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BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
1st 9 Weeks
Domain
Seeing
Structure in
Expressions
Seeing
Structure in
Expressions
Creating
Equations
Creating
Equations
Page 1 of 26
Content
Content Standard Description
Standard
# and
Identifier
12, 12a, Interpret expressions that represent a quantity in terms of
its context.* [A-SSE1]
12b
a). Interpret parts of an expression such as terms,
factors, and coefficients. [A-SSE1a]
b). Interpret complicated expressions by viewing one
or more of their parts as a single entity. [A-SSE1b]
Use the structure of an expression to identify ways to
13
rewrite it. [A-SSE2]
20
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. [A-CED1]
22
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]
AHSGE
ACT/Quality
Core
Standards
Description
G.1.a
F.1.b.
G.1.c
AHSGE:
VII-8
item spec
pg 70-71
Standards
for
Mathematic
al Practice
1, 2, 4, 7
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill
– Algebra 2
1.1, 1.4
2, 7
Precalculus
1.2
D.2.b, E.1.a,
E.1.d, E.2.a,
, G.1.a
1, 2, 4, 5
1.3, 1.4, 1.5,
1.6
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
1.4, 1.5, 1.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
1st 9 Weeks
Domain
Content
Content Standard Description
Standard
# and
Identifier
For a function that models a relationship between two
Arithmetic
18
quantities, interpret key features of graphs and tables in
with
terms of the quantities, and sketch graphs showing key
Polynomials
features given a verbal description of the relationship.
and
Key features include intercepts; intervals where the
Rational
function is increasing, decreasing, positive, or negative;
Expressions
relative maximums and minimums; symmetries; end
behavior; and periodicity.* [F-IF4]
Seeing
Structure in
Expressions
12, 12b
Interpret expressions that represent a quantity in terms of
its context.* [A-SSE1]
b). Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A-SSE1b]
Interpreting
Functions
32
Creating
Equations
21
Compare properties of two functions each represented in
a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). [F-IF9] .
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales. [A-CED2]
Creating
Equations
22
Interpreting
Functions
29
Page 2 of 26
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]
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.*
[F-IF5]
AHSGE
ACT/Quality
Core
Standards
Description
AHSGE:
V-2 item
spec pg 4851
G.1.a
Standards
for
Mathematic
al Practice
2, 4, 5, 6, 7,
8
Quality
Core
Prerequisite
s Skill
1, 2, 4, 7
6, 7
Textbook
Resources
McGraw Hill
– Algebra 2
2.1, 2.1
extend
2.2, 2.2
extend, 2.4,
2.6, 2.7, 2.7
explore
Precalculus
2.2, 2.2
extend
D.2.a, D.2.b,
D.1.c, E.1.d,
E.2.a, E.2.c
1, 2, 4, 5
2.4
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
2.6, 2.7, 2.7
explore, 2.8
E.2.a, E.2.b
2, 4, 6
Precalculus
2.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
1st 9 Weeks
Domain
Content
Content Standard Description
Standard
# and
Identifier
Interpreting 30, 30a Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
Functions
technology for more complicated cases.* [F-IF7]
a. Graph square root, cube root, and piecewise-defined
functions, including step functions and absolute value
functions. [F-IF7b]
Interpreting
Functions
32
Building
Functions
34
Creating
Equations
21
Creating
Equations
22
Page 3 of 26
Compare properties of two functions each represented in
a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). [F-IF9]
Identify the effect on the graph of replacing f(x) by f(x) +
k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology.
Include recognizing even and odd functions from their
graphs and algebraic expressions for them. [F-BF3]
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales. [A-CED2]
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]
AHSGE
AHSGE:
V-I, 4
item specs
pg 40-42
ACT/Quality
Core
Standards
Description
F.2.d, G.2.a
E.2.b
Standards
for
Mathematic
al Practice
2, 7
Quality
Textbook
Core
Resources
Prerequisite McGraw Hill
s Skill
– Algebra 2
Precalculus 2.6
6, 7
Precalculus
2.7, 2.7
explore
4, 5, 7
Precalculus
2.7, 2.7
explore
D.2.a, D.2.b,
D.1.c, E.1.d,
E.2.a, E.2.c
1, 2, 4, 5
3.1
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
3.1, 3.2, 3.3,
3.4
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
1st 9 Weeks
Domain
Reasoning
with
Equations
and
Inequalities
Page 4 of 26
Content
Content Standard Description
Standard
# and
Identifier
Explain why the x-coordinates of the points where the
27
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.* [A-REI11]
AHSGE
ACT/Quality
Core
Standards
Description
D.1.a, D.1.b
Standards
for
Mathematic
al Practice
2, 4, 5, 6
Quality
Textbook
Core
Resources
Prerequisite McGraw Hill
s Skill
– Algebra 2
Precalculus 3.1
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
Content Standard Description
Vector
and
Matrix
Quantitie
s
Vector
and
Matrix
Quantitie
s
Vector
and
Matrix
Quantitie
s
Vector
and
Matrix
Quantitie
s
7
(+) Use matrices to represent and manipulate data, e.g., to
represent payoffs or incidence relationships in a network. (Use
technology to approximate roots.) [N-VM6]
8
(+) Multiply matrices by scalars to produce new matrices, e.g.,
as when all of the payoffs in a game are doubled. [N-VM7]
I.1.a., I.1.b,
I.1.f.
3.5
9
(+) Add, subtract, and multiply matrices of appropriate
dimensions. [N-VM8]
I.1.a., I.1.f.
3.5, 3.6
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]
I.1.a.,
I.1.b., I.1.f.
3.6
Page 5 of 26
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
I.1.f.
Standards
for
Mathematic
al Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
McGraw
Hill –
Algebra 2
3.5
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
Content Standard Description
Vector
and
Matrix
Quantitie
s
Reasonin
g with
Equation
s and
Inequaliti
es
Seeing
Structure
in
Expressio
ns
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.
[N-VM10]
26
(+) Find the inverse of a matrix if it exists and use it to solve
systems of linear equations (using technology for matrices of
dimensions 3x3 or greater). [A-REI9]
I.1.e.
1, 2, 4, 7
3.8
Interpret expressions that represent a quantity in terms of its
context.* [A-SSE1]
a). Interpret parts of an expression such as terms, factors, and
coefficients. [A-SSE1a]
b). Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A-SSE1b]
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.* [F-IF5]
G.1.a
1, 2, 4, 7
4.1, 4.6,
4.7, 4.7
extend, 4.7
explore
Interpreti
ng
Functions
Interpreti
ng
Functions
Page 6 of 26
12, 12a,
12b
29
32
Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in tables,
or by verbal descriptions). [F-IF9]
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
I.1.c., I.1.e.,
I.1.d.
E.2.a, E.2.b
Standards
for
Mathematic
al Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
McGraw
Hill –
Algebra 2
3.7
(example
1), 3.8
2, 4, 6
Precalculus
4.1
6, 7
Precalculus
4.1
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
Content Standard Description
Creating
Equation
s
21
Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate
axes with labels and scales. [A-CED2]
Reasonin
g with
Equation
s and
Inequaliti
es
27
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.* [A-REI11]
Seeing
Structure
in
Expressio
ns
Arithmeti
c with
Polynomi
als and
Rational
Expressio
ns
13
Use the structure of an expression to identify ways to rewrite it.
[A-SSE2]
18
Prove polynomial identities and use them to describe numerical
relationships. [A-APR4]
Page 7 of 26
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
D.2.a,
D.2.b,
D.1.c,
E.1.d, E.2.a,
E.2.c
D.1.a, D.1.b
Standards
for
Mathematic
al Practice
Quality Core
Prerequisites
Skill
2, 4, 5, 6
Precalculus
4.2, 4.2
extend
F.1.b, G.1.c
2, 7
Precalculus
4.3, 4.5
1, 2, 4, 5
7, 8
Textbook
Resources
McGraw
Hill –
Algebra 2
4.2, 4.2
extend
4.3, 4.5,
4.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
Creating
Equation
s
20
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. [A-CED1]
Interpreti
ng
Functions
31
The
Complex
Number
System
The
Complex
Number
System
The
Complex
Number
System
The
Complex
Number
System
Page 8 of 26
Content Standard Description
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
D.2.b,
E.1.a, E.1.d,
E.2.a, ,
G.1.a
Standards
for
Mathematic
al Practice
Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of
the function. [F-IF8]
E.3.a, E.3.b,
E.3.c, E.3.d
2, 7
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. [NCN1]
C.1.a
2, 6
2
Use the relation i2 = –1 and the commutative, associative, and
distributive properties to add, subtract, and multiply complex
numbers. [N-CN2]
C.1.b
2, 7, 8
3
(+) Find the conjugate of a complex number; use conjugates to
find moduli and quotients of complex numbers. [N-CN3]
C.1.a
5
(+) Extend polynomial identities to the complex numbers. [NCN8]
AHSG
E: VII8 item
spec pg
70-71
1, 2, 4, 5
Quality Core
Prerequisites
Skill
Textbook
Resources
McGraw
Hill –
Algebra 2
4.3, 4.5,
4.6, 4.8
4.3, 4.5,
4.7, 4.7
extend, 4.7
explore
4.4
4.4
4.4
4.4, 4.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
2nd 9 Weeks
Domain
Content
Standard
# and
Identifier
The
Complex
Number
System
Creating
Equation
s
Reasonin
g with
Equation
s and
Inequaliti
es
Building
Functions
4
Solve quadratic equations with real coefficients that have
complex solutions. [N-CN7]
23
Rearrange formulas to highlight a quantity of interest, using the
same reasoning as in solving equations. [A-CED4]
1, 2, 4, 5, 7
25
Recognize when the quadratic formula gives complex
solutions, and write them as a+bi for real numbers a and b. [AREI4b]
2, 7, 8
34
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. [A-CED1]
22
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. [ACED3]
Creating
Equation
s
Page 9 of 26
Content Standard Description
AHSGE
AHSG
E: VII8 item
spec pg
70-71
ACT/Qualit
y Core
Standards
Descriptio
n
E.1.c.
Standards
for
Mathematic
al Practice
Quality Core
Prerequisites
Skill
1, 7
Precalculus
E.2.b.
1, 2, 4, 5
D.2.a,
D.2.b,
E.2.c.
1, 2, 4, 5
Textbook
Resources
McGraw
Hill –
Algebra 2
4.5, 4.6
4.6
4.6 and
supplemen
t for a + bi
Precalculus
4.7, 4.7
extend, 4.7
explore
4.8
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Understand that polynomials form a system analogous
Arithme
15
to the integers; namely, they are closed under the
tic with
operations of addition, subtraction, and multiplication;
Polynom
add, subtract, and multiply polynomials. [A-APR1]
ials and
Rational
Expressi
ons
Rewrite simple rational expressions in different forms;
Arithme
19
write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x),
tic with
b(x), q(x), and r(x) are polynomials with the degree of
Polynom
r(x) less than the degree of b(x), using inspection, long
ials and
division, or for the more complicated examples, a
Rational
computer algebra system. [A-APR6]
Expressi
ons
Relate the domain of a function to its graph and, where
Interpre
29
applicable, to the quantitative relationship it describes.*
ting
[F-IF5]
Function
s
Interpre 30, 30b Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
ting
technology for more complicated cases.* [F-IF7]
Function
b. Graph polynomial functions, identifying zeros when
s
suitable factorizations are available, and showing end
behavior. [F-IF7c]
Page 10 of 26
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
A.1.b
2, 7
5.1
F.1.b
2, 5, 7, 8
5.2
E.2.a., E.2.b.
2, 4, 6
Precalculus
5.3
F.2.d, G.2.a.
5, 6
Precalculus
5.3, 5.4, 5.4 extend,
5.6, 5.7, 5.7 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
3rd 9 Weeks
AHSGE
Domain
Content
Content Standard Description
Standar
d # and
Identifie
r
Compare properties of two functions each represented in
Interpre
32
a different way (algebraically, graphically, numerically
ting
in tables, or by verbal descriptions). [F-IF9]
Function
s
Seeing
12, 12b Interpret expressions that represent a quantity in terms
of its context.* [A-SSE1]
Structur
b). Interpret complicated expressions by viewing one
e in
or
more of their parts as a single entity. [A-SSE1b]
Expressi
ons
Create equations and inequalities in one variable and use
Creating
20
them to solve problems. Include equations arising from
Equatio
linear and quadratic functions, and simple rational and
ns
exponential functions. [A-CED1]
Reasoni
ng with
Equatio
ns and
Inequalit
ies
Page 11 of 26
27
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.* [A-REI11]
AHSGE
: VII-8
item
spec pg
70-71
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
6, 7
Precalculus
5.3
G.1.a
1, 2, 4, 7
5.4, 5.4 extend
D.2.b, E.1.a.,
E.1.d., E.2.a.,
G.1.a
1, 2, 4, 5
5.5, 5.5 extend, 5.6,
5.7, 5.7 extend
D.1.a, D.1.b.
2, 4, 5, 6
Precalculus
5.5, 5.5 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Know and apply the Remainder Theorem: For a
Arithme
16
polynomial p(x) and a number a, the remainder on
tic with
division by x – a is p(a), so p(a) = 0 if and only if (x – a)
Polynom
is a factor of p(x). [A-APR2]
ials and
Rational
Expressi
ons
(+) Know the Fundamental Theorem of Algebra; show
The
6
that it is true for quadratic polynomials. [N-CN9]
Complex
Number
System
Identify zeros of polynomials when suitable
Arithme
17
factorizations are available, and use the zeros to
tic with
construct a rough graph of the function defined by the
Polynom
polynomial. [A-APR3]
ials and
Rational
Expressi
ons
Prove polynomial identities and use them to describe
Arithme
18
numerical relationships. [A-APR4]
tic with
Polynom
ials and
Rational
Expressi
ons
Page 12 of 26
ACT/Quality
Core
Standards
Description
F.1.a.
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
2, 3, 8
Precalculus
5.6
F.2.c., E.1.b.
F.1.b., F.2.a.,
F.2.b., E.1.a.,
F.2.d.
5.7. 5.7 extend
1, 2, 4, 5, 8
7, 8
Precalculus
5.7. 5.7 extend
5.7, 5.7 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Compare properties of two functions each represented in
Interpre
32
a different way (algebraically, graphically, numerically
ting
in tables, or by verbal descriptions). [F-IF9]
Function
s
Building 33, 33a Write a function that describes a relationship between
two quantities.* [F-BF1]
Function
a. Combine standard function types using arithmetic
s
operations. [F-BF1b]
Relate the domain of a function to its graph and, where
Interpre
29
applicable, to the quantitative relationship it describes.*
ting
[F-IF5]
Function
s
Building 35, 35a Find inverse functions. [F-BF4]
a.Solve an equation of the form f(x) = c for a simple
Function
function
f that has an inverse, and write an expression
s
for the inverse. [F-BF4a]
Create equations in two or more variables to represent
Creating
21
relationships between quantities; graph equations on
Equatio
coordinate axes with labels and scales. [A-CED2]
ns
Interpre 30, 30a Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
ting
technology for more complicated cases.* [F-IF7]
Function
a. Graph square root, cube root, and piecewise-defined
s
functions, including step functions and absolute value
functions. [F-IF7b]
Page 13 of 26
ACT/Quality
Core
Standards
Description
C.1.d.
E.2.a., E.2.b.
AHSGE
: V-I, 4
item
spec 4041
D.2.a., D.2.b.,
D.1.c., E.1.d.,
E.2.a., E.2.c
F.2.d., G.2.a.
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
6, 7
Precalculus
6.1, 6.3, 6.3 extend
1, 2, 3, 4, 5,
6, 7, 8
2, 4, 6
6.1
Precalculus
6.2, 6.3, 6.3 extend
2, 4, 5, 7
6.2
1, 2, 4, 5
6.3, 6.3 extend
5, 6
Precalculus
6.3, 6.3 extend, 6.4, 6.4
extend,
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Identify the effect on the graph of replacing f(x) by f(x)
Building
34
+ k, k f(x), f(kx), and f(x + k) for specific values of k
Function
(both positive and negative); find the value of k given
s
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]
Use the structure of an expression to identify ways to
Seeing
13
rewrite it. [A-SSE2]
Structur
e in
Expressi
ons
Solve simple rational and radical equations in one
Reasoni
24
variable, and give examples showing how extraneous
ng with
solutions may arise. [A-REI2]
Equatio
ns and
Inequalit
ies
Explain why the x-coordinates of the points where the
Reasoni
27
graphs of the equations y = f(x) and y = g(x) intersect are
ng with
the solutions of the equation f(x) = g(x); find the
Equatio
solutions approximately, e.g., using technology to graph
ns and
the functions, make tables of values, or find successive
Inequalit
approximations. Include cases where f(x) and/or g(x) are
ies
linear, polynomial, rational, absolute value, exponential,
and logarithmic functions.* [A-REI11]
Page 14 of 26
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
4, 5, 7
Precalculus
6.3, 6.3 extend, 6.4, 6.4
extend
F.1.b., G.1.c.
2, 7
Precalculus
6.4, 6.4 extend, 6.5
G.1.b., G.1.c.,
G.1.d., G.1.e.,
G.1.f, G.1.g.
1, 2, 3, 7
Precalculus
6.7, 6.7 extend
D.1.a., D.1.b.
2, 4, 5, 6
Precalculus
6.7, 6.7 extend
E.2.b.
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Relate the domain of a function to its graph and, where
Interpre
29
applicable, to the quantitative relationship it describes.*
ting
[F-IF5]
Function
s
Interpre 30, 30c Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using
ting
technology for more complicated cases.* [F-IF7]
Function
c.) Graph exponential and logarithmic functions,
s
showing intercepts and end behavior, and trigonometric
functions, showing period, midline, and amplitude. [FIF7e]
Write a function defined by an expression in different
Interpre
31
but equivalent forms to reveal and explain different
ting
properties of the function. [F-IF8]
Function
s
Compare properties of two functions each represented in
Interpre
32
a different way (algebraically, graphically, numerically
ting
in tables, or by verbal descriptions). [F-IF9]
Function
s
Identify the effect on the graph of replacing f(x) by f(x)
Building
34
+ k, k f(x), f(kx), and f(x + k) for specific values of k
Function
(both positive and negative); find the value of k given
s
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]
Page 15 of 26
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
E.2.a., E.2.b.
2, 4, 6
Precalculus
7.1, 7.3
F.2.d., G.2.a.
5, 6
Precalculus
7.1, 7.3
E.3.a., E.3.b.,
E.3.c, E.3.d.
2, 7
E.2.b.
7.1, 7.8, 7.8 extend
6, 7
Precalculus
7.1
4, 5, 7
Precalculus
7.1, 7.3
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Domain
Seeing
Structur
e in
Expressi
ons
Creating
Equatio
ns
3rd 9 Weeks
AHSGE
Content
Content Standard Description
Standar
d # and
Identifie
r
Use the structure of an expression to identify ways to
13
rewrite it. [A-SSE2]
20
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. [A-CED1]
Reasoni
ng with
Equatio
ns and
Inequalit
ies
27
Linear,
Quadrati
c, and
Exponen
tial
Models
36
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.* [A-REI11]
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. [F-LE4]
Page 16 of 26
AHSGE
: VII-8
item
spec pg
70-71
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
F.1.b., G.1.c.
2, 7
Precalculus
7.2, 7.2 extend, 7.3,
7.4, 7.7, 7.8, 7.8 extend
D.2.b., E.1.a.,
E.1.d., E.2.a.,
G.1.a.
1, 2, 4, 5
D.1.a., D.1.b.
2, 4, 5, 6
G.2.b.
4, 5, 7
7.2, 7.2 extend, 7.4,
7.5, 7.6, 7.6 extend,
7.8, 7.8 extend
Precalculus
7.2, 7.2 extend, 7.6, 7.6
extend
7.2, 7.2 extend, 7.8, 7.8
extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
3rd 9 Weeks
AHSGE
Domain
Content
Content Standard Description
Standar
d # and
Identifie
r
Represent constraints by equations or inequalities, and
Creating
22
by systems of equations and/or inequalities, and
Function
interpret solutions as viable or nonviable options in a
s
modeling context. [A-CED3]
Building
Function
s
33, 33a
Page 17 of 26
Write a function that describes a relationship between
two quantities.* [F-BF1]
a. Combine standard function types using arithmetic
operations. [F-BF1b]
ACT/Quality
Core
Standards
Description
Standards
for
Mathemati
cal Practice
D.2.a., D.2.b.,
E.2.c.
1, 2, 4, 5
7.8, 7.8 extend
1, 2, 3, 4, 5,
6, 7, 8
7.8, 7.8 extend
C.1.d.
Quality
Core
Prerequisit
es Skill
Textbook Resources
McGraw Hill – Algebra
2
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Content Standard Description
Interpre
ting
Function
s
Building
Function
s
29
Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.* [FIF5]
34
Interpre
ting
Function
s
Creating
Equatio
ns
32
Identify the effect on the graph of replacing f(x) by f(x) + k,
k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing
even and odd functions from their graphs and algebraic
expressions for them. [F-BF3]
Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). [F-IF9]
20
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. [A-CED1]
Creating
Equatio
ns
22
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]
Page 18 of 26
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
E.2.a, E.2.b.
E.2.b.
AHSG
E: VII8 item
spec pg
70-71
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill –
Algebra 2
2, 4, 6
Precalculus
8.3, 8.4
4, 5, 7
Precalculus
8.3
6, 7
Precalculus
8.4
D.2.b.,
E.1.a.,
E.1.d.,
E.2.a.,
G.1.a.
1, 2, 4, 5
8.6, 8.6
extend
D.2.a.,
D.2.b.,
E.2.c.
1, 2, 4, 5
8.6, 8.6
extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Reasoni
ng with
Equatio
ns and
Inequalit
ies
Reasoni
ng with
Equatio
ns and
Inequalit
ies
24
Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may
arise. [A-REI2]
27
Creating
Equatio
ns
Seeing
Structur
e in
Expressi
ons
23
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.* [A-REI11]
Rearrange formulas to highlight a quantity of interest, using
the same reasoning as in solving equations. [A-CED4]
12, 12b
Page 19 of 26
Content Standard Description
Interpret expressions that represent a quantity in terms of its
context.* [A-SSE1]
b). Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A-SSE1b]
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
G.1.b.,
G.1.c.,
G.1.d.,
G.1.e.,
G.1.f.,
G.1.g.
D.1.a.,
D.1.b.
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill –
Algebra 2
1, 2, 3, 7
Precalculus
8.6, 8.6
extend
2, 4, 5, 6
Precalculus
8.6, 8.6
extend
1, 2, 4, 5, 7
G.1.a.
1, 2, 4, 7
9.1, 9.3
9.2, 9.3, 9.4
enrichment,
9.5
enrichment,
9.6, 9.6
enrichment,
9.6 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Creating
Equatio
ns
21
Create equations in two or more variables to represent
relationships between quantities; graph equations on
coordinate axes with labels and scales. [A-CED2]
Interpre
ting
Function
s
32
Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). [F-IF9]
Reasoni
ng with
Equatio
ns and
Inequalit
ies
27
Conic
Sections
28, 28a
Creating
Equatio
ns
23
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.* [A-REI11]
Create graphs of conic sections, including parabolas,
hyperbolas, ellipses, circles, and degenerate conics, from
second-degree equations.
a. Formulate equations of conic sections from their
determining characteristics.
Rearrange formulas to highlight a quantity of interest, using
the same reasoning as in solving equations. [A-CED4]
Page 20 of 26
Content Standard Description
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
D.2.a.,
D.2.b.,
D.1.c.,
E.1.d.,
E.2.a.,
E.2.c.
D.1.a.,
D.1.b.
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
1, 2, 4, 5
Textbook
Resources
McGraw Hill –
Algebra 2
9.3
6, 7
Precalculus
9.6, 9.6
enrichment,
9.6 extend
2, 4, 5, 6
Precalculus
9.7
Precalculus
9.2, 9.3, 9.4,
9.5, 9.6
E.3.a.,
E.3.b.,
E.3.c., E.3.d
1, 2, 4, 5, 7
10.2
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Seeing
Structur
e in
Expressi
ons
Seeing
Structur
e in
Expressi
ons
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
14
12, 12b
Page 21 of 26
Content Standard Description
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
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.* [A-SSE4]
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill –
Algebra 2
3, 4, 7, 8
10.3
10.7
Interpret expressions that represent a quantity in terms of its
context.* [A-SSE1]
b). Interpret complicated expressions by viewing one or
more of their parts as a single entity. [A-SSE1b]
G.1.a.
1, 2, 4, 7
39
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"). [S-CP1]
H.1.a.,
H.1.b.,
H.1.c.,
H.1.e.
1, 2, 4, 6, 7
0.4, 0.5, 0.6
40
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. [S-CP3]
H.1.f.
1, 2, 4, 6, 7
0.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
41
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
42
Page 22 of 26
Content Standard Description
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. [S-CP4]
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
H.1.d.,
H.1.f.
Standards for
Mathematical
Practice
1, 2, 3, 4, 5, 6,
7, 8
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill –
Algebra 2
0.6
Example: Collect data from a random sample of students in
your school on their favorite subject among mathematics,
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.
Recognize and explain the concepts of conditional
probability and independence in everyday language and
everyday situations. [S-CP5]
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.
H.1.d.,
H.1.f.
1, 4, 6, 8
0.4, 0.5, 0.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Content Standard Description
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
43
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]
44
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]
45
(+) 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]
Page 23 of 26
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
H.1.f.
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
Textbook
Resources
McGraw Hill –
Algebra 2
1, 4, 5, 7
0.5
H.1.d.
1, 4, 5, 6, 7
0.5
H.1.d.
1, 4, 5, 6, 7
0.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
4th 9 Weeks
Domain
Content
Standard
# and
Identifier
Conditio
nal
Probabil
ity and
the
Rules of
Probabil
ity
Using
Probabil
ity to
Make
Decision
s
Using
Probabil
ity to
Make
Decision
s
46
(+) Use permutations and combinations to compute
probabilities of compound events and solve problems. [SCP9]
38
(+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a
hockey goalie at the end of a game). [S-MD7]
37
(+) Use probabilities to make fair decisions (e.g., drawing
by lots, using a random number generator). [S-MD6]
Page 24 of 26
Content Standard Description
AHSGE
ACT/Qualit
y Core
Standards
Descriptio
n
H.1.b
H.1.a,
H.1.b,
H.1.c,
H.1.d,
H.1.e,
H.1.f.
H.1.a,
H.1.b,
H.1.c,
H.1.d,
H.1.e,
H.1.f.
Standards for
Mathematical
Practice
Quality
Core
Prerequisite
s Skill
1, 4, 5, 6, 7
Textbook
Resources
McGraw Hill –
Algebra 2
0.4
1, 4, 5, 6, 7
Precalculus
11.3, 11.4,
11.6
1, 4, 5, 6, 7
Precalculus
11.4
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
Essential Vocabulary
st
1 9 Weeks
Chapter 1: algebraic expressions,
order of operations, formula, real
numbers, rational numbers, irrational
numbers, integers, whole numbers,
natural numbers, open sentence,
equation, solution, absolute value,
empty set, constraint, extraneous
solution, set-builder notation,
compound inequality, intersection,
union
Chapter 2: one-to-one function, onto
function, discrete relation,
continuous relation, vertical line test,
independent variable, dependent
variable, function notation, linear
relation, nonlinear relation, linear
equation, standard form, y-intercept,
x-intercept, root, slope, slopeintercept form, point-slope form,
parallel, perpendicular, piecewisedefined function, piecewise-linear
function, step function, greatest
integer function, absolute value
function, family of graphs, parent
graph, parent function constant
function, identity function, quadratic
function, translation, reflection, line
of reflection, dilation, linear
inequality, boundary
Chapter 3: system of equations,
Page 25 of 26
nd
2 9 Weeks
Chapter 3: scalar, scalar
multiplication, determinant, secondorder determinant, third-order
determinant, diagonal rule, identity
matrix, square matrix, inverse matrix,
matrix equation, variable matrix,
constant matrix
Chapter 4: quadratic function,
quadratic term, linear term, constant
term, parabola, axis of symmetry,
vertex, maximum value, minimum
value, quadratic equation, standard
form, root, zero, factored form, FOIL
method, imaginary unit, pure
imaginary number, complex number,
complex conjugates, completing the
square, Quadratic Formula,
discriminant, vertex form, quadratic
inequality
3rd 9 Weeks
Chapter 5: simplify, degree of a
polynomial, synthetic division,
polynomial in one variable, leading
coefficient, polynomial function,
power function, quartic function,
quintic function, end behavior,
Location Principle, relative
maximum, relative minimum,
extrema, turning points, prime
polynomials, quadratic form,
synthetic substitution, depressed
polynomial
Chapter 6: composition of functions,
inverse relation, inverse function,
square root function, radical
function, square root inequality, nth
root, radical sign, index, radicand,
principal root, rationalizing the
denominator, like radical
expressions, conjugate, radical
equation, extraneous solution,
radical inequality
Chapter 7: exponential function,
exponential growth, asymptote,
growth factor, exponential decay,
decay factor, exponential equation,
compound interest, exponential
inequality, logarithm, logarithmic
function, logarithmic equation,
logarithmic inequality, common
4th 9 Weeks
Chapter 8: reciprocal function,
hyperbola, rational function, vertical
asymptote, horizontal asymptote,
oblique asymptote, point
discontinuity, rational equation,
weighted average, rational inequality
Chapter 9: parabola, focus, directrix,
latus rectum, standard form, general
form, circle, center, radius, ellipse,
focus, major axis, minor axis, center,
vertices, co-vertices, constant sum,
hyperbola, transverse axis, conjugate
axis, foci, vertices, co-vertices,
constant difference
Chapter 10: arithmetic means, series,
arithmetic series, partial sum, sigma
notation, geometric means,
geometric series, mathematical
induction, induction hypothesis
Prerequisites Chapter: outcome,
probability experiment, sample
space, tree diagram, permutation,
factorial, combination, probability,
probability model, uniform or simple
probability model, theoretical
probability, experimental probability,
simple event, compound event,
mutually exclusive event, odds,
independent events, dependent
events, conditional probability, two-
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II
break-even point, consistent,
inconsistent, independent,
dependent, substitution method,
elimination method, system of
inequalities, linear programming,
feasible region, bounded,
unbounded, optimize, ordered triple
Page 26 of 26
logarithm, Change of Base Formula,
natural base – e, natural base
exponential function, natural
logarithm
way frequency table
Chapter 11: random variable,
discrete random variable, continuous
random variable, probability
distribution, theoretical probability
distribution, experimental probability
distribution, Law of Large Numbers,
expected value, binomial
experiment, binomial, distribution,
inferential statistics, statistical
inference, confidence interval,
maximum error of estimate,
hypothesis test, null hypothesis,
alternative hypothesis, critical
region, left-tailed test, two-tailed
test, right-tailed test