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BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Seeing
Structure in
Expressions
Content
Standard #
and
Identifier
12, 12a, 12b
Content Standard Description
1st 9 Weeks
AHSGE
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]
Use the structure of an expression to identify
ways to rewrite it. [A-SSE2]
ACT/Quality
Core Standards
Description
Standards for
Mathematical
Practice
G.1.a
1, 2, 4, 7
F.1.b.
G.1.c
2, 7
Quality Core
Prerequisites
Skill
Textbook
Resources
1.1, 1.4
Seeing
Structure in
Expressions
Creating
Equations
13
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]
AHSGE: D.2.b, E.1.a,
VII-8
E.1.d, E.2.a, ,
item
G.1.a
spec pg
70-71
1, 2, 4, 5
1.3, 1.4,
1.5, 1.6
Creating
Equations
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]
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
1.4, 1.5, 1.6
Page 1 of 31
Precalculus
1.2
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Arithmetic
with
Polynomials
and Rational
Expressions
Content
Standard #
and
Identifier
18
Content Standard Description
1st 9 Weeks
AHSGE
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.*
[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]
Page 2 of 31
ACT/Quality
Core Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
2, 4, 5, 6, 7, 8
AHSGE:
V-2
item
spec pg
48-51
G.1.a
D.2.a, D.2.b,
D.1.c, E.1.d,
E.2.a, E.2.c
2.1, 2.1
extend
1, 2, 4, 7
6, 7
1, 2, 4, 5
Textbook
Resources
2.2, 2.2
extend, 2.4,
2.6, 2.7, 2.7
explore
Precalculus
2.2, 2.2
extend
2.4
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Creating
Equations
Content
Standard #
and
Identifier
22
Interpreting
Functions
29
Interpreting
Functions
30, 30a
Interpreting
Functions
32
Page 3 of 31
Content Standard Description
1st 9 Weeks
AHSGE
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]
Graph functions expressed symbolically and
show key features of the graph, by hand in
simple cases and using technology for more
complicated cases.* [F-IF7]
a. Graph square root, cube root, and
piecewise-defined functions, including step
functions and absolute value functions. [FIF7b]
Compare properties of two functions each
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
descriptions). [F-IF9]
ACT/Quality
Core Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
E.2.a, E.2.b
2, 4, 6
Precalculus
2.6
2, 7
Precalculus
2.6
6, 7
Precalculus
2.7, 2.7
explore
AHSGE: F.2.d, G.2.a
V-I, 4
item
specs pg
40-42
2.6, 2.7, 2.7
explore, 2.8
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Building
Functions
Content
Standard #
and
Identifier
34
Creating
Equations
21
Creating
Equations
22
Reasoning
with
Equations
and
Inequalities
27
Page 4 of 31
Content Standard Description
1st 9 Weeks
AHSGE
ACT/Quality
Core Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
4, 5, 7
Precalculus
Textbook
Resources
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]
E.2.b
D.2.a, D.2.b,
D.1.c, E.1.d,
E.2.a, E.2.c
1, 2, 4, 5
3.1
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]
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]
D.2.a, D.2.b,
E.2.c
1, 2, 4, 5
3.1, 3.2,
3.3, 3.4
D.1.a, D.1.b
2, 4, 5, 6
Precalculus
2.7, 2.7
explore
3.1
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Seeing
Structure in
Expressions
Content
Standard #
and
Identifier
12, 12a, 12b
Interpreting
Functions
29
Interpreting
Functions
32
Creating
Equations
21
Reasoning
with
Equations
and
Inequalities
27
Page 5 of 31
Content Standard Description
1st 9 Weeks
AHSGE
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]
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]
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]
ACT/Quality
Core Standards
Description
G.1.a
E.2.a, E.2.b
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
1, 2, 4, 7
Textbook
Resources
4.1, 4.6,
4.7, 4.7
extend, 4.7
explore
2, 4, 6
Precalculus
4.1
6, 7
Precalculus
4.1
D.2.a, D.2.b,
D.1.c, E.1.d,
E.2.a, E.2.c
1, 2, 4, 5
D.1.a, D.1.b
2, 4, 5, 6
4.2, 4.2
extend
Precalculus
4.2, 4.2
extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Seeing
Structure in
Expressions
Arithmetic
with
Polynomials
and Rational
Expressions
Creating
Equations
Content
Standard #
and
Identifier
13
Content Standard Description
1st 9 Weeks
AHSGE
Use the structure of an expression to identify
ways to rewrite it. [A-SSE2]
ACT/Quality
Core Standards
Description
F.1.b, G.1.c
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
2, 7
Precalculus
18
Prove polynomial identities and use them to
describe numerical relationships. [A-APR4]
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]
Interpreting
Functions
31
E.3.a, E.3.b,
E.3.c, E.3.d
2, 7
The
Complex
Number
System
The
Complex
Number
System
1
Write a function defined by an expression in
different but equivalent forms to reveal and
explain different properties of the function. [FIF8]
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. [N-CN1]
C.1.a
2, 6
Use the relation i2 = –1 and the commutative,
associative, and distributive properties to add,
subtract, and multiply complex numbers. [NCN2]
C.1.b
2, 7, 8
Page 6 of 31
2
7, 8
AHSGE: D.2.b, E.1.a,
VII-8
E.1.d, E.2.a, ,
item
G.1.a
spec pg
70-71
1, 2, 4, 5
Textbook
Resources
4.3, 4.5
4.3, 4.5, 4.6
4.3, 4.5,
4.6, 4.8
4.3, 4.5,
4.7, 4.7
extend, 4.7
explore
4.4
4.4
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
The
Complex
Number
System
The
Complex
Number
System
The
Complex
Number
System
Creating
Equations
Reasoning
with
Equations
and
Inequalities
Building
Functions
Page 7 of 31
Content
Standard #
and
Identifier
3
Content Standard Description
1st 9 Weeks
AHSGE
(+) Find the conjugate of a complex number;
use conjugates to find moduli and quotients of
complex numbers. [N-CN3]
5
(+) Extend polynomial identities to the
complex numbers. [N-CN8]
4
Solve quadratic equations with real
coefficients that have complex solutions. [NCN7]
23
Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving
equations. [A-CED4]
Recognize when the quadratic formula gives
complex solutions, and write them as a+bi for
real numbers a and b. [A-REI4b]
25
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]
ACT/Quality
Core Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
C.1.a
Textbook
Resources
4.4
4.4, 4.6
E.1.c.
1, 7
Precalculus
1, 2, 4, 5, 7
4.6
2, 7, 8
AHSGE: E.2.b.
VII-8
item
spec pg
70-71
1, 2, 4, 5
4.5, 4.6
4.6 and
supplement
for a + bi
Precalculus
4.7, 4.7
extend, 4.7
explore
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Creating
Equations
Page 8 of 31
Content
Standard #
and
Identifier
22
Content Standard Description
1st 9 Weeks
AHSGE
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]
ACT/Quality
Core Standards
Description
D.2.a, D.2.b,
E.2.c.
Standards for
Mathematical
Practice
1, 2, 4, 5
Quality Core
Prerequisites
Skill
Textbook
Resources
4.8
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Trigonometric
Functions
Content
Standard #
and
Identifier
39
Trigonometric
Functions
37
Trigonometric
Functions
38
Creating
Equations
21
Interpreting
Functions
29
Page 9 of 31
Content Standard Description
2nd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
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.
Understand radian measure of an angle
as the length of the arc on the unit
circle subtended by the angle. [F-TF1]
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. [F-TF2]
Create equations in two or more
variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
[A-CED2]
G.3.g
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.*
[F-IF5]
E.2.a, E.2.b.
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
12.1, 12.6
G.3.c
6
G.3.b
2, 3, 6
12.6
1, 2, 4, 5
12.7
D.2.a, D.2.b, D.1.c,
E.1.d, E.2.a, E.2.c
2, 4, 6
12.2, 12.6
Precalculus
12.7
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Interpreting
Functions
Content
Standard #
and
Identifier
30, 30c
Trigonometric
Functions
40
Building
Functions
33, 33a
Page 10 of 31
Content Standard Description
2nd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
5, 6
Precalculus
12.7, 12.8, 12.8
explore
Precalculus
12.7, 12.8, 12.8
explore
Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases.* [F-IF7]
c.) Graph exponential and logarithmic
functions, showing intercepts and end
behavior, and trigonometric functions,
showing period, midline, and
amplitude. [F-IF7e]
F.2.d, G.2.a.
Choose trigonometric functions to
model periodic phenomena with
specified amplitude, frequency, and
midline.* [F-TF5]
Write a function that describes a
relationship between two quantities.*
[F-BF1]
a. Combine standard function
types using arithmetic operations. [FBF1b]
G.3.g
4, 5, 7
C.1.d.
1, 2, 3, 4, 5, 6,
7, 8
12.8, 12.8
explore
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Building
Functions
Content
Standard #
and
Identifier
34
Vector and
Matrix
Quantities
7
Vector and
Matrix
Quantities
8
Vector and
Matrix
Quantities
Vector and
Matrix
Quantities
9
Page 11 of 31
10
Content Standard Description
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]
(+) 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]
(+) Multiply matrices by scalars to
produce new matrices, e.g., as when all
of the payoffs in a game are doubled.
[N-VM7]
(+) Add, subtract, and multiply
matrices of appropriate dimensions.
[N-VM8]
(+) 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]
2nd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
E.2.b.
4, 5, 7
Precalculus
Textbook
Resources
12.8, 12.8
explore
I.1.f.
3.5
I.1.a., I.1.b, I.1.f.
3.5
I.1.a., I.1.f.
3.5, 3.6
I.1.a., I.1.b., I.1.f.
3.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Vector and
Matrix
Quantities
Reasoning
with
Equations
and
Inequalities
Page 12 of 31
Content
Standard #
and
Identifier
11
26
Content Standard Description
(+) 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]
(+) 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]
2nd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
I.1.c., I.1.e., I.1.d.
I.1.e.
Quality Core
Prerequisites
Skill
Textbook
Resources
3.7 (example 1),
3.8
2, 4, 5, 6
3.8
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Arithmetic
with
Polynomials
and
Rational
Expressions
Arithmetic
with
Polynomials
and
Rational
Expressions
Interpreting
Functions
Page 13 of 31
Content
Standard #
and
Identifier
15
19
29
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
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]
A.1.b
2, 7
5.1
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. [A-APR6]
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.*
[F-IF5]
F.1.b
2, 5, 7, 8
5.2
E.2.a., E.2.b.
2, 4, 6
Precalculus
5.3
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Interpreting
Functions
Content
Standard #
and
Identifier
30, 30b
Interpreting
Functions
32
Seeing
Structure in
Expressions
12, 12b
Creating
Equations
20
Page 14 of 31
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
F.2.d, G.2.a.
Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases.* [F-IF7]
b. Graph polynomial functions,
identifying zeros when suitable
factorizations are available, and
showing end behavior. [F-IF7c]
Compare properties of two functions
each represented in a different way
(algebraically, graphically,
numerically in tables, or by verbal
descriptions). [F-IF9]
Interpret expressions that represent a
quantity in terms of its context.* [ASSE1]
b). Interpret complicated
expressions by viewing one or more of
their parts as a single entity. [ASSE1b]
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]
AHSGE:
VII-8
item spec
pg 70-71
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
5, 6
Precalculus
5.3, 5.4, 5.4
extend, 5.6,
5.7, 5.7 extend
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
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Reasoning
with
Equations
and
Inequalities
Arithmetic
with
Polynomials
and
Rational
Expressions
The
Complex
Number
System
Arithmetic
with
Polynomials
and
Rational
Expressions
Page 15 of 31
Content
Standard #
and
Identifier
27
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
2, 4, 5, 6
Precalculus
5.5, 5.5 extend
Precalculus
5.6
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]
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). [A-APR2]
D.1.a, D.1.b.
F.1.a.
2, 3, 8
6
(+) Know the Fundamental Theorem
of Algebra; show that it is true for
quadratic polynomials. [N-CN9]
F.2.c., E.1.b.
2, 3, 8
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., F.2.a.,
F.2.b., E.1.a., F.2.d.
16
1, 2, 4, 5, 8
5.7. 5.7 extend
Precalculus
5.7. 5.7 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Arithmetic
with
Polynomials
and
Rational
Expressions
Interpreting
Functions
Content
Standard #
and
Identifier
18
32
Building
Functions
33, 33a
Interpreting
Functions
29
Building
Functions
35, 35a
Page 16 of 31
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Prove polynomial identities and use
them to describe numerical
relationships. [A-APR4]
7, 8
Compare properties of two functions
each represented in a different way
(algebraically, graphically,
numerically in tables, or by verbal
descriptions). [F-IF9]
Write a function that describes a
relationship between two quantities.*
[F-BF1]
a. Combine standard function
types using arithmetic operations. [FBF1b]
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.*
[F-IF5]
Find inverse functions. [F-BF4]
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. [F-BF4a]
6, 7
C.1.d.
E.2.a., E.2.b.
Quality Core
Prerequisites Skill
5.7, 5.7 extend
Precalculus
1, 2, 3, 4, 5, 6,
7, 8
2, 4, 6
2, 4, 5, 7
Textbook
Resources
6.1, 6.3, 6.3
extend
6.1
Precalculus
6.2, 6.3, 6.3
extend
6.2
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Creating
Equations
Content
Standard #
and
Identifier
21
Interpreting
Functions
30, 30a
Building
Functions
34
Seeing
Structure in
Expressions
13
Page 17 of 31
Content Standard Description
Create equations in two or more
variables to represent relationships
between quantities; graph equations on
coordinate axes with labels and scales.
[A-CED2]
Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using 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]
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]
Use the structure of an expression to
identify ways to rewrite it. [A-SSE2]
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
AHSGE:
V-I, 4
item spec
40-41
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
D.2.a., D.2.b.,
D.1.c., E.1.d.,
E.2.a., E.2.c
1, 2, 4, 5
F.2.d., G.2.a.
5, 6
Precalculus
6.3, 6.3 extend,
6.4, 6.4 extend,
4, 5, 7
Precalculus
6.3, 6.3 extend,
6.4, 6.4 extend
2, 7
Precalculus
6.4, 6.4 extend,
6.5
E.2.b.
F.1.b., G.1.c.
6.3, 6.3 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Reasoning
with
Equations
and
Inequalities
Reasoning
with
Equations
and
Inequalities
Interpreting
Functions
Page 18 of 31
Content
Standard #
and
Identifier
24
27
29
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
Solve simple rational and radical
equations in one variable, and give
examples showing how extraneous
solutions may arise. [A-REI2]
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
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]
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.*
[F-IF5]
D.1.a., D.1.b.
2, 4, 5, 6
Precalculus
6.7, 6.7 extend
E.2.a., E.2.b.
2, 4, 6
Precalculus
7.1, 7.3
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Interpreting
Functions
Content
Standard #
and
Identifier
30, 30c
Interpreting
Functions
31
Interpreting
Functions
32
Page 19 of 31
Content Standard Description
Graph functions expressed
symbolically and show key features of
the graph, by hand in simple cases and
using technology for more complicated
cases.* [F-IF7]
c.) Graph exponential and logarithmic
functions, showing intercepts and end
behavior, and trigonometric functions,
showing period, midline, and
amplitude. [F-IF7e]
Write a function defined by an
expression in different but equivalent
forms to reveal and explain different
properties of the function. [F-IF8]
Compare properties of two functions
each represented in a different way
(algebraically, graphically,
numerically in tables, or by verbal
descriptions). [F-IF9]
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
F.2.d., G.2.a.
5, 6
Precalculus
E.3.a., E.3.b., E.3.c,
E.3.d.
2, 7
6, 7
Textbook
Resources
7.1, 7.3
7.1, 7.8, 7.8
extend
Precalculus
7.1
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Building
Functions
Seeing
Structure in
Expressions
Creating
Equations
Page 20 of 31
Content
Standard #
and
Identifier
34
13
20
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Quality Core
Prerequisites Skill
4, 5, 7
Precalculus
7.1, 7.3
F.1.b., G.1.c.
2, 7
Precalculus
D.2.b., E.1.a.,
E.1.d., E.2.a.,
G.1.a.
1, 2, 4, 5
7.2, 7.2 extend,
7.3, 7.4, 7.7,
7.8, 7.8 extend
7.2, 7.2 extend,
7.4, 7.5, 7.6,
7.6 extend, 7.8,
7.8 extend
E.2.b.
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]
Use the structure of an expression to
identify ways to rewrite it. [A-SSE2]
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]
Standards for
Mathematical
Practice
AHSGE:
VII-8
item spec
pg 70-71
Textbook
Resources
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Reasoning
with
Equations
and
Inequalities
Linear,
Quadratic,
and
Exponential
Models
Creating
Functions
Page 21 of 31
Content
Standard #
and
Identifier
27
36
22
Content Standard Description
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
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]
D.1.a., D.1.b.
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]
D.2.a., D.2.b.,
E.2.c.
G.2.b.
Standards for
Mathematical
Practice
Quality Core
Prerequisites Skill
Textbook
Resources
2, 4, 5, 6
Precalculus
7.2, 7.2 extend,
7.6, 7.6 extend
4, 5, 7
7.2, 7.2 extend,
7.8, 7.8 extend
1, 2, 4, 5
7.8, 7.8 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Building
Functions
Page 22 of 31
Content
Standard #
and
Identifier
33, 33a
Content Standard Description
Write a function that describes a
relationship between two quantities.*
[F-BF1]
a. Combine standard function
types using arithmetic operations. [FBF1b]
3rd 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
C.1.d.
Standards for
Mathematical
Practice
1, 2, 3, 4, 5, 6,
7, 8
Quality Core
Prerequisites Skill
Textbook
Resources
7.8, 7.8 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Interpreting
Functions
Content
Standard #
and
Identifier
29
Building
Functions
34
Interpreting
Functions
32
Creating
Equations
20
Page 23 of 31
Content Standard Description
Relate the domain of a function to its
graph and, where applicable, to the
quantitative relationship it describes.*
[F-IF5]
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]
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]
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
E.2.a, E.2.b.
2, 4, 6
Precalculus
8.3, 8.4
E.2.b.
4, 5, 7
Precalculus
8.3
6, 7
Precalculus
8.4
AHSGE: D.2.b., E.1.a.,
VII-8
E.1.d., E.2.a., G.1.a.
item
spec pg
70-71
1, 2, 4, 5
Textbook
Resources
8.6, 8.6 extend
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Creating
Equations
Content
Standard #
and
Identifier
22
Reasoning
with
Equations
and
Inequalities
Reasoning
with
Equations
and
Inequalities
24
Creating
Equations
23
Page 24 of 31
27
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
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]
Solve simple rational and radical
equations in one variable, and give
examples showing how extraneous
solutions may arise. [A-REI2]
D.2.a., D.2.b., E.2.c.
1, 2, 4, 5
G.1.b., G.1.c.,
G.1.d., G.1.e.,
G.1.f., G.1.g.
1, 2, 3, 7
Precalculus
8.6, 8.6 extend
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. [ACED4]
D.1.a., D.1.b.
2, 4, 5, 6
Precalculus
8.6, 8.6 extend
1, 2, 4, 5, 7
8.6, 8.6 extend
9.1, 9.3
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Seeing
Structure in
Expressions
Content
Standard #
and
Identifier
12, 12b
Creating
Equations
21
Interpreting
Functions
32
Reasoning
with
Equations
and
Inequalities
27
Page 25 of 31
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Interpret expressions that represent a
quantity in terms of its context.* [ASSE1]
b). Interpret complicated
expressions by viewing one or more
of their parts as a single entity. [ASSE1b]
G.1.a.
1, 2, 4, 7
Create equations in two or more
variables to represent relationships
between quantities; graph equations
on coordinate axes with labels and
scales. [A-CED2]
Compare properties of two functions
each represented in a different way
(algebraically, graphically,
numerically in tables, or by verbal
descriptions). [F-IF9]
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
D.2.a., D.2.b.,
D.1.c., E.1.d., E.2.a.,
E.2.c.
1, 2, 4, 5
D.1.a., D.1.b.
Quality Core
Prerequisites
Skill
Textbook
Resources
9.2, 9.3, 9.4
enrichment,
9.5
enrichment,
9.6, 9.6
enrichment,
9.6 extend
9.3
6, 7
Precalculus
9.6, 9.6
enrichment,
9.6 extend
2, 4, 5, 6
Precalculus
9.7
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Content
Standard #
and
Identifier
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
functions.* [A-REI11]
Conic
Sections
28, 28a
Creating
Equations
23
Seeing
Structure in
Expressions
14
Seeing
Structure in
Expressions
12, 12b
Conditional
Probability
43
Page 26 of 31
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. [ACED4]
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.* [ASSE4]
Interpret expressions that represent a
quantity in terms of its context.* [ASSE1]
b). Interpret complicated
expressions by viewing one or more
of their parts as a single entity. [ASSE1b]
Describe events as subsets of a
sample space (the set of outcomes),
E.3.a., E.3.b., E.3.c.,
E.3.d
G.1.a.
H.1.a., H.1.b.,
H.1.c., H.1.e.
Precalculus
9.2, 9.3, 9.4,
9.5, 9.6
1, 2, 4, 5, 7
10.2
3, 4, 7, 8
10.3
1, 2, 4, 7
10.7
1, 2, 4, 6, 7
0.4, 0.5, 0.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Content
Standard #
and
Identifier
and the
Rules of
Probability
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Quality Core
Prerequisites
Skill
Textbook
Resources
using characteristics (or categories) of
the outcomes, or as unions,
intersections, or complements of
other events ("or," "and," "not"). [SCP1]
Conditional
Probability
and the
Rules of
Probability
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 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.
Conditional
Probability
and the
Rules of
Probability
45
Construct and interpret two-way
frequency tables of data when two
categories are associated with each
object being classified. Use the twoway table as a sample space to decide
if events are independent and to
approximate conditional probabilities.
[S-CP4]
H.1.d., H.1.f.
Example: Collect data from a random
sample of students in your school on
their favorite subject among
mathematics, science, and English.
Page 27 of 31
Standards for
Mathematical
Practice
1, 2, 4, 6, 7
0.6
1, 2, 3, 4, 5, 6, 7,
8
0.6
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Content
Standard #
and
Identifier
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
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.
Conditional
Probability
and the
Rules of
Probability
46
Conditional
Probability
and the
Rules of
Probability
47
Conditional
Probability
and the
Rules of
Probability
48
Page 28 of 31
H.1.d., H.1.f.
1, 4, 6, 8
0.4, 0.5, 0.6
Find the conditional probability of A
given B as the fraction of B's
outcomes that also belong to A, and
interpret the answer in terms of the
model. [S-CP6]
H.1.f.
1, 4, 5, 7
0.5
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]
H.1.d.
1, 4, 5, 6, 7
0.5
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.
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Domain
Conditional
Probability
and the
Rules of
Probability
Conditional
Probability
and the
Rules of
Probability
Using
Probability
to Make
Decisions
Using
Probability
to Make
Decisions
Page 29 of 31
Content
Standard #
and
Identifier
49
50
42
41
Content Standard Description
4th 9 Weeks
AHSGE
ACT/Quality Core
Standards
Description
Standards for
Mathematical
Practice
Quality Core
Prerequisites
Skill
Textbook
Resources
(+) 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]
(+) Use permutations and
combinations to compute
probabilities of compound events and
solve problems. [S-CP9]
H.1.d.
1, 4, 5, 6, 7
0.6
H.1.b
1, 4, 5, 6, 7
0.4
(+) 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]
(+) Use probabilities to make fair
decisions (e.g., drawing by lots, using
a random number generator). [SMD6]
H.1.a, H.1.b, H.1.c,
H.1.d, H.1.e, H.1.f.
1, 4, 5, 6, 7
Precalculus
11.3, 11.4, 11.6
H.1.a, H.1.b, H.1.c,
H.1.d, H.1.e, H.1.f.
1, 4, 5, 6, 7
Precalculus
11.4
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Essential Vocabulary
1st 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
Page 30 of 31
2nd 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 12: trigonometry,
trigonometric ratio, trigonometric
function, sine, cosine, tangent,
cosecant, secant, cotangent,
reciprocal functions, inverse sine,
inverse cosine, inverse tangent, angle
of elevation, angle of depression,
standard position, initial side,
terminal side, coterminal angles,
radian, central angle, arc length, unit
circle, circular function, periodic
function, cycle, period, amplitude,
frequency, phase shift, vertical shift,
midline
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
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,
BCSS Mathematics Pacing Guide 2013 - 2014
Algebra II with Trig
Essential Vocabulary
st
1 9 Weeks
inequality, boundary
Chapter 3: system of equations,
break-even point, consistent,
inconsistent, independent,
dependent, substitution method,
elimination method, system of
inequalities, linear programming,
feasible region, bounded,
unbounded, optimize, ordered triple
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
Page 31 of 31
nd
2 9 Weeks
3rd 9 Weeks
function, logarithmic equation,
logarithmic inequality, common
logarithm, Change of Base Formula,
natural base – e, natural base
exponential function, natural
logarithm
4th 9 Weeks
independent events, dependent
events, conditional probability, twoway 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