2016-2017 Math Nation Algebra 2 Scope & Sequence: MAFS Topics and Standards Alignment
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TABLE OF CONTENTS
SECTIONS PAGES IN THIS DOC
Section 1: Function Overview 2-4
Section 2: Linear Functions 5-9
Section 3: Piecewise-Defined Functions 10-12
Section 4: Quadratics Functions – Part 1 13-16
Section 5: Quadratics Functions – Part 2 17-23
Section 6: Polynomials Functions 24-27
Section 7: Rational Expressions and Equations 28-29
Section 8: Expressions and Equations with Radicals and Rational Exponents 30-32
Section 9: Exponential and Logarithmic Functions 33-37
Section 10: Sequences and Series 38-39
Section 11: Probability 40-44
Section 12: Statistics 45-46
Section 13: Trigonometry – Part 1 47
Section 14: Trigonometry – Part 2 48
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SECTION 1: FUNCTIONS
Section 1 - Topic 1:
Adding Functions
MAFS.912.A-APR.1.1 Understand that
polynomials form a system analogous to the
integers; namely, they are closed under the
operations of addition, subtraction, and
multiplication; add, subtract, and multiply
polynomials.
In this topic, students will add and subtract
polynomial functions.
Section 1 - Topic 2:
Multiplying Functions
MAFS.912.A-APR.1.1 Understand that
polynomials form a system analogous to the
integers; namely, they are closed under the
operations of addition, subtraction, and
multiplication; add, subtract, and multiply
polynomials.
In this topic, students will multiply
polynomial functions.
Section 1 - Topic 3:
Dividing Rational Expressions
MAFS.912.A-APR.4.6 Rewrite simple rational
expressions in different forms; write 𝑎(𝑥)/𝑏(𝑥) in
the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥),
𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree
of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using
inspection, long division, or, for the more
complicated examples, a computer algebra
system.
In this topic, students will rewrite a rational
expression as the quotient in the form of a
polynomial added to the remainder
divided by the divisor. Students will use
polynomial long division to divide a
polynomial by a polynomial.
Section 1 - Topic 4:
Using Synthetic Division to Divide Functions
MAFS.912.A-APR.4.6 Rewrite simple rational
expressions in different forms; write 𝑎(𝑥)/𝑏(𝑥) in
the form 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥), where 𝑎(𝑥), 𝑏(𝑥), 𝑞(𝑥), and 𝑟(𝑥) are polynomials with the degree
of 𝑟(𝑥) less than the degree of 𝑏(𝑥), using
inspection, long division, or, for the more
complicated examples, a computer algebra
system.
In this topic, students will use synthetic
division as a method of rewriting rational
expressions when the divisor is in the form
𝑥 − 𝑐.
Section 1 - Topic 5:
Composition of Functions
MAFS.912.F-BF.1.1c Write a function that
describes a relationship between two
quantities.
c. Compose functions. For example, if 𝑇(𝑦) is the temperature in the atmosphere as a
function of height and ℎ(𝑡) is the height of a
weather balloon as a function of time, then
𝑇(ℎ(𝑡)) is the temperature at the location of
the weather balloon as a function of time.
In this topic, students will write a function to
model a real-world context by composing
functions and the information within the
context.
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Section 1 - Topic 6:
Inverse Functions - Part 1
MAFS.912.F-BF.2.4a,c Find inverse functions.
a. Solve an equation of the form 𝑓(𝑥) = 𝑐 for a
simple function, 𝑓, that has an inverse and
write an expression for the inverse.
For example, 𝑓(𝑥) = 2 × 3 or 𝑓(𝑥) = (𝑥 +
1)/(𝑥– 1) for 𝑥 ≠ 1.
c. Read values of an inverse function from a
graph or a table, given that the function has
an inverse.
In this topic, students will investigate inverse
functions. will use a graph or a table of a
function to determine values of the
function’s inverse. Students will find the
inverse of a function.
Section 1 - Topic 7:
Inverse Functions - Part 2
MAFS.912.F-BF.2.4a,b,c,d Find inverse
functions.
a. Solve an equation of the form 𝑓(𝑥) = 𝑐 for a
simple function, 𝑓, that has an inverse and
write an expression for the inverse.
For example, 𝑓(𝑥) = 2 × 3 or 𝑓(𝑥) = (𝑥 +1)/(𝑥– 1) for 𝑥 ≠ 1.
b. Verify by composition that one function is
the inverse of another.
c. Read values of an inverse function from a
graph or a table, given that the function has
an inverse.
d. Produce an invertible function from a non-
invertible function by restricting the domain.
In this topic, students will continue to work
with inverses. Students will use compositions
to determine if two functions are inverses.
Students will restrict domains to create
invertible functions.
Section 1 - Topic 8:
Recognizing Even and Odd Functions
MAFS.912.F-BF.2.3 Identify the effect on the
graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓(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.
In this topic, students will investigate
features of even and odd functions.
Students will determine if functions are
even or odd by examining equations,
tables, and graphs.
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Section 1 - Topic 9:
Key Features of Graphs of Functions
MAFS.912.F-IF.3.7a Graph functions expressed
symbolically and show key features of the
graph, by hand in simple cases and using
technology in more complicated cases. A.
Graph linear and quadratic functions and
show intercepts, maxima, and minima. This
section focuses on linear functions.
MAFS.912.F-IF.2.4 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. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; end
behavior; and periodicity.
In this topic, students will review key
features of graphs of functions. (solutions,
y-intercepts, positive/negative,
increasing/decreasing, maximum,
minimum,).
Section 1 - Topic 10:
Transformations of Functions – Part 1
MAFS.912.F-BF.2.3 Identify the effect on the
graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓 (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.
In this topic, students will review
transformations of functions. Students will
investigate horizontal shifts of functions.
Students will also consider multiple
transformations on a function.
Section 1 - Topic 11:
Transformations of Functions – Part 2
MAFS.912.F-BF.2.3 Identify the effect on the
graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓 (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.
In this topic, students will review
transformations of functions. Students will
investigate horizontal shifts of functions.
Students will also consider multiple
transformations on a function.
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SECTION 2: LINEAR FUNCTIONS, EQUATIONS, AND INEQUALITIES
Section 2 - Topic 1:
Linear Equations in One Variable - Part 1
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems.
MAFS.912.A-REI.1.1 Explain each step in solving
a simple equation as following from the
equality of numbers asserted at the previous
step, starting from the assumption that the
original equation has a solution.
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
MAFS.912.A-SSE.1.1a Interpret expressions that
represent a quantity in terms of its context.
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
In this topic, students will justify the steps to
solve equations. Students will create and
solve equations representing real-world
situations. Additionally, students will
interpret expressions and what the terms
represent.
Section 2 - Topic 2:
Linear Equations in One Variable - Part 2
MAFS.912.A-CED.1.4 Rearrange formulas to
highlight a quantity of interest using the same
reasoning as in solving equations.
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems.
In this topic, students will solve equations
with multiple variables for a specific
variable.
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Section 2 - Topic 3:
Linear Equations and Inequalities in Two
Variables
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-CED.1.3 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.
MAFS.912.F-LE.2.5 Interpret the parameters in a
linear or an exponential function in terms of a
context.
MAFS.912.A-SSE.1.1a Interpret expressions that
represent a quantity in terms of its context.
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
In this topic, students will represent real-
world situations with linear functions.
Students will graph the functions and
interpret key features of the graph.
Section 2 - Topic 4:
Key Features of Linear Functions
MAFS.912.F-IF.2.4 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. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; end
behavior; and periodicity.
In this topic, students will review the key
features of linear functions.
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Section 2 - Topic 5:
Classifying Linear Functions and Finding
Inverses
MAFS.912.F-BF.2.4 Find inverse functions.
a. Solve an equation of the form f(x) = c for a
simple function, f, that has an inverse and
write an expression for the inverse. For
example, 𝑓(𝑥) = 2𝑥³ or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for
𝑥 ≠ 1.
b. Verify by composition that one function is
the inverse of another.
c. Read values of an inverse function from a
graph or a table, given that the function has
an inverse.
d. Produce an invertible function from a non-
invertible function by restricting the domain.
In this topic, students will classify linear
functions as even, odd, or neither.
Additionally, students will find the inverse of
a linear function, if it exists.
Section 2 - Topic 6:
Solving Linear Systems - Investigating
Graphing, Substitution, and Elimination
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear
equations in two variables.
MAFS.912.A-REI.4.11 Explain why the x-
coordinates of the points where the graphs of
the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect
are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately (e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations).
In this topic, students investigate solutions
to systems of linear equations. Students will
solve systems by graphing and substitution.
Additionally, students will explore
equivalent systems of equations.
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Section 2 - Topic 7:
Solving Linear Systems Using Elimination
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear
equations in two variables.
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-SSE.1.1a Interpret expressions that
represent a quantity in terms of its context.
a. Interpret parts of an expression, such as
terms, factors, and coefficients.
In this topic, students will solve systems
using the elimination method. Additionally,
student will interpret different terms in a
system of equations.
Section 2 - Topic 8:
Solving Linear Systems Using Substitution
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear
equations in two variables.
MAFS.912.A-CED.1.3 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.
In the topic, students will solve systems of
equations by substitution. They will explore
why the x-coordinates of the points where
the graphs of the equations 𝑦 = 𝑓(𝑥) and
𝑦 = 𝑔(𝑥) intersect are the solutions of the
equation 𝑓(𝑥) = 𝑔(𝑥).
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Section 2 - Topic 9:
Systems of Linear Equations in Three Variables -
Part 1
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear
equations in two variables.
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
In this topic, students will write and solve
systems of linear equations in three
variables that represent real-world
situations.
Section 2 - Topic 10:
Systems of Linear Equations in Three Variables -
Part 2
MAFS.912.A-REI.3.6 Solve systems of linear
equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear
equations in two variables.
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
In this topic, students will write and solve
systems of linear equations in three
variables that represent real-world
situations.
Section 2 - Topic 11:
Systems of Linear Inequalities
MAFS.912.A-CED.1.3 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.
In this topic students will create systems of
linear inequalities from real-world situations.
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SECTION 3: PIECEWISE-DEFINED FUNCTIONS
Section 3 - Topic 1:
Introduction to Piecewise-Defined Functions -
Part 1
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
In this topics, students will explore and
evaluate piecewise-defined functions.
Additionally, students will define key
features for graphs of piecewise-defined
functions.
Section 3 - Topic 2:
Introduction to Piecewise-Defined Functions -
Part 2
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
In this topics, students will explore and
evaluate piecewise-defined functions.
Additionally, students will define key
features for graphs of piecewise-defined
functions.
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Section 3 - Topic 3:
Graphing and Writing Piecewise-Defined
Functions - Part 1
MAFS.912.A.F-IF.2.4 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.
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales.
In this topic, students will graph piece-
wise defined functions. Additionally,
students will write piece-wise defined
functions and describe key features of
the graphs.
Section 3 - Topic 4:
Graphing and Writing Piecewise-Defined
Functions - Part 2
MAFS.912.A.F-IF.2.4 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.
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales.
In this topic, students will graph piece-
wise defined functions. Additionally,
students will write piece-wise defined
functions and describe key features of
the graphs.
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Section 3 - Topic 5:
Real World Examples of Piecewise-Defined
Functions
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales.
In this topic, students will look at real
world examples of piecewise-defined
functions. Students will write and graph
the function that represents the situation.
Section 3 - Topic 6:
Absolute Value Functions
MAFS.912.F-IF.3.7b Graph functions expressed
symbolically and show key features of the graph
by hand in simple cases and using technology for
more complicated cases.
b. Graph square root, cube root, and piecewise-
defined functions, including step functions and
absolute value functions.
MAFS.912.A.F-IF.2.4 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.
MAFS.912.A-CED.1.2 Create equations in two or
more variables to represent relationships between
quantities; graph equations on coordinate axes
with labels and scales.
In this topic, students will explore
absolute value functions. Students will
make the connection that absolute
value functions can be written as
piecewise-defined function. Students will
write and graph absolute value
functions.
Section 3 - Topic 7:
Transformations of Piecewise–Defined Functions
MAFS.912.F-BF.2.3 Identify the effect on the graph
of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓(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.
In this topic, students will apply their
knowledge of transformations of
functions to piecewise-defined functions.
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SECTION 4: QUADRATICS PART 1
Section 4 - Topic 1:
Real-Life Examples of Quadratic Functions
MAFS.912.F-IF.2.4 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.
MAFS.912.CED.1.1 Create equations and inequalities in
one variable and use them to solve problems.
MAFS.912.A-CED.1.2 Create equations in two or more
variables to represent relationships between quantities;
graph equations on coordinate axes with labels and
scales.
In this topic, students will determine
and relate the key features of a
function within a real-world context
by examining the function’s graph.
Students will also consider using the
gravitational constant to write a
quadratic function to represent a
real-life situation.
Section 4 - Topic 2:
Solving Quadratic Equations by Factoring
MAFS.912.A-SSE.2.3 Choose and produce an equivalent
form of an expression to reveal and explain properties of
the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the
function it defines.
MAFS.912.A-REI.1.1
Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the
original equation has a solution.
In this topic, students will factor a
quadratic expression to find the
solutions.
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Section 4 - Topic 3:
Solving Quadratic Equations by Factoring -
Special Cases - Part 1
MAFS.912.A-SSE.2.3 Choose and produce an equivalent
form of an expression to reveal and explain properties of
the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of
the function it defines.
MAFS.912.A-REI.2.4.b Solve quadratic equations in one
variable.
b. Solve quadratic equations by inspection (e.g., for 𝑥2 =49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will look at
special cases of factoring. This topic
focuses on perfect square trinomials.
Section 4 - Topic 4:
Solving Quadratic Equations by Factoring -
Special Cases - Part 2
MAFS.912.A-SSE.2.3 Choose and produce an equivalent
form of an expression to reveal and explain properties of
the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the
function it defines.
MAFS.912.A-REI.2.4.b Solve quadratic equations in one
variable.
b. Solve quadratic equations by inspection (e.g., for 𝑥2 =49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will look at
special cases of factoring. This topic
focuses on difference of two
squares.
Section 4 - Topic 5:
Complex Numbers - Part 1
MAFS.912.N-CN.1.1 Know there is a complex number, 𝑖,
such that 𝑖2 = −1, and every complex number has the
form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.
MAFS.912.N-CN.1.2 Use the relation 𝑖2 = −1 and the
commutative, associative, and distributive properties to
add, subtract, and multiply complex numbers.
In this topic, students will use I to
represent imaginary numbers.
Students will add, subtract, and
multiply complex numbers and use
𝑖2 = −1 to write the answer as a
complex number.
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Section 4 - Topic 6:
Complex Numbers - Part 2
MAFS.912.N-CN.1.1 Know there is a complex number, 𝑖,
such that 𝑖2 = −1, and every complex number has the
form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real.
MAFS.912.N-CN.1.2 Use the relation 𝑖2 = −1 and the
commutative, associative, and distributive properties to
add, subtract, and multiply complex numbers.
In this topic, students will use I to
represent imaginary numbers.
Students will add, subtract, and
multiply complex numbers and use
𝑖2 = −1 to write the answer as a
complex number.
Section 4 - Topic 7:
Solving Quadratic Equations by Completing
the Square
MAFS.912.A-REI.2.4 Solve quadratic equations in one
variable.
a. Use the method of completing the square to transform
any quadratic equation in 𝑥 into an equation of the form
(𝑥 – 𝑝)2 = 𝑞 that has the same solutions. Derive the
quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for 𝑥2 =49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the
initial form
MAFS.912.N-CN.3.7 Solve quadratic equations with real
coefficients that have complex solutions.
In this topic, students will transform a
quadratic equations by completing
the square and then solve the
equation by taking the square root.
Section 4 - Topic 8:
Solving Quadratics Using the Quadratic
Formula - Part 1
MAFS.912.N-CN.3.7 Solve quadratic equations with real
coefficients that have complex solutions.
MAFS.912.A-REI.2.4.b Solve quadratic equations in one
variable.
b. Solve quadratic equations by inspection (e.g., for 𝑥2 =
49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
them as 𝑎 ± 𝑏𝑖 for real numbers 𝑎 and 𝑏.
In this topic, students will use the
quadratic formula to solve
quadratics.
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Section 4 - Topic 9:
Solving Quadratics Using the Quadratic
Formula - Part 2
MAFS.912.N-CN.3.7 Solve quadratic equations with real
coefficients that have complex solutions.
MAFS.912.A-REI.2.4 Solve quadratic equations in one
variable.
b. Solve quadratic equations by inspection (e.g., for 𝑥2 =49), taking square roots, completing the square, the
quadratic formula, and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
them as 𝑎 ± 𝑏𝑖 for real numbers 𝑎 and 𝑏.
MAFS.912.A-CED.1.1 Create equations and inequalities in
one variable and use them to solve problems.
MAFS.912.A-CED.1.2 Create equations in two or more
variables to represent relationships between quantities;
graph equations on coordinate axes with labels and
scales.
In this topic, students will use the
quadratic formula to solve
quadratics.
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SECTION 5: QUADRATICS – PART 2
Section 5 – Topic 1:
Graphing Quadratics in Standard Form
MAFS.912.F-IF.3.7a Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
MAFS.912.F-IF.3.9 Compare properties of two
functions each represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For example,
given a graph of one quadratic function and
an algebraic expression for another, say which
has the larger maximum.
MAFS.912.A-REI.2.4.b Solve quadratic
equations in one variable.
b. Solve quadratic equations by inspection
(e.g., for 𝑥2 = 49), taking square roots,
completing the square, the quadratic formula,
and factoring, as appropriate to the initial form
of the equation. Recognize when the
quadratic formula gives complex solutions and
write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will review the key
features of a quadratic function. Additionally,
they will use key features to sketch the graph
of the quadratic.
Section 5 – Topic 2:
Writing Quadratic Equations in Standard Form
from a Graph
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
In this topic, students will identify key features
from a graph and use those to write the
equation represented by the graph.
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Section 5 – Topic 3:
Graphing Quadratics in Vertex Form - Part 1
MAFS.912.F-IF.3.7a Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
MAFS.912.A-REI.2.4.b Solve quadratic
equations in one variable.
b. Solve quadratic equations by inspection
(e.g., for 𝑥2 = 49), taking square roots,
completing the square, the quadratic formula,
and factoring, as appropriate to the initial form
of the equation. Recognize when the
quadratic formula gives complex solutions and
write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students will identify key features
from the vertex form. Students will use the
features to graph the function.
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Section 5 – Topic 4:
Graphing Quadratics in Vertex Form - Part 2
MAFS.912.F-IF.3.7a Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
a. Graph linear and quadratic functions and
show intercepts, maxima, and minima.
MAFS.912.F-IF.3.8.a Write a function defined by
an expression in different but equivalent forms
to reveal and explain different properties of
the function.
a. Use the process of factoring and completing
the square in a quadratic function to show
zeros, extreme values, and symmetry of the
graph, and interpret these in terms of a
context.
MAFS.912.F-IF.3.9 Compare properties of two
functions each represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For example,
given a graph of one quadratic function and
an algebraic expression for another, say which
has the larger maximum.
MAFS.912.A-REI.2.4.b Solve quadratic
equations in one variable.
b. Solve quadratic equations by inspection
(e.g., for 𝑥2 = 49), taking square roots,
completing the square, the quadratic formula,
and factoring, as appropriate to the initial form
of the equation. Recognize when the
quadratic formula gives complex solutions and
write them as 𝑎 ± 𝑏i for real numbers 𝑎 and 𝑏.
In this topic, students write functions in vertex
form and identify key features. Students will use
the features to graph the function.
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Section 5, Topic 5:
Writing Quadratic Equations in Vertex Form
from a Graph
MAFS.912.F-IF.3.8.a Write a function defined by
an expression in different but equivalent forms
to reveal and explain different properties of
the function.
a. Use the process of factoring and completing
the square in a quadratic function to show
zeros, extreme values, and symmetry of the
graph, and interpret these in terms of a
context.
MAFS.912.A-CED.1.2 Create equations in two
or more variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
In this topic, students will use the vertex and
other features to write the equation of the
quadratic in vertex form.
Section 5, Topic 6:
Converting Quadratic Equations
MAFS.912.A-SSE.2.3b Choose and produce an
equivalent form of an expression to reveal and
explain properties of the quantity represented
by the expression b. Complete the square in a
quadratic expression to reveal the maximum or
minimum value of the function it defines.
In this topic, students will write quadratic
equations in different forms.
Section 5, Topic 7:
Writing Quadratic Equations When Given a
Focus and Directrix
MAFS.912.G-GPE.1.2 Derive the equation of a
parabola given a focus and directrix.
In this topic, students will use the understand
the relationship between the directrix and
focus of a parabola and use those features to
write the equation of the parabola.
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Section 5 - Topic 8:
Systems of Equations with Quadratics - Part 1
MAFS.912.A-REI.3.7 Solve a simple system
consisting of a linear equation and a quadratic
equation in two variables algebraically and
graphically. For example, find the points of
intersection between the line 𝑦 = − 3𝑥 and the
circle 𝑥2 + 𝑦2 = 3.
MAFS.912.A-REI.4.11 Explain why the x-
coordinates of the points where the graphs of
the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect
are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately (e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations). Include cases where 𝑓(𝑥)
and/or 𝑔(𝑥) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.
In this topic, students will solve systems of
equations that contain linear and quadratic
equations, as well as systems of two
quadratics.
Section 5 - Topic 9:
Systems of Equations with Quadratics - Part 2
MAFS.912.A-REI.3.7 Solve a simple system
consisting of a linear equation and a quadratic
equation in two variables algebraically and
graphically. For example, find the points of
intersection between the line 𝑦 = − 3𝑥 and the
circle 𝑥2 + 𝑦2 = 3.
MAFS.912.A-REI.4.11 Explain why the x-
coordinates of the points where the graphs of
the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect
are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately (e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations). Include cases where 𝑓(𝑥)
and/or 𝑔(𝑥) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.
In this topic, students will solve systems of
equations that contain linear and quadratic
equations, as well as systems of two
quadratics.
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Section 5 - Topic 10:
Transformations with Quadratic Functions
MAFS.912.F-BF.2.3 Identify the effect on the
graph of replacing 𝑓(𝑥) by 𝑓(𝑥) 𝑘, 𝑘𝑓(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.
In this topic, students will apply their knowledge
of transformations of functions specifically to
quadratic functions.
Section 5 - Topic 11:
Key Features of Quadratic Functions
MAFS.912.F-IF.2.4 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. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; end
behavior; and periodicity.
In this topic, students will review all the key of
quadratic functions.
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Section 5 – Topic 12:
Classifying Quadratic Functions and Finding
Inverses
MAFS.912.F-BF.2.4 Find inverse functions.
a. Solve an equation of the form 𝑓(𝑥) = 𝑐 for a
simple function, f, that has an inverse and write
an expression for the inverse. For example,
𝑓(𝑥) = 2𝑥³ or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1.
b. Verify by composition that one function is
the inverse of another.
c. Read values of an inverse function from a
graph or a table, given that the function has
an inverse.
d. Produce an invertible function from a non-
invertible function by restricting the domain.
MAFS.912.F-BF.2.3 Identify the effect on the
graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓(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.
In this topic, students will classify quadratic
functions as even, odd, or neither.
Additionally, they will find inverses of quadratic
functions and restrict domains to produce and
invertible function.
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SECTION 6: POLYNOMIALS FUNCTIONS
Section 6 - Topic 1:
Classifying Polynomials and Closure Property
MAFS.912.A-APR.1.1 Understand that
polynomials form a system analogous to the
integers; namely, they are closed under the
operations of addition, subtraction, and
multiplication; add, subtract, and multiply
polynomials.
MAFS.912.A-APR.3.4 Prove polynomial identities
and use them to describe numerical
relationships.
In this topic, students will classify polynomials
which leads into a review of the closure
property as applied to polynomials.
Section 6 - Topic 2:
Polynomial Identities - Part 1
MAFS.912.A-SSE.1.2 Use the structure of an
expression to identify ways to rewrite it. For
example, see 𝑥4– 𝑦4 as (𝑥2)2 – (𝑦2)2, thus
recognizing it as a difference of squares that
can be factored as (𝑥2 – 𝑦2)(𝑥2 + 𝑦2).
MAFS.912.A-APR.3.4 Prove polynomial identities
and use them to describe numerical
relationships.
In this topic, students will prove polynomial
identities. Students will use those identities to
write equivalent expressions and describe
numerical relationships.
Section 6 - Topic 3:
Polynomial Identities - Part 2
MAFS.912.A-SSE.1.2 Use the structure of an
expression to identify ways to rewrite it. For
example, see 𝑥4– 𝑦4 as (𝑥2)2 – (𝑦2)2, thus
recognizing it as a difference of squares that
can be factored as (𝑥2 – 𝑦2)(𝑥2 + 𝑦2).
MAFS.912.A-APR.3.4 Prove polynomial identities
and use them to describe numerical
relationships.
In this topic, students will prove polynomial
identities. Students will use those identities to
write equivalent expressions and describe
numerical relationships.
Section 6 - Topic 4:
Recognizing End Behavior of Graphs of
Polynomials
MAFS.912.F-IF.2.4 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.
In this topic, students will review graphs and
make generalities about end behavior of
polynomial functions. Students will use those
generalities to determine the end behavior
when given a polynomial function.
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Section 6 - Topic 5:
Using Successive Differences
MAFS.912.F-IF.2.4 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.
MAFS.912.F-IF.2.6 Calculate and interpret the
average rate of change of a function
(presented symbolically or as a table) over a
specified interval. Estimate the rate of change
from a graph.
In this topic, students will explore rate of
change and successive differences of different
polynomial functions. They will use their findings
to classify polynomial functions.
Section 6 - Topic 6:
Understanding Zeroes of Polynomials
MAFS.912.F-IF.2.4 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. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; end
behavior; and periodicity.
MAFS.912.A-APR.2.3 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.
In this topic, students will explore zeroes of
polynomial functions and how this relates to
the degree of the function.
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Section 6 - Topic 7:
Factoring Polynomials
MAFS.912.A-SSE.2.3 Choose and produce an
equivalent form of an expression to reveal and
explain properties of the quantity represented
by the expression.
MAFS.912.A-SSE.1.2 Use the structure of an
expression to identify ways to rewrite it. For
example, see 𝑥4– 𝑦4 as (𝑥2)2 – (𝑦2)2, thus
recognizing it as a difference of squares that
can be factored as (𝑥2 – 𝑦2)(𝑥2 + 𝑦2).
MAFS.912.A-APR.2.3 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.
In this topic, students will apply their prior
knowledge of factoring and polynomial
identities to factor polynomials of higher
degrees.
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Section 6 - Topic 8:
Sketching Graphs of Polynomials
MAFS.912.A-APR.2.3 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.
MAFS.912.F-IF.3.7c Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
c. Graph polynomial functions, identifying zeros
when suitable factorizations are available and
showing end behavior.
MAFS.912.A-SSE.2.3 Choose and produce an
equivalent form of an expression to reveal and
explain properties of the quantity represented
by the expression.
MAFS.912.A-SSE.1.2 Use the structure of an
expression to identify ways to rewrite it. For
example, see 𝑥4– 𝑦4 as (𝑥2)2 – (𝑦2)2, thus
recognizing it as a difference of squares that
can be factored as (𝑥2 – 𝑦2)(𝑥2 + 𝑦2).
In this topic, students will apply their knowledge
of zeroes and end behavior of polynomials to
sketch the graph of polynomial functions of
higher degrees.
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SECTION 7: RATIONAL EXPRESSIONS AND EQUATIONS
Section 7, Topic 1:
The Remainder Theorem
MAFS.912.A-APR.2.2 Know and apply the
Remainder Theorem: For a polynomial 𝑝(𝑥)
and a number 𝑎, the remainder on division by
𝑥 – 𝑎 is 𝑝(𝑎), so 𝑝(𝑎) = 0 if and only if (𝑥 – 𝑎) is a
factor of 𝑝(𝑥).
In this topic, students will understand and apply
the remainder theorem to determine if an
expression is a factor of a polynomial function.
Section 7, Topic 2:
Solving Rational Equations
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
MAFS.912.A-CED.1.3 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. For example, represent
inequalities describing nutritional and cost
constraints on combinations of different foods.
In this topic, students will solve a rational
equation in one variable.
Section 7, Topic 3:
Solving Systems of Rational Equations
MAFS.912.A-REI.4.11 Explain why the x-
coordinates of the points where the graphs of
the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect
are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥);
find the solutions approximately (e.g., using
technology to graph the functions, make
tables of values, or find successive
approximations). Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.
MAFS.912.A-REI.1.2 Solve simple rational and
radical equations in one variable, and give
examples showing how extraneous solutions
may arise.
In this topic, students will solve a system of
rational equations.
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Section 7, Topic 4:
Using Rational Equations to Solve Real World
Problems
MAFS.912.A-CED.1.1 Create equations and
inequalities in one variable and use them to
solve problems. Include equations arising from
linear and quadratic functions and simple
rational, absolute, and exponential functions.
MAFS.912.A-CED.1.3 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. For example, represent
inequalities describing nutritional and cost
constraints on combinations of different foods.
In this topic, students will use rational equations
solve real-world situations.
Section 7, Topic 5:
Graphing Rational Functions
MAFS.912.F-IF.3.7d Graph functions expressed
symbolically and show key features of the
graph by hand in simple cases and using
technology for more complicated cases.
d. Graph rational functions, identifying zeros
and asymptotes when suitable factorizations
are available and showing end behavior.
MAFS.912.F-IF.3.9 Compare properties of two
functions each represented in a different way
(algebraically, graphically, numerically in
tables, or by verbal descriptions). For example,
given a graph of one quadratic function and
an algebraic expression for another, say which
has the larger maximum.
In this topic, students will explore the key
features of rational functions and use those to
graph the function.
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SECTION 8: EXPRESSIONS AND EQUATIONS WITH RADICALS AND RATIONAL EXPONENTS
Section 8 - Topic 1:
Expressions with Radicals and
Radical Exponents – Part 1
MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 5
1
3 to be the cube root of 5 because
we want (5
1
3 ) 3 =
5 (
1
3)3, to hold, so
(51
3 ) 3 must equal 5.
MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
In this topic, students will
understand rational exponents
using the properties of integer
exponents. Students will also
convert between expressions with
radicals and rational exponents.
Section 8 - Topic 2:
Expressions with Radicals and
Radical Exponents – Part 2
MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer exponents to
those values, allowing for a notation for radicals in terms of rational
exponents. For example, we define 5
1
3 to be the cube root of 5 because
we want (5
1
3 ) 3 =
5 (
1
3)3, to hold, so
(51
3 ) 3 must equal 5.
MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
In this topic, students will
understand rational exponents
using the properties of integer
exponents. Students will also
convert between expressions with
radicals and rational exponents.
Section 8 - Topic 3:
Solving Equations with Radicals
and Rational Exponents - Part 1
MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one
variable, and give examples showing how extraneous solutions may
arise.
In this topic, students will write and
solve equations with radicals and
rational exponents. Students will
also understand what extraneous
solutions are.
Section 8 - Topic 4:
Solving Equations with Radicals
and Rational Exponents - Part 2
MAFS.912.A-CED.1.1 Create equations and inequalities in one variable
and use them to solve problems. Include equations arising from linear
and quadratic functions and simple rational, absolute, and exponential
functions.
MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one
variable, and give examples showing how extraneous solutions may
arise.
MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of
interest using the same reasoning as in solving equations. For example,
rearrange Ohm’s law, 𝑉 = 𝐼𝑅, to highlight resistance, 𝑅.
In this topic, students will write and
solve equations with radicals and
rational exponents. Students will
also understand what extraneous
solutions are.
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Section 8 – Topic 5:
Graphing Square Root and Cube
Root Functions- Part One
MAFS.912.F-IF.3.7 b Graph functions expressed symbolically and show
key features of the graph by hand in simple cases and using
technology for more complicated cases.
b. Graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions.
MAFS.912.F-IF.2.4 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. Key features include: intercepts; intervals
where the function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end behavior; and
periodicity.
MAFS.912.F-IF.3.9 Compare properties of two functions each
represented in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say which
has the larger maximum.
MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it describes. For
example, if the function h(n) gives the number of person-hours it takes
to assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function.
MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓 (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.
In this topic, students will graph
square root and cube root
functions. Students will use the
graphs to solve real-world
problems. Additionally, students
will apply their knowledge of
transformations of functions.
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Section 8 - Topic 6:
Graphing Square Root and Cube
Root Functions – Part Two
MAFS.912.F-IF.3.7 b Graph functions expressed symbolically and show
key features of the graph by hand in simple cases and using
technology for more complicated cases.
b. Graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions.
MAFS.912.F-IF.2.4 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. Key features include: intercepts; intervals
where the function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end behavior; and
periodicity.
MAFS.912.F-IF.3.9 Compare properties of two functions each
represented in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say which
has the larger maximum.
MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and,
where applicable, to the quantitative relationship it describes. For
example, if the function ℎ(𝑛) gives the number of person-hours it takes
to assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function.
MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing 𝑓(𝑥) by
𝑓(𝑥) + 𝑘, 𝑘𝑓(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.
In this topic, students will graph
square root and cube root
functions. Students will use the
graphs to solve real-world
problems. Additionally, students
will apply their knowledge of
transformations of functions.
2016-2017 Math Nation Algebra 2 Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 9: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Section 9 - Topic 1:
Real World Exponential Growth and
Decay - Part 1
MAFS.912.A-CED.1.1 Create equations and inequalities in one
variable and use them to solve problems. Include equations
arising from linear and quadratic functions and simple rational,
absolute, and exponential functions.
MAFS.912.A-CED.1.2 Create equations in two or more variables
to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
MAFS.912.A-CED.1.3 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. For example, represent inequalities describing
nutritional and cost constraints on combinations of different
foods.
MAFS.912.F-IF.3.8.b 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.
MAFS.912.F-LE.2.5 Interpret the parameters in a linear or an
exponential function in terms of a context.
In this topic, students will explore and
solve problems involving exponential
growth and decay in the context of real-
world situations.
2016-2017 Math Nation Algebra 2 Scope & Sequence: MAFS Topics and Standards Alignment
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Section 9 - Topic 2:
Real World Exponential Growth and
Decay - Part 2
MAFS.912.A-CED.1.1 Create equations and inequalities in one
variable and use them to solve problems. Include equations
arising from linear and quadratic functions and simple rational,
absolute, and exponential functions.
MAFS.912.A-CED.1.2 Create equations in two or more variables
to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
MAFS.912.A-CED.1.3 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. For example, represent inequalities describing
nutritional and cost constraints on combinations of different
foods.
MAFS.912.F-IF.3.8.b 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.
MAFS.912.F-LE.2.5 Interpret the parameters in a linear or an
exponential function in terms of a context.
Students will write an equation in one
variable that represents a real-world
context. Students will write and solve an
equation in one variable that represents
a real-world context. Students will identify
the quantities in a real-world situation
that should be represented by distinct
variables.
In this topic, students will explore and
solve problems involving exponential
growth and decay in the context of real-
world situations.
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Section 9 - Topic 3:
Interpreting Exponential Equations
MAFS.912.F-IF.3.8b 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.
MAFS.912.A-CED.1.1 Create equations and inequalities in one
variable and use them to solve problems. Include equations
arising from linear and quadratic functions and simple rational,
absolute, and exponential functions.
MAFS.912.A-SSE.2.3c Choose and produce an equivalent form of
an expression to reveal and explain properties of the quantity
represented by the expression.
c. Use the properties of exponents to transform expressions for
exponential functions.
MAFS.912.A-SSE.1.1b Interpret expressions that represent a
quantity in terms of its context.
b. Interpret complicated expressions by viewing one or more of
their parts as a single entity.
In this topic, students will write
exponential functions in equivalent forms
to make observations about what the
function represents in a real-world
context. Additionally, they will use the
functions to solve problems.
Section 9 - Topic 4:
Euler’s Number
In this video, students will investigate how
we derive Euler's Number. Euler's Number
will be used in succeeding videos.
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Section 9 - Topic 5:
Graphing Exponential Functions
MAFS.912.F-IF.2.4 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. Key
features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior; and periodicity.
MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points
where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥)
intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the
solutions approximately (e.g., using technology to graph the
functions, make tables of values, or find successive
approximations). Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are
linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.
In this topic, students will graph
exponential functions and find the
solution for a system of exponential
functions.
Section 9 - Topic 6:
Transformations of Exponential
Functions
MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing
𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘𝑓 (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.
In this topic, students will apply their
knowledge of transformations of
functions to exponential functions.
Section 9 - Topic 7:
Key Features of Exponential
Functions
MAFS.912.F-IF.2.4 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. Key
features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior; and periodicity.
Include recognizing even and odd functions from their graphs
and algebraic expressions for them.
In this topic, students will explore the key
features of exponential functions.
Section 9 - Topic 8:
Logarithmic Functions - Part 1
MAFS.912.F-BF.2.4 Find inverse functions.
a. Solve an equation of the form 𝑓(𝑥) = 𝑐 for a simple function,
𝑓, that has an inverse and write an expression for the inverse.
For example, 𝑓(𝑥) = 2 × 3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1.
In this topic, students will discover that a
logarithmic function is the inverse of an
exponential function.
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Section 9 - Topic 9:
Logarithmic Functions - Part 2
MAFS.912.F-BF.2.4 Find inverse functions.
a. Solve an equation of the form 𝑓(𝑥) = 𝑐 for a simple function,
𝑓, that has an inverse and write an expression for the inverse.
For example, 𝑓(𝑥) = 2 × 3 or 𝑓(𝑥) = (𝑥 + 1)/(𝑥– 1) for 𝑥 ≠ 1.
MAFS.912.F-IF.3.7e. Graph functions expressed symbolically and
show key features of the graph by hand in simple cases and
using technology for more complicated cases.
e. Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude and using phase shift.
In this topic, students will continue to
build their understanding of logarithmic
functions, as well as graph the functions.
Section 9 - Topic 10:
Common and Natural Logarithms
MAFS.912.F-LE.1.4 For exponential models, express as a logarithm
the solution to 𝑎𝑏𝑐𝑡 = 𝑑, where 𝑎, 𝑐, and 𝑑 are numbers and the
base, 𝑏, is 2, 10, or 𝑒; evaluate the logarithm using technology.
MAFS.912.F-BF.2.a: Use the change of base formula.
In this topic, students will extend their
knowledge of logarithms to bases other
than 10. Students will learn and apply the
Change of Base formula.
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SECTION 10: SEQUENCES AND SERIES
Section 10 - Topic 1:
Arithmetic Sequences - Part 1
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function that
describes a relationship between two
quantities.
a. Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
In this topic, students will write an explicit and
recursive formula for an arithmetic sequence.
Students will apply the formula to real-world
situations.
Section 10 - Topic 2:
Arithmetic Sequences - Part 2
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function that
describes a relationship between two
quantities.
a. Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
In this topic, students will write an explicit and
recursive formula for an arithmetic sequence.
Students will apply the formula to real-world
situations.
Section 10 - Topic 3:
Geometric Sequences - Part 1
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function that
describes a relationship between two
quantities.
a. Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
In this topic, students will write an explicit and
recursive formula for a geometric sequence.
Students will apply the formula to real-world
situations.
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Section 10 - Topic 4:
Geometric Sequences - Part 2
MAFS.912.F-BF.1.2 Write arithmetic and
geometric sequences both recursively and
with an explicit formula, use them to model
situations, and translate between the two
forms.
MAFS.912.F-BF.1.1a Write a function that
describes a relationship between two
quantities.
a. Determine an explicit expression, a recursive
process, or steps for calculation from a
context.
In this topic, students will write an explicit and
recursive formula for a geometric sequence.
Students will apply the formula to real-world
situations.
Section 10 - Topic 5:
Introduction to Geometric Series – Part 1
MAFS.912.A-SSE.2.4 Derive the formula for the
sum of a finite geometric series (when the
common ratio is not 1), and use the formula to
solve problems. For example, calculate
mortgage payments.
In this topic, students will be introduced to the
concept of geometric series.
Section 10 - Topic 6:
Introduction to Geometric Series – Part 2
MAFS.912.A-SSE.2.4 Derive the formula for the
sum of a finite geometric series (when the
common ratio is not 1), and use the formula to
solve problems. For example, calculate
mortgage payments.
In this topic, students will derive the formula for
a sum of a finite geometric series with a
common ratio not equal to 1.
Section 10 - Topic 7:
Sum of Geometric Series
MAFS.912.A-SSE.2.4 Derive the formula for the
sum of a finite geometric series (when the
common ratio is not 1), and use the formula to
solve problems. For example, calculate
mortgage payments.
In this topic, students will apply the formula for
the sum of a finite geometric series.
Section 10 - Topic 8:
Calculating Loan Payments
MAFS.912.A-SSE.2.4 Derive the formula for the
sum of a finite geometric series (when the
common ratio is not 1), and use the formula to
solve problems. For example, calculate
mortgage payments.
In this topic, students will use the formula for
the sum of a finite geometric series to
calculate loan payments.
2016-2017 Math Nation Algebra 2 Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 11: PROBABILITY
Section 11 - Topic 1:
Sets and Venn Diagrams - Part 1
MAFS.912.S-CP.1.1 Describe events as subsets
of a sample space (the set of outcomes) using
characteristics (or categories) of the
outcomes, or as unions, intersections, or
complements of other events (“or,” “and,”
“not”).
In this topic, students will explore and be able
to identify the basic elements of Venn diagrams
including intersection, union, and complement.
Section 11 - Topic 2:
Sets and Venn Diagrams - Part 2
MAFS.912.S-CP.1.1 Describe events as subsets
of a sample space (the set of outcomes) using
characteristics (or categories) of the
outcomes, or as unions, intersections, or
complements of other events (“or,” “and,”
“not”).
In this topic, students will create and analyze
Venn diagrams using the various components
of intersection, union, and complement.
Section 11 - Topic 3:
Probability and the Addition Rule - Part 1
MAFS.912.S-CP.2.7 Apply the Addition Rule,
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) – 𝑃(𝐴 𝑎𝑛𝑑 𝐵), and
interpret the answer in terms of the model.
MAFS.912.S-CP.1.4 Construct and interpret two-
way frequency tables of data when two
categories are associated with each object
being classified. Use the two-way table as a
sample space to decide if events are
independent and to approximate conditional
probabilities. For example, collect data from a
random sample of students in your school on
their favorite subject among math, science,
and English. Estimate the probability that a
randomly selected student from your school
will favor science given that the student is in
tenth grade. Do the same for other subjects
and compare the results.
In this topic, students will find probability of one
event taking place and apply the addition rule
to find the probability that one event OR a
separate event will take place.
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Section 11 - Topic 4:
Probability and the Addition Rule - Part 2
MAFS.912.S-CP.2.7 Apply the Addition Rule,
𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) – 𝑃(𝐴 𝑎𝑛𝑑 𝐵), and
interpret the answer in terms of the model.
MAFS.912.S-CP.1.4 Construct and interpret two-
way frequency tables of data when two
categories are associated with each object
being classified. Use the two-way table as a
sample space to decide if events are
independent and to approximate conditional
probabilities. For example, collect data from a
random sample of students in your school on
their favorite subject among math, science,
and English. Estimate the probability that a
randomly selected student from your school
will favor science given that the student is in
tenth grade. Do the same for other subjects
and compare the results.
In this topic, students will find probability of one
event taking place and apply the addition rule
to find the probability that one event OR a
separate event will take place.
Section 11 - Topic 5:
Probability and Independence
MAFS.912.S-CP.1.5 Recognize and explain the
concepts of conditional probability and
independence in everyday language and
everyday situations. For example, compare
the chance of having lung cancer if you are a
smoker with the chance of being a smoker if
you have lung cancer.
MAFS.912.S-CP.1.2 Understand that two events
𝐴 and 𝐵 are independent if the probability of 𝐴
and 𝐵 occurring together is the product of
their probabilities, and use this characterization
to determine if they are independent.
In this topic, students will determine whether or
not two events are dependent or independent,
and use that knowledge to calculate
probabilities of those events.
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Section 11 - Topic 6:
Conditional Probability
MAFS.912.S-CP.1.3 Understand the conditional
probability of 𝐴 given 𝐵 as 𝑃(𝐴 𝑎𝑛𝑑 𝐵)/𝑃(𝐵),
and interpret independence of 𝐴 and 𝐵 as
saying that the conditional probability of 𝐴
given 𝐵 is the same as the probability of 𝐴 and
the conditional probability of 𝐵 given 𝐴 is the
same as the probability of 𝐵.
MAFS.912.S-CP.2.6 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.
MAFS.912.S-CP.1.5 Recognize and explain the
concepts of conditional probability and
independence in everyday language and
everyday situations. For example, compare
the chance of having lung cancer if you are a
smoker with the chance of being a smoker if
you have lung cancer.
MAFS.912.S-CP.1.2 Understand that two events
𝐴 and 𝐵 are independent if the probability of 𝐴
and 𝐵 occurring together is the product of
their probabilities, and use this characterization
to determine if they are independent.
In this topic, students will find the conditional
probability of various real-world situations, as
well as determine and justify independence of
two events,
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Section 11 - Topic 7
Two-Way Frequency Tables - Part 1
MAFS.912.S-CP.1.4 Construct and interpret two-
way frequency tables of data when two
categories are associated with each object
being classified. Use the two-way table as a
sample space to decide if events are
independent and to approximate conditional
probabilities. For example, collect data from a
random sample of students in your school on
their favorite subject among math, science,
and English. Estimate the probability that a
randomly selected student from your school
will favor science given that the student is in
tenth grade. Do the same for other subjects
and compare the results.
MAFS.912.S-CP.1.3 Understand the conditional
probability of 𝐴 given 𝐵 as 𝑃(𝐴 𝑎𝑛𝑑 𝐵)/𝑃(𝐵),
and interpret independence of 𝐴 and 𝐵 as
saying that the conditional probability of 𝐴
given 𝐵 is the same as the probability of 𝐴 and
the conditional probability of 𝐵 given 𝐴 is the
same as the probability of 𝐵.
MAFS.912.S-CP.1.5 Recognize and explain the
concepts of conditional probability and
independence in everyday language and
everyday situations. For example, compare
the chance of having lung cancer if you are a
smoker with the chance of being a smoker if
you have lung cancer.
MAFS.912.S-CP.2.6 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.
In this topic, students will find and interpret
probability from a two-way frequency table.
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Section 11 - Topic 8
Two-Way Frequency Tables - Part 2
MAFS.912.S-CP.1.4 Construct and interpret two-
way frequency tables of data when two
categories are associated with each object
being classified. Use the two-way table as a
sample space to decide if events are
independent and to approximate conditional
probabilities. For example, collect data from a
random sample of students in your school on
their favorite subject among math, science,
and English. Estimate the probability that a
randomly selected student from your school
will favor science given that the student is in
tenth grade. Do the same for other subjects
and compare the results.
MAFS.912.S-CP.1.3 Understand the conditional
probability of 𝐴 given 𝐵 as 𝑃(𝐴 𝑎𝑛𝑑 𝐵)/𝑃(𝐵),
and interpret independence of 𝐴 and 𝐵 as
saying that the conditional probability of 𝐴
given 𝐵 is the same as the probability of 𝐴 and
the conditional probability of 𝐵 given 𝐴 is the
same as the probability of 𝐵.
MAFS.912.S-CP.1.5 Recognize and explain the
concepts of conditional probability and
independence in everyday language and
everyday situations. For example, compare
the chance of having lung cancer if you are a
smoker with the chance of being a smoker if
you have lung cancer.
MAFS.912.S-CP.2.6 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.
In this topic, students will create two-way
frequency tables, as well as find and interpret
probability from the tables they create.
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SECTION 12: STATISTICS
Section 12 - Topic 1:
Statistics and Parameters
MAFS.912.S-IC.1.1 Understand statistics as a
process for making inferences about
population parameters based on a random
sample from that population.
In this topic, students will identify the
population, sample, variable of interest,
parameters, and statistics of interest in various
real-world situations.
Section 12 - Topic 2:
Statistical Studies – Part 1
MAFS.912.S-IC.1.1 Understand statistics as a
process for making inferences about
population parameters based on a random
sample from that population.
MAFS.912.S-IC.2.3 Recognize the purposes of
and differences among sample surveys,
experiments, and observational studies; explain
how randomization relates to each.
In this topic, students will learn the different
ways to gather data, as well as the 3 principles
of experimental design, and use this
knowledge to identify the best method of data
collection different situations.
Section 12 - Topic 3:
Statistical Studies – Part 2
MAFS.912.S-IC.2.3 Recognize the purposes of
and differences among sample surveys,
experiments, and observational studies; explain
how randomization relates to each.
MAFS.912.S-IC.1.1 Understand statistics as a
process for making inferences about
population parameters based on a random
sample from that population.
In this topic, students will identify bias in various
sampling techniques, and determine which
sampling techniques work for differing
situations.
Section 12 - Topic 4:
The Normal Distribution – Part 1
MAFS.912.S-ID.1.4 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 tables to estimate areas under the normal
curve.
MAFS.912.S-IC.2.6 Evaluate reports based on
data.
In this topic, students will use the Empirical Rule
to determine the percentage of values
between two data points.
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Section 12 - Topic 5:
The Normal Distribution – Part 2
MAFS.912.S-ID.1.4 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 tables to estimate areas under the normal
curve.
MAFS.912.S-IC.2.6 Evaluate reports based on
data.
In this topic, students will calculate and
interpret the z-score in various real-world
situations.
Section 12 - Topic 6:
The Normal Distribution – Part 3
MAFS.912.S-ID.1.4 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 tables to estimate areas under the normal
curve.
MAFS.912.S-IC.2.6 Evaluate reports based on
data.
In this topic, students will find the probability
that an event will occur using the mean and
standard deviation to calculate the z-score.
Students will combine their knowledge of z-
core and the Empirical Rule to interpret data.
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SECTION 13: TRIGONOMETRY – PART 1
Section 13 - Topic 1
The Unit Circle - Part 1
MAFS.912.F-TF.1.2 Explain how the unit circle in the
coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian
measures of angles traversed counterclockwise around the
unit circle.
In this topic, students will use their
knowledge of special right triangles to
find the angles measure of the angles
formed by rays intersecting the unit circle
and coordinates on the unit circle.
Section 13 - Topic 2
The Unit Circle - Part 2
MAFS.912.F-TF.1.2 Explain how the unit circle in the
coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian
measures of angles traversed counterclockwise around the
unit circle.
In this topic, students will use their
knowledge of special right triangles to
find the angles measure of the angles
formed by rays intersecting the unit circle
and coordinates on the unit circle.
Section 13 - Topic 3
Radian Measure - Part 1
MAFS.912.F-TF.1.1 Understand radian measure of an angle
as the length of the arc on the unit circle subtended by the
angle; convert between degrees and radians.
MAFS.912.F-TF.1.2 Explain how the unit circle in the
coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian
measures of angles traversed counterclockwise around the
unit circle.
In this topic, students will find missing
angles and radian measures on a unit
circle using knowledge of converting
between degrees and radians.
Section 13 - Topic 4
Radian Measure - Part 2
MAFS.912.F-TF.1.1 Understand radian measure of an angle
as the length of the arc on the unit circle subtended by the
angle; convert between degrees and radians.
MAFS.912.F-TF.1.2 Explain how the unit circle in the
coordinate plane enables the extension of trigonometric
functions to all real numbers, interpreted as radian
measures of angles traversed counterclockwise around the
unit circle.
In this topic, students will find missing
angles and radian measures on a unit
circle using knowledge of special right
triangle and reference angles.
Section 13 - Topic 5
More Conversions with Radians
MAFS.912.F-TF.1.1 Understand radian measure of an angle
as the length of the arc on the unit circle subtended by the
angle; convert between degrees and radians.
In this topic, students will find equivalent
forms of trigonometric functions by
converting between degrees and
radians.
Section 13 - Topic 6
Arc Measure
MAFS.912.F-TF.1.1 Understand radian measure of an angle
as the length of the arc on the unit circle subtended by the
angle; convert between degrees and radians.
In this topic, students will find the length of
the arc on the unit circle subtended by
the angle. Students will also use the arc
length to find the measure of the central
angle, as well as apply their knowledge of
arc length to real-world scenarios.
2016-2017 Math Nation Algebra 2 Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 48
SECTION 14: TRIGONOMETRY – PART 2
Section 14 - Topic 1:
Pythagorean Identity
MAFS.912.F-TF.3.8 Prove the Pythagorean
identity
In this topic, students will prove the Pythagorean
Identitiy, and use it to calculate trigonometric
ratios.
Section 14 - Topic 2:
Sine and Cosine Graph – Part 1
MAFS.912.F-TF.2.5 Choose trigonometric
functions to model periodic phenomena with
specified amplitude, frequency, and midline.
In this topic, students will explore periodic
functions and identify the period, amplitude,
and frequency; and use special right triangle
ratios to graph trigonometric functions.
Section 14 - Topic 3:
Sine and Cosine Graph – Part 2
MAFS.912.F-TF.2.5 Choose trigonometric
functions to model periodic phenomena with
specified amplitude, frequency, and midline.
In this topic, students will explore periodic
functions and identify the period, amplitude,
frequency and midline, and use special right
triangle ratios to graph trigonometric functions.
Section 14 - Topic 4:
Transformations of Trigonometric Functions
MAFS.912.F-TF.2.5 Choose trigonometric
functions to model periodic phenomena with
specified amplitude, frequency, and midline.
In this topic, students will use and apply their
knowledge of transformations to graph various
trigonometric functions. Students will identify key
features of trigonometric functions including
period, amplitude and frequency.
Section 14 - Topic 5:
Modeling with Trigonometric Graphs
MAFS.912.F-TF.2.5 Choose trigonometric
functions to model periodic phenomena with
specified amplitude, frequency, and midline.
In this topic, students will use and apply their
knowledge of transformations solve real-world
problems using trigonometric functions. Students
will identify key features of trigonometric
functions including period, amplitude and
frequency.