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COURSE CONTENT
MATHEMATICS
ALGEBRA II
QUALITY
CCRS
EVIDENCE OF STUDENT
ATTAINMENT
CONTENT STANDARDS
RESOURCES
CORE
FIRST SIX WEEKS
27
Explain why the x-coordinates of the points where the graphs of equations y = f(x) and
y = g(x) intersect are solutions of the equations 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. [AREI11]
28
[F-IF.7d] Create graphs of conic sections, including parabolas, hyperbolas, ellipses,
circles, and degenerate conics, from second-degree equations. (Alabama)
Example: Graph x2 - 6x +y2 - 12y + 41 = 0 or y2 - 4x + 2y + 5 = 0.
a.
21
D.2.a
D.2.b
E.2.c
Formulate equations of conic sections from their determining characteristics.
(Alabama)
Example: Write the equation of an ellipse with center (5, -3), a horizontal
major axis of length 10, and a minor axis of length 4.
Answer: (x - 5)/25 +(y + 3)/4 = 1.
Create equations in two or more variables to represent relations between quantities;
graph equations on coordinate axes with labels and scales. [A-CED2]
Students:Given two functions (linear,
polynomial, rational, absolute value,
exponential, and logarithmic) that
intersect (e.g., y= 3x and y= 2x), - Graph
each function and identify the
intersection point(s), - Explain solutions
for f(x) = g(x) as the x-coordinate of the
points of intersection of the graphs, and
explain solution paths (e.g., the values
that make 3x = 2xtrue, are the xcoordinate intersection points of y=3x
and y=2x, - Use technology, tables, and
successive approximations to produce
the graphs, as well as to determine the
approximation of solutions.
Students:
Given a second degree conic equation,






Graph parabolas.
Graph hyperbolas.
Graph ellipses.
Graph circles.
Graph degenerate conics.
Given the determining
characteristics of a conic
section, formulate its equation.
Students:
Given a contextual situation expressing a
relationship between quantities with two
or more variables,

Pages 640-645
Pages 83-89
Model the relationship with
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
equations and graph the
relationship on coordinate axes
with labels and scales.
20
D.2.a
D.2.b
D.1.c
E.1.d
E.2.a
E.2.c
Create equations in one variable and use them to solve problems.[A-CED1]
(Please Note: This standard must be
taught in conjunction with the preceding
standard).
Students:
Given a contextual situation that may
include linear, quadratic, exponential, or
rational functional relationships in one
variable,

7
Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence
relationships in a network. [N-VM6]
8
Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs
of a game are doubled. [N-VM7]
Model the relationship with
equations or inequalities and
solve the problem presented in
the contextual situation for the
given variable.
(Please Note: This standard must be
taught in conjunction with the standard
that follows).
Students:
Given a contextual situation,

Pages 171-178
Represent the data in a matrix
and interpret the value of each
entry.
Students:
Given a matrix,

Pages 282-288
Pages 171-178
Pages 179-186
Use scalar multiplication to
produce a new matrix and
interpret the value of the new
entries.
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
9
Add, subtract, and multiply matrices of appropriate dimensions. [N-VM8]
Students:
Given two matrices,


10
Understand that, unlike multiplication of numbers, matrix multiplication for square
matrices is not a commutative operation, but still satisfies the associative and
distributive properties. [N-VM9]
Determine whether arithmetic
operations (add, subtract,
multiply) are defined.
Perform arithmetic (add,
subtract, multiply) operations
to form new matrices.
Students:
Given two square matrices,

Pages 171-178
Pages 179-186Pages 171-178
Pages 171-178
Demonstrate that
multiplication is not
commutative.
Given a matrix expression with square
matrices,

11
Understand that the zero and identity matrices play a role in matrix addition and
multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse. [NVM10]
Show that the associative and
distributive properties are
satisfied.
Students:
Given a matrix,


Pages 171-178
Add the zero matrix to show
that the matrix does not
change.
Multiply by the identity matrix
to show that the matrix does
not change.
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
Given a square matrix,




21
D.2.a
D.2.b
E.2.c
Create equations in two or more variables to represent relations between quantities;
graph equations on coordinate axes with labels and scales. [A-CED2]
Students:
Given a contextual situation expressing a
relationship between quantities with two
or more variables,

26
I.1.e
Find the inverse of a matrix, if it exists and use it to solve systems of linear equations
(using technology for matrices of dimension 3 x 3 or greater). [A-REI9]
Find the determinant.
If the determinant is non-zero,
find the multiplicative inverse.
Find the multiplicative inverse,
if it is defined, and show that
the determinant is not zero.
If the multiplicative inverse is
not defined, show that the
determinant is equal to zero.
Pages 83-89
Model the relationship with
equations and graph the
relationship on coordinate axes
with labels and scales.
(Please Note: This standard must be
taught in conjunction with the preceding
standard).
Students:
Given a variety of matrices,

Determine the inverse of the
matrix, if it exists, and explain
the conditions under which the
inverse does not exist.
Given a system of linear equations,

Convert the system to a matrix
equation and use this equation
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
to find the solution to the
original system, if one exists,
using technology for
dimension 3 x 3 or greater.
SECOND SIX WEEKS
33
[F-BF.1] Write a function that describes a relationship between two quantities.*
a.
Combine standard function types using arithmetic operations.
Example: Build a function that models the temperature of a cooling body by
adding a constant function to a decaying exponential, and relate these
functions to the model.
Students:
Given two functions represented
differently (algebraically, graphically,
numerically in tables, or by verbal
descriptions),


20
21
D.2.a
D.2.b
D.1.c
E.1.d
E.2.a
E.2.c
D.2.a
D.2.b
E.2.c
[A-CED.1T] Create equations and inequalities in one variable and use them to solve
problems.Include equations arising from linear and quadratic functions, and simple
rational and exponential functions.
Create equations in two or more variables to represent relations between quantities;
graph equations on coordinate axes with labels and scales. [A-CED2]
Use key features to compare
the functions,
Explain and justify the
similarities and differences of
the functions.
Students:
Given a contextual situation that may
include linear, quadratic, exponential, or
rational functional relationships in one
variable,

Pages 385-392
Pages 18-25
Pages 27-32
Pages 33-39
Model the relationship with
equations or inequalities and
solve the problem presented in
the contextual situation for the
given variable.
(Please Note: This standard must be
taught in conjunction with the standard
that follows).
Students:
Given a contextual situation expressing a
relationship between quantities with two
or more variables,
Pages 83-89
5
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MATHEMATICS
ALGEBRA II

29
34
F.2.d
E.2.a
G.2.a
G.3.d
G.3.e
G.3.f
[F-IF.5T] Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
Example: If the functionh(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.*
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), 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-BF3]
Model the relationship with
equations and graph the
relationship on coordinate axes
with labels and scales.
(Please Note: This standard must be
taught in conjunction with the preceding
standard).
Students:
Given a contextual situation that is
functional,

Model the situation with a
graph and construct the graph
based on the parameters given
in the domain of the context.
Students:
Given a function in algebraic form,



Pages 61-67
Pages 109-116
Graph the function, f(x),
conjecture how the graph of
f(x) + k, k f(x), f(kx), and f(x +
k) for specific values of k(both
positive and negative) will
change from f(x), and test the
conjectures,
Describe how the graphs of the
functions were affected (e.g.,
horizontal and vertical shifts,
horizontal and vertical
stretches, or reflections),
Use technology to explain
possible effects on the graph
from adding or multiplying the
input or output of a function by
a constant value,
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COURSE CONTENT
MATHEMATICS
ALGEBRA II

Recognize if a function is even
or odd.
Given the graph of a function and the
graph of a translation, stretch, or
reflection of that function,


29
22
F.2.d
E.2.a
G.2.a
G.3.d
G.3.e
G.3.f
Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. [F-IF5]
Students:
Given a contextual situation that is
functional,

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. [A-CED3]
Determine the value which was
used to shift, stretch, or reflect
the graph,
Recognize if a function is even
or odd.
Model the situation with a
graph and construct the graph
based on the parameters given
in the domain of the context.
Students:
Given a contextual situation involving
constraints,


Pages 61-67
Write equations or inequalities
or a system of equations or
inequalities that model the
situation and justify each part
of the model in terms of the
context,
Solve the equation, inequalities
or systems and interpret the
solution in the original context
including discarding solutions
to the mathematical model that
Pages 146-152
Pages 154-160
Pages 161-167
Pages 189-197
Pages 198-204
Pages 282-288
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MATHEMATICS
ALGEBRA II


13
14
H.2.a
H.2.b
H.2.c
H.2.d
H.2.e
Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Students:

[A-SSE.4T] 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.*
cannot fit the real world
situation (e.g., distance cannot
be negative),
Solve a system by graphing the
system on the same coordinate
grid and determine the point(s)
or region that satisfies all
members of the system,
Determine the point(s) of the
region satisfying all members
of the system that maximizes
or minimizes the variable of
interest in the case of a system
of inequalities.
Pages 238-245
Make sense of algebraic
expressions by identifying
structures within the
expression which allow them
to rewrite it in useful ways.
Students:

Present and defend the
derivation of the formula for
the sum of a finite geometric
series. One approach:
S = a + ar + ar2 + ar3 + . . . +
arn
rS = ar + ar2 + ar3+ . . . + arn+1
rS - S = arn+1 - a = a(rn+1 - 1)
S = a(rn+1 - 1)/(r - 1),

Recognize geometric series
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MATHEMATICS
ALGEBRA II
which exist in problem
situations and use the sum
formula to simplify and solve
problems.
33
Combine standard function types using arithmetic operations. [F-BF1b]
Students:
Given two functions represented
differently (algebraically, graphically,
numerically in tables, or by verbal
descriptions),


12
F.1.b
G.1.c
[A-SSE.1T] Interpret expressions that represent a quantity in terms of its context.*
a.
b.
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a
single entity.For example, interpret P(1+r)nas the product of P and a factor
not depending on P.
Use key features to compare
the functions,
Explain and justify the
similarities and differences of
the functions.
Students:
Given a contextual situation and an
expression that does model it,


Pages 385-392
ALGEBRA II
Pages 5-10
Pages 27-32
Pages 83-89
Connect each part of the
expression to the
corresponding piece of the
situation,
Interpret parts of the
expression such as terms,
factors, and coefficients.
THIRD SIX WEEKS
13
H.2.a
H.2.b
H.2.c
H.2.d
H.2.e
Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Students:

Pages 11-17
Make sense of algebraic
expressions by identifying
structures within the
expression which allow them
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
to rewrite it in useful ways.
32
C.1.d
Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]
Students:
Given two functions represented
differently (algebraically, graphically,
numerically in tables, or by verbal
descriptions),


30
[F-IF.7T] Graph functions expressed symbolically, and show key features of the
graph, by hand in simple cases and using technology for more complicated cases.*
a.
b.
c.
Graph square root, cube root, and piecewise-defined functions, including
step functions and absolute value functions.
Graph polynomial functions, identifying zeros when suitable factorizations
are available, and showing end behavior.
Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and
amplitude.
Use key features to compare
the functions,
Explain and justify the
similarities and differences of
the functions.
Students:
Given a symbolic representation of a
function (including linear, quadratic,
square root, cube root, piecewise-defined
functions, polynomial, exponential,
logarithmic, trigonometric, and (+)
rational),


a.
b.
Pages 69-74
Pages 101-107
Produce an accurate graph (by
hand in simple cases and by
technology in more
complicated cases) and justify
that the graph is an alternate
representation of the symbolic
function,
Identify key features of the
graph and connect these
graphical features to the
symbolic function, specifically
for special functions:
quadratic or linear (intercepts,
maxima, and minima),
square root, cube root, and
10
COURSE CONTENT
MATHEMATICS
ALGEBRA II
c.
d.
e.
f.
31
Write a function defined by an expression in different but equivalent forms to reveal
and explain different properties of the function. [F-IF8]
piecewise-defined functions,
including step functions and
absolute value functions
(descriptive features such as
the values that are in the range
of the function and those that
are not),
polynomial (zeros when
suitable factorizations are
available, end behavior),
(+) rational (zeros and
asymptotes when suitable
factorizations are available,
end behavior),
exponential and logarithmic
(intercepts and end behavior),
trigonometric functions
(period, midline, and
amplitude).
Students:
Given a contextual situation containing a
function defined by an expression,




Pages 451-458
Pages 509-515
Use algebraic properties to
rewrite the expression in a
form that makes key features
of the function easier to find,
Manipulate a quadratic
function by factoring and
completing the square to show
zeros, extreme values, and
symmetry of the graph,
Explain and justify the
meaning of zeros, extreme
values, and symmetry of the
graph in terms of the
contextual situation,
Apply exponential properties
to expressions and explain and
11
COURSE CONTENT
MATHEMATICS
ALGEBRA II
justify the meaning in a
contextual situation.
35
[F-BF.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.
Example: f(x) =2x3 or f(x) = (x+1)/(x-1) for x≠ 1.
Students:
Given a function in algebraic form,




Graph the function, f(x),
conjecture how the graph of
f(x) + k, k f(x), f(kx), and f(x +
k) for specific values of k(both
positive and negative) will
change from f(x), and test the
conjectures,
Describe how the graphs of the
functions were affected (e.g.,
horizontal and vertical shifts,
horizontal and vertical
stretches, or reflections),
Use technology to explain
possible effects on the graph
from adding or multiplying the
input or output of a function by
a constant value,
Recognize if a function is even
or odd.
Given the graph of a function and the
graph of a translation, stretch, or
reflection of that function,


1
C.1.a
Know that there is a complex number i such that i2 = –1, and every complex number
Students:
Determine the value which was
used to shift, stretch, or reflect
the graph,
Recognize if a function is even
or odd.
Pages 246-252
12
COURSE CONTENT
MATHEMATICS
ALGEBRA II
has the form a + bi with a and b real. [N-CN1]
Given an equation wherex2 is less than
zero,


2
C.1.b
Use the relationship i2 = –1 and the commutative, associative, and distributive
properties to add, subtract, and multiply complex numbers. [N-CN2]
Students:

3
Find the conjugate of a complex number; use conjugates to find moduli and quotients
of complex number. [N-CN3]
Explain by repeated reasoning
from square roots in the
positive numbers what
conditions a solution must
satisfy, how defining a
number iby the equation i2= 1 would satisfy those
conditions, and extend the real
numbers to a set called the
complex numbers,
Explain how adding and/or
multiplying i by any real
number results in a complex
number and is real when the
multiplier is zero.
Pages 246-252
Produce equivalent expressions
in the form a + bi, where a and
b are real for combinations of
complex numbers by using
addition, subtraction, and
multiplication and justify that
these expressions are
equivalent through the use of
properties of operations and
equality (Tables 3 and 4).
Students:
Given a complex number,

Pages 245-252
Find the conjugate and the
modulus.
13
COURSE CONTENT
MATHEMATICS
ALGEBRA II
Given a quotient of complex numbers,

4
E.1.c
5
Solve quadratic equations with real coefficients that have complex solutions. [N-CN7]
Students:
Given a contextual situation in which a
quadratic solution is necessary find all
solutions real or complex.
[N-CN.8] (+) Extend polynomial identities to the complex numbers.
Example: Rewrite x2 + 4 as (x + 2i)(x - 2i).
Students:

6
F.2.c
Multiply by 1 by multiplying
the numerator and denominator
by the conjugate of the
denominator to write the
indicated quotient as a single
complex number.
Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials. [N-CN9]
Use properties of operations on
polynomials and the definition
of ito justify that: a2+ b2 =
(a+bi)(a-bi)
Students:
Given a polynomial,

Pages 256-262
Pages 264-272
Pages 358-365
determine the number of
possible roots realizing that
some of them may be complex
or used more than once.
Given a quadratic polynomial,

Show that it has two roots (real
or complex) and find them.
14
COURSE CONTENT
MATHEMATICS
ALGEBRA II
20
D.2.a
D.2.b
D.1.c
E.1.d
E.2.a
E.2.c
Create equations in one variable and use them to solve problems.[A-CED1]
Students:
Given a contextual situation that may
include linear, quadratic, exponential, or
rational functional relationships in one
variable,

Pages 342-349
Model the relationship with
equations or inequalities and
solve the problem presented in
the contextual situation for the
given variable.
(Please Note: This standard must be
taught in conjunction with the standard
that follows).
FOURTH SIX WEEKS
21
D.1.a
D.2.b
E.2.c
Create equations in two or variables to represent relationships between quantities;
graph equations or coordinate axes with labels and scales. [A-CED2]
Students:
Given a contextual situation expressing a
relationship between quantities with two
or more variables,

15
F.1.a
F.1.b
F.2.c
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. [A-APR1]
Model the relationship with
equations and graph the
relationship on coordinate axes
with labels and scales.
(Please Note: This standard must be
taught in conjunction with the preceding
standard).
Students:

Pages 229-236
Pages 303-309
Use the repeated reasoning
from prior knowledge of
properties of arithmetic on
integers to progress
consistently to rules for
arithmetic on polynomials,
15
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MATHEMATICS
ALGEBRA II

16
E.1.a
F.1.b
F.2.a
F.2.b
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)= o if and only of (x – a) is a factor of
p(x). [A-APR2]
Students:
Given a polynomial p(x):


17
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-APR3]


[A-APR.4T] Prove polynomial identities and use them to describe numerical
relationships.
Example: The polynomial identity (x2 + y2)2 = (x2 -y2)2 + (2xy)2 can be used to
generate Pythagorean triples.
Pages 352-357
Identify when (x - a) is a factor
of the given polynomial p(x),
Identify when (x - a)is not a
factor, then the remainder
when p(x) is divided by (x - a)
is p(a).
Students:
Given any polynomial,

18
Accurately perform
combinations of operations on
various polynomials.
Pages 358-365
Analyze and determine if
suitable factorizations exist,
Use the root determined by
these factorizations to
construct a graph of the given
polynomials. The graph should
include all real roots,
Utilize techniques such as
plotting points between and
outside roots or use technology
to find the general shape of the
graph.
Students:

Use properties of operations on
polynomials to justify
identities such as:
16
COURSE CONTENT
MATHEMATICS
ALGEBRA II
1.
2.
3.
4.
5.

19
6
D.2.b
E.1.a
E.1.d
E.2.a
G.1.a
Rewrite simple ration 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
that the degree of b(x), using inspection, long division, or for the more complicated
examples, a computer algebra system. [A-APR6]
F.2.c
Know the Fundamental Theorem of Algebra; show that it is true for quadratic
polynomials. [N-CN9]
(a+b)2 = a2 + 2ab + b2
(a+b)(c+d) = ac + ad + bc + bd
a2 - b2 = (a+b)(a-b)
x2 + (a+b)x + ab = (x + a)(x +
b)
(x2 + y2)2 = (x2 - y2)2 + (2xy)2,
Use these identities to describe
numerical relationships (e.g.,
identity 3 can be used to
mentally compute 79 x 81, or
identity 5 can be used as a
generator for Pythagorean
triples).
Students:
Given a rational expression in the form
a(x)/b(x),

Rewrite rational expressions of
the form q(x) + r(x)/b(x) with
the degree of r(x) less than the
degree of b(x),choosing the
most appropriate technique
from inspection when b(x)is a
common factor of the terms of
a(x), long division for other
examples and a computer
algebra system for more
complicated examples.
Students:
Given a polynomial,

Pages 311-317
Pages 358-365
determine the number of
possible roots realizing that
some of them may be complex
17
COURSE CONTENT
MATHEMATICS
ALGEBRA II
or used more than once.
Given a quadratic polynomial,

16
E.1.a
F.1.b
F.2.a
F.2.b
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)= o if and only of (x – a) is a factor of
p(x). [A-APR2]
Students:
Given a polynomial p(x):


17
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-APR3]


F.1.b
G.1.c
[A-SSE.1T] Interpret expressions that represent a quantity in terms of its context.*
Pages 352-357
Identify when (x - a) is a factor
of the given polynomial p(x),
Identify when (x - a)is not a
factor, then the remainder
when p(x) is divided by (x - a)
is p(a).
Students:
Given any polynomial,

12
Show that it has two roots (real
or complex) and find them.
Pages 358-365
Analyze and determine if
suitable factorizations exist,
Use the root determined by
these factorizations to
construct a graph of the given
polynomials. The graph should
include all real roots,
Utilize techniques such as
plotting points between and
outside roots or use technology
to find the general shape of the
graph.
Students:
Given a contextual situation and an
Pages 264-272
Pages 219-227
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
expression that does model it,
a.
b.
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a
single entity.For example, interpret P(1+r)nas the product of P and a factor
not depending on P.


Connect each part of the
expression to the
corresponding piece of the
situation,
Interpret parts of the
expression such as terms,
factors, and coefficients.
FIFTH SIX WEEKS
13
23
H.2.a
H.2.b
H.2.c
H.2.d
H.2.e
Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Students:

[A-CED.4T] Rearrange formulas to highlight a quantity of interest, using the same
reasoning as in solving equations.
Example: Rearrange Ohm's law V = IR to highlight resistance R.
Make sense of algebraic
expressions by identifying
structures within the
expression which allow them
to rewrite it in useful ways.
Pages 407-414
Pages 415-421
Pages 429-435
Students:

Rearrange formulas which
arise in contextual situations to
isolate variables that are of
interest for particular
problems. For example, if the
electric company charges for
power by the formula COST =
0.03 KWH + 15, a consumer
may wish to determine how
many kilowatt hours they may
use to keep the cost under
particular amounts, by
considering KWH< (COST 15)/0.03 which would yield to
keep the monthly cost under
$75, they need to use less than
2000 KWH.
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COURSE CONTENT
MATHEMATICS
ALGEBRA II
24
Solve simple rational and radical equations in one variable, and give examples
showing how extraneous roots may arise. [A-REI2]
Students:



25
[A-REI.4b] Recognize when the quadratic formula gives complex solutions and write
them as a ± bi form for real numbers a and b. (Alabama)
Pages 570-578
Solve problems involving
rational and radical equations
in one variable,
Identify extraneous solutions
to these equations if any,
Produce examples of equations
that would or would not have
extraneous solutions and
communicate the conditions
that lead to the extraneous
solutions.
Students:






Solve quadratic equations
where both sides of the
equation have evident square
roots by inspection,
Transform quadratic equations
to a form where the square root
of each side of the equation
may be taken, including
completing the square,
Use the method of completing
the square on the equation in
standard form (ax2+bx+c=0) to
derive the quadratic formula,
Identify quadratic equations
which may be solved
efficiently by factoring, and
then use factoring to solve the
equation,
Use the quadratic formula to
solve quadratic equations,
Explain when the roots are real
or complex for a given
quadratic equation, and when
20
COURSE CONTENT
MATHEMATICS
ALGEBRA II

32
C.1.d
Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]
Students:
Given two functions represented
differently (algebraically, graphically,
numerically in tables, or by verbal
descriptions),


30
Graph exponential and logarithmic functions , showing intercepts and end behavior,
and trigonometric functions, showing period, midline, and amplitude. [F-IF7e]
complex write them as a ±
bi for real numbersa and b,
Demonstrate that a proposed
solution to a quadratic equation
is truly a solution by making
the original true.
Use key features to compare
the functions,
Explain and justify the
similarities and differences of
the functions.
Students:
Given a symbolic representation of a
function (including linear, quadratic,
square root, cube root, piecewise-defined
functions, polynomial, exponential,
logarithmic, trigonometric, and (+)
rational),


Pages 219-227
Pages 837-843
Pages 845-852
Produce an accurate graph (by
hand in simple cases and by
technology in more
complicated cases) and justify
that the graph is an alternate
representation of the symbolic
function,
Identify key features of the
graph and connect these
graphical features to the
symbolic function, specifically
21
COURSE CONTENT
MATHEMATICS
ALGEBRA II
for special functions:
a.
b.
c.
d.
e.
f.
36
G.3.c
For exponential models, express as a logarithm the solution to ab ct = d, where a, c, and
d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology.
[F-LE4]
quadratic or linear (intercepts,
maxima, and minima),
square root, cube root, and
piecewise-defined functions,
including step functions and
absolute value functions
(descriptive features such as
the values that are in the range
of the function and those that
are not),
polynomial (zeros when
suitable factorizations are
available, end behavior),
(+) rational (zeros and
asymptotes when suitable
factorizations are available,
end behavior),
exponential and logarithmic
(intercepts and end behavior),
trigonometric functions
(period, midline, and
amplitude).
Students:
Given a contextual situation involving
exponential growth or decay,



Pages 461-467
Pages 509-515
Develop an exponential
function which models the
situation,
Rewrite the exponential
function as an equivalent
logarithmic function,
Use logarithmic properties to
rearrange the logarithmic
function, to isolate the
variable, and use technology to
find an approximation of the
22
COURSE CONTENT
MATHEMATICS
ALGEBRA II
solution.
37
G.3.b
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle. [F-TF1]
Students:
Given a unit circle and an angle that is
defined in terms of a fractional part of a
revolution,


38
Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measure of angles
traversed counterclockwise around the unit circle. [F-TF2]
39
Define the six trigonometric functions using ratios of the sides of a right triangle,
coordinates on the unit circle, and the reciprocal of other functions.
Use the definition of one
radian as the measure of the
central angle of a unit circle
which subtends (cuts off) an
arc of length one to determine
measures of other central
angles as a fraction of a
complete revolution (2π for the
unit circle),
Create a circle in the
coordinate plane other than a
unit circle, and show that an
arc equal in length to the radius
defines a triangle inside the
circle, similar to one in the unit
circle for an arc of length one,
so the angle must have the
same measure.
Students:
Given a contextual situation in which a
decision needs to be made,

Pages 799-806
Pages 830-836
Pages 830-836
Use probability concepts to
analyze, justify, and make
objective decisions.
Students:
Given scenarios involving chance,
Pages 790-798
Pages 799-806
Pages 830-836
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COURSE CONTENT
MATHEMATICS
ALGEBRA II


40
Choose trigonometric functions to model periodic phenomena with specified
amplitude, frequency, and midline. [F-TF5]
Determine the sample space
and a variety of simple and
compound events that may be
defined from the sample space,
Use the language of union,
intersection, and complement
appropriately to define events.
Students:
Given a contextual situation of a periodic
phenomenon that may be modeled by a
trigonometric function,


Pages 837-843
Create a trigonometric function
to model the phenomena,
Use features such as the
specified amplitude, frequency,
and midline of the function to
justify the model.
SIXTH SIX WEEKS
41
[S-MD.6T] (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a
random number generator).
Students:
Given a contextual situation in which a
decision needs to be made,

Pages P9-P12
Use a random probability
selection model to produce
unbiased decisions.
.
42
Analyze decisions and strategies using probability concepts (e.g. product testing,
medical testing, pulling a hockey goalie from the end of a game). [S-MD7]
Students:
Given a contextual situation and
scenarios involving two events,
Pages 742-750
Pages 752-759
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COURSE CONTENT
MATHEMATICS
ALGEBRA II


43
H.1.a-c, e
Describe events as subsets of a sample space(the set of outcomes, using characteristics
or categories of the outcomes, or as unions, intersections, or compliments of other
events) “or”, “and”, not”
Students:
Given scenarios involving chance,


44
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying 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. [S-CP4]
Explain the meaning of
independence from a formula
perspective P(A∩B) = P(A) x
P(B) and from the intuitive
notion that A occurring has no
impact on whether B occurs or
not,
Compare these two
interpretations within the
context of the scenario.
Determine the sample space
and a variety of simple and
compound events that may be
defined from the sample space,
Use the language of union,
intersection, and complement
appropriately to define events.
Students:
Given scenarios involving two
events A and B both when A and B are
independent and when Aand B are
dependent,

Pages P13-P15
Pages P16-P19
Determine the probability of
each individual event, then
limit the sample space to those
outcomes where B has
occurred and calculate the
probability of A, compare
the P(A)and the P(A given B),
and explain the equality or
difference in the original
25
COURSE CONTENT
MATHEMATICS
ALGEBRA II

context of the problem,
Justify that P(A given B) =
P(A∩B)/P(B).
.
45
Construct and interpret two-way frequency tables of data when two categories are
associated each object being classified. Use the two-way table as a sample space to
decide if events are independent and to approximate conditional probabilities. [S-CP4]
Students:
Given a contextual situation consisting
of two events A and B,

46
Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations. [S-CP5]


47
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-CP6]
Use the definition of
conditional probability P(B|A)
= P(A and B)/P(A) to
determine the probability of
the compound event (A and B)
when the P(A|B) and the P(A)
are known or may be
determined. Interpret the
probability as it relates to the
context.
Students:
Given a contextual situation,

Pages 742-750
Pages P16-P19
Choose the appropriate
counting technique
(permutation or combination),
Find the number of ways an
event(s) can occur,
Use these counts to determine
probabilities of the event,
including compound events.
Students:
Given a contextual situation consisting
of two events,
Pages P16-P19
26
COURSE CONTENT
MATHEMATICS
ALGEBRA II


48
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. [S-CP7]
Determine the probability of
each individual event, then
limit the sample space to those
outcomes where B has
occurred and calculate the
probability of A, compare
the P(A)and the P(A given B),
and explain the equality or
difference in the original
context of the problem,
Determine the probability of
each individual event, then
limit the sample space to those
outcomes where B has
occurred and calculate the P(A
and B), compare the ratio
of P(A and B) and P(B) to P(A
given B), and explain the
equality or difference in the
original context of the
problem.
Students:
Given a contextual situation consisting
of two events,




Pages P13-P15
Determine the simple
probability of each event,
Determine the P(A or B) and
P(A and B),
Interpret the Addition Rule by
counting outcomes in the four
events A, B, A and B, A or B
and showing the relationship to
P(A or B) = P(A) + P(B) - P(A
and B),
Interpret the Addition Rule in
the case that the P(A and B) =
27
COURSE CONTENT
MATHEMATICS
ALGEBRA II
0.
49
Apply the general Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8]
Students:
Given a contextual situation consisting
of two events A and B,

50
Use permutations and combinations to compute probabilities of compound events and
solve problems. [S-CP9]
Use the definition of
conditional probability P(B|A)
= P(A and B)/P(A) to
determine the probability of
the compound event (A and B)
when the P(A|B) and the P(A)
are known or may be
determined. Interpret the
probability as it relates to the
context.
Students:
Given a contextual situation,



Pages P16-P19
Pages P9-P12
Choose the appropriate
counting technique
(permutation or combination),
Find the number of ways an
event(s) can occur,
Use these counts to determine
probabilities of the event,
including compound events.
28