ALGEBRA II PACING GUIDE
No.
Days
10
Strand & Page
Numbers
Chapter 1
Linear Review
FIRST NINE WEEKS
SOL
A.4
The student will solve multistep
linear and quadratic equations in
two variables, including:
d) solving multistep linear
equations algebraically and
graphically;
f) solving real-world problems
involving equations and
systems of equations.
Student Essential Knowledge and Skills
Solve multistep linear equations in one variable.
Confirm algebraic solutions to linear and quadratic
equations, using a graphing calculator.
Determine if a linear equation in one variable has one,
an infinite number, or no solutions.†
Resources
Kuta Software
Worksheets https://www.kut
asoftware.com/f
ree.html
IXL –
https://www.ixl.
com/math/algeb
ra-1
Sections J.1 –
J.9, K.1 – K.15,
T.1 – T.5
Vocabulary
Order of Operations
Expression
Variable
Coefficient
Leading Coeffienct
Term
Linear
Inequality
Slope
Khan Academy –
https://www.kh
anacademy.org/
math/algebra/so
lving-linearequations-andinequalities
10
Chapter 2
Absolute Value
• Equations &
Inequalities
AII.4
The student will solve,
algebraically and graphically,
a) absolute value equations
and inequalities;
AII.6
The student will recognize the
general shape of function
(absolute value, . . . ) families
and will convert between
graphic and symbolic forms of
functions. A transformational
approach to graphing will be
employed.
•
Solve absolute value equations and
inequalities algebraically and graphically.
•
Recognize graphs of parent functions.
•
Given a transformation of a parent
function, identify the graph of the
transformed function.
•
Given the equation and using a
transformational approach, graph a
function.
Kuta Software
Worksheets https://www.kut
asoftware.com/f
ree.html
IXL https://www.ixl.
com/math/algeb
ra-2
Sections B.3 –
B.4, C.7 – C.9
Khan Academy https://www.kh
Absolute Value
Transformation
Equation
Inequalities
Vertex
Maximum
Minimum
20
Chapter 3
Quadratics
• Expressions &
Operations
• Equations &
Inequalities
• Functions
AII.1
The student, given rational,
radical, or polynomial
expressions, will
d) factor polynomials
completely.
SOL AII.4
The student will solve,
algebraically and graphically,
b) quadratic equations over
the set of complex numbers
SOL AII.7
The student will investigate
and analyze functions
algebraically and graphically.
Key concepts include
b)
zeros;
c)
x- and y-intercepts;
AII.8
The student will investigate
and describe the relationships
among solutions of an
equation, zeros of a function,
x-intercepts of a graph, and
factors of a polynomial
expression.
•
Given the graph of a function, identify the
parent function.
•
Given the graph of a function, identify the
transformations that map the preimage to
the image in order to determine the
equation of the image.
•
Using a transformational approach, write
the equation of a function given its graph.
•
Factor polynomials by applying general
patterns including difference of squares,
sum and difference of cubes, and perfect
square trinomials.
•
Factor polynomials completely over the
integers.
•
Verify polynomial identities including the
difference of squares, sum and difference
of cubes, and perfect square trinomials.
•
Solve a quadratic equation over the set of
complex numbers using an appropriate
strategy.
•
Calculate the discriminant of a quadratic
equation to determine the number of real
and complex solutions.
•
Describe the relationships among
solutions of an equation, zeros of a
function, x-intercepts of a graph, and
factors of a polynomial expression.
•
Define a polynomial function, given its
zeros.
anacademy.org/
math/algebra2/
polynomial_and
_rational
Kuta Software
Worksheets https://www.kut
asoftware.com/f
ree.html
IXL https://www.ixl.
com/math/algeb
ra-2
Sections K.1 –
K.19
Khan Academy https://www.kh
anacademy.org/
math/algebra2/
polynomial_and
_rational
Factors
Prime
Polynomials
Binomial
Monomial
Difference of Squares
Quadratic
Zero Product Property
Solutions or Roots
X-Intercepts
Zeros
Quadratic Formula
•
3
Benchmark
Testing
Determine a factored form of a
polynomial expression from the xintercepts of the graph of its
corresponding function.
ALGEBRA II PACING GUIDE
No.
Days
5
11
Strand & Page
Numbers
Chapter 4
Complex
Numbers
• Expressions &
Operations
Chapter 5
Rationals
• Expression &
Operations
2014-2015
SOL
AII.3
The student will perform
operations on complex
numbers,
express the results in simplest
form using patterns of the
powers of i, and identify field
properties that are valid for
the complex numbers.
AII.1
The student, given rational
expressions, will
Student Essential Knowledge and
Skills
• Recognize that the square
root of –1 is represented as i.
•
•
Determine which field
properties apply to the
complex number system.
Simplify radical expressions
containing negative rational
numbers and express in a+bi
form.
•
Simplify powers of i.
•
Add, subtract, and multiply
complex numbers.
•
Place the following sets of
numbers in a hierarchy of
subsets: complex, pure
imaginary, real, rational,
irrational, integers, whole,
and natural.
•
Write a real number in a+bi
form.
•
Write a pure imaginary
number in a+bi form.
•
Add, subtract, multiply, and
divide rational algebraic
expressions.
SECOND NINE WEEKS
Resources
Kuta Software
Worksheets https://www.kutasoftwar
e.com/free.html
IXL https://www.ixl.com/mat
h/algebra-2
Sections H.1 – H.8
Vocabulary
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Irrational Numbers Real
Numbers
Complex Numbers
Properties of Equality &
Inequality
Khan Academy https://www.khanac
ademy.org/math/pre
calculus/imaginary_c
omplex_precalc
Kuta Software
Worksheets https://www.kutasoftwar
e.com/free.html
IXL –
Rational
Discontinuity
Hole
Asymptote:
Horizontal
• Equations &
Inequalities
• Functions
7
Chapter 6
Systems
• Equations &
Inequalities
a) add, subtract, multiply,
divide, and simplify rational
algebraic expressions;
SOL AII.4
The student will solve,
algebraically and graphically,
c) equations containing
rational algebraic expressions;
AII.6
The student will recognize the
general shape of function ( . . .
, rational, . . . ) families and will
convert between graphic and
symbolic forms of functions. A
transformational approach to
graphing will be employed.
AII.7
The student will investigate
and analyze functions
algebraically
and graphically. Key concepts
include
e)
asymptotes
AII.5
The student will solve
nonlinear systems of
equations,
including linear-quadratic and
quadratic-quadratic,
algebraically and graphically.
•
Simplify a rational algebraic
expression with common
monomial or binomial
factors.
https://www.ixl.com/mat
h/algebra-2
Sections N.1 – N.7
Vertical
Common Denominator
Least Common Multiple
Khan Academy https://www.khanacade
my.org/math/algebra2/ra
tional-expressions
•
Solve equations containing
rational algebraic
expressions with monomial
or binomial denominators
algebraically and
graphically.
•
Predict the number of
solutions to a nonlinear
system of two equations.
Kuta Software
Worksheets https://www.kutasoftwar
e.com/free.html
•
Solve a linear-quadratic
system of two equations
algebraically and
graphically.
IXL https://www.ixl.com/mat
h/algebra-1
Sections U.1 – U.15
•
Solve a quadratic-quadratic
system of two equations
algebraically and
graphically.
Khan Academy https://www.khanacade
my.org/math/algebra2/sy
stems_eq_ineq/systems_
tutorial_precalc/e/syste
ms_of_equations
Systems
Substitution
Elimination
Graphing
12
Mid-Term
Review & Testing
7
Chapter 7
Radicals
• Expressions &
Operations
• Equations &
Inequalities
3
Benchmark
Testing
AII.1
The student, given rational,
radical, or polynomial
expressions, will
b) add, subtract, multiply,
divide, and simplify radical
expressions containing rational
numbers and variables, and
expressions containing rational
exponents;
c) write radical expressions as
expressions containing rational
exponents and vice versa
AII.4
The student will solve,
algebraically and graphically,
d) equations containing
radical expressions.
•
Simplify radical expressions
containing positive rational
numbers and variables.
•
Convert from radical
notation to exponential
notation, and vice versa.
•
Add and subtract radical
expressions.
•
Multiply and divide radical
expressions not requiring
rationalizing the
denominators.
•
Solve an equation containing
a radical expression
algebraically and
graphically.
•
Verify possible solutions to
an equation containing
rational or radical
expressions
Kuta Software
Worksheets https://www.kutasoftwar
e.com/free.html
IXL –
https://www.ixl.com/mat
h/algebra-2
Sections N.1 – N.7
Khan Academy https://www.khanacade
my.org/math/algebra2/ra
tional-expressions
Square Root
Cube Root
Nth Root
Simplest Radical Form
Radical Properties:
Product
Quotient
Exponential Form
Negative Exponent
Zero Exponent
Properties:
Product of Powers
Power of a Power
Power of a Product
Quotient of Powers
Power of a Quotient
ALGEBRA II PACING GUIDE
No.
Days
8
7
Strand & Page
Numbers
Chapter 8
Sequences &
Series
• Expressions &
Operations
Chapter 9
Composition of
Functions
• Functions
THIRD NINE WEEKS
SOL
AII.2
The student will investigate
and apply the properties of
arithmetic and geometric
sequences and series to solve
real-world problems, including
writing the first n terms,
finding the nth term, and
evaluating summation
formulas. Notation will
include and an.
AII.7
The student will investigate
and analyze functions
algebraically
and graphically. Key concepts
include
h) composition of multiple
functions.
Student Essential Knowledge and
Skills
• Distinguish between a sequence
and a series.
•
Generalize patterns in a
sequence using explicit and
recursive formulas.
•
Use and interpret the notations
, n, nth term, and an.
•
Given the formula, find an (the
nth term) for an arithmetic or a
geometric sequence.
•
Given formulas, write the first n
terms and find the sum, Sn, of the
first n terms of an arithmetic or
geometric series.
•
Given the formula, find the sum
of a convergent infinite series.
•
Model real-world situations
using sequences and series.
•
Find the composition of two
functions.
•
Use composition of functions to
verify two functions are
inverses.
Resources
Kuta Software Worksheets https://www.kutasoftware.c
om/free.html
IXL –
https://www.ixl.com/math/
algebra-2
Sections BB.1- BB.19
Vocabulary
Sequences
Series
Arithmetic
Geometric
Infinite
Sigma
Summation Notation
Khan Academy https://www.khanacademy.
org/math/integralcalculus/sequences_series_
approx_calc
Kuta Software Worksheets https://www.kutasoftware.c
om/free.html
IXL –
https://www.ixl.com/math/
algebra-2
Sections O.1 – O.9
Function
Function Notation
Composition
Khan Academy https://www.khanacademy.
org/math/algebra2/function
s_and_graphs/function_exp
ressions/e/combiningfunctions-with-arithmeticoperations
12
Chapter 10
Graphs/Function
s
• Functions
AII.6
The student will recognize the
general shape of function
(absolute value, square root,
cube root, rational,
polynomial, exponential, and
logarithmic) families and will
convert between graphic and
symbolic forms of functions. A
transformational approach to
graphing will be employed.
Graphing calculators will be
used as a tool to investigate
the shapes and behaviors of
these functions.
AII.7
The student will investigate
and analyze functions
algebraically
and graphically. Key concepts
include
a) domain and range, including
limited and discontinuous
domains and ranges;
b) zeros;
c) x- and y-intercepts;
d) intervals in which a function
is increasing or decreasing;
f) end behavior;
g) inverse of a function; and
•
Recognize graphs of parent
functions.
•
Given a transformation of a
parent function, identify the
graph of the transformed
function.
•
Given the equation and using a
transformational approach,
graph a function.
•
Given the graph of a function,
identify the parent function.
•
Given the graph of a function,
identify the transformations that
map the preimage to the image
in order to determine the
equation of the image.
•
Using a transformational
approach, write the equation of
a function given its graph.
•
Identify the domain, range,
zeros, and intercepts of a
function presented algebraically
or graphically.
Kuta Software Worksheets https://www.kutasoftware.c
om/free.html
IXL https://www.ixl.com/math/
algebra-2
Multiple Sections
Khan Academy https://www.khanacademy.
org/math/algebra/algebrafunctions
Square Root
Cube Root
Zero Product Property
Relations
Functions
Domain
Range
Parent Functions
Inverse
Exponential
Logarithmic
Graphing calculators will be
used as a tool to assist in
investigation of
functions.
AII.8
The student will investigate
and describe the relationships
among solutions of an
equation, zeros of a function,
x-intercepts of a graph, and
factors of a polynomial
expression.
•
Describe
restricted/discontinuous
domains and ranges.
•
Given the graph of a function,
identify intervals on which the
function is increasing and
decreasing.
•
Find the equations of vertical
and horizontal asymptotes of
functions.
•
Describe the end behavior of a
function.
•
Find the inverse of a function.
•
Graph the inverse of a function
as a reflection across the line
y = x.
•
Investigate exponential and
logarithmic functions, using the
graphing calculator.
•
Convert between logarithmic
and exponential forms of an
equation with bases consisting
of natural numbers.
•
Describe the relationships
among solutions of an equation,
zeros of a function, x-intercepts
of a graph, and factors of a
polynomial expression.
•
Define a polynomial function,
given its zeros.
5
7
Chapter 11
Curve of Best Fit
Chapter 12
Variation
• Statistics
AII.9
The student will collect and
analyze data, determine the
equation of the curve of best
fit, make predictions, and
solve real-world problems,
using mathematical models.
Mathematical models will
include polynomial,
exponential, and logarithmic
functions.
AII.10
The student will identify,
create, and solve real-world
•
Determine a factored form of a
polynomial expression from the
x-intercepts of the graph of its
corresponding function.
•
For a function, identify zeros of
multiplicity greater than 1 and
describe the effect of those zeros
on the graph of the function.
•
Given a polynomial equation,
determine the number of real
solutions and nonreal solutions.
•
Collect and analyze data.
•
Investigate scatterplots to
determine if patterns exist and
then identify the patterns.
•
Find an equation for the curve
of best fit for data, using a
graphing calculator. Models will
include polynomial,
exponential, and logarithmic
functions.
•
Make predictions, using data,
scatterplots, or the equation of
the curve of best fit.
•
Given a set of data, determine
the model that would best
describe the data.
Kuta Software Worksheets https://www.kutasoftware.c
om/free.html
IXL https://www.ixl.com/math/
precalculus/linearregression
Correlation
Linear
Quadratic
Quartic
Exponential
Logarithmic
Khan Academy https://www.khanacademy.
org/math/probability/regres
sion
Kuta Software Worksheets https://www.kutasoftware.c
om/free.html
Variation
Direct
Inverse
problems involving inverse
variation, joint variation, and a
combination of direct and
inverse variations.
3
Benchmark
Testing
•
Translate “y varies jointly as x
and z” as y = kxz.
•
Translate “y is directly
proportional to x” as y = kx.
•
Translate “y is inversely
•
Given a situation, determine the
value of the constant of
proportionality.
•
Set up and solve problems,
including real-world problems,
involving inverse variation, joint
variation, and a combination of
direct and inverse variations.
k
proportional to x” as y = x .
IXL https://www.ixl.com/math/
algebra-2
Sections Q.1 – Q.7
Khan Academy https://www.khanacademy.
org/math/algebra2/rationalexpressions/direct_inverse_
variation
Joint
ALGEBRA II PACING GUIDE
6
10
Chapter 13
Permutations &
Combinations
• Statistics
Chapter 14
Statistics
• Statistics
AII.12
The student will compute and
distinguish between
permutations and
combinations and use
technology for applications.
AII.11
The student will identify
properties of a normal
distribution and apply those
properties to determine
probabilities associated with
areas under the standard
normal curve.
FOURTH NINE WEEKS
•
Compare and contrast
permutations and combinations.
•
Calculate the number of
permutations of n objects taken
r at a time.
•
Calculate the number of
combinations of n objects taken
r at a time.
•
Use permutations and
combinations as counting
techniques to solve real-world
problems.
•
Identify the properties of a
normal probability distribution.
•
Describe how the standard
deviation and the mean affect
the graph of the normal
distribution.
•
Compare two sets of normally
distributed data using a standard
normal distribution and zscores.
•
Represent probability as area
under the curve of a standard
normal probability distribution.
•
Use the graphing calculator or a
standard normal probability
Kuta Software Worksheets https://www.kutasoftware.com/f
ree.html
IXL https://www.ixl.com/math/algebr
a-2
Sections CC.1- CC.12
Permutation
Combination
Fundamental
Counting Principle
Khan Academy https://www.khanacademy.org/
math/probability
Kuta Software Worksheets https://www.kutasoftware.com/f
ree.html
IXL https://www.ixl.com/math/algebr
a-2
Sections CC.13- CC.21
Khan Academy https://www.khanacademy.org/
math/probability
Probability
Mean
Median
Mode
Box-&-Whisker
Plots
Stem & Leaf
Standard
Deviation
Variance
Z-Score
Normal
Distribution
Scatterplot
Outliers
Histograms
table to determine probabilities
or percentiles based on z-scores.
18
9
SOL Review &
Testing
Final Exam
Review & Testing