ADVANCED MATHEMATICS II
(SECONDARY)
SELECTIVE UNIT 4 (S04)
(Conics (11.1-11.5))
(July 2013)
Unit Statement: The student will be introduced to the graphs and equations for the four
conic sections: circle, ellipse, parabola and hyperbola. This selective unit is beneficial for
the student with interests in architecture and engineering, particularly optical engineering,
due to conics’ many real world applications.
Essential Outcomes: (must be assessed for mastery)
1. The Student Will define parabolas, circles, ellipses and hyperbolas geometrically.
[11.1-11.3, pp. 724-741]
2. TSW use the parameters of a parabola (focus, directrix) to graph a parabola with both a
horizontal axis and vertical axis. [11.1 pp. 724]
3. TSW graph an ellipse given an equation by identifying the major axis, minor axis and
foci. [11.2, pp. 732]
4. TSW define eccentricity and find the equation of an ellipse from its eccentricity and
foci. [11.2, pp. 732]
5. TSW graph a hyperbola given an equation by identifying vertices, transverse axis,
asymptotes and foci. [11.3, pp. 741]
6.
TSW write equations of parabolas, ellipses and hyperbolas given an original equation
and a description of an applied horizontal or vertical shift. [11.4, pp. 750]
7. TSW sketch graphs of parabolas, ellipses and hyperbolas that have been shifted
horizontally and/or vertically. [11.4, pp. 750]
8. TSW determine if a conic in the form Ax2+Cy2+Dx+Ey+F=0 based on the values of A
and C. [11.4, pp. 750]
a. If A or C is zero, the conic is a parabola.
b. If A=C, the conic is a circle.
c. If A and C have the same sign and A ≠B, the conic is an ellipse.
d. If A and C have opposite signs, the conic is a hyperbola.
e. If A and C both equal zero, it is a degenerate conic.
9. TSW graph a rotated conic. [11.5, pp. 757]
10. TSW identify a conic of the form Ax2+Cy2+Dx+Ey+F=0 by the discriminant B2-4AC.
[11.5, pp. 757]
a. If the discriminant is zero, the conic is a parabola.
b. If the discriminant is less than zero, the conic is an ellipse.
c. If the discriminant is more than zero, the conic is a hyperbola.
QSI ADV MATHEMATICS II S04
Copyright © 1988-2013
49
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)
Projects/Group Work (Interim and/or Summative Assessment)
o Students create a picture utilizing a minimum of 15 conics (teacher can
determine requirements and diversity of conics) on Geogebra.
o Group Work, Section 11.1: The Effects of Gravity (Instructor’s Guide)
o Group Work, Section 11.3: Sketching Hyperbolas
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.or
QSI ADV MATHEMATICS II S04
Copyright © 1988-2013
50
SUGGESTED RUBRIC ADVANCED MATH II S04
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
1. TSW define parabolas, ellipses and
hyperbolas geometrically.
2. TSW use the parameters of a
parabola (focus, directrix) to graph a
parabolas with both a horizontal axis
and vertical axis.
3. TSW graph an ellipse from an
equation by identifying the major
axis, minor axis and foci.
4.
‘A’* LEVEL
TSW use the geometric definition of one (or
more) parabolas to create equations of parabolas.
TSW compare, analyze and draw conclusions on
families of parabolas with varying parameters
(focus, directrix).
TSW graph an ellipse from an equation by
identifying the major axis, minor axis and
foci.
TSW define eccentricity and find
the equation of an ellipse from its
eccentricity and foci.
5. TSW graph a hyperbola given an
equation by identifying vertices,
transverse axis, asymptotes and foci.
TSW define eccentricity and find the
equation of an ellipse from its eccentricity and
foci.
TSW create an algorithm on how to find the
TSW graph a hyperbola given an equation by
equation of a hyperbola by inspecting a graph of a identifying vertices, transverse axis,
hyperbola.
asymptotes and foci.
6. TSW write equations of parabolas,
ellipses and hyperbolas given an original
equation and a description of an applied
horizontal or vertical shift.
QSI ADV MATHEMATICS II S04
Copyright © 1988-2013
‘B’ LEVEL
TSW define parabolas, ellipses and
hyperbolas geometrically.
TSW use the parameters of a parabola (focus,
directrix) to graph a parabolas with both a
horizontal axis and vertical axis.
TSW write equations of parabolas, ellipses
and hyperbolas given an original equation and
a description of an applied horizontal or
vertical shift.
51
Comments
7. TSW sketch graphs of parabolas,
ellipses and hyperbolas that have been
shifted horizontally and/or vertically.
TSW sketch graphs of parabolas, ellipses and
hyperbolas that have been shifted horizontally
and/or vertically.
8. TSW determine if a conic in the form
Ax2+Cy2+Dx+Ey+F=0 based on the
values of A and C. [11.4]
a. If A or C is zero, the conic is a
parabola.
b. If A=C, the conic is a circle.
c. If A and C have the same sign and A
≠B, the conic is an ellipse.
d. If A and C have opposite signs, the
conic is a hyperbola.
e. If A and C both equal zero, it is a
degenerate conic.
TSW determine if a conic in the form
Ax2+Cy2+Dx+Ey+F=0 based on the values of
A and C.
If A or C is zero, the conic is a parabola.
If A=C, the conic is a circle.
If A and C have the same sign and A ≠B, the
conic is an ellipse.
If A and C have opposite signs, the conic is a
hyperbola.
If A and C both equal zero, it is a degenerate
conic.
9. TSW graph a rotated conic.
Given the graph of a rotated conic, the student
will derive a method for finding equation of the
conic.
10. TSW identify a conic of the form
Ax2+Cy2+Dx+Ey+F=0 by the discriminant
B2-4AC.
a. If the discriminant is zero, the conic is a
parabola.
b. If the discriminant is less than zero, the
conic is an ellipse.
c. If the discriminant is more than zero,
the conic is a hyperbola.
QSI ADV MATHEMATICS II S04
Copyright © 1988-2013
TSW graph a rotated conic.
TSW identify a conic of the form
Ax2+Cy2+Dx+Ey+F=0 by the discriminant B24AC.
If the discriminant is zero, the conic is
a parabola.
If the discriminant is less than zero,
the conic is an ellipse.
If the discriminant is more than zero,
the conic is a hyperbola.
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