NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Number and Quantity
The Real Number System (N.RN)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Extend the properties
of exponents to
rational exponents.
N-RN.1 Explain how the definition of the meaning of
rational exponents follows from extending the properties of
integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents. For example, we
define
to be the cube root of 5 because we want
=
to hold, so
must equal 5.
AII-N.RN.1 Explore how the meaning of rational exponents follows
from extending the properties of integer exponents.
e.g., We define
to be the cube root of 5 because we want
=
to hold, so
must equal 5.
N-RN.2 Rewrite expressions involving radicals and rational
exponents using the properties of exponents.
NYSED: Includes expressions with variable factors, such as
.
AII-N.RN.2 Convert between radical expressions and expressions with
rational exponents using the properties of exponents.
Note: All radical expressions involving variables assume the
variables are representing positive numbers. Includes expressions
with variable factors, such as
, being equivalent to
which equals
.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Number and Quantity
Quantities (N-Q)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Reason quantitatively
and used units to
solve problems. ★
N-Q.2 Define appropriate quantities for the purpose of
descriptive modeling.
PARCC: This standard will be assessed in Algebra II by ensuring that some
modeling tasks (involving Algebra II content or securely held content from
previous grades and courses) require the student to create a quantity of
interest in the situation being described (i.e., this is not provided in the
task). For example, in a situation involving periodic phenomena, the
student might autonomously decide that amplitude is a key variable in a
situation, and then choose to work with peak amplitude.
STANDARD REMOVED
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Number and Quantity
The Complex Number System (N.CN)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Perform arithmetic
operations with
complex numbers.
N-CN.1 Know there is a complex number i such that
= –1, and every complex number has the form a + bi
with a and b real.
AII-N.CN.1 Know there is a complex number i such that
= –1, and
every complex number has the form a + bi with a and b real.
N-CN.2 Use the relation
= –1 and the commutative,
associative, and distributive properties to add, subtract, and
multiply complex numbers.
AII-N.CN.2 Use the relation
= –1 and the commutative, associative,
and distributive properties to add, subtract, and multiply complex
numbers.
Note: Tasks include simplifying powers of i.
Use complex numbers
in polynomial
identities and
equations.
N-CN.7 Solve quadratic equations with real coefficients
that have complex solutions.
STANDARD REMOVED
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Seeing Structure in Expressions (A.SSE)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Interpret the
structure of
expressions.
A-SSE.2 Use the structure of an expression to identify ways
to rewrite it. For example, see
as
,
thus recognizing it as a difference of squares that can be
factored as
.
NYSED: Includes factoring by grouping.
PARCC: i.) Tasks are limited to polynomial, rational, or exponential
expressions. ii.) Examples: see x
4
-y
4
as (x
2
)
2
-(y
2
)
2
, thus recognizing it as a
difference of squares that can be factored as (x
2
-y
2
) (x
2
+y
2
). In recognizing
the equation x
2
+2x+1+y
2
=9, see the opportunity to rewrite the first three
terms as (x+1)
2
, thus recognizing the equation of a circle with radius 3 and
center (-1,0). See (x
2
+4)/ (x
2
+3) as ((x
2
+3) +1)/(x
2
+3), thus recognizing an
opportunity to write it as 1+1/ (x
2
+3).
AII-A.SSE.2 Recognize and use the structure of an expression to
identify ways to rewrite it.
(Shared standard with Algebra I)
e.g.
• 81x
4
- 16y
4
is equivalent to (9x
2
)
2
- (4y
2
)
2
or
(9x
2
- 4y
2
) (9x
2
+ 4y
2
) or (3x + 2y) (3x - 2y) (9x
2
+ 4y
2
)
•
is equivalent to
=
+
= 1 +
• 3x
3
- 5x
2
- 48x + 80 is equivalent to 3x (x
2
- 16) - 5(x
2
- 16),
which when factored completely is (3x - 5) (x + 4) (x - 4)
Notes:
• Includes factoring by grouping and factoring the sum and
difference of cubes.
• Tasks are limited to polynomial, rational, or exponential
expressions. Quadratic expressions include leading
coefficients other than 1.
• This standard is a fluency expectation for Algebra II. The
ability to see structure in expressions and to use this
structure to rewrite expressions is a key skill in everything
from advanced factoring (e.g., grouping) to summing
series, to rewriting of rational expressions, to examining
the end behavior of the corresponding rational function.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Seeing Structure in Expressions (A.SSE)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Write expressions in
equivalent forms to
reveal their
characteristics. ★
A-SSE.3 Choose and produce an equivalent form of an
expression to reveal and explain properties of the quantity
represented by the expression.
AII-A.SSE.3 Choose and produce an equivalent form of an expression
to reveal and explain properties of the quantity represented by the
expression. (Shared standard with Algebra I)
AII-A.SSE.3a Factor a quadratic expression to reveal the zeros of
the function it defines.
A-SSE.3c Use the properties of exponents to transform
expressions for exponential functions. For example the
expression
can be rewritten as
to reveal the approximate equivalent monthly interest rate if
the annual rate is 15%.
PARCC: i) Tasks have a real-world context. As described in the standard,
there is interplay between the mathematical structure of the expression and
the structure of the situation such that choosing and producing an equivalent
form of the expression reveals something about the situation. ii) Tasks are
limited to exponential expressions with rational or real exponents.
AII-A.SSE.3c Use the properties of exponents to rewrite exponential
expressions.
(Shared standard with Algebra I)
Note: Tasks include rewriting exponential expressions with rational
coefficients in the exponent.
A-SSE.4 Derive the formula for the sum of a finite
geometric series (when the common ratio is not 1), and use
the formula to solve problems. For example, calculate
mortgage payments.
NYSED: Includes using summation notation.
STANDARD REMOVED
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Arithmetic with Polynomials and Rational Expressions (A.APR)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand the
relationship between
zeros and factors of
polynomials.
A-APR.2 Know and apply the Remainder Theorem: For
a polynomial p(x) and a number a, the remainder on
division by x – a is p(a), so p(a) = 0 if and only if (x – a)
is a factor of p(x).
AII-A.APR.2 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-APR.3 Identify zeros of polynomials when suitable
factorizations are available, and use the zeros to
construct a rough graph of the function defined by the
polynomial.
PARCC: i) Tasks include quadratic, cubic, and quartic polynomials and
polynomials for which factors are not provided. For example, find the
zeros of (x
2
-1) (x
2
+1).
AII-A.APR.3 Identify zeros of polynomial functions when suitable
factorizations are available.
(Shared standard with Algebra I)
Use polynomial identities
to solve problems.
A-APR.4 Prove polynomial identities and use them to
describe numerical relationships. For example, the
polynomial identity
can be used to generate Pythagorean triples.
STANDARD REMOVED
Rewrite rational
expressions.
A-APR.6 Rewrite simple rational expressions in
different forms; write (a(x)) ⁄(b(x)) in the form
q(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.
AII-A.APR.6 Rewrite simple rational expressions in different forms;
write (a(x)) ⁄(b(x)) in the form q(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).
Note: This standard is a fluency expectation for Algebra II. This
standard sets an expectation that students will divide polynomials
with remainders by inspection in simple cases. For example, one
can view the rational expression
as
which is 1 +
.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Creating Equations (A.CED) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Create equations that
describe numbers or
relationships. ★
A-CED.1 Create equations and inequalities in one variable
and use them to solve problems. Include equations arising
from linear and quadratic functions, and simple rational and
exponential functions. (Tasks are limited to linear,
quadratic, or exponential equations with integer exponents.)
PARCC: i) Tasks are limited to exponential equations with rational or real
exponents and rational functions. ii) Tasks have a real-world context.
AII-A.CED.1 Create equations and inequalities in one variable to
represent a real-world context.
(Shared standard with Algebra I)
Note: This is strictly the development of the model
(equation/inequality). Tasks include linear, quadratic, rational,
and exponential functions.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Reasoning with Equations and Inequalities (A.REI)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand solving
equations as a process
of reasoning and
explain the reasoning.
A-REI.1 Explain each step in solving a simple equation as
following from the equality of numbers asserted at the
previous step, starting from the assumption that the
original equation has a solution. Construct a viable
argument to justify a solution method.
PARCC: i) Tasks are limited to simple rational or radical equations.
AII-A.REI.1b Explain each step when solving rational or radical
equations as following from the equality of numbers asserted at the
previous step, starting from the assumption that the original equation
has a solution. Construct a viable argument to justify a solution
method.
A-REI.2 Solve simple rational and radical equations in
one variable, and give examples showing how extraneous
solutions may arise.
AII-A.REI.2 Solve rational and radical equations in one variable,
identify extraneous solutions, and explain how they arise.
Note: Radical equations may include but are not limited to those of
the form x
3/5
= 8 and 3x
3/4
+ 5 = 86.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Reasoning with Equations and Inequalities (A.REI)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve equations and
inequalities in one
variable.
A-REI.4 Solve quadratic equations in one variable.
AII-A.REI.4 Solve quadratic equations in one variable.
Note: Solutions may include simplifying radicals.
A-REI.4b Solve quadratic equations by inspection (e.g., for
= 49), taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial
form of the equation. Recognize when the quadratic formula
gives complex solutions and write them as a ± bi for real
numbers a and b.
PARCC: i) In the case of equations that have roots with nonzero imaginary
parts, students write the solutions as a±bi for real numbers a and b.
AII-A.REI.4b Solve quadratic equations by:
i) inspection,
ii) taking square roots,
iii) factoring,
iv) completing the square,
v) the quadratic formula, and
vi) graphing.
Write complex solutions in a bi form.
(Shared standard with Algebra I)
Notes:
• An example for inspection would be x
2
= -81, where a
student should know that the solutions would include ±9i.
• An example where students need to factor out a leading
coefficient while completing the square would be
4x
2
+ 8x - 9 = 0.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Algebra
Reasoning with Equations and Inequalities (A.REI)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Solve systems of
equations.
A-REI.6 Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear
equations in two variables.
PARCC/NYSED: i) Tasks are limited to 3x3 systems only. Systems of 3
linear equations with 3 variables only.
STANDARD REMOVED
A-REI.7 Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically. For example, find the points of
intersection between the line and the circle
.
AII-A.REI.7b Solve a system consisting of a linear equation and a
quadratic equation in two variables algebraically and graphically.
(Shared standard with Algebra I)
Note: Conics are limited to parabolas and circles.
Represent and solve
equations and
inequalities
graphically.
A-REI.11 Explain why the x-coordinates of the points
where the graphs of the equations y=f(x) and y=g(x) intersect
are the solutions of the equation f(x)=g(x); find the solutions
approximately, e.g., using technology to graph the functions,
make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial,
rational, absolute value, exponential, and logarithmic
functions.
PARCC: i) Tasks may involve any of the function types mentioned in the
standard.
AII-A.REI.11 Given the equations y = f(x) and y = g(x):
i) recognize that each x-coordinate of the intersection(s) is the solution
to the equation f(x) = g(x);
ii) find the solutions approximately using technology to graph the
functions or make tables of values;
iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and
iv) interpret the solution in context. ★
(Shared standard with Algebra I)
Note: Tasks include cases where f(x) and/or g(x) are linear, polynomial,
absolute value, square root, cube root, trigonometric, exponential,
and logarithmic functions.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Interpreting Functions (F. IF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand the
concept of a function
and use function
notation.
F-IF.3 Recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of the
integers. For example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥
1.
PARCC: i) This standard is supporting work in Algebra II. This standard
should support the major work in F-BF.2 for coherence.
AII-F.IF.3 Recognize that a sequence is a function whose domain is a
subset of the integers.
(Shared standard with Algebra I)
Notes:
• In Algebra II, sequences will be defined/written recursively and
explicitly in subscript notation.
• This standard is a fluency expectation for Algebra II. Fluency in
translating between recursive definitions and closed forms is
helpful when dealing with many problems involving sequences
and series, with applications ranging from fitting functions to
tables to problems in finance.
Interpret functions
that arise in
applications in terms
of the context. ★
F-IF.4 For a function that models a relationship between
two quantities, interpret key features of graphs and tables
in terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship. Key
features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior; and
periodicity.
PARCC: i) Tasks have a real-world context. ii) Tasks may involve
polynomial, exponential, logarithmic, and trigonometric functions.
AII-F.IF.4 For a function that models a relationship between two
quantities:
i) interpret key features of graphs and tables in terms of the quantities;
and
ii) sketch graphs showing key features given a verbal description of the
relationship.
(Shared standard with Algebra I)
Notes:
• Algebra II key features include: intercepts, zeros; intervals where the
function is increasing, decreasing, positive, or negative; relative
maxima and minima; symmetries; end behavior; and periodicity.
• Tasks may involve real-world context and may include polynomial,
square root, cube root, exponential, logarithmic, and trigonometric
functions.
F-IF.6 Calculate and interpret the average rate of change
of a function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a
graph.
PARCC: i) Tasks have a real-world context. ii)Tasks may involve
polynomial, exponential, logarithmic, and trigonometric functions.
AII-F.IF.6 Calculate and interpret the average rate of change of a
function over a specified interval.
(Shared standard with Algebra I)
Notes:
• Functions may be presented by function notation, a table of values,
or graphically.
• Algebra II tasks have a real-world context and may involve
polynomial, square root, cube root, exponential, logarithmic, and
trigonometric functions.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Interpreting Functions (F.IF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Analyze functions
using different
representations.
F-IF.7 Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using technology
for more complicated cases. ★
AII-F.IF.7 Graph functions and show key features of the graph by hand and
using technology when appropriate. ★
(Shared standard with Algebra I)
F-IF.7c Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end behavior.
AII-F.IF.7c Graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
F-IF.7e Graph exponential and logarithmic functions, showing
intercepts and end behavior, and trigonometric functions, showing
period, midline, and amplitude.
AII-F.IF.7e Graph cube root, exponential and logarithmic functions,
showing intercepts and end behavior; and trigonometric functions, showing
period, midline, and amplitude.
Note: Trigonometric functions include sin(x), cos(x) and tan(x).
F-IF.8 Write a function defined by an expression in different but
equivalent forms to reveal and explain different properties of the
function.
AII-F.IF.8 Write a function in different but equivalent forms to reveal and
explain different properties of the function.
(Shared standard with Algebra I)
F-IF.8b Use the properties of exponents to interpret expressions
for exponential functions. For example, identify percent rate of
change in functions such as
,
and classify them as representing
exponential growth or decay.
NYSED: Includes A=Pe
rt
and A=P(1+r/n))
nt
AII-F.IF.8b Use the properties of exponents to interpret exponential
functions, and classify them as representing exponential growth or decay.
Note:
Tasks also include real world problems that involve compounding
growth/decay (A = P(1 + (r/n))
nt
) and continuous compounding
growth/decay (A = Pe
rt
).
F-IF.9 Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in tables, or
by verbal descriptions). For example, given a graph of one
quadratic function and an algebraic expression for another, say
which has the larger maximum.
PARCC: Tasks may involve polynomial, exponential, logarithmic and
trigonometric functions.
AII-F.IF.9 Compare properties of two functions each represented in a
different way (algebraically, graphically, numerically in tables, or by verbal
descriptions).
(Shared standard with Algebra I)
Note:
Tasks may involve polynomial, square root, cube root, exponential,
logarithmic, and trigonometric functions.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Building Functions (F.BF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Build a function that
models a relationship
between two
quantities. ★
F-BF.1 Write a function that describes a relationship
between two quantities.
AII-F.BF.1 Write a function that describes a relationship between two
quantities.
(Shared standard with Algebra I)
F-BF.1a Determine an explicit expression, a recursive
process, or steps for calculation from a context.
PARCC: i) Tasks have a real-world context ii) Tasks may involve linear
functions, quadratic functions, and exponential functions.
AII-F.BF.1a Determine a function from context. Determine an
explicit expression, a recursive process, or steps for calculation from a
context.
(Shared standard with Algebra I)
Notes:
• Tasks may involve linear functions, quadratic functions, and
exponential functions.
• In Algebra II, sequences will be defined/written recursively
and explicitly in subscript notation.
F-BF.1b Combine standard function types using arithmetic
operations. For 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.
AII-F.BF.1b Combine standard function types using arithmetic
operations.
e.g., 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.
F-BF.2 Write arithmetic and geometric sequences both
recursively and with an explicit formula, use them to model
situations, and translate between the two forms.
AII-F.BF.2 Write arithmetic and geometric sequences both recursively
and with an explicit formula, use them to model situations, and
translate between the two forms.
Note:
In Algebra II, sequences will be defined/written recursively and
explicitly in subscript notation.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Building Functions (F.BF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Build new functions
from existing
functions.
F-BF.3 Identify the effect on the graph of replacing f(x) by
f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k
(both positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an explanation
of the effects on the graph using technology. Include
recognizing even and odd functions from their graphs and
algebraic expressions for them.
PARCC: i) Tasks may involve polynomial, exponential, logarithmic, and
trigonometric functions ii) Tasks may involve recognizing even and odd
functions.
AII-F.BF.3b Using f(x) + k, k f(x), f(kx), and f(x + k):
i) identify the effect on the graph when 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);
ii) find the value of k given the graphs;
iii) write a new function using the value of k; and
iv) use technology to experiment with cases and explore the effects on
the graph.
Include recognizing even and odd functions from their graphs.
(Shared standard with Algebra I)
Note:
Algebra II tasks may involve polynomial, square root, cube root,
exponential, logarithmic, and trigonometric functions.
F-BF.4 Find inverse functions.
STANDARD REMOVED
F-BF.4a Solve an equation of the form f(x) = c for a simple
function f that has an inverse and write an expression for the
inverse. For example,
or
f(x) = (x+1)/(x–1) for x ≠ 1.
AII-F.BF.4a Find the inverse of a one-to-one function both
algebraically and graphically.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Building Functions (F.BF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Build new functions
from existing
functions.
AII-F.BF.5a Understand inverse relationships between exponents
and logarithms algebraically and graphically.
AII-F.BF.6 Represent and evaluate the sum of a finite arithmetic
or finite geometric series, using summation (sigma) notation.
AII-F.BF.7 Explore the derivation of the formulas for finite
arithmetic and finite geometric series. Use the formulas to solve
problems. ★
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Linear, Quadratic and Exponential Models (F.LE) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Construct and compare
linear, quadratic and
exponential models and solve
problems
F-LE.2 Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a description
of a relationship, or two input-output pairs (include reading these
from a table).
PARCC: Tasks will include solving multi-step problems by constructing linear
and exponential functions.
AII-F.LE.2 Construct a linear or exponential function
symbolically given:
i) a graph;
ii) a description of the relationship;
and iii) two input-output pairs (include reading these from
a table).
(Shared standard with Algebra I)
F-LE.4 For exponential models, express as a logarithm the
solution to
where a, c, and d are numbers and the base
b is 2, 10, or e; evaluate the logarithm using technology.
AII-F.LE.4 Use logarithms to solve exponential
equations, such as ab
ct
= d (where a, b, c, and d are real
numbers and b > 0) and evaluate the logarithm using
technology.
Interpret expressions for
functions in terms of the
situation they model.
F-LE.5 Interpret the parameters in a linear or exponential
function in terms of a context.
PARCC: i) Tasks have a real-world context. ii) Tasks are limited to exponential
functions with domains not in the integers.
AII-F.LE.5 Interpret the parameters in a linear or
exponential function in terms of a context.
(Shared standard with Algebra I)
Note:
Algebra II tasks have a real-world context and
exponential functions are not limited to integer domains.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Functions
Trigonometric Functions (F.TF)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Extend the domain of
trigonometric functions using
the unit circle.
F-TF.1 Understand radian measure of an angle as
the length of the arc on the unit circle subtended by
the angle.
AII-F.TF.1 Understand radian measure of an angle as the length of the
arc on the unit circle subtended by the angle.
F-TF.2 Explain how the unit circle in the
coordinate plane enables the extension of
trigonometric functions to all real numbers,
interpreted as radian measures of angles traversed
counterclockwise around the unit circle.
NYSED: Includes the reciprocal trigonometric functions.
AII-F.TF.2 Apply concepts of the unit circle in the coordinate
plane to calculate the values of the six trigonometric functions
given angles in radian measure.
AII-F.TF.4 Use the unit circle to explain symmetry (odd and even)
and periodicity of trigonometric functions.
Note:
Focus of this standard is on cos(x), sin(x) and tan(x).
Model periodic phenomena
with trigonometric functions.
★
F-TF.5 Choose trigonometric functions to model
periodic phenomena with specified amplitude,
frequency, and midline.
AII-F.TF.5 Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, horizontal shift, and
midline.
Prove and apply
trigonometric identities.
F-TF.8 Prove the Pythagorean identity
and use it to find sin(θ), cos(θ), or
tan(θ) given sin(θ), cos(θ), or tan(θ) and the
quadrant of the angle.
AII-F.TF.8 Prove the Pythagorean identity sin
2
(θ) + cos
2
(θ) = 1. Find
the value of any of the six trigonometric functions given any other
trigonometric function value and when necessary find the
quadrant of the angle.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Geometry
Expressing Geometric Properties with Equations (G.GPE)
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Translate between the
geometric description and
the equation for a conic
section.
G-GPE.2 Derive the equation of a parabola given a
focus and directrix.
STANDARD REMOVED
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Statistics and Probability ★
Interpreting Categorical and Quantitative Data (S.ID) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Summarize, represent, and
interpret data on a single
count or measurement
variable.
S-ID.4 Use the mean and standard deviation of a data
set to fit it to a normal distribution and to estimate
population percentages. Recognize that there are data
sets for which such a procedure is not appropriate.
Use calculators, spreadsheets, and tables to estimate
areas under the normal curve.
AII-S.ID.4a. Recognize whether or not a normal curve is
appropriate for a given data set.
AII-S.ID.4b If appropriate, determine population percentages
using a graphing calculator for an appropriate normal curve.
Summarize, represent, and
interpret data on two
categorical and quantitative
variables.
S-ID.6 Represent data on two quantitative variables
on a scatter plot, and describe how the variables are
related.
AII-S.ID.6 Represent bivariate data on a scatter plot, and describe
how the variables’ values are related.
Note:
It’s important to keep in mind that the data must be linked to the
same “subjects”, not just two unrelated quantitative variables. Do
not assume that an association between two variables implies that
one causes another to change.
S-ID.6a Fit a function to the data; use functions fitted
to data to solve problems in the context of the data.
Use given functions or choose a function suggested by
the context. Emphasize linear, quadratic, and
exponential models.
PARCC: i) Tasks have a real-world context. ii) Tasks are limited to
exponential functions with domains not in the integers and
trigonometric functions.
AII-S.ID.6a Fit a function to real-world data; use functions fitted to
data to solve problems in the context of the data.
(Shared standard with Algebra I)
Note:
Algebra II emphasis is on quadratic, exponential, and power
models, including the regression capabilities of the calculator.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Statistics and Probability ★
Making Inferences and Justifying Conclusions (S.IC) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand and evaluate
random processes
underlying statistical
experiments.
S-IC.1 Understand statistics as a process for making
inferences about population parameters based on a
random sample from that population.
STANDARD REMOVED
S-IC.2 Decide if a specified model is consistent with
results from a given data-generating process, e.g.,
using simulation. For example, a model says a
spinning coin falls heads up with probability 0.5.
Would a result of 5 tails in a row cause you to
question the model?
AII-S.IC.2 Determine if a value for a sample proportion or sample
mean is likely to occur based on a given simulation.
Note:
For the purposes of this course, if the statistic falls within two
standard deviations of the mean (95% interval centered on the
population parameter), then the statistic is considered likely
(plausible, usual).
Make inferences and justify
conclusions from sample
surveys, experiments and
observational studies.
S-IC.3 Recognize the purposes of and differences
among sample surveys, experiments, and
observational studies; explain how randomization
relates to each.
AII-S.IC.3 Recognize the purposes of and differences among surveys,
experiments, and observational studies. Explain how randomization
relates to each.
S-IC.4 Use data from a sample survey to estimate a
population mean or proportion; develop a margin of
error through the use of simulation models for random
sampling.
AII-S.IC.4 Given a simulation model based on a sample proportion
or mean, construct the 95% interval centered on the statistic (+/-
two standard deviations) and determine if a suggested parameter is
plausible.
S-IC.5 Use data from a randomized experiment to
compare two treatments; use simulations to decide if
differences between parameters are significant.
STANDARD REMOVED
S-IC.6 Evaluate reports based on data.
AII-S.IC.6a Use the tools of statistics to draw conclusions from
numerical summaries.
AII-S.IC.6b Use the language of statistics to critique claims from
informational texts. For example, causation vs correlation, bias,
measures of center and spread.
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Statistics and Probability ★
Conditional Probability and Rules of Probability (S.CP) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Understand independence
and conditional probability
and use them to interpret
data.
S-CP.1 Describe events as subsets of a sample space
(the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,”
“and,” “not”).
AII-S.CP.1 Describe events as subsets of a sample space (the set of
outcomes) using characteristics (or categories) of the outcomes, or as
unions, intersections, or complements of other events (“or,” “and,”
“not”).
S-CP.2 Understand that two events A and B are
independent if the probability of A and B occurring
together is the product of their probabilities, and use
this characterization to determine if they are
independent.
STANDARD REMOVED
S-CP.3 Understand the conditional probability of A
given B as
P (A and B)/P(B), and interpret independence of A
and B as saying that the conditional probability of A
given B is the same as the probability of A, and the
conditional probability of B given A is the same as the
probability of B.
STANDARD REMOVED
S-CP.4 Construct and interpret two-way frequency
tables of data when two categories are associated with
each object being classified. Use the two-way table as
a sample space to decide if events are independent and
to approximate conditional probabilities. For example,
collect data from a random sample of students in your
school on their favorite subject among math, science,
and English. Estimate the probability that a randomly
selected student from your school will favor science
given that the student is in tenth grade. Do the same
for other subjects and compare the results.
AII-S.CP.4 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 calculate conditional probabilities.
S-CP.5 Recognize and explain the concepts of
conditional probability and independence in everyday
language and everyday situations. For example,
compare the chance of having lung cancer if you are
a smoker with the chance of being a smoker if you
have lung cancer.
STANDARD REMOVED
NYSED Algebra II Draft Updated June 2019: Specific modeling domains, clusters and standards are indicated by a star symbol ★.
New York State Next Generation Mathematics Learning Standards
Algebra II Crosswalk
Statistics and Probability ★
Conditional Probability and Rules of Probability (S.CP) ★
Cluster
NYS P-12 CCLS
NYS Next Generation Learning Standard
Use the rules of probability
to compute probabilities of
compound events in a
uniform probability model.
S-CP.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.
STANDARD REMOVED
S-CP.7 Apply the Addition Rule,
P(A or B) = P(A) + P(B) – P(A and B), and interpret
the answer in terms of the model.
AII-S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A
and B), and interpret the answer in terms of the model.
