ADVANCED MATHEMATICS II

(SECONDARY)

essential UNIT 3 (e03)

(Polynomials Complex Numbers (3.2-3.6))

(July 2013)

Unit Statement: In this unit the student will study polynomial functions including their shape, end behavior and critical values. The students will learn how to find all real and complex roots of a polynomial function, which will lead into a study of operations with complex numbers.

Essential Outcomes:(must be assessed for mastery)

  1. The Student Will determine the end behavior of a polynomial function by looking at the function’s leading degree and leading coefficient [3.2, pp. 232]
  1. TSWgraph a polynomial function by:
  1. Identifying all zeros by factoring
  2. Using multiplicity of factors to determine the function’s behavior at each zero
  3. Utilize knowledge of end behavior [3.2, pp. 232]
  1. TSWdetermine the maximum number of extrema possible for a given polynomial based on it’s degree and use a GDC to find the specific value of extrema. [3.2, pp. 232]
  1. TSW use long division on polynomials and write the dividend as the product of its divisor and quotient plus remainder (P(x)=D(x)Q(x)+R(x)). [3.3, pp.246]
  1. TSWuse synthetic division and The Remainder Theorem to evaluate a function at a point. [3.3, pp. 246]
  1. TSW find all zeros of a polynomial by using synthetic division and The Factor Theorem. [3.3, pp. 246]
  1. TSWusesynthetic division and The Rational Zeros test to find all zeros of a polynomial. [3.4, pp. 253]
  1. TSW perform addition, subtraction, multiplication and division on complex numbers [3.5, pp. 264]
  1. TSW find complex solutions to quadratics and recognize complex solutions come in pairs called complex conjugates [3.5, pp. 264]
  1. TSW find all real and complex zeros of a polynomial using the Zeros Theorem and the Conjugate Zeros Theorem. [3.6, pp. 269]
  1. TSW write a polynomial as a product of its linear and quadratic factors following from The Fundamental Theorem of Algebra. [3.6, pp.269]
  1. TSW engage in one or more interactive activities or projects that requires inquiry, analysis, application and/or interpretation of unit objectives (TSWs).

Introduced and Practiced Outcomes:

  1. The Student Willapply the Intermediate Value Theorem. [3.2, pp. 232]
  1. TSW utilize Descartes’ Rule of Sign to determine the maximum number of possible positive and negative real zeros of a polynomial. [3.4, pp. 253]
  1. TSW utilize the Upper and Lower Bounds Theorem to determine the upper and lower bounds for all possible zeros of a polynomial. [3.4, pp. 253]

Suggested Assessment Tools and Strategies:

  • Attached Rubric or teacher generated rubric that assesses ALL essential outcomes (TSWs)
  • Warm up practice (Formative Assessment)
  • Group quizzes to practice TSW’s (Formative Assessment)
  • Unit assessments (Interim Assessment)
  • *TSW 12: Projects/Group Work (Interim and/or Summative Assessment)
  • Focus on Modeling: Fitting Polynomial Curves to Data
  • Discovery Project: Zeroing in on a Zero
  • Group Work 1: Section 3.2: The Waste Free Box (Found in Instructor’s Guide.)
  • Group Work 2: Section 3.2: My Mother’s Gifts (Found in Instructor’s Guide.)
  • Group Work 1: Section 3.4: Supply and Demand (Found in Instructor’s Guide.)

Suggested Resources:

(See Course Outcomes for more detailed descriptions.)

  • Geogebra graphing software
  • Free to download at
  • TI-Smartview Emulator Software for TI-84 Plus to enable a class display.
  • Purchasable at
  • Graphics Display Calculator for every student. Texas Instruments, TI-84 Plus is recommended.
  • Student Solutions Manual
  • Complete Solutions Manual
  • Study Guide
  • Instructor’s Guide
  • Solution Builder

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Additional Resources:

These materials will not be provided automatically but schools are encouraged to purchase them when possible.

  • Enhanced WebAssign
  • Text-Specific DVDs
  • PowerLecture with ExamView CD-ROM

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Technology Links:

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QSI ADV MATHEMATICS II E03

Copyright © 1988-2013

1

QSI ADV MATHEMATICS II E03

Copyright © 1988-2013

SUGGESTED RUBRICADVANCED MATH II E03

Student Name: ______Date: ______

  • To receive a ‘B’, the student must show ‘B’ level mastery on all essential outcomes (TSWs).
  • The teacher’s discretion on the student’s holistic performance on the unit, including such items as: the above ‘A’ level rubric, the unit project, group work and class discussions will determine ‘A’ level mastery.

TSW / ‘A’* LEVEL / ‘B’ LEVEL / Comments
  1. The Student Will determine the end behavior of a polynomial function by looking at the function’s leading degree and leading coefficient.
/ The Student Will determine the end behavior of a polynomial function by looking at the function’s leading degree and leading coefficient.
  1. TSWgraph a polynomial function by:
  2. Identifying all zeros by factoring
  3. Using multiplicity of factors to determine the function’s behavior at each zero
  4. Utilize knowledge of end behavior
/ TSW compare how altering components of a polynomial function (such as it’s leading coefficient or multiplicity of factors) affects its graph and communicate clear conclusions. / TSW graph a polynomial function by:
  1. Identifying all zeros by factoring
  2. Using multiplicity of factors to determine the function’s behavior at each zero
  3. Utilize knowledge of end behavior
.
  1. TSW determine the maximum number of extrema possible for a given polynomial based on it’s degree and use a GDC to find the specific value of extrema.
/ TSW assess when a viewing window is inappropriate for a polynomial and clearly justify their reasoning. / TSW determine the maximum number of extrema possible for a given polynomial based on it’s degree and use a GDC to find the specific value of extrema.
  1. TSW use long division on polynomials and write the dividend as the product of its divisor and quotient plus remainder (P(x)=D(x)Q(x)+R(x)).
/ TSW use long division on polynomials and write the dividend as the product of its divisor and quotient plus remainder (P(x)=D(x)Q(x)+R(x)).
  1. TSW use synthetic division and The Remainder Theorem to evaluate a function at a point.
/ TSW use synthetic division and The Remainder Theorem to evaluate a function at a point.
  1. TSW find all zeros of a polynomial by using synthetic division and The Factor Theorem.
/ TSW find all zeros of a polynomial by using synthetic division and The Factor Theorem.
  1. TSWuse synthetic division and The Rational Zeros test to find all zeros of a polynomial.
/ TSW use The Rational Zeros test to list all possible zeros of a polynomial, then utilize trial and error in synthetic division to determine all zeros of a polynomial. After dividing down to a manageable degree, the student may factor to find remaining zeros.
  1. TSW perform addition, subtraction, multiplication and division on complex numbers
/ TSW perform addition, subtraction, multiplication and division on complex numbers.
  1. TSW find complex solutions to quadratics and recognize complex solutions come in pairs called complex conjugates.
/ TSW justify why complex conjugates must come in pairs. / TSW find complex solutions to quadratics and recognize complex solutions come in pairs called complex conjugates.
  1. TSW find all real and complex zeros of a polynomial using the Zeros Theorem and the Conjugate Zeros Theorem.
/ TSWcreate a polynomial with real coefficients given one complex root and all real roots. / TSW find all real and complex zeros of a polynomial using the Zeros Theorem and the Conjugate Zeros Theorem
  1. TSW write a polynomial as a product of its linear and quadratic factors.
/ TSW create a polynomial given it’s zeros and their multiplicity. / TSW write a polynomial as a product of its linear and quadratic factors.
  1. TSW engage in one or more interactive activities or projects that requires inquiry, analysis, application and/or interpretation of unit objectives (TSWs).
/ The teacher should assess for mastery with an individualized rubric for the assignment.

1

QSI ADV MATHEMATICS II E03

Copyright © 1988-2013