Course: Pre-Calculus
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
2010 – 2011
Concept (Big Idea): Graphs of Other Trig Functions
Concept Pacing: 32 days
Enduring
Essential Questions:
Understanding:
1. How do the periods of the trigonometric function differ?
The characteristics of
2. What are the domains and ranges of each of the trig functions?
the trigonometric
3. How do you sketch each of the 6 basic trig functions?
functions and their
4. Explain how the graphs of the secant and cosecant are related to the cosine and sine functions, respectively, and explain why
applications to real
that relationship exists.
world situations.
5. When given an equation of a tangent or cotangent function, how do you determine the amplitude, the period, the horizontal and
vertical translations of the graph?
6. When given an equation of a secant or cosecant function, how do you determine the amplitude, the period, the horizontal and
vertical translations of the graph?
7. When given the graphs of trig functions, how do you determine the values of A, B, C and D in order write their equations.
Unit 1: Graphs of other trigonometric functions
Unit Pacing: ~5 days
Vocabulary: relation, function, graph of a function, input, output, domain, range, vertical line test, independent and dependent variables, evaluate, solution,
asymptote, horizontal asymptote, vertical asymptote, end behavior, odd intercepts, cosine, tangent, cotangent, secant, cosecant, amplitude, period, reciprocal,
reciprocal function, increases without bound, decreases without bound, odd function, even function
Resources: LH textbook 4.6; graphing calculator, websites
Matrix
#
Established Goals
TEKS Knowledge & Skill
P.3: The student uses
functions and their
properties, tools and
technology, to model and
solve meaningful problems
Established Goals
TEKS Student Expectation
P.3A: investigate properties
of trigonometric and
polynomial functions;
240
Students Will Know…
Students will be able to….
 The relationship of the
graphs trigonometric
reciprocal functions to the
sine, cosine, and tangent
functions.
 Trigonometric functions
have unique and
recognizable graphs.
 Trigonometric functions can
be used to model real world
situations.
 Trigonometric functions are
periodic.
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Sketch the 6 basic trig functions.
Use the 6 trig functions to graph other trig graphs
that have changes in amplitude, period, phase shift,
and vertical shift
Given graphs of trig functions, write their equations.
Using calculators, sketch graphs of any trig function
or combination of trig functions involving sine,
cosine, tangent, cotangent, secant. or cosecant.
Identify graphs of the basic trig functions as being
odd, even, or neither.
Identify the domains and ranges of each of the trig
functions.
Student Work Products/Assessment Evidence
Performance Tasks
Understand the characteristics of 6 basic trig functions.
Sketch the graphs of the trig functions.
Write equations of the trig functions given their graphs.
© 2010 Austin Independent School District
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student work samples,
observations, etc.)
Discussions, worksheets, problems from book, tests & quizzes
Pre-Calculus Page 1 of 8
updated 11/20/10
Course: Pre-Calculus
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Lesson/Activity/Module
Name
Teacher
Resource
Student
Resource
Graphs of Other Trig
Functions
Textbook
LH 4.6
Textbook
LH 4.6
Learning Plan
Technology (Media, website, etc.)
Other (Include Pre-Teach
Suggestions, Intervention
Suggestions, Anchors of Support - all
as links)
2010 – 2011
Assessment (Prep
for Assessment,
TAKS Stems links)
Graphing calculator
patrick just math tutoring
www.patrickjmt.com
regents prep
www.regentsprep.org
purple math
www.purplemath.com
tutorial-go to key index
http://mathdemos.gcsu.edu/mathdemos/
Concept (Big Idea): Vectors and Dot Products
Enduring Understanding:
Perform basic vector operations, represent them
graphically, find the dot products of two vectors, and
determine whether two vectors are orthogonal.
Concept Pacing:
Essential Questions:
1. What is a vector and when does it make sense to model real world situations using vectors?
2. How is a vector drawn and described?
3. What is the process to add two vectors graphically and what does it mean?
4. How does a scalar affect a vector?
5. What is the difference in meaning of vector addition and multiplication by a scalar versus
finding the dot product of two vectors.
6. What is the process to determine the dot product of two vectors?
7. What is a unit vector and how do you determine its value?
8. How do you determine when two vectors are orthogonal and what does it tell you?
Unit 2: Vectors and Dot Products
Unit Pacing: 3-4 days
Vocabulary: force, velocity, magnitude, direction, directed line segment, initial point, terminal point, distance, equivalent, directed line segments, same
magnitude, same direction, distance formula, slope, standard position, components, component form of a vector, zero vector, equal vectors, scalar
multiplication, scalar addition, scalars, parallelogram law, resultant, vector addition, scalar multiplication, negative of a vector, tip to tail, unit vector, standard
unit vectors, horizontal and vertical components of a vector, linear combination, orthogonal vectors
Resources: LH textbook 6.3,6.4: graphing calculator; websites
Arc 1 (if applicable):
Arc Pacing:
Resources: LH textbook 4.7: graphing calculator; websites
© 2010 Austin Independent School District
Pre-Calculus Page 2 of 8
updated 11/20/10
Course: Pre-Calculus
Matrix
#
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Established Goals
TEKS Knowledge & Skill
P.3: The student uses
functions and their
properties, tools and
technology, to model and
solve meaningful
problems
241
335
P.6: The student uses
vectors to model physical
situations. The student is
expected to:
Established Goals
TEKS Student Expectation
P.3E: Solve problems from
physical situations using
trigonometry, including the
use of Law of Sines, Law of
Cosines, and area formulas
and incorporate radian
measure where needed.
P.6A: use the concept of
vectors to model situations
defined by magnitude and
direction; and
P.6B: analyze and solve
vector problems generated
by real-life situations.
336
Students Will Know…
Students will be able to….
 What vectors
represent.
 Vector operations.
 The effect of a scalar
on a vector.
 Dot products.
 Unit vectors.
 Component form.
 Orthogonal vectors.
 How vectors can be
applied to real world
situations.

 What vectors
represent.
 Vector operations.
 The effect of a scalar
on a vector.
 Dot products.
 Unit vectors.
 Component form.
 Orthogonal vectors.
 How vectors can be
applied to real world
situations
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2010 – 2011
Perform basic vector operations. represent vectors,
including sums, difference, and scalars, graphically.
Determine when vectors are equivalent.
Determine the magnitude of a vector.
Determine if vectors have the same direction.
Find the component form of a vector determine given an
initial point and terminal point.
Find a unit vector.
Write a vector given an initial point and terminal point in
linear combination, (i,j), form.
Find the dot products of two vectors.
Determine whether two vectors are orthogonal.
Apply vector concepts to application problems in
Physics and other real world situations.
Perform basic vector operations. represent vectors,
including sums, difference, and scalars graphically.
Determine when vectors are equivalent.
Determine the magnitude of a vector.
Determine if vectors have the same direction.
Find the component form of a vector determine given an
initial point and terminal point.
Find a unit vector.
write a vector given an initial point and terminal point in
linear combination, (i,j), form.
Find the dot products of two vectors.
Determine whether two vectors are orthogonal.
Apply the vector concepts to application problems in
Physics and other real world situations.
Student Work Products/Assessment Evidence
Performance Tasks
Graph vectors, their sums and differences and vectors involving scalars
Perform operations involving vectors algebraically.
Find dot products.
Determine whether two vectors are orthogonal
© 2010 Austin Independent School District
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
work samples, observations, etc.)
Discussions, worksheets, Problems from book, Tests & quizzes
Pre-Calculus Page 3 of 8
updated 11/20/10
Course: Pre-Calculus
2010 – 2011
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Learning Plan
Lesson/Activity/
Module Name
Teacher
Resource
Student
Resource
Technology (Media,
website, etc.)
Vectors in a
Plane and Dot
Products
Textbook LH
6.3,6.4
Textbook LH
6.3,6.4
Graphing Calculator
Other (Include Pre-Teach Suggestions, Intervention
Suggestions, Anchors of Support - all as links)
Assessment (Prep for
Assessment, TAKS
Stems links)
atrick just math
tutoring
www.patrickjmt.com
Concept (Big Idea): Inverse Trigonometric functions
Concept Pacing:
Enduring Understanding:
Essential Questions:
1. How do you graph the inverse relation of y = sin (x) and why is the inverse relation not a function?
The characteristics of the inverse trigonometric
2. How do you determine the domain and range of the inverse sine function using the graph of the
functions and their applications to real world
situations
sine function.
3. What are the domains and ranges of the inverses of the remaining trigonometric functions?
4. How do you determine the value of Arcsin (1/2) and what does your answer represent?
5. What is the process in determining the composite sin(arctan(-1/3)?) and what does your answer
represent?
Unit 3: Inverse Trigonometric Functions
Unit Pacing: 3-4 days
Vocabulary: relation, function, graph of a function, input, output, domain, range, vertical line test, independent variable, dependent variable, evaluate, solution,
asymptote, horizontal asymptote, vertical asymptote, end behavior, odd intercepts, cosine, tangent, cotangent, secant, cosecant, amplitude, period, reciprocal,
reciprocal functions, increases, increases without bound, decreases, decreases without bound, odd function, even function,
Resources: LH textbook 4.7: graphing calculator; websites
Matrix
#
240A
Established Goals
TEKS Knowledge &
Skill
P.3: The student uses
functions and their
properties, tools and
technology, to model
and solve meaningful
problems.
Established Goals
TEKS Student
Expectation
P.3B: use functions
such as logarithmic,
exponential,
trigonometric,
polynomial, etc. to
model real-life data;
© 2010 Austin Independent School District
Students Will Know…
 Inverse trigonometric functions have unique
and recognizable graphs.
 Domains and ranges.
 Inverse trigonometric functions are periodic.
 Values of compositions of trigonometric.
 Inverse trigonometric functions are
determined.
 Inverse trigonometric functions can be used to
model real world situations.
Pre-Calculus Page 4 of 8
Students will be able to….
 Graph the inverse trigonometric functions.
 Identify the domains and ranges of the
inverse trig functions.
 Write equations of inverse trigonometric
functions from their graphs.
 Restrict the domain of the inverse function
given a function.
 Evaluate inverse trig functions Evaluate
compositions of trigonometric functions
updated 11/20/10
Course: Pre-Calculus
2010 – 2011
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Student Work Products/Assessment Evidence
Performance Tasks
Understand the characteristics of basic inverse trig functions.
Sketch the graphs of the inverse trig functions.
Write equations of inverse trig functions.
Understand how to find values using inverse trig
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
work samples, observations, etc.)
Discussions, worksheets, problems from book, tests & quizzes
Learning Plan
Technology (Media, website, etc.)
Lesson/Activity/Module
Name
Teacher
Resource
Student
Resource
Inverse Trig Functions
LH Textbook 4.7
LH Textbook 4.7
Graphing Calculator
Supplemental
worksheet on
Inverse Trig
Supplemental
worksheet on
Inverse Trig
patrick just math tutoring
www.patrickjmt.com
Other (Include Pre-Teach
Suggestions, Intervention
Suggestions, Anchors of)
Assessment (Prep
for Assessment,
TAKS Stems links)
regents prep
www.regentsprep.org
purple math
www.purplemath.com
tutorial-go to key index
http://mathdemos.gcsu.edu/mathdemos/
Concept (Big Idea): Parametrics Equations
Enduring Understanding:
Parametric equations can be changed to rectangular
coordinates and used to model real world situations.
© 2010 Austin Independent School District
Concept Pacing:
Essential Questions:
1. How do you sketch a plane curve when represented by a pair of parametric equations?
2. What is the process to change from given parametric equations to a rectangular
equation in x and y.
3. How does restriction of the values of t affect the domain and range of the rectangular
equation?
4. When sketching a graph from given parametric equations, is the resultant graph
necessarily a function?
5. How do you find a set of parametric equations from a given graph or a given equation
in rectangular coordinates?
6. In what ways do parametric equations have connections to the physical world?
Pre-Calculus Page 5 of 8
updated 11/20/10
Course: Pre-Calculus
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
2010 – 2011
Unit 4: Parametric Equations
Unit Pacing: 5 Days
Vocabulary: relation, function, graph of a function, input, output, domain, range, vertical line test, independent variable, dependent variable, evaluate, solution,
plane curve, variables, rectangular equation, parameter, parametric equation, eliminate the parameter, sketching a plane curve, orientation, arrows, indicate
orientation
Resources: LH textbook 10.6; graphing calculator, websites
Arc 1 (if applicable):
Arc Pacing:
Resources(if applicable): LH textbook 10.6; graphing calculator, websites
Matrix
#
271
230
Established Goals
TEKS Knowledge & Skill
P.1: The student defines functions,
describes characteristics of functions,
and translates among verbal,
numerical, graphical, and symbolic
representations of functions, including
polynomial, rational, power (including
radical), exponential, logarithmic,
trigonometric, and piecewise-defined
functions. The student is expected to:
Established Goals
TEKS Student Expectation
P.1D: recognize and use
connections among
significant values of a
function (zeros, maximum
values, minimum values,
etc.), points on the graph of
a function, and the symbolic
representation of a function;
and
Students Will Know…
 Graphing from given
parametric equation.
 Changing from parametric to
rectangular equations.
 Direction of motion.
 Domain and Range of
parametrically defined
functions.
 Sketch curves represented by
parametric functions.
 Identify direcdtion of motion.
 Restrict domain and range of
Rewrite sets of parametric
 parametric functions as rectangular
coordinates using substitution.
 Find a set of parametric equations
from rectangular coordinates.
P.5: The student uses conic sections,
their properties, and parametric
representations, as well as tools and
technology, to model physical
situations. The student is expected
to:
P.5C: convert between
parametric and rectangular
forms of functions and
equations to graph them;
and
P.5D: use parametric
functions to simulate
problems involving motion.
 Graphing from given
parametric equation.
 Changing from parametric to
rectangular equations.
 Direction of motion.
 Domain and Range of
parametrically defined
functions.
 Applications of parametric
equations to real world
situations
 Sketch curves represented by
parametric functions.
 Identify direcdtion of motion.
 Restrict domain and range of
Rewrite sets of parametric
 parametric functions as rectangular
coordinates using substitution.
 Find a set of parametric equations
from rectangular coordinates.
 Apply parametric equations for real
world situations.
239
Students will be able to….
Student Work Products/Assessment Evidence
Performance Tasks
Sketch the graphs given parametric equations.
Convert from parametric to rectangular equations.
Find a set of parametric equations from rectangular coordinates.
© 2010 Austin Independent School District
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
work samples, observations, etc.)
Discussions, worksheets, problems from book, tests & quizzes
Pre-Calculus Page 6 of 8
updated 11/20/10
Course: Pre-Calculus
2010 – 2011
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Lesson/Activity/Module
Name
Teacher Resource
Learning Plan
Student Resource
Technology (Media,
website, etc.)
Parametric
Equations
LH Textbook 10.6
LH Textbook 10.6
PTII:IV.1.1 Activity 1
Avoiding the Crash
PTII:IV.1.1 Activity 1
Avoiding the Crash
PTII:IV.1.1 Activity 3
Free Falling Bodies
PTII:IV.1.1 Activity 3
Free Falling Bodies
Other (Include Pre-Teach
Suggestions, Intervention
Suggestions, Anchors of
Support - all as links)
Assessment (Prep
for Assessment,
TAKS Stems links)
Graphing Calculator
patrick just math
tutoring
www.patrickjmt.com
Concept (Big Idea): Parametrics Equations
Concept Pacing:
Enduring Understanding:
Essential Questions:
Recognize and graph
1. How are the various conic sections generated from a plane and a double napped cone?
various conic sections and
2. Given equations of different conics, how do you determine whetherthe equation is a circle, parabola, ellipse, or hyperbola?
apply conics to real world
3. How do we use the distance formula to algebraically develop the standard equation of a parabola?
situations.
4. What are the standard forms of each of the conic sections?
5. Describe the process of completing the square to change the equation of a parabola (and other conic sections) from
general form to standard form?
6. How do you write the equation of a parabola given the focus and directrix?
7. How do you determine the axes of symmetry from the equations of each of the conic sections?
8. How do you determine the coordinates the vertices and co-vertices from the equation of an ellipse?
9. What is the relationship between the values of a, b, and c for ellipses and hyperbolas?
10. How do you determine the equations of the asymptotes from the equation of a hyperbola?
11. What does the eccentricity of an ellipse tell you?
Unit 5: Conics: Parabolas, Ellipses, Circles, and Hyperbolas
Unit Pacing: 9 days
Vocabulary: relation, function, graph of a function, input, output, domain, range, vertical line test, independent variable, dependent variable, domain, evaluate,
solution, asymptote, conic section, locus, parabola, opens, upward, opens downward, equidistant, fixed point, focus, directrix, vertex, axis, standard form of the
equation of a parabola, perpendicular, directed distance, focal chord, latus rectum, tangent, symmetry, tangent, tangent line, reflexive property, horizontal axis,
vertical axis foci, completing the square, perfect square trinomial, ellipse, foci, vertices, major axis, minor axis, center, standard form, Pythagorean Theorem,
eccentricity, hyperbola, transverse axis, conjugate axis, asyptotes
Resources (if applicable) LH textbook 10.2,10.3,10.4: graphing calculator; websites
Arc 1 (if applicable):
Arc Pacing:
Resources(if applicable): LH textbook 10.2,10.3,10.4: graphing calculator; websites
© 2010 Austin Independent School District
Pre-Calculus Page 7 of 8
updated 11/20/10
Course: Pre-Calculus
2010 – 2011
Austin ISD Curriculum Road Map
Fourth Six Weeks – Jan 4 – Feb 17. (32 days)
Matrix
#
Established Goals
TEKS Knowledge & Skill
Established Goals
TEKS Student Expectation
Students Will Know…
Students will be able to….
P.5A: use conic sections to
model motion, such as the
graph of velocity vs. position
of a pendulum and motions
of planets;
 How conic sections are
generated from cones
 Standard forms of
parabolas, ellipses,
circles, and hyperbolas.
 Graphing conic sections.
 How to use translations to
graph from basic conic
graphs.
 Relationships between a,
b, and c for ellipses and
hyperbolas.
 Characteristics of conics.


341
P.5: The student uses
conic sections, their
properties, and parametric
representations, as well as
tools and technology, to
model physical situations.
342
P.5B: use properties of
conic sections to describe
physical phenomena such
as the reflective properties of
light and sound;
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Recognize various conic sections.
Graph conic equations including (when applicable)
center point, vertice(s), covertices, focal point(s),
directrix, vertices, covertices, major And minor axes,
transverse and conjugates axes, and asymptotes.
Write equations of conics in standard form.
Write equations from given information or graphs.
Identify and determine characteristics of conic
sections.
Solve applications problems involving conics.
Determine the eccentricity of an ellipse and tell what
it means.
Identify the relationship and determine the values of
a, b, and c for ellipses and hyperbolas.
Apply conics to real world situations.
Student Work Products/Assessment Evidence
Other Evidence (i.e. unit tests, open ended exams, quiz, essay, student
work samples, observations, etc.)
Performance Tasks
Graphing conic sections.
Writing equations of conic sections.
Determine characteristics of conic sections.
Change from general form to standard form by completing the square.
Solving application problems involving conics.
Lesson/Activity/Module
Name
Conic Sections
Teacher
Resource
LH
Textbook
10.2,10.3,
10.4
Student
Resource
LH
Textbook
10.2,10.3,
10.4
Workshee
t on Conic
Sections
Workshee
t on Conic
Sections
© 2010 Austin Independent School District
Discussions, worksheets, Problems from book, Tests & quizzes
Learning Plan
Technology (Media, website, etc.)
Graphing Calculator
patrick just math tutoring: www.patrickjmt.com
regents prep: www.regentsprep.org
purple math: www.purplemath.com
Other
Assessment
(Include Pre-Teach
Suggestions,
Intervention
Suggestions,
Anchors of Support
- all as links)
(Prep for
Assessment,
TAKS Stems
links)
tutorial-go to key index: http://mathdemos.gcsu.edu/mathdemos/
Pre-Calculus Page 8 of 8
updated 11/20/10