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Essentials to Algebra 2 Curriculum Map 2012-13
Pacing
Sept
5th –
Sept.
28th
Unit/Essential
Questions
Unit 1: Equations
and Inequalities
How do you solve
absolute value
equation/inequality
and plot on the
number line?
Essential KnowledgeContent/Performance Indicators
(What students must learn)
A2.A.1 Solve absolute value equations
and inequalities involving linear
expressions in one variable
Essential Skills
(What students will be able to do)
Review of Algebra Topics
Student will be able to
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simplify expressions
write and evaluate algebraic
expressions
represent mathematical phrases and
real world quantities using
algebraic expressions
solve multi step equations and
check
distinguish between solution, no
solution and identity
solve literal equations
solve multi step inequalities and
graph them
write inequality from a sentence
using key word at least, at most,
fewer, less, more …
Algebra 2 and Trig. Topics
Students will be able to
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solve absolute value equations and
check
solve absolute value inequalities
and check for extraneous solution
distinguish between an “and”
problem and an “or” problem and
accordingly write the solution
Vocabulary
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Term
Constant
term
Like terms
Coefficient
Expression
Equation
Literal
Equation
Inequality
Absolute
Value
Extraneous
solution
Resources
Pearson NYS Algebra 2
1-3: Algebraic Expressions
(1 day)
1-4: Solving equations.
(4 day)
Supplement with additional
worksheets on equations
with fractional coefficients
1-5: Solving Inequalities
(1 day)
1-6 Absolute Value
Equations
(3 - 4 days)
Essentials to Algebra 2 Curriculum Map 2012-13
Oct 1st
–
Oct
19th
Unit 2: Linear
Equations and
Functions
A2.A.5 Use direct and inverse variation to
solve for unknown values
A2.A.37 Define a relation and function
How do you
distinguish between
Direct and Inverse
variation?
How do you
distinguish between a
relation and a
function?
How do you find the
domain and range of
a function?
How do you
transformation with
functions?
A2.A.38 Determine when a relation is a
function
A2.A.39 Determine the domain and range
of a function from its equation
A2.A.40 Write functions in functional
notation
A2.A.41 Use functional notation to
evaluate functions for given values in the
domain
A2.A.46 Perform transformations with
functions and relations:
f(x + a) , f(x) + a, f(−x), − f(x), af(x)
Review of Algebra Topics
Student will be able to
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Determine if a function is linear
Graph a linear function
with/without a calculator.
Find the Slope of a linear function
given an equation, graph or 2
points
Find the equation for a linear
function given two points or a point
and a graph.
Algebra 2 and Trig. Topics
Student will be able to
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Distinguish between a relation and
a function.
Determine if a relation is a function
given a set of ordered pair,
mapping diagram, graph or table of
values
Distinguish between direct and
indirect variation
Determine of a given function is
direct given a function rule, graph
or table of values
Solve word problems related to
direct and indirect variation (ref. to
regents questions from jmap.org)
Distinguish between parallel and
perpendicular lines.
Do linear regression using a
graphing calculator
Determine the correlation between
the data sets by viewing or plotting
a scatter-plot.
Perform vertical and horizontal
translations
Graph absolute value equations and
perform related translations
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Relation
Function
Vertical line
test
Function Rule
Function
notation
Domain
Range
Direct
Variation
Constant of
Variation
Linear
function
Linear
equation
x-intercept
y-intercept
Slope
Standard
form of linear
function
Slope
intercept form
of linear
function
Point slope
form of linear
function
Line of best
fit
Scatter plot
Correlation
Correlation
coefficient
Regression
Absolute
value
2.1 Relations and functions
Emphasis on domain and
Range
(2 days)
2.2 Direct Variation
(2 days)
2.3 Linear Functions and
slope-intercept Form
(3 days)
2.4 More about Linear
Equations
(1 day)
2.5 Using Linear Model
(1 day)
2.6 Families of functions
(2 – 3 days)
2.7 Absolute value
Functions and Graphs
(1 - 2 days)
Essentials to Algebra 2 Curriculum Map 2012-13
Oct
22nd –
Nov
2nd
Unit 3: Linear
Systems
How can you use a
graph to find the
solution of a system?
How do you solve a
system of equations
by substitution or
elimination?
A.G.7 Graph and solve systems of linear
equations and inequalities with rational
coefficients in two variables
Review of Algebra Topics
Student will be able to
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A.A.10 Solve systems of two linear
equations in two variables algebraically.
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A2.PS.5 Choose an effective approach to
solve systems a problem from a variety of
strategies (numeric, graphic, algebraic)
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How can you solve a
system of inequalities
graphically?
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How can you solve
systems involving
three equations?
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Find the point where the two lines
intersect
Identify the solution to a system of
two lines
Identify a consistent system
Identify an inconsistent system
Identify an independent and
dependent system
Solve a system of equations by
substitution
Solve a system of equations by
elimination
Use substitution or elimination to
solve word problems
Algebra 2 and Trig. Topics
Student will be able to
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Solve a system of inequalities
graphically.
Use a system of inequalities to
model a real situation
Solve a linear and absolute-value
system
solve a system of three equations
using elimination
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System of
equations
Linear system
solution of a
system
inconsistent
system
consistent
system
independent
system
dependent
system
equivalent
systems
at least
at most
3 -1 Solving System Using
Tables and Graphs
(1 - 2 days)
3 - 2 Solving Systems
Algebraically
(2 - 3 days)
3 - 3 Systems of
Inequalities
(2 - 3 days)
3 - 5 Systems with Three
Variables
OPTIONAL
Essentials to Algebra 2 Curriculum Map 2012-13
Nov 5th
–
Dec
21st
Unit 4: Quadratic
Equations and
Functions
How do you perform
transformations of
functions?
How do you factor
completely all types
of quadratic
expressions?
How do you use the
calculator to find
appropriate
regression formulas?
How do you use
imaginary numbers to
find square roots of
negative numbers?
How do you solve
quadratic equations
using a variety of
techniques?
How do you
determine the kinds
of roots a quadratic
will have from its
equation?
How do you find the
solution set for
quadratic
inequalities?
How do you solve
systems of linear and
quadratic equations
graphically and
algebraically?
A2.A.46 Perform transformations with
functions and relations:
f (x + a) , f(x)+ a, f (−x), − f (x), af (x)
A2.A.40 Write functions in functional
notation
A2.A.39 Determine the domain and
range of a function from its
equation
A2.A.7 Factor polynomial expressions
completely, using any combination of the
following techniques: common factor
extraction, difference of two perfect
squares, quadratic trinomials
A2.S.7 Determine the function for the
regression model, using appropriate
technology, and use the regression
function to interpolate and extrapolate
from the data
Review of Algebra Topics
Students will be able to
- use definitions of domain and
range to sketch a quadratic
- factor the difference of two squares
- factor completely
- solve quadratic equations by
factoring
- use a quadratic equation to model a
real situation
- determine a quadratic equation,
given integer roots
- graph linear and quadratic
functions
Algebra 2 and Trig Topics
Students will be able to
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A2.A.20 Determine the sum and
product of the roots of a quadratic
equation by examining its coefficients
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A2.A.21 Determine the quadratic
equation, given the sum and product of
its roots
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A2.A.13 Simplify radical expressions
A2.A.24 Know and apply the
technique of completing the square
A2.A.25 Solve quadratic equations,
using the quadratic formula
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A2.A.2 Use the discriminant to
determine the nature of the roots of a
quadratic equation
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A2.A.4 Solve quadratic inequalities in
one and two variables, algebraically and
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perform horizontal and vertical
translations of the graph of y = x2
graph a quadratic in vertex form:
f(x) =a(x - h)2 + k
identify and label the vertex as ( h ,
k)
identify and label the axis of
symmetry of a parabola
graph parabolas in the form of y =
a x2 with various values of a
graph a quadratic in vertex form:
f(x) = ax2+bx+c
find the axis of symmetry
algebraically using the standard
form of the equation
identify the y-intercept as ( 0, c )
find the vertex of a parabola
algebraically using the standard
form of the equation
identify the range of parabolas
sketch a graph of a parabola after
finding the axis of symmetry, the
vertex, and the y-intercept
use the calculator to find a
quadratic regression equation
factor using “FOIL”
finding a GCF
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Parabola
Quadratic
function
Vertex form
Axis of
symmetry
Vertex of
the parabola
Maximum
Minimum
Standard
form
Domain and
Range
Regressions
Factoring
Greatest
Common
Factor
Perfect
square
trinomial
Difference
of two
squares
Zero of a
function
(root)
Discriminan
t
Imaginary
numbers
Complex
numbers
Conjugates
4-1 Quadratic functions and
transformations
(2 – 3 days)
4-2 Standard form of a
quadratic function
(2 days)
4-3 Modeling with quadratic
functions
(1 - 2 days)
4-4 Factoring quadratic
expressions (4 days)
4-5 Quadratic equations (12 days)
4-6 Completing the square
(2 -3 days)
4-7 Quadratic Formula (2
days)
4-8 Complex Numbers
(4 - 5 days)
Additional resource at
www.emathinstruction.com
Quadratic Inequalities Page
256-257 (1 day)
4-9 Quadratic Systems
(2 days)
Essentials to Algebra 2 Curriculum Map 2012-13
graphically
A2.A.3
Solve systems of equations
involving one linear equation and one
quadratic equation algebraically
Note: This includes rational
equations that result in linear
equations with extraneous roots.
A2.N6 Write square roots of negative
numbers in terms of i
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A2.N9 Perform arithmetic operations on
complex numbers and write the answer in
the form a+bi
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perfect square trinomials
difference of two squares
zero product property
finding the sum and product of
roots
writing equations knowing the
roots or knowing the sum and
product of the roots
solve by taking square roots
solve by completing the square
solve by using the quadratic
formula
use the discriminant to find the
nature of the roots
simplify expressions containing
complex numbers (include
rationalizing the denominator)
solve quadratic inequalities
solve systems of quadratics
algebraically
Essentials to Algebra 2 Curriculum Map 2012-13
Jan 2nd
– Jan
11th
Unit 5: Polynomials
How do you perform
arithmetic operations
with polynomial
expressions?
How do you factor
polynomials?
How do you solve
polynomial equation?
How do you expand a
polynomial to the nth
Order?
How do you find the
nth term of a binomial
expansion?
A2.N.3 Perform arithmetic operations
with polynomial expressions containing
rational coefficients
A2.A.7 Factor polynomial expressions
completely, using any combination of the
following techniques: common factor
extraction, difference of two perfect
squares, quadratic trinomials
Review of Algebra Topics
Student will be able to
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Algebra 2 and Trig Topics
Students will be able to
A2.A.26 Find the solution to polynomial
equations of higher degree that can be
solved using factoring and/or the
quadratic formula
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A2.A.50 Approximate the solution to
polynomial equations of higher degree by
inspecting the graph
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A2.A.36 Apply the binomial theorem to
expand a binomial and determine a
specific term of a binomial expansion
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Jan
14th –
Jan
18th
MIDTERM REVIEW
January 22nd – January 25th Midterm Exam Week
combine like terms
subtract polynomial expressions
multiply monomials, binomials and
trinomials
recognize and classify polynomials
factor polynomials using common
factor extraction, difference of two
perfect squares and or trinomial
factoring.
Write a polynomial function given
its roots.
Solve polynomial equations /find
the roots graphically.
Apply the Binomial Theorem to
expand a binomial expression
Find a specific term of a binomial
expansion.
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Polynomial
Monomial
Binomial
Trinomial
Degree
Root
Solution
Zero
Property
5-1 Polynomial Functions
(1 day)
5-2 Polynomials, Linear
Factors and Zeros
(1 day)
5-3 Solving Polynomial
Equations
(2 days)
5-7 The Binomial Theorem
(2 days)
Essentials to Algebra 2 Curriculum Map 2012-13
Jan
28th –
Mar 8
Unit 6: Radical
Functions, Rational
Exponents,
Function
Operations
How do you write
algebraic expressions
in simplest radical
form?
How do you simplify
by rationalizing the
denominator?
A2.N.1 Evaluate numerical expressions
with negative and/or fractional
exponents, without the aid of a calculator
(when the answers are rational numbers
A2.N.2 Perform arithmetic operations
with expressions containing irrational
numbers in radical form
A2.N.4 Perform arithmetic operations on
irrational expressions
A2.A.8 Use rules of exponents to
simplify expressions involving negative
and/or rational exponents
How do you express
sums and differences
of radical expressions
in simplest form?
A2.A.9 Rewrite expressions that contain
negative exponents using only positive
exponents
How do you write
radicals with
fractional exponents?
A2.A.10 Rewrite algebraic expressions
with fractional exponents as radical
expressions
How do you change
an expression with a
fractional exponent
into a radical
expression?
A2.A.11 Rewrite radical expressions as
algebraic expressions with fractional
exponents
How do you solve
radical equations?
How do you add,
subtract, multiply,
and divide functions?
A2.A.12 Evaluate exponential
expressions
A2.A.13 Simplify radical expressions
A2.A.14 Perform basic operations on
radical expressions
A2.N.5 Rationalize a denominator
containing a radical expression
A2.A.15 Rationalize denominators of
algebraic radical expressions
A2.A.22 Solve radical equations
Review of Algebra Topics
Student will be able to
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Use rules of positive and negative
exponents in algebraic
computations
Use squares and cubes of numbers
Know square roots of perfect
squares from 1-15
Algebra 2 and Trig Topics
Students will be able to
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Simplify radical expressions
Multiply and divide radical
expressions
Add and subtract radical
expressions
Use rational exponents
Solve radical equations and check
for extraneous roots
Add, subtract, multiply, and divide
functions
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Exponents
Conjugates
Radicals
Rationalize
the
denominator
Extraneous
roots
f- 1(x)
inverse of a
function
one to one
onto
Page 360 Properties of
exponents (2days)
6-1 Simplify radical
expressions (2 days)
6-2 Multiply and divide
radical expressions (2-3
days)
6-3 Binomial Radical
Expressions (1 day)
6-4 Rational Exponents
(2 days)
6-5 Solve radical equations
(2-3 days)
Essentials to Algebra 2 Curriculum Map 2012-13
Mar 11
– April
19
Unit 7:Exponential
and Logarithmic
Functions
How do you model a
quantity that changes
regularly over time
by the same
percentage?
How are exponents
and logarithms
related?
How are exponential
functions and
logarithmic functions
related?
A2.A.6 Solve an application with results
in an exponential function.
A2.A.12 Evaluate exponential
expressions, including those with base e.
Students will be able to:
- model exponential growth and
decay
- explore the properties of functions
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of the form y  ab
graph exponential functions that
have base e
write and evaluate logarithmic
expressions
graph logarithmic functions
derive and use the properties of
logarithms to simplify and expand
logarithms.
solve exponential and logarithmic
equations
evaluate and simplify natural
logarithmic expressions
solve equations using natural
logarithms
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x
A2.A.53 Graph exponential functions of
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the form. y  b for positive values of b,
including b = e.
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x
A2.A.18 Evaluate logarithmic
expressions in any base
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A2.A.54 Graph logarithmic functions,
using the inverse of the related
exponential function.
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A2.A.51 Determine the domain and range
of a function from its graph.
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A2.A.19 Apply the properties of
logarithms to rewrite logarithmic
expressions in equivalent forms.
A2.A. 27 Solve exponential equations
with and without common bases.
A2.A. 28 Solve a logarithmic equations
by rewriting as an exponential equation.
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asymptote
change of
base
formula
common
logarithm
exponentia
l equation
exponentia
l function
exponentia
l decay
exponentia
l growth
logarithm
logarithmic
equation
logarithmic
function
natural
logarithmic
function
7 -1 Exploring Exponential
Models (1 day)
7 – 3 Logarithmic Functions
as Inverses
(2 days)
7 - 4 Properties of
Logarithms
(2 – 3 days)
7 - 5 Exponential and
Logarithmic Equations
(3 days)
7 - 6 Natural Logarithms
pg 478
(2 days)
Essentials to Algebra 2 Curriculum Map 2012-13
April
22May
24
Unit 8: Rational
Expressions and
Functions
How do we perform
arithmetic operations
on rational
expressions?
How do we simplify
a complex fraction?
How do we solve a
rational equation?
A2.A.16 Perform arithmetic operations
with rational expressions and rename to
lowest terms
A2.A.17 Simplify complex fractional
expressions
A2.A.23 Solve rational equations and
inequalities
Review of Algebra Topics
All topics in this unit except complex
fractions are taught in Integrated Algebra.
In Algebra most problems involve
monomials and simple polynomials. In
Algebra 2 factoring becomes more complex
and may require more than one step to factor
completely.
Algebra 2 Topics
Students will be able to
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Simplify a rational expression to
lowest terms by factoring and
reducing
State any restrictions on the
variable
Multiply and divide rational
expressions
Add and subtract rational
expressions
Simplify a complex fraction
Solve rational equations
(inequalities will be saved for the
Alg 2 course)
Simplest form
Rational
Expression
 Common
factors
 Reciprocal
 Least
Common
Multiple
 Lowest
Common
Denominato
r
 Common
factors
 Complex
Fraction
 Rational
equation
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8-4 Rational Expressions (34 days)
8-5 Adding and Subtracting
Rational Expressionsincludes simplifying
complex fractions (4-5
days)
8-6 Solving Rational
Equations (2 -3 days)
Essentials to Algebra 2 Curriculum Map 2012-13
optional
Unit 9: Probability
How do you calculate
the probability of an
event?
A2.S.9 Differentiate between situations
requiring permutations and those
requiring combinations
Algebra 2 Topics
Students will be able to
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A2.S.10 Calculate the number of possible
permutations (nPr) of n items taken r at a
time
A2.S.12 Use permutations, combinations,
and the Fundamental Principle of
Counting to determine the number of
elements in a sample space and a specific
subset (event)
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A2.S.13 Calculate theoretical
probabilities, including geometric
applications
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A2.S.14 Calculate empirical probabilities
A2.S.15 Know and apply the binomial
probability formula to events involving
the terms exactly, at least, and at most
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Use permutations, combinations,
and the Fundamental Principle of
Counting to determine the number
of elements in a sample space and a
specific subset (event)
Determine theoretical and
experimental probabilities for
events, including geometric
applications
Find the probability of the event A
and B
Find the probability of event A or
B
Know and apply the binomial
probability formula to events
involving the terms exactly, at
least, and at most
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Permutation
Combinatio
n
Factorial
Counting
Principle
Event
Outcome
Sample
Space
Theoretical
probability
Experiment
al
Probability
Dependent
events
Independent
events
Mutually
exclusive
11-1 Permutations and
Combinations (2-3 days)
11-2 Probability(1-2 days)
11-3 Probability of Multiple
Events(1-2 days)
11-8 Binomial Distributions
(2-3 days)
Essentials to Algebra 2 Curriculum Map 2012-13
optional
Unit 10: Statistics
What methods are
there for analyzing
data?
A2.S.1 Understand the differences among
various kinds of studies (e.g., survey,
observation, controlled experiment)
Algebra 2 Topics
Students will be able to
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A2.S.2 Determine factors which may
affect the outcome of a survey
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A2.S.3 Calculate measures of central
tendency with group frequency
distributions
A2.S.4 Calculate measures of dispersion
(range, quartiles, interquartile range,
standard deviation, variance) for both
samples and populations
A2.S.5 Know and apply the
characteristics of the normal distribution
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Calculate measures of central
tendency given a frequency table
Calculate measures of dispersion
(range, quartiles, interquartile
range, standard deviation, variance)
for both samples and populations
(standard deviation & variance
using graphing calculator)
Calculate probabilities using the
normal distribution (use the normal
curve given on the Algebra 2
reference sheet)
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May
28thJune
10th
June
11th June
20nd
REVIEW FOR FINAL EXAM
FINAL Exam Week
Survey
Experiment
Bias
Sample
Population
Standard
deviation
Variance
Central
tendency
Outlier
Frequency
distribution
Dispersion
Quartiles
Interquartile
range
Binomial
probability
Normal
Distribution
11-5 Analyzing Data (1-2
days)
11-6 Standard Deviation (12 days)
11-7 Samples and Surveys
(1-2 days)
11-9 Normal Distributions
(2-3 days)