Advanced Mathematics II

advanced mathematics II

(SECONDARY)

essential UNIT 2 (e02)

(Quadratic, Rational, Inverse Combined Functions)

(1.6, 2.6-2.7, 3.1, 3.7)

(July 2013)

Unit Statement: In this unit, the student will continue his/her study of functions. The students will determine when an inverse function exists and identify algebraic and geometric properties of inverse functions. The student will combine functions through addition, subtraction, multiplication, division and composition and reason about how such combinations affect the properties of the original functions. The student will study the properties of quadratic and rational functions and use this knowledge to graph such functions.

Essential Outcomes: (must be assessed for mastery)

1. The Student Will transform any form of a quadratic function into standard form (f(x)=a(x-h)2+k) and sketch a graph of the function. [3.1, pp. 224]

2. TSW find the minimum/maximum value of a quadratic in the following ways:

i. Identifying the vertex in standard form, (h,k).

ii. Finding the x-coordinate of the vertex using the equationwhen the quadratic is of the form f(x)=ax2+bx+c.

iii. Graphing on a GDC and utilizing calculator’s feature for finding the minimum/maximum value. [3.1, pp. 224]

3. TSW set up and use functions as models of real life situations. [1.6 pp.57]

4. TSW combine functions utilizing the operations of addition, subtraction, multiplication and division, and identify the combined function’s new domain. [2.6, pp. 190]

5. TSW find the composition of two or more functions and identify the composite function’s new domain. [2.6, pp. 190]

6. TSW determine if a function is one-to-one. [2.7, pp. 199]

7. TSW determine if a function has an inverse and, if so, find the inverse of the function. [2.7, pp. 199]

8. TSW graph a rational function by hand by identifying all horizontal, vertical and slant asymptotes, intercepts and plotting points. [3.7, pp. 277]

9. TSW engage in one or more interactive activities or projects that require inquiry, analysis, application and/or interpretation of unit objectives (TSWs)

Introduced and Practiced Outcomes:

1. The Student Will use transformations to graph a rational function. [3.7, pp. 277]

Suggested Assessment Tools and Strategies:

· Attached Rubric or teacher generated rubric that assesses ALL essential outcomes (TSWs)

o Warm up practice (Formative Assessment)

o Group quizzes to practice TSW’s (Formative Assessment)

o Unit assessments (Interim Assessment)

· *TSW 10 Projects/Group Work (Interim and/or Summative Assessment)

o Discovery Project: Iteration and Chaos

o Group Work 1 Section 1.6: How Many People (Found in Instructor’s Guide)

o Group Work 2 Section 1.6: Some Like It Hot (Found in Instructor’s Guide)

o Group Work 3 Section 2.7: Functions in the Classroom Revisited (Found in Instructor’s Guide)

o Group Work Section 3.1: The Penny Drop (Found in Instructor’s Guide)

o Discovery Projects

§ http://www.stewartmath.com/media/5_inside_discovery.php

o Focus on Problem Solving

§ http://www.stewartmath.com/media/5_inside_focus.php

Suggested Resources:

(See Course Outcomes for more detailed descriptions.)

· Geogebra graphing software

o Free to download at www.geogebra.org

· TI-Smartview Emulator Software for TI-84 Plus to enable a class display.

o Purchasable at http://education.ti.com

· 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

(http://www.stewartmath.com/media/5_inside_supplements.php)

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

(http://www.stewartmath.com/media/5_inside_supplements.php)

Technology Links:

www.explorelearning.com

www.quia.com

www.stewartmath.com

www.nctm.org

www.geogebra.org

QSI ADV MATHEMATICS II E02

SUGGESTED RUBRIC ADV MATH II E02

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 transform any form of a quadratic function into standard form (f(x)=a(x-h)2+k) and sketch a graph of the function. / The Student Will transform any form of a quadratic function into standard form (f(x)=a(x-h)2+k) and sketch a graph of the function.
2. TSW find the minimum/maximum value of a quadratic in the following ways:
a. Identifying the vertex in standard form, (h,k).
b. Finding the x-coordinate of the vertex using the equationwhen the quadratic is of the form f(x)=ax2+bx+c.
c. Graphing on a GDC and utilizing calculator’s feature for finding the minimum/maximum value. / TSW correctly analyze real life situations modeled by quadratic equations and draw conclusions regarding critical values (maximum, minimum, intercepts) on the graph. / TSW find the minimum/maximum value of a quadratic in the following ways:
i. Identifying the vertex in standard form, (h,k).
ii. Finding the x-coordinate of the vertex using the equationwhen the quadratic is of the form f(x)=ax2+bx+c.
iii. Graphing on a GDC and utilizing calculator’s feature for finding the minimum/maximum value.
3. TSW set up and use functions as models of real life situations. / TSW set up and use non-linear models of real life situations and analyze the model to draw conclusions. / TSW set up and use linear functions as models of real life situations.
4. TSW combine functions utilizing the operations of addition, subtraction, multiplication and division, and identify the combined function’s new domain. / Given graphs of f(x) and g(x) the student will perform operations by drawing the resultant graph. / TSW combine functions utilizing the operations of addition, subtraction, multiplication and division, and identify the combined function’s new domain
5. TSW find the composition of two or more functions and identify the composite function’s new domain. / 1) The student can analyze real life contexts that require compositions of functions and justify the new domain within the context of the situation. One example of a real life composition function is a car dealership offering both a deduction and a percent discount.
2) Given graphs of f(x) and g(x), the student will perform graphical analysis to determine the composite functions. / TSW find the composition of two or more functions and identify the composite function’s new domain.
6. TSW determine if a function is one-to-one. / TSW assess if a function is one to one analytically. / TSW determine if a function is one-to-one graphically (Horizontal Line Test).
7. TSW determine if a function has an inverse and, if so, find the inverse of the functions. / TSW determine if a function has an inverse and, if so, find the inverse of the functions.
8. TSW graph a rational function by hand by identifying all horizontal, vertical and slant asymptotes, intercepts and plotting points. / TSW create a rational function given characteristics and/or a graph. / TSW graph a rational function by hand by identifying all horizontal, vertical and slant asymptotes, intercepts and plotting points.
9. TSW engage in one or more interactive activities or projects that require inquiry, analysis, application and/or interpretation of unit objectives (TSWs) / The teacher should assess for mastery with an individualized rubric for the assignment.

QSI ADV MATHEMATICS II E02