Madison Public Schools
Advanced Algebra and Trigonometry
Written by:
Debra Ann Wahle
Reviewed by:
Matthew A. Mingle
Director of Curriculum and Instruction
Kathryn Lemerich
Supervisor of Mathematics and Business
Approval date:
October 14, 2014
Members of the Board of Education:
Lisa Ellis, President
Kevin Blair, Vice President
Shade Grahling, Curriculum Committee Chairperson
David Arthur
Johanna Habib
Thomas Haralampoudis
Leslie Lajewski
James Novotny
Madison Public Schools
359 Woodland Road
Madison, NJ 07940
www.madisonpublicschools.org
Course Overview
Description
Advanced Algebra and Trigonometry includes an emphasis on essential algebraic skills as well as the
study of functions, conics, introductory trigonometry, sequences and series. In connection with the
Common Core State Standards, this course examines the concepts of: Number and Quantity,
Algebra, Functions, Modeling, and Probability and Statistics. This course also incorporates the 8
Standards for Mathematical Practice as identified in the Common Core State Standards.
The course is designed for the college-prep student who has completed Algebra II but requires
greater mastery of the skills and knowledge needed to continue on to Pre-Calculus. It is
recommended for juniors who wish to take Pre-calculus during their senior year and for
college-bound seniors who desire additional mathematical knowledge beyond Algebra 2. This course
will both strengthen and extend the Algebra II concepts and prerequisites for Pre-Calculus, such as:
factoring and quadratic functions, applications of quadratic, exponential and logarithmic functions,
rational functions, triangle trigonometry including the laws of sines and cosines, radian measure,
inverse trigonometric functions, the unit circle, systems, matrices and more.
Goals
This course aims to:
● enable students to make sense of various types of problems and the reasonableness of their
answers
● build student confidence with the various approaches to solving a problem and persevere in
solving them
● encourage students to become abstract thinkers who make sense of quantities and their
relationships in problem situations
● develop students’ ability to cooperatively discuss, make conjectures and critique ideas of one
another
● use, apply, and model mathematics to solve problems arising in everyday life, society, and the
workplace
● consider the variety of available tools when solving a mathematical problem
● communicate mathematical ideas precisely and effectively to others
● determine a pattern or analyze structure within mathematical content to apply to related
ideas
● use repeated reasoning to follow a multi-step process through to completion
Suggested activities and resources page
Unit 1 Overview
Unit Title: Linear and Quadratic Functions
Unit Summary:
This unit will revisit, explore, and extend previously learned concepts with respect to linear and
quadratic functions. Students will briefly examine all aspects of a linear function including, but not
limited to, slope and intercepts. Students will solve quadratic functions with real and imaginary
roots, as well as graph quadratic functions. Emphasis will be placed on the use of linear and
quadratic models to examine real-world scenarios.
Suggested Pacing: 11 lessons
Learning Targets
Unit Essential Questions:
● How can a linear function be used to model a real-world situation?
● How can a quadratic function be used to model a real-world situation?
● Why are imaginary numbers necessary when solving quadratic functions?
Unit Enduring Understandings:
● Real-world situations can be modeled using various types of functions: linear, quadratic or
others.
Evidence of Learning
Unit Benchmark Assessment Information:
Go to link:
https://docs.google.com/a/madisonnjps.org/file/d/0B16knUWDCx7rcldSY0dzeFliRE0/edit
Objectives
(Students will be able to…)
Apply the distance
and midpoint
formulas.
Use slope to
determine whether
lines are parallel,
perpendicular or
neither.
Write the equation
of a line.
Model real-world
scenarios using
linear functions.
Essential
Content/Skills
Suggested
Assessments
Content:
Distance formula,
midpoint formula,
slope, general form
of a line,
slope-intercept
form, point-slope
form, intercept form
Give students a list
of problems which
are varied in the
information which is
given. Ask student
which linear form
would be most
appropriate to write
the equation.
Skills:
Find the midpoint of
a line segment.
Find the intersecting
point of two lines.
Use slope to
determine if lines
are parallel,
perpendicular or
neither.
Write the equation
of a line given
certain geometric
properties of the
line.
Model a word
problem using a
linear function and
its graph.
Place students in
groups of 3 to draw
diagrams on p. 16
WE # 16, 20, 22
(Advanced
Mathematics Text)
Place students in
groups of 3. Each
group randomly
picks a pre-selected
word problem (3
different ones- see
Advanced
Mathematics page
23 # 12, 14, 16 ).
Students have 20
minutes to discuss,
graph and solve in
their own notes then
10 minutes to place
on large post-it
paper (which has a
piece of graph paper
already taped to it).
Museum Walk.
Play Algebra 1, “I
Have, Who Has”
card game
Standards
(NJCCCS CPIs, CCSS, NGSS)
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
A-CED-1: Create equations and
inequalities in one variable and use
them to solve problems.
A-CED-2: Create equations in two
or more variables to represent
relationships between quantities,
graph equations on coordinate
axes with labels and scales.
A-REI-10 : Represent and solve
equations and inequalities.
Understand that the graph of an
equation in two variables is the set
of all its solutions plotted in the
coordinate plane, often forming a
curve (which could be a line).
F-IF-B.4: For a function that
models a relationship between
two quantities, interpret key
features of graphs, and sketch key
features given a verbal description
of the relationship.
F-IF.B.6: Calculate and interpret
the average rate of change of a
function over a specified interval.
Estimate the rate of change from a
graph.
F-BF -1b: Build a function that
models a relationship between two
quantities
Pacing
5
lessons
Add, subtract,
multiply and divide
complex numbers.
Solve quadratic
equations by
factoring,
completing the
square or using the
quadratic formula.
Analyze the
discriminant to
determine the
nature of roots.
Locate important
characteristics of a
parabola and sketch
its graph.
Model real-world
scenarios using
quadratic functions.
Content:
Complex numbers,
factoring,
completing the
square, quadratic
formula, domain,
range, discriminant,
real and imaginary
roots, parabola, axis
of symmetry,
vertex, x and y
intercepts.
Skills:
Locate vertex, axis
of symmetry and
intercepts of a
parabola.
Choose then apply
most convenient
method to solve a
quadratic equation.
Graph quadratic
functions.
Write a quadratic
function to model a
real-world situation.
Make a notebook
foldable with flaps
on top and sides to
fold in to display
domain and range of
a quadratic function.
Kuta.com
worksheets with
various quadratic
solving methods
Play Algebra 2, “I
Have, Who Has”
card game
Give students a page
with various
quadratic functions
and various graphs.
Have them match
the functions to
their graphs.
Use page 47 # 12
(Advanced
Mathematics) as a
physics application
modeling problem.
Quiz Questions:
Describe a
real-world context
in which a quadratic
function can be
used?
Why are complex
numbers necessary
when solving
quadratic
equations?
A-REI.B.4: Solve quadratic
equations in one variable.
F-LE.A.1: Distinguish between
situations that can be modeled
with linear functions and with
exponential functions. Does this
fit? It looks like these lessons
solely focus on quadratics.
N-CN.C.7: Solve quadratic
equations with real coefficients
that have complex solutions.
A-APR.B.3: Identify zeros of
polynomials when suitable
factorizations are available and
use zeros to construct a rough
graph of the function defined by
the polynomial.
F-IF-B.4: For a function that
models a relationship between
two quantities, interpret key
features of graphs, and sketch key
features given a verbal
description of the relationship.
F.IF.C.7: Graph functions
expressed symbolically and show
key features of the graph, by
hand in simple cases and using
technology for more complicated
cases.
F.IF.C.8: Write a function defined
by an expression in different but
equivalent forms to reveal and
explain different properties of the
function.
6
Lessons
Unit 2 Overview
Unit Title: Polynomials and Polynomial Functions
Unit Summary:
In this unit, students will solve polynomial equations, with and without technology, using various
methods of factoring, including the rational root theorem. Graphs of such equations will be explored
and key characteristics, such as minimum and maximum points, will be located. The unit will
conclude with the study and application of general theorems about polynomial equations.
Application problems will be a focus of this unit.
Suggested Pacing: 14 lessons
Learning Targets
Unit Essential Questions:
● What are the differences between the graphs of different polynomial functions?
● How can one find the zeros of a polynomial equation?
● How can one locate the minimum or maximum of a polynomial function?
● How can technology be used to approximate the roots of a polynomial function?
Unit Enduring Understandings:
● The number of roots of an equation is the same as the highest degree of the polynomial.
● Higher degree polynomials have distinctive shapes that differ from each other.
● There are various methods for solving higher degree polynomial equations.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Identify a
polynomial
function.
Evaluate a
polynomial
equation using
synthetic
substitution.
Determine zeros of
a polynomial
function.
Apply the
Remainder and
Factor Theorems.
Compare and
contrast linear,
quadratic, cubic,
quartic, and
quintic functions.
Essential
Content/Skills
Content:
quadratic, cubic,
quartic, quintic,
synthetic
substitution, zeros,
remainder theorem,
factor theorem.
Suggested
Assessments
Create a Venn
Diagram that
compares and
contrasts Linear,
Quadratic, Cubic,
Quartic and Quintic
Functions
Skills:
Classify polynomial
functions as
constant, linear,
quadratic, cubic,
quartic or quintic.
Use synthetic
substitution to find
zeros of a
polynomial
function.
Apply the remainder
and factor theorems.
Make a notebook
foldable explaining
the remainder and
factor theorems.
Standards
(NJCCCS CPIs, CCSS, NGSS)
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
N-CN.C.7: Solve quadratic
equations with real coefficients
that have complex solutions.
A.APR.B.3: Identify zeros of
polynomials when suitable
factorizations are available, and
use the zeros to construct a
rough graph of the function
defined by the polynomial.
F-IF.C.8: Write a function
defined by an expression in
different but equivalent forms
to reveal and explain different
properties of the function.
Pacing
3 lessons
Sketch the graph of a
polynomial
function.
Recognize the effect
a squared or cubed
factor has on the
graph of a
polynomial
function.
Write a polynomial
function for a given
situation.
Find the minimum
or maximum value
of a function.
Content:
double root, triple
root,
minimum value,
maximum value
Skills:
Sketch the graph of a
polynomial function
in factored or
non-factored form.
Determine the
equation of a
polynomial function
given its graph.
Locate the minimum
or maximum value
of a polynomial
function.
Short Quiz/Matching
activity: Provide
students withl a list
of polynomial
functions which they
must match to their
graphs.
Students create a
foldable of all types
of polynomial
functions with their
associated graphs.
Journal writing:
What happens to a
graph when there is
a double root?
Triple root?
Play “Green Globs”.
Students must
create a polynomial
equation which hits
the most number of
points given on a
grid.
Group work:
Students complete
“Using Technology”
resource book
exploration on p. 11
A.APR.B.3: Identify zeros of
polynomials when suitable
factorizations are available, and
use the zeros to construct a
rough graph of the function
defined by the polynomial.
A-SSE.A.2: Use the structure of
an expression to identify ways
to rewrite it.
F-IF.C.8: Write a function
defined by an expression in
different but equivalent forms
to reveal and explain different
properties of the function.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
5
lessons
Solve a higher
degree polynomial
equation by
factoring.
Use the rational root
theorem to solve a
polynomial
equation.
Recognize and solve
a polynomial
equation that has a
quadratic form.
Apply general
theorems about
polynomial
equations.
Content: factoring,
quadratic form,
rational root
theorem,
Fundamental
Theorem of Algebra,
Complex Conjugates
Theorem, sum and
product of roots.
Skills:
Factor or use the
rational root
theorem to solve a
higher degree
polynomial.
Use the rational root
theorem to solve
polynomial
equations, given all
real and imaginary
roots.
Solve a polynomial
equation that has a
quadratic form.
Understand the
Fundamental
Theorem of Algebra.
“Checking Main
Ideas” found in
resource book
p. 20.
Provide students
with various
polynomial
equations and ask
them to write down
the type of solving
process they would
use to find the roots.
Quiz: Given various
higher degree
equations, student
must explain why or
why they are not in
quadratic form then
solve those that are.
Make a foldable of
four theorems: The
Fundamental
Theorem of Algebra,
The Complex
Conjugates
Theorem,
Odd-Degree
Theorem, and Sum
and Product of
Roots Theorem.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
N-CN 9: Know the Fundamental
Theorem of Algebra; show it is
true for quadratic polynomials.
A-SSE.A.2: Use the structure of
an expression to identify ways
to rewrite it.
F-IF.C.8: Write a function
defined by an expression in
different but equivalent forms
to reveal and explain different
properties of the function.
6 lessons
Unit 3 Overview
Unit Title: Inequalities
Unit Summary:
In this unit, students will solve and graph linear and polynomial inequalities in one or two variables.
They will also solve and graph absolute value inequalities and graph systems of inequalities. Linear
programming models will be set up and used to examine a function’s feasible region by using the
corner-point principle.
Suggested Pacing: 10 lessons
Learning Targets
Unit Essential Questions:
● How does a combined inequality differ from a single inequality?
● How does one interpret the solutions to a system of inequalities?
● Why might one use linear programming?
Unit Enduring Understandings:
● The solutions to inequalities in two variables reside in a shaded-region.
● Linear Programming is a method for solving certain decision-making problems where a
quantity needs to be maximized or minimized.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Solve and graph
linear inequalities in
one variable
(including absolute
value).
Solve and graph
polynomial
inequalities in one
variable.
Compare and
contrast the
similarities and
differences in
solving equations
vs. inequalities
Essential
Content/Skills
Suggested
Assessments
Content:
linear inequalities,
disjunction,
conjunction,
polynomial
inequality, intervals,
sign graph.
Self-assessment:
Give students a list
of polynomial
inequalities to graph
by hand then have
them check their
own graphs on a
graphing calculator
or computer,
reworking if
necessary.
Skills:
Graph the solution
set of an inequality
on a number line.
Recognize if the
solution set of a
combined inequality
is the empty set.
Solve combined
inequalities
algebraically.
Represent the
solutions to a
real-world scenario
as a combined
inequality.
Perform a sign
analysis in the
intervals
determined by the
zeros of a
polynomial
equation.
Journal entry: Ask
students to write a
combined inequality
which has no
solution and explain
why.
Graphic organizer:
Compare and
contrast the
similarities and
differences in
solving equations
versus inequalities.
Standards
(NJCCCS CPIs, CCSS, NGSS)
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
A-SSE.A.2: Use the structure of
an expression to identify ways
to rewrite it.
A.APR.B.3: Identify zeros of
polynomials when suitable
factorizations are available, and
use the zeros to construct a
rough graph of the function
defined by the polynomial
A-CED.A.1: Create equations
and inequalities in one variable
and use them to solve problems.
A-REI.D.11: Represent and
solve equations and inequalities
graphically.
Pacing
5 lessons
Graph polynomial
inequalities in two
variables.
Graph the solution
set of a system of
inequalities.
Explain what linear
programming can be
used for.
Content:
Shaded regions,
system of
inequalities, linear
programming,
feasible solution,
feasible region,
corner-point
principle,
maximizing profit.
Skills:
Solve certain
application
problems using
linear programming.
Determine if a point
is above, on, or
below the graph of
an equation.
Sketch the graph of
an inequality.
Sketch the graph of a
system of
inequalities.
Utilize linear
programming to
maximize profit or
minimize a cost.
Journal entry:
Students explain the
the process of linear
programming and
what it can be used
for.
Journal entry:
Students describe a
business situation
where linear
programming would
be a helpful tool.
Collaborative:
Group students to
work on and analyze
a business scenario
using linear
programming then
create a poster to
display to the class.
A-CED.A.3: Represent
constraints by equations or
inequalities, and by systems of
equations and/or inequalities,
and interpret solutions as viable
or nonviable options in a
modeling context.
5 lessons
Unit 4 Overview
Unit Title: Functions
Unit Summary:
In this unit, students will build on their previous knowledge of functions by combining them in a
variety of ways. They will explore the relationships between graphs of functions and their algebraic
rules. Functions of more than one variable will also be considered. Technology will be used as a tool
as functions are applied to real-world situations.
Suggested Pacing: 14 lessons
Learning Targets
Unit Essential Questions:
● What is a function?
● In what type of real-world scenario can a function be useful?
● Why would one need to compose a function?
● How can one determine from an equation which type of symmetry a graph will have?
Unit Enduring Understandings:
● Not all functions have inverses.
● Graphs of functions can be transformed in various ways.
● Arithmetic operations and compositions can be performed on functions.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Identify a function.
Determine the
domain, range and
zeros of a function.
Graph a function.
Perform operations
on functions (ie.
add, subtract,
multiply, divide,
compose).
Determine domains
of resultant
functions after
operations have
been applied.
Essential
Content/Skills
Content:
Function, domain,
range, zeros,
dependent and
independent
variable,
vertical-line test,
composite function
Skills:
Determine if a
relation is a function
given data in various
formats (ie. table,
equation, graph).
Apply the
vertical-line test.
Find the domain and
range of a function.
Perform arithmetic
operations with
functions.
Find composite
functions.
Suggested
Assessments
“Algebra, Trig. and
Pre-Calcu Laughs”
resource book pun
sheet “What did the
Teacher Function
Say?”
Partner activity:
Have each student
create a function.
Pair students to find
domains of each of
their functions and
find the composite
of their two
functions (both
ways) and their
resulting domains.
Have each pair of
students assigned to
another pair of
students to check
each other’s work.
Standards
(NJCCCS CPIs, CCSS, NGSS)
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
F.IF.C.7: Graph functions
expressed symbolically and
show key features of the graph,
by hand in simple cases and
using technology for more
complicated cases.
F-BF.A..1: Write a function
that describes the relationship
between two quantities.
(arithmetic and composite are
included here).
Pacing
5 lessons
Reflect graphs in the
x-axis, y-axis, and
the line y=x.
Determine if an
equation has
symmetry in the
x-axis, y-axis, line
y=x and/or the
origin.
Use symmetry to
sketch graphs.
Classify functions as
even or odd.
Content:
Reflection,
symmetry, axis of
symmetry, point of
symmetry, even
function, odd
function,.
Skills:
Draw the reflection
of a graph.
Algebraically
determine types of
symmetry.
Sketch a graph using
its symmetry.
Determine
periodicity and
amplitude from
graphs.
Stretch, shrink (both
vertically and
horizontally), and
translate graphs.
Quiz: Students are
given equations and
must show all of the
algebraic steps
needed to determine
the type of
symmetry it has, if
any.
Content:
Period, fundamental
period, amplitude,
stretch and shrink
(horizontally and
vertically),
translate.
Skills:
Determine the
fundamental period
and amplitude of a
graph.
Find the function
value at a given
location (ie. f(100))
using the
fundamental period.
Sketch a stretched
or shrunk graph
given an original
graph and a rule for
its changed graph
(ie. y = f(x) to
y = 2f(x)).
Partner activity:
Each pair of students
is given an equation
to determine
whether it is even or
odd and must write a
justification of their
conclusion. They
hand off their paper
to another pair of
students who must
check/comment on
the response then
explain something
that could be done
to the original
equation which
would change it
from even to odd or
vice versa.
Students create an
index study card of
all types of
transformed graphs
(horizontal and
vertical shrinks and
stretches) with
function
representations of
each (see page. 142
in Advanced
Mathematics)
F.IF.C.7: Graph functions
expressed symbolically and
show key features of the graph,
by hand in simple cases and
using technology for more
complicated cases.
4 lessons
F-BF.B.3: Identify the effect on
the graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and f(x +k)
for specific values of k (both
positive and negative), find the
value of k given the graphs.
Experiment with cases and
illustrate an explanation of the
effects on the graph using
technology. Include
recognizing even and odd
functions from their graphs and
algebraic expressions for them.
F-IF.B.4: For a function that
models a relationship between
two quantities, interpret key
features of graphs and tables in
terms of the quantities, and
sketch graphs showing key
features given a verbal
description of the relationship.
F.IF.C.7: Graph functions
expressed symbolically and
show key features of the graph,
by hand in simple cases and
using technology for more
complicated cases.
F-BF.3: Build new functions
from existing functions.
3 lessons
Find the inverse of a
function, it it exists.
Sketch the graph of
an inverse function.
Describe
characteristics of an
inverse function.
Content:
inverse functions,
inverse function
notation,
horizontal-line test.
one-to-one
functions.
Skills:
Determine whether
or not two functions
are inverses of each
other (using
composite
functions).
Sketch the graph of
an inverse function.
Find an inverse
function by
interchanging the
domain and range.
Apply the
horizontal-line test
to a function to
determine if it is
one-to-one.
Individual practice:
“Algebra, Trig. and
Pre-Calculaughs” p.
30
Provide students
with a page of
pre-made graphs
and equations to
determine if they
have inverses and if
so, to sketch the
inverse on top of the
original graph. (use
different color for
inverse graph).
Journal Entry:
Have students write
about the various
characteristics
(graphically etc.) of
an inverse function
and how to find one.
F-BF.B.4 (a,b,c) : Find inverse
functions. (includes writing
inverse function, verifying by
composition that one function is
the inverse of another and
reading values of an inverse
function from a table or graph).
2 lessons
Unit 5 Overview
Unit Title: Probability
Unit Summary:
Students will first be introduced to the basic concepts of probability; probability of a single event, of
either of two events and of two events occurring together. Students will explore the concepts of
permutations and combinations. Probability principles will then be explored in the context of
real-world problems. Graphing calculator technology will be used to enhance student
understanding.
Suggested Pacing: 8 lessons
Learning Targets
Unit Essential Questions:
● How is the probability of an event determined and described?
● How can probability be applied to real-world situations?
Unit Enduring Understandings:
● There are many types of probabilities.
● Probability is a tool which can be used for decision-making.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Find the sample
space of an
experiment.
Find the probability
of a single event.
Find the probability
of either of two
events.
Explain what it
means for events to
be equally likely.
Essential
Content/Skills
Content:
Probability, sample
space, theoretical
probability,
empirical
probability, with
replacement,
without
replacement,
experiment, event,
mutually exclusive,
equally likely,
random.
Provide examples of
situations where
events would and
would not be equally
likely.
Skills:
Find probability of a
single event given
they are equally
likely.
Find the probability
of events occurring
together.
Content:
Tree diagram,
dependent events,
independent events,
conditional
probability. with or
without
replacement.
Determine the
difference between
finding the
probability of a
single event versus
the probability of
two events
occurring together.
Determine and
explain whether two
events are
dependent or
independent.
Skills:
Use a tree diagram
to calculate
probabilities of
possible outcomes.
Distinguish between
dependent and
independent events.
Understand the
meaning of
conditional
probability.
Suggested
Assessments
Standards
(NJCCCS CPIs, CCSS, NGSS)
Partner Activity:
Students complete
“Assessing Risk”
activity and present
findings to the class.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
Journal writing:
Have students
compare and
contrast the
procedures for
finding the
probability of a
single event versus
that of either of two
events.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Journal writing:
Students explain
what is means for
events to be equally
likely and give an
example of a
situation where
events would not be
equally likely.
Journal writing:
Students explain
two ways of
choosing balls of
different color from
a jar of two yellow
and three green
balls.
(ie. P(YG) + P(GY)
or
1- P(same color))
Give students a list
of two events.
Students must write
whether or not the
events are
“independent” or
“dependent” and
explain why.
Pacing
2 lessons
S.MD.B.6: Use probabilities to
make fair decisions.
S-CP.B.6: Find the conditional
probability of A given B as the
fraction of B’s outcomes that
also belong to A and interpret
the answer in terms of the
model.
S.MD.B.6: Use probabilities to
make fair decisions.
S-CP.B.6: Find the conditional
probability of A given B as the
fraction of B’s outcomes that
also belong to A and interpret
the answer in terms of the
model.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
3 lessons
Apply probability
formulas.
Distinguish between
permutations and
combination.
Compute
permutations and
combinations.
Content:
permutation,
combination, The
Counting Principle,
factorial.
Skills:
Determine if a word
problem requires
the use of a
permutation or
combination
formula to solve.
Apply permutation
and combination
formulas to solve
problems.
Use the graphing
calculator to
compute
permutations and
combinations.
“Why Should You
Never Allow a
Mathematician…?”
pun worksheet from
“Algebra, Trig. and
Pre-Calculaughs”
Provide students
will a list of word
situations to which
they must state
whether it
represents a
permutation or
combination and
explain why.
S.MD.B.6: Use probabilities to
make fair decisions.
HSS-CP.B.9: Use permutations
and combinations to compute
probabilities of compound
events and solve problems.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
3 lessons
Unit 6 Overview
Unit Title: Statistics
Unit Summary:
In this unit, students learn to represent data graphically, to summarize data using statistics, and to
analyze samples. Sets of data will be graphed in a variety of ways, including, stem-and-leaf plots,
box-and-whisker plots, histograms and frequency polygons. Students will also find various
measures of central tendency and measures of dispersion for sets of data. Normal distributions will
be introduced, for which students will use the standard normal table to find the percent of data in a
given interval. Real-world application will be an emphasis and graphing calculator technology will be
used as an integral tool.
Suggested Pacing: 8 lessons
Learning Targets
Unit Essential Questions:
● In what real-world situations would varying types of data displays be appropriate?
● How can one use various data displays to make inferences?
● What is a “normal distribution” and how can it be used in real-world scenarios?
Unit Enduring Understandings:
● Data displays of various formats provide useful insight into data characteristics/trends.
● The “normal” or “bell-shaped” curve has useful applications.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Find and examine
usefulness of
measures of
central tendency:
mean, median and
mode.
Display a set of
data using a
stem-and-leaf plot,
a histogram, a
frequency
polygon, or a
cumulative
frequency
polygon.
Interpret
information on a
frequency
polygon.
Essential
Content/Skills
Content:
Descriptive
statistics, inferential
statistics,
stem-and-leaf-plot,
histogram,
frequency table,
frequency polygon,
cumulative
frequency, mean,
median mode
Skills:
Find the mean,
median, and mode
for a set of data.
Summarize data in
stem-and-leaf plots.
Read and
understand data
from a frequency (or
cumulative
frequency) polygon.
Suggested
Assessments
Have students
discuss, in small
groups, the
strengths and
weaknesses of each
type of average.
Each student writes
a journal entry
about their group
discussion.
Make a
venn-diagram
comparing
histograms and
stem-and-leaf plots.
“Alternative
Assessment”, 53
Writing assignment:
For a set of data,
suppose you are
given only a
frequency polygon
(with integer labels
on the frequency
axis). Explain how
to estimate the mean
of the data from the
graph.
Standards
(NJCCCS CPIs, CCSS, NGSS)
S-IC.B.6:
Evaluate reports based on
data.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Pacing
2 lessons
Draw a
box-and-whisker
plot for a set of data.
Use a
box-and-whisker
plot and a
stem-and-leaf plot to
compare data.
Create a
box-and-whisker
plot on a graphing
calculator.
Content:
Box-and-whisker
plot, range,
interquartile range,
lower and upper
extremes, median,
lower and upper
quartiles, outliers,
back-to-back
stem-and-leaf plots.
Skills:
Draw a
box-and-whisker
plot to display data.
Create a
back-to-back
stem-and-leaf plot.
Create side-by-side
box-and-whisker
plots.
Analyze data in a
plot (find extremes,
range, median,
lower and upper
quartiles,
interquartile range,
and outliers, if any.)
Journal writing:
How does one
mathematically
determine if a piece
of data is considered
an outlier?
Cooperative
learning: Have
students google the
ages of the first 41
U.S. Presidents at
the time each took
office. Make a
stem-and-leaf plot of
the data and list all
relevant information
(extremes, range,
median, lower and
upper quartiles,
interquartile range,
outliers). Once they
complete the
information, they
are to make a
box-and-whisker
plot using the data.
Both plots can be
made into a poster
and displayed
around the room for
a museum walk.
Project idea :
Students make a
back-to-back stem
-and-leaf plot to
compare the ages at
which individual
female and male
musicians (specific
genre) won Grammy
Awards during the
years of
1980-Present.
S-IC.B.6:
Evaluate reports based on data.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
2 lessons
Explain what
variance and
standard deviation
measure.
Find the variance
and standard
deviation of a set of
data.
Convert data to
standard values.
Recognize uniform,
skewed, and normal
distributions.
Determine the
percent of data
within a given
interval (for a
normal
distribution).
Find percentiles.
Content:
Statistic, measures
of dispersion,
standard deviation,
variance, standard
value (z-score),
normal distribution,
skewed data,
standard normal
distribution,
standard normal
table, percentiles,
Skills:
Utilize formulas to
calculate variance
and standard
deviation of a set of
data.
Compute the
standard value (ie.
z-score) for date
values.
Use the standard
normal table to find
the percent of data
in a given interval
on a normal
distribution.
Analyze real-world
situations by
examining area
under the curve of a
normal distribution.
Activity on page 662
of “Advanced
Mathematics”
Have students
create a
symmetrical
foldable of a normal
distribution and
label percentiles
and other relevant
information.
Quiz or journal entry
to assess student
understanding of
normal
distributions.:
Provide students
with scenarios such
as : “The car does
not give nearly the
gas mileage it is
supposed to give”
and have students
tell what
information they
need to evaluate the
statement. See
margin of TE
“Advanced
Mathematics” p.
667
S-ID.A.4:
Use the mean and standard
deviation of a data set to fit it to
a normal distribution and to
estimate population
percentages. Recognize that
there are data sets for which
such a procedure is not
appropriate. Use calculators,
spreadsheets, and table to
estimate areas under the normal
curve.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
4
Lessons
Unit 7 Overview
Unit Title: Exponential Functions/Logarithms
Unit Summary:
In this unit, students will study the laws of exponents and logarithms. Real-world applications
problems will be examined throughout. Integral, rational and real exponents will be utilized while
students simplify exponential expressions and investigate exponential growth and decay models.
The number “e” and the function “ex” will be used as students apply them to compound interest
problems. In the final portion of the unit, students simplify logarithmic expressions, examine
models based on logarithms and solve exponential equations using logarithms. Graphing calculator
technology will be used to assist with concepts.
Suggested Pacing: 13 lessons
Learning Targets
Unit Essential Questions:
● In what real-world contexts can exponential functions be utilized?
● In what real-world contexts can logarithms be utilized?
● How are expressions involving exponents and logarithms related?
Unit Enduring Understandings:
● The characteristics of exponential and logarithmic functions and their graphs are useful in
solving real-world problems.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Define and apply
integral exponents.
Define and apply
rational exponents.
Essential
Content/Skills
Content:
Laws of exponents,
integral exponents,
rational exponents,
growth and decay,
Skills:
Simplify expressions
involving integral
exponents.
Apply a
growth/decay
model to application
problems.
Simplify expressions
involving rational
exponents.
Solve equations by
changing both sides
to the same base.
Suggested
Assessments
“Alternative
Assessment” p. 15
Partner activity:
Have students
research the cost of
two items (ie...a
gallon of milk)
twenty years ago
and the cost today.
Determine the rate
of increase or
decrease in the costs
over the years.
Think-Pair-Share
Class Exercises from
“Advanced
Mathematics” text
sections 5.1-5.2
Circuit activity using
index cards with
problems to
simplify.
Journal writing:
Explain why a power
cannot be
“distributed” over
addition or
subtraction.
((use a-2+ b-2)-1
substituting 1 for a
and 2 for b to show
mathematically).
Standards
(NJCCCS CPIs, CCSS, NGSS)
N-RN.A.2: Rewrite
expressions involving radicals
and rational exponents using
the properties of exponents.
A-SSE.A.2: Use the structure
of an expression to identify
ways to rewrite it.
F-IF.C.8: Write a function
defined by an expression in
different but equivalent forms
to reveal and explain different
properties of the function.
b. Use the properties of
exponents to interpret
expressions for exponential
functions. For example,
identify percent rate of change
in functions such as y=
(1.02)t, y =(0.97)t, y
=(1.01)12t, y = (1.2)t/10, and
classify them as representing
exponential growth or decay.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Pacing
4 lessons
Define and use
exponential
functions.
Define and apply the
natural exponential
function.
Content:
Exponential
function, irrational
exponents, Rule of
72, doubling time,
half-life, the number
“e”, the function
“ex”, limits,
compound
interest,effective
annual yield.
Skills:
Understand what an
exponential function
and its graph look
like.
Estimate, using a
graphing calculator,
the value of
expressions
containing irrational
exponents.
Given the half-life,
find the amount of a
substance after a
specified period of
time.
Apply the rule of 72
to determine the
doubling time of a
quantity.
Calculate the
amount of money
after specified
periods of time
given it is
compounded at
various interest
period.
“Alternative
Assessment” p.
15-16
Journal Entry:
Explain the
difference between
simple and
compound interest.
Journal Entry:
Explain that an
exponential function
is and how it can be
used.
Journal Entry or
Quiz Question: How
does the number “e”
relate to the idea of a
limit?
Journal Entry or
Quiz Question:
“ A bank advertises
that its 6% annual
interest rate
compounded daily is
equivalent to a
6.14% effective
annual yield. What
does this mean?”
F-IF.C.8: Write a function
defined by an expression in
different but equivalent forms
to reveal and explain different
properties of the function.
b. Use the properties of
exponents to interpret
expressions for exponential
functions. For example,
identify percent rate of change
in functions such as y=
(1.02)t, y =(0.97)t, y
=(1.01)12t, y = (1.2)t/10, and
classify them as representing
exponential growth or decay.
F-LE.A.4: For exponential
models, express as a logarithm
the solution to abct = d where
a,c,and c are numbers and the
base b is 2, 10,or e; evaluate
the logarithm using
technology.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
3 lessons
Define and apply
logarithms.
Prove and apply
laws of logarithms.
Solve exponential
equations.
Change logarithms
from one base to
another.
Content:
Common logarithm,
natural logarithms,
laws of logs,
exponential
equation,
change-of-base
formula
Skills:
Use common
logarithms to find
decibel levels given
specified intensity of
sounds.
Write expressions
written in terms of
separate logarithms
as a single log.
Simplify logarithmic
expressions.
(including natural
logs).
Apply the
change-of-base
formula to rewrite
(non-base 10)
logarithms.
“Alternative
Assessment” p. 17
Activity: Distribute
one index card with
a law of log practice
problem on it and
another with an
answer to a problem
on it to each
student. Students
place the answer
card in the corner of
their desk. Each
student individually
works out his/her
problem then must
find the answer card
associated with their
problem. --When
they find it, they are
to swap question
cards with the
person who had the
answer on their desk
(leave original
answer card on
desk). If the person
is not done with the
problem, they must
help each other.
Return to desk to
work out next
problem and so on.
Journal entry:
Explain a situation
where it might be
necessary to change
the base of a
logarithm.
F-LE.A.4: For exponential
models, express as a logarithm
the solution to abct = d where
a,c,and c are numbers and the
base b is 2, 10,or e; evaluate the
logarithm using technology.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
6
lessons
Unit 8 Overview
Unit Title: Sequences and Series
Unit Summary:
This unit introduces finite and infinite sequences and series. With regard to sequences, students
learn to identify arithmetic and geometric sequences and to define them explicitly and recursively.
Students will also find the limit, if it exists, of an infinite sequence. With regard to series, students
will find the sums of finite and infinite series. Sigma notation will be introduced and used to
represent a series.
Suggested Pacing: 14 lessons
Learning Targets
Unit Essential Questions:
● How are sequences and series determined and described?
● How can sequences and series be useful applications?
● Do all series have limits?
Unit Enduring Understandings:
● Not all series have a limit.
● Sequences and Series can be used to describe and analyze real-world scenarios.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be able to…)
Determine if a
sequence is
arithmetic or
geometric.
Compare and
contrast geometric
and arithmetic
sequences.
Sketch the graph of a
sequence.
Find a formula for
the nth term of a
sequence.
Use sequences
defined recursively
to solve problems.
Find the sum of the
first n terms of an
arithmetic or
geometric series.
Essential
Content/Skills
Content:
Arithmetic
sequence, geometric
sequence, common
difference, common
ratio, terms,
graphing a
sequence, recursive
definition, explicit
definition, series,
finite and infinite
sequences and
series, sum of finite
arithmetic series,
sum of finite
geometric series.
Skills:
Distinguish an
arithmetic sequence
from a geometric
sequence.
Sketch graphs of
sequences.
Find an indicated
term of a sequence.
Write a recursive
definition for a
sequence.
Find the specified
sum of a series.
Write a formula for a
specified term or
the nth term of a
series.
Suggested
Assessments
Make a Venn
Diagram comparing
and contrasting
arithmetic
sequences and
geometric
sequences.
Standards
(NJCCCS CPIs, CCSS, NGSS)
F-IF.A.3: Recognize that
sequences are functions,
sometimes defined
recursively, whose domain is a
subset of the integers.
“Alternative
Assessment” p. 39
F-BF.A.1: Determine an
explicit expression, a
recursive process, or steps for
calculation from a context.
Cooperative
Learning: Students
jigsaw Exercises
21-35 on pages
482-485 in
Advanced
Mathematics text.
F-BF.A.2: Write arithmetic
and geometric sequences both
recursively and with an
explicit formula, use them to
model situations, and
translate between the two
forms.
Students make a
sequence and series
foldable. See
http://mrsleblancs
math.pbworks.com/
w/file/fetch/611526
97/Sequences%20F
oldable.pdf
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Pacing
6
Lessons
Find or estimate the
limit of an infinite
sequence.
Content:
Limits, infinite
sequence, no limit,
Determine if a limit
of an infinite
sequence exists.
Skills:
Find a limit of an
infinite sequence, if
it exists.
Use a calculator to
estimate the limit of
an infinite sequence.
Paired Partners:
Have one partner
work 10 given
problems and the
other work 10
different problems.
When they are done,
they must share
results and explain
their answers to
each other.
Journal writing:
Explain the
difference between a
sequence that has
“no limit” and a
sequence that has an
“infinite limit”.
All students are
assigned page
496-497 WE # 2, 4,
6, 8, 10, 12, 14, 21,
26 in Advanced
Mathematics text.
Students are to find
the limits of each
problem then when
time is called (15
min.), they are to
stick the post-it
(with the number of
the problem on it)
on the board under
the correct limit
(which had been
previously written)
Students continue to
synthesize
information by
writing in their
foldable.
F-BF.A.1: Determine an explicit
expression, a recursive process,
or steps for calculation from a
context.
F-BF.A.2: Write arithmetic and
geometric sequences both
recursively and with an explicit
formula, use them to model
situations, and translate
between the two forms.
3 lessons
Find the sum of an
infinite geometric
series.
Express an infinite,
repeating decimal as
an infinite series.
Content:
Limit, sum, nth
partial sum,
sequence of partial
sums, converge,
diverge, sum of
infinite geometric
series.
Skills:
Calculate the sum of
an infinite geometric
series.
Determine the
interval of
convergence in an
infinite geometric
series.
Journal writings:
Explain why there is
no infinite geometric
series with the first
term 10 and sum 4.
Explain why the sum
of an infinite
geometric series is
positive if and only if
the first term is
positive.
Students continue to
synthesize
information by
writing in their
foldable.
F.BF.A.2: Write arithmetic and
geometric sequences both
recursively and with an explicit
formula, use them to model
situations, and translate
between the two forms.
3 lessons
F.LE.A.2: Construct linear and
exponential functions,
including arithmetic and
geometric sequences, given
a graph, a description of a
relationship, or two
input-output pairs.
A-SSE.A.2: Use the structure of
an expression to identify ways
to rewrite it.
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
Rewrite an infinite,
repeating decimal as
an infinite series.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Represent a series
using Sigma
Notation.
Recognize known
sums including; sum
of integers, sum of
squares and sum of
cubes.
Content:
Series, Sigma
Notation, summand,
limits of summation,
index, Properties of
Finite Sums, sum of
integers, sum of
squares, sum of
cubes
Skills:
Express a series that
is given in Sigma
Notation into
expanded form and
vice versa.
Determine an
appropriate
summand for a given
series.
Recognize and use 3
known sums.
In groups of 3,
students create 5
series using Sigma
Notation. They
write down only the
expanded version of
the series on a piece
of paper. Groups
swap papers and
express the given
series in Sigma
notation. When
done, switch papers
back to original
group to check for
accuracy. Two
groups pair up to
discuss answers.
F-BF.A.2: Write arithmetic and
geometric sequences both
recursively and with an explicit
formula, use them to model
situations, and translate
between the two forms.
A-SSE.A.2: Use the structure of
an expression to identify ways
to rewrite it.
2
Lessons
Unit 9 Overview
Unit Title: Trigonometry
Unit Summary:
Students have previous knowledge of basic trigonometric ratios from Geometry. In this unit, they
will expand their knowledge using trigonometric functions. Initially, students will convert between
degree and radian measures of angles and find arc lengths as well as areas of sectors of circles.
Students will be introduced to the six trigonometric functions using the coordinate of the point
where the terminal ray of an angle in standard position intersects a circle centered at the origin.
They then evaluate and graph the trigonometric functions. Finally, students will determine inverse
functions which they will also evaluate. Application problems will be infused throughout the unit.
Suggested Pacing: 19 lessons
Learning Targets
Unit Essential Questions:
● What are trigonometric functions useful in real life?
● How do trigonometric functions relate to their graphs?
● What is the relationship between a function and its inverse?
Unit Enduring Understandings:
● Trigonometry involves the study of triangles.
● Trigonometry is useful in many real-world application problem, including physics and
geology.
● Not all functions have inverses.
Evidence of Learning
Unit Benchmark Assessment Information:
Objectives
(Students will be
able to…)
Find the measure of
an angle in either
degrees or radians.
Determine
coterminal angles.
Find the arc length
and area of a sector
of a circle.
Essential
Content/Skills
Content:
Revolution, degree,
minutes, seconds,
arc length, radian
measure, standard
position, quadrantal
angle, sector, arc
length, apparent
size.
Skills:
Solve problem
involving apparent
size.
Convert degree
measures to radians
and vice versa.
Find coterminal
angles, one positive
and one negative,
with a given angle.
Calculate the arc
length and area of a
sector.
Approximate
distances given the
apparent size of an
object.
Suggested
Assessments
Give students two
index cards, one
with a degree
measure and one
with radians. Have
students find their
matches and tape
them on the board.
Circuit Activity: Use
coterminal pairs of
angles in (mixed)
radian and degree
measures . Students
must find the
coterminal angle
then move to the
next card.
Have students look
up the diameter and
apparent size of a
planet then
determine how far it
is from Earth.
Standards
(NJCCCS CPIs, CCSS, NGSS)
9.1.12.A.1
Apply critical thinking and
problem-solving strategies
during structured learning
experiences.
9.1.12.F.2
Demonstrate a positive work
ethic in various settings,
including this classroom and
during structured learning
experiences.
Pacing
4 lessons
Use definitions of
sine and cosine to
find values of those
functions.
Solve simple
trigonometric
equations.
Content:
Sine, cosine,
domain, range, unit
circle, circular
functions, periodic
functions,
fundamental period,
Skills:
Use special right
triangles and the
unit circle to
determine
trigonometric
ratios.
Find cosine and sine
of an angle with a
terminal ray in
standard position.
Sketch the graphs of
cosine and sine
functions.
Determine which
quadrant an angle
lies in given its sine
or cosine as positive
or negative.
Explain what is
meant by “circular
functions.”
Solve trigonometric
equations with
infinitely many
solutions.
Sketch the unit
circle and use it to
solve problems.
Understand special
right triangles.
Plot points on a sine
and cosine wave.
Journal Writing:
Explain what is
meant by “circular
functions”?
Have students
sketch the unit circle
labeling all standard
angles zero through
two pi and their
corresponding sines
and cosines.
Explain how angles
in each quadrant
relate to each other.
See “Activity” p. 269
in Advanced
Mathematics text.
F-TF.A.3: (+) Use special
triangles to determine
geometrically the values of sine,
cosine, tangent for ᵰ/3, ᵰ/4,
and ᵰ/6, and use the unit circle
to express the values of sine,
cosine, and tangent for x, ᵰ + x,
and 2ᵰ - x in terms of their
values for x, where x is any real
number.
6 lessons
Find the values of
the tangent,
cotangent, secant,
and cosecant
functions.
Sketch the functions’
(listed above)
graphs.
Express
trigonometric ratios
in terms of a
reference angle.
Sketch the graphs of
tangent and secant
trigonometric
functions.
Content:
tangent, cotangent,
secant, cosecant,
significant digits,
vertical asymptotes,
reference angles.
Skills:
Find “other”
trigonometric
function values to
four significant
digits.
Given the value of
one of the five
trigonometric
functions of an
angle, calculate the
other four.
Give students a list
of functions to graph
by hand. When
complete, they are
to check their
graphs using a
graphing calculator
or online graphing
tool.
6
Lessons
Go to link below for
reference angle
online practice:
http://www.mathwa
rehouse.com/trigon
ometry/reference-a
ngle/finding-referen
ce-angle.php
Find reference
angles of given
trigonometric
ratios.
Use tangent and
secant ratios to
sketch their graphs.
Find values of the
inverse
trigonometric
functions with and
without a calculator.
Content:
Inverse function,
one-to-one function,
intervals.
Skills:
Understand the
definition of a
one-to-one function.
Understand the
concept of an
inverse function.
Determine if a
function has an
inverse.
Calculate a
function’s inverse
with and without a
calculator to the
nearest tenth of a
degree or hundredth
of a radian.
Gallery walk –
Determining if
situations (real,
graphic, or
trigonometric) are
inverses of each
other. Groups will
read from 8 posters
and comment on
each.
http://www.onlinem
athlearning.com/inv
erse-functions-algeb
ra.html
F-TF.B.6: (+) Understand that
restricting a trigonometric
function to a domain on which it
is always increasing or always
decreasing allows its inverse to
be constructed.
F-TF.B.7: (+) Use inverse
functions to solve trigonometric
equations that arise in modeling
contexts; evaluate the solutions
using technology, and interpret
them in terms of the context.
3
Lessons