter 7, pp. 422 – 477)
Semester Two:
                Unit 7: Exponential and Logarithmic Functions (Chapter 6, pp. 352 – 421)
                Unit 8: Rational Functions and Radical Functions (Chapter 8, pp. 478 – 559)
                Unit 9: Discrete Mathematics: Series and Patterns (Chapter 11, pp. 688 – 761)
                Unit 10: Conic Sections (Chapter 9, pp. 560 – 625)
                Unit 11: Discrete Mathematics: Counting Principles and Probability (Chapter 10, pp. 626 – 687)
                Unit 12: Discrete Mathematics: Statistics (Chapter 12, pp. 762 – 825) 

Unit Outline:

Semester One:
Unit 1: Data and Linear Representations (Chapter 1, pp. 2 – 83)
It is the goal of the instructor that the students will:

• convert between the slope-intercept, point-slope, and standard forms of a linear equation

• calculate the slope (rate of change) and the y-intercept of a linear equation and explain their meaning in a real-world context

• convert between the written, equation, graphic, and tabular form of a linear equation

• calculate the linear equation given two points, given a point and a slope, and given a parallel or perpendicular line and a point

• design and solve a direct variation, including finding its constant of variation

• compute the linear regression and median-median equation and correlation for a set of data and explain their meaning and applications in a real-world context

• identify a linear pattern in a table of data

• simplify and solve linear equations and inequalities, literal equations, and absolute value equations and inequalities

• memorize the properties of equality and inequality and apply them

Unit 2: Numbers and Functions (Chapter 2, pp. 84 – 153)
It is the goal of the instructor that the students will:

• classify numbers by their type

• memorize and apply the properties of addition and multiplication and the distributive property

• memorize and apply the properties of exponents

• simplify complex fractions

• determine whether a relation is a function and determine its domain and range

• add, subtract, multiply, divide, and compose functions and determine the new domain and range

• calculate the inverse of a function and prove algebraically that it is the inverse

• graph piecewise, absolute value, and step functions by hand and on the graphics calculator, and know their applications

• identify the transformations an equation would go through compared to its parent equation

• form an equation given its parent and the transformations it should go through

Unit 3: Systems of Linear Equations & Inequalities (Chapter 3, pp. 154 – 213)
It is the goal of the instructor that the students will:

• identify a system of equations as consistent, inconsistent, dependent, or independent

• solve a system of equations by graphing, substitution and elimination

• solve mixture and part-part-whole problems

• solve a system of inequalities by graphing

• organize and solve a problem involving linear programming

• graph a set of parametric equations by hand and on the graphics calculator

• create an equation in two variables by removing a parameter

• create a set of parametric equations by adding a parameter

• apply parametric equations to describe the path of a projectile and to graph equations and their inverses

Unit 4: Matrices (Chapter 4, pp. 214 – 271)
It is the goal of the instructor that the students will:

• memorize, identify, and apply the parts of a matrix

• create a matrix to arrange data

• add, subtract, multiply, scalar multiply, and calculate the inverse and determinant of matrices

• perform a geometric transformation through the application of a matrix

• simulate connections in a network in a matrix

• code and un-code a message through the use of matrices

• solve a system of equations using matrices by the A^-1B method, using row operations, and Cramer’s Rule

Unit 5: Quadratic Functions (Chapter 5, pp. 272 – 351)
It is the goal of the instructor that the students will:

• convert between the general and standard (h-k) forms of a quadratic equation

• identify the vertex, axis of symmetry, minimum/maximum, domain, range, and end behavior of a quadratic equation

• calculate the rate of change and the y-intercept of a quadratic equation and explain their meaning in a real-world context

• convert between the written, equation, graphic, and tabular form of a quadratic equation

• compute the quadratic regression and quadratic interpolation equation and correlation for a set of data and explain their meaning and applications in a real-world context

• identify a quadratic pattern in a table of data

• simplify and solve quadratic equations and inequalities using factoring, the quadratic formula, completing the square and taking the square root, the sign-pattern method, and graphing

• identify and apply the relationship between roots and factors

• identify and factor/multiply the special cases involving the difference of two perfect squares and perfect square trinomials

• identify the transformations a quadratic equation would go through compared to its parent equation

• derive (prove) the quadratic formula

• identify the discriminant of a quadratic equation and use it to classify the roots of the equation

• add, subtract, multiply, divide, and compute the conjugate of complex numbers

• graph a complex number on the complex plane and calculate its modulus

Unit 6: Polynomial Functions (Chapter 7, pp. 422 – 477)
It is the goal of the instructor that the students will:

• classify polynomials by degree and number of terms

• add, subtract, multiply and evaluate polynomials

• graph a polynomial by hand and on the graphics calculator

• compute the cubic or quartic regression or interpolation equation for a set of data and use it to make predictions

• identify a cubic or quartic pattern in a table of data

• identify the local and absolute minimums/maximums, turning points, roots, and end behavior model of a polynomial equation

• solve a polynomial equation by factoring (including factoring by grouping and factoring the sum or difference of two perfect cubes), synthetic division, graphing, and by substitution of a variable

• divide polynomials by long division and synthetic division

• apply the factor theorem and remainder theorem in polynomial division

• apply the location principle, multiplicity of roots, rational root theorem, and the fundamental theorem of Algebra in solving polynomial equations

Semester Two:

Unit 7: Exponential and Logarithmic Functions (Chapter 6, pp. 352 – 421)
It is the goal of the instructor that the students will:

• identify the y-intercept, rate of change, base, the initial population, asymptote, domain, range, and the transformations in an exponential or logarithmic equation

• identify an exponential or logarithmic pattern in a table of data

• classify an equation as exponential growth or decay

• calculate interest and total value of an investment in a compound interest problem

• compute the exponential or logarithmic regression equation for a set of data and use it to make predictions

• convert between exponential and logarithmic forms of an equation

• evaluate exponential and logarithmic equations by applying the “one-to-one” property

• apply logarithms to pH, population growth, radioactive decay, magnitude of earthquakes, cooling, and sound intensity problems

• memorize and apply the properties of logarithms to simplify, expand, and solve logarithmic and exponential equations

• identify and apply common and natural logarithms

• identify the irrational number e, derive its value, and apply it to natural logarithmic and continuous interest problems

Unit 8: Rational Functions and Radical Functions (Chapter 8, pp. 478 – 559)
It is the goal of the instructor that the students will:

• design and solve an indirect variation, joint variation, or combined variation including finding its constant of variation

• identify the y-intercept, zeros, rate of change, domain, range, asymptotes, holes, and transformations of a rational equation

• graph rational and radical equations by hand and on the calculator

• simplifying rational and radical expressions involving multiplication, division, addition, or subtraction and complex fractions

• solve rational and radical equations and inequalities algebraically and graphically

• identify the y-intercept, zeros, rate of change, domain, range, and transformations of a radical equation

• compute a rational equation given its y-intercept, zeros, asymptotes, holes, and transformations

• compute the power regression equation for a radical set of data

Unit 9: Discrete Mathematics: Series and Patterns (Chapter 11, pp. 688 – 761)
It is the goal of the instructor that the students will:

• derive an explicit, implicit, or recursive formula for a sequence

• convert a series to summation notation, and a vice versa

• memorize and apply summation algebra to compute the sum of a series

• identify an arithmetic sequence/series and its common difference and initial term

• identify a geometric sequence/series and its common ratio and initial term

• calculate an arithmetic or geometric mean

• memorize and evaluate the formulas to find the sum of an arithmetic or geometric series

• prove a mathematical property using mathematical induction

• identify whether an infinite geometric series converges or diverges

• identify and apply the patterns found in Pascal’s Triangle to two-outcome experiments and the Binomial Theorem

• expand or find the nth term of a binomial applying the Binomial Theorem

Unit 10: Conic Sections (Chapter 9, pp. 560 – 625)
It is the goal of the instructor that the students will:

• classify a conic section by analyzing its equation

• graph a conic section by hand and on the calculator

• compute the distance and the midpoint between two points and relate them to the diameter and center of a circle

• identify the focus, directrix, axis of symmetry, vertex, and transformations of a parabola from a graph and an equation

• identify the center, radius, and transformations of a circle from a graph and an equation

• identify the center, major and minor axis, foci, vertices, co-vertices, and transformations of an ellipse from a graph and an equation

• identify the center, transverse axis, vertices, co-vertices, conjugate axis, asymptotes, and transformations of a hyperbola from a graph and an equation

• memorize and apply the definition of each conic section to sketch the conic section and derive its standard equation

• calculate and explain the meaning of the eccentricity of a conic section

• solve a system of conic sections

Unit 11: Discrete Mathematics: Counting Principles and Probability (Chapter 10, pp. 626 – 687)
It is the goal of the instructor that the students will:

• explain and apply the difference between experimental and theoretical probability

• identify a trial, experiment, sample space, and event in a probability situation

• design a tree diagram to display all the possible outcomes in a sample space

• apply the fundamental counting principle, permutations, or combinations correctly to a particular probability scenario

• calculate n!, nCr, or nPr using memorized formulas and on the calculator

• identify inclusive vs. mutually exclusive or independent vs. dependent or conditional probability events and apply the correct probability formula to each

• calculate the complement of an event

• construct a Venn diagram to organize data

• simulate a probability scenario using manipulatives or the calculator to find an experimental probability

Unit 12: Discrete Mathematics: Statistics (Chapter 12, pp. 762 – 825)
It is the goal of the instructor that the students will:

• calculate the measures of central tendency for a set of data (mean, median, mode) individually or from a frequency table

• describe how outliers effect each measure of central tendency

• construct a frequency table to manage a set of data

• construct a stem and leaf plot, histogram, relative frequency table, circle graph, or boxplot for a set of data by hand and (some) on the calculator and identify their key parts

• identify the shape of a histogram, stem and leaf plot, or boxplot, and explain what it tells you about the data

• calculate the measures of deviation for a set of data (mean variation, variance, standard deviation)

• identify a binomial distribution/experiment and calculate the binomial probability of the experiment

• identify a normal distribution of data and calculate z-scores to find the probability of an event or given the probability, determine the event restrictions

Instructional Strategies:

                Correcting of Homework/Questions (10%)
                Opening Motivational Activity (10%)
                Lecture/Discussion (50%)
                Small group/independent work (20%)
                Daily Homework Quiz (10%) 

Grading:

Percentage breakdown:
Homework (10%)
Quizzes (15%)
Projects (20%)
Tests (35%)
Semester Project (20%) 

Homework

                Homework is extremely important to learning Algebra.  In order to be successful on the quizzes, tests and projects, and with Algebra in general, you MUST do and understand the problems you are assigned for homework.  Homework, however, is where you practice the new math skills you are learning.  Treat homework like any other practice: practice hard, practice often, and learn from your successes and your failures.  It is okay to have some failures in practice as long as you learn from your mistakes.  This is the reason homework does not make up a large percentage of your overall grade, and is also the reason why I use a rubric to grade your homework, rather than a strict percentage of the number you got correct.  The rubric I will use to assess your homework is: 

All homework will be corrected at the beginning of class on the day it is due.  You will be given an answer sheet, and you are to correct your own homework in red pen.  While you correct your homework, be sure to write-in the correct answers to any problems you got wrong or simply did not get.  Try to determine what you did wrong on your own, and make notes on your homework to help you remember how to do those problems correctly in the future.  When everyone is finished correcting their papers, you will then have the opportunity to ask questions on problems you still do not understand.  I will collect your homework afterwards so I can grade your homework.  It is my intent to provide written feedback on some assignments before returning them to you as time allows.

A sheet listing all homework to be done for a chapter will be distributed when we begin each chapter.  Refer to this sheet to find the specific problems assigned for a particular section, as well as any extra directions I might give you to follow for the assignment.  The homework sheet will also list the objectives for each section.  Review these objectives regularly and be sure you have accomplished each objective.

                All homework is to be done in pencil on loose-leaf paper.  Write your full name, the class period, and assignment number on the top of your homework sheet.

Usually you will be given two days to complete a homework assignment once discussion on the section is finished.  Begin working on the assignment the same day it is assigned or earlier.  If you are having many problems with an assignment, plan time to get help outside of class from me, the Learning Center, Peer Tutoring, another student, or from Mr. Schoeneck during ELP.  NEVER come to class with your assignment not done for any reason, including “I didn’t understand the assignment!” or “I didn’t have time to print my graphs!”  Only a minimal amount of time will be given for questions in class, so be sure to get your questions answered outside of class if you have many questions.  Time will not be “given” for you to print off calculator graphs in class, but you might find some “downtime” on some class days which allow you to do some printing.  Assignments are due at the beginning of class on the day assigned unless otherwise told.

                Assigned homework is for your benefit.  To make the most of it, you should include all work and personal notes so when it comes time to study, you will be reminded of what you did right or wrong, and how to correct it. 

                Your homework grade will be determined by dividing the number of points you received by the number of points possible for the quarter.  A separate homework grade will be given for each quarter.

Quizzes

                On the day a homework assignment is due, you will have a quiz covering the content of that assignment.  The quiz will have a few questions similar to those found in the homework assignment.  The quiz will usually be given in the last 5 minutes of the class period, and must be turned in as you leave the class.  The chapter vocabulary quiz will be given on the day the chapter review is due.  Your daily quiz grade will be determined by dividing the number of points you received by the number of points possible for the quarter.  A separate quiz grade will be given for each quarter.

Projects

                Approximately one project will be assigned for each chapter having you apply the concepts learned in that chapter.  A rubric for grading each project will be supplied when the project is assigned.

                Some projects will be group projects.  With group projects, you are to only work with other students in your group.  It will be considered cheating to work with a student outside your group and questions should be directed to me.  If a project is an individual project, it will be considered cheating if you get help from, or work together with, another student in the class.  You may only get help from a teacher or a peer tutor (in the LC).

Tests

                Tests will be given after each unit to assess your understanding of the concepts studied in that unit.  The semester exam period will be used to give the final chapter test(s), rather than a comprehensive exam.

Semester Project

                For one semester project, you will form a group and pick a section of the MESA Exploratorium to take care of.  You will assess the exhibits themselves and their webpages and make improvements.  You will also be responsible for setting up and monitoring a month-long exhibition keeping the exhibits you set up in working order and accessible to the public.

                For the other semester project, you will form a group and create an Advanced Algebra letterbox.  Your group will need to try some of the Advanced Algebra letterboxes already placed, then hide a box of your own using all of the different concepts you learned throughout the year or during a chapter.

                The class will be divided so half of the class will do the MESA Exploratorium first semester and the letterbox second semester.  The other half of the class will do the letterbox first semester and the MESA Exploratorium second semester. 

Major Grades

                All projects and tests are considered MAJOR GRADES.  Failure to complete even one of these will result in an F grade for the semester.  Although homework and daily quizzes are not “major” grades, failure to practice your Algebra skills will result in a poor grade for the class.

Absences/Late Work

                If you have an excused unplanned absence (due to illness, etc.), you will have as many days you were absent to make-up late tests without penalty.  Homework and daily quizzes may also be “made up” within this time, but you are not required to do so.  It is to your advantage to make up missed homework and quizzes, as they are more likely to help your overall grade than to harm your grade.  (If you do not make up the homework or quiz, the grade goes in as “excused” which doesn’t hurt or help your grade.)  Projects have specific due-dates, and are due on that day or the day you come back from your absence or they are considered late.

                I do not accept unexcused late homework.  Homework not turned in on the day it is due will receive a grade of zero and you will be expected to take the daily quiz.  Tests and projects not completed on time will result in a 5% reduction in the final grade per school day.  After 2 weeks or 10 school days the grade will be a zero grade and you will automatically fail the semester.

Pre-planned absences need to be cleared following normal school procedures, with assignments indicated on the form due when indicated or they will be considered late.  It is your responsibility, not the instructor’s, to be sure you are following these procedures and getting make-up work in on time, so make appropriate use of your planner.

Semester/Quarter/Midterm Grades

                Note that semester grades are cumulative, meaning I use the indicated percentage breakdown to determine grades.  (I do NOT use 40% Q1, 40% Q2, and 20% Semester Exam.)  Quarter grades and midterm grades are only for those grades recorded during that quarter using the same percentage breakdown as for the semester grade.  For the second and fourth quarter midterm grades, I typically give students both the current quarter grade as well as the current semester grade.

                Your current quarter grade and current semester grade will be posted when the grades for a chapter are completed and at midterm (sometimes these will coincide).  These reports will be sent home to your parents as well - a copy of which must be signed by a parent and returned to me.

Representing Your Savior by Using Your Talents

                By virtue of being in this class, you have shown yourself to be blessed by God with mathematical ability.  God asks us to use our gifts and talents to serve and represent Him.  As such, you will be asked to represent your Savior and your school in various math competitions during the year.  Participation in these meets does not automatically make you a member of the KML Math Team.  You must meet the other criteria of being a team member to be considered a member of the math team.  Various extra credit opportunities are given for participation in these competitions.

                Another way you can serve God with your talents is to use your abilities to help others with their math by becoming a peer tutor.  I will omit the lowest test grade for the semester to any student that is a peer tutor during that semester.  In order to take advantage of this, you must sign-up to be a peer tutor with Mrs. Boeldt at the beginning of the semester.  The peer tutoring can be done during the school day or during ELP.

Student Materials:

Pencil
Pen     
TI-83/84 type graphics calculator         
Three-ring binder (at least 1” width)
Red pen                
Notebook                             
Textbook              
Student Planner   
Loose-leaf paper

Classroom Procedures:
·   Be in the classroom in your assigned desk quietly working on the opening activity when the bell rings or you will be considered tardy
·   Begin working on the opening activity upon arrival in the classroom
·   Bring the above materials to class each day
·   Respect classmates and teachers
·   Participate courteously in class activities
·   Be attentive to the class discussion and provide appropriate input to the discussion when called upon or given permission after raising your hand
·   Finish all work on time and completely
·   Find a “study-buddy” whom you can call for help with an assignment, or to get the assignment when you are absent.  When you are absent, see me the first day you return for make-up work responsibilities
·   Take notes of what is discussed in class and what is demonstrated on the board or overhead 

Extra Information about your Honors Advanced Algebra class:

A typical class day would be:
·   Enter class and begin working on the opening activity (typically correcting the assignment due).
·   Attendance and homework grading will be done while you are working on the opening activity.
·   Questions taken on homework due.
·   Discussion on the new lesson.
·   Lesson investigation activities/class practice.
·   Lesson wrap-up.
·   Daily quiz. 

A typical homework session should include:
·   Review and self-evaluation of the objectives for the section of HW to be done.
·   Review and clarification of your notebook notes for that day including vocabulary.
·   Reading the section in the textbook the HW is for.
·   Completion of the HW assigned (in pencil in your notebook) or review for test.
·   Pre-reading the objectives for the next section.
·   Progress check/work on the chapter project. 

For extra practice on a section you can:
·   use the odd problems in a section (the answers are in the back of the text)
·   use the odd problems from the chapter reviews
·   make corrections on your homework
·   use the extra practice problems in the back of the text
·   go to the textbook’s website for extra problems and tutoring 

Your calculator:
·   don’t be afraid to investigate what it can do
·   don’t use it as a crutch to do simple calculations your should do in your head
·   store the calculator safely in your locker - don’t leave it unattended on a table or in your book bag, especially during exam week or the last day of school before vacation
·   be sure you have your name engraved on it
·   you may have games on it, but no games are allowed to be played during any class
·   you must maintain enough free memory on your calculator so it can function for class work
·   calculator programs provided by the school for use in class take precedence over game programs - at no time should these programs be deleted to make room for games
·   the school reserves the right to delete offensive and unnecessary programs from your calculator at any time
·   no password programs are allowed on your calculator
·   repeated abuse of these calculator rules is grounds for a detention 

Assignments and section objectives are printed in detail on the chapter homework sheet

Assignments are posted on the smaller white board near the closet door

Graph paper is provided for free - no need to buy any

Always have your binder, and keep all work, notes, and papers organized and neat

Mr. Kuehl’s email address is tkuehl@wi.rr.com or tkuehl@kmlhs.org.  Both email addresses are checked fairly regularly, even on weekends and in the late evening.

The textbook’s website is go.hrw.com. It has many helpful resources.

The class website can be found at the school website under Departments.  It has many useful resources, including printable graph paper, the complete course syllabus, and a listing of the assignments that are due.