Download Pacing

CURRICULUM MAP: ALGEBRA 2 and TRIG.
RCSD- Department of Mathematics
2010 - 2011
Note for teachers: The Pacing below is a general guideline on how much time you need to spend on each unit. Feel free to adjust according to your students needs. We chose to
start with 3 Trig. units since it is a new and interesting topic that will capture student interest and attention at the start of the school year. However, you may choose to move the
units around as it serves you best. Make sure you refer to the Performance Indicators as you go along. The primary text is Algebra 2 by Pearson.
Refer to http://www.jmap.org and http://emathinstruction.com for additional practice
Pacing
Sept
3rd –
Sept
14th
Unit/Essential
Questions
Unit 1: Intro to Trig
What are the six
trigonometric ratios
in relation to right
triangles?
What is the unit
circle and how is it
used in
trigonometry?
How do we find the
values of the six
trigonometric
functions?
What is radian
measure and how do
we convert between
radians and degrees?
Essential KnowledgeContent/Performance Indicators
(What students must learn)
A2.A.55 Express and apply the six
trigonometric functions as ratios of the
sides of a right triangle
Essential Skills
(What students will be able to do)
Students will be able to
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A2.A.57 Sketch and use the reference
angle for angles in standard position
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A2.A.59 Use the reciprocal and cofunction relationships to find the value of
the secant, cosecant, and cotangent of 0º,
30º, 45º, 60º, 90º, 180º, and 270º angles
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A2.A.60 Sketch the unit circle and
represent angles in standard position
A2.A.61 Determine the length of an arc of
a circle, given its radius and the measure
of its central angle
A2.A.62 Find the value of trigonometric
functions, if given a point on the terminal
Resources
Pearson Algebra 2
A2.A.56 Know the exact and approximate
values of the sine, cosine, and tangent of
0º, 30º, 45º, 60º, 90º, 180º, and 270º
angles
A2.A.58 Know and apply the co-function
and reciprocal relationships between
trigonometric ratios
Vocabulary
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Find missing angle using inverse
trig functions
Understand the concept of the unit
circle and its relation to
trigonometry
Sketch a given angle on the unit
circle
Find both negative and positive
coterminal angles
Find the sine and cosine of an
angle on the unit circle
Distinguish between exact and
approximate values of trig.
functions
Find the exact value of a
sine/cosine function
Convert between radians and
degrees
Find the length of the intercepted
arc
Find the value of trig. function
given a point on the unit circle
Find the terminal point on the unit
circle given a trig. angle.
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Trig. Ratios
Inverse
Trig
functions
Unit Circle
Standard
side
Initial side
Terminal
side
Coterminal
angle
Exact value
Central
angle
Intercepted
arc
Radian
14-3 Right triangles and
Trig Ratios
13-2 Angles and Unit Circle
13-3 Radian measure
side of angle θ
A2.A.64 Use inverse functions to find the
measure of an angle, given its sine,
cosine, or tangent
A2.A.66 Determine the trigonometric
functions of any angle, using technology
A2.M.1 Define radian measure
A2.M.2 Convert between radian and
degree measures
Sept
15th –
Sept
28th
Unit 2 Trig
Functions and
Graphing
What are the
characteristics of the
graphs of the
trigonometric
functions?
A2.A.63 Restrict the domain of the sine,
cosine, and tangent functions to ensure the
existence of an inverse function
A2.A.65 Sketch the graph of the inverses
of the sine, cosine, and tangent functions
A2.A.69 Determine amplitude, period,
frequency, and phase shift, given the
graph or equation of a periodic function
Students will be able to
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How do you write a
trigonometric
equation represented
by a graph?
How do you sketch
the graphs of the six
trigonometric
functions?
A2.A.70 Sketch and recognize one cycle
of a function of the
form y = Asin Bx or y = Acos Bx
A2.A.71 Sketch and recognize the graphs
of the functions y = sec(x) , y = csc(x),
y = tan(x), and y = cot(x)
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A2.A.72 Write the trigonometric function
that is represented by a given periodic
graph
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Find the amplitude, frequency,
period and phase shift of a sine
curve given its equation or graph
Find the amplitude, frequency,
period and phase shift of a cosine
curve given its equation or graph
Graph a sine or cosine curve given
its equation
Write the trig. Function given its
graph
Recognize and sketch the inverse
trig. Functions (know its domain
and range).
Recognize and sketch the
reciprocal trig. Functions (know its
domain and range)
Graph all trig function with a
graphing calculator
Solve trig. functions graphically
using a graphing calculator by
finding the points of intersection
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Periodic
function
Cycle
Period
Amplitude
Frequency
Phase shift
Domain
Range
Sine curve
Cosine
curve
13-1 Exploring Periodic
Functions
13-4 The Sine Function
13-5 The Cosine Function
13-6 the Tangent Function
13-7 Translating Sine and
cosine Function
13-8 Reciprocal
Trigonometric Functions
Sept
29th –
Oct 8th
Unit 3 Trig
Applications (Laws)
How do you use the
Law of Sines to find
missing parts of
oblique triangles?
How do you use the
Law of Cosines to
find missing parts of
oblique triangles?
How do you use the
trigonometry to find
the area of oblique
triangles?
How many distinct
triangles are possible
given certain parts of
oblique triangles?
A2.A.73 Solve for an unknown side or
angle, using the Law of Sines or the Law
of Cosines
Students will be able to
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A2.A.74 Determine the area of a triangle
or a parallelogram, given the measure of
two sides and the included angle
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A2.A.75 Determine the solution(s) from
the SSA situation (ambiguous case)
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Use the Law of Sines to find a
missing angle or missing side
Use the Law of Cosines to find a
missing angle or missing side
Find the area of a triangle or a
parallelogram
Find the possible number of
triangles given an angle and two
sides
Apply the Law of Sines and Law of
Cosines to word problems
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Law of
Sine
Law of
Cosine
Oblique
triangle
14-4 Area and the Law of
Sines
14-5 The Law of Cosines
Page 927 The Ambiguous
Case
Oct
12th –
Oct
21st
Unit 4: Equations
and Inequalities
How do you solve
absolute value
equation/inequality
and plot on the
number line?
A2.A.1 Solve absolute value equations
and inequalities involving linear
expressions in one variable
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
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Term
Constant
term
Like terms
Coefficient
Expression
Equation
Literal
Equation
Inequality
Absolute
Value
Extraneous
solution
1-3: Algebraic Expressions
1-4: Solving equations.
Supplement with additional
worksheets on equations
with fractional coefficients
1-5: Solving Inequalities
1-6 Absolute Value
Equations and inequalities
Oct
22nd –
Oct
27th
Unit 5: 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?
A2.A.38 Determine when a relation is a
function
Review of Algebra Topics
Student will be able to
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A2.A.39 Determine the domain and range
of a function from its equation
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A2.A.40 Write functions in functional
notation
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How do you find the
domain and range of
a function?
A2.A.41 Use functional notation to
evaluate functions for given values in the
domain
How do you
transformation with
functions?
A2.A.46 Perform transformations with
functions and relations:
f(x + a) , f(x) + a, f(−x), − f(x), af(x)
Algebra 2 and Trig. Topics
Student will be able to
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A2.A.52 Identify relations and functions,
using graphs
A2.S.8 Interpret within the linear
regression model the value of the
correlation coefficient as a measure of the
strength of the relationship
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.
Draw a scatter plot and find the
line of best fit
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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 if 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
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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
Overview of Chapter 2 with
special emphasis on
transformation.
Go over review questions on
page 80
perform related translations
Oct
28th –
Dec 3rd
Unit 6: 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
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
Students will be able to
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A2.A.39 Determine the domain and
range of a function from its
equation
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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
A2.A.20 Determine the sum and
product of the roots of a quadratic
equation by examining its coefficients
A2.A.21 Determine the quadratic
equation, given the sum and product of
its roots
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
A2.A.2 Use the discriminant to
determine the nature of the roots of a
quadratic equation
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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
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
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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
4-2 Standard form of a
quadratic function
4-3 Modeling with quadratic
functions
4-4 Factoring quadratic
expressions
4-5 Quadratic equations
4-6 Completing the square
4-7 Quadratic Formula
4-8 Complex Numbers
Additional resources at
www.emathinstruction.com
Quadratic Inequalities Page
256-257
Powers of complex numbers
Page 265
4-9 Quadratic Systems
10-3 Circles
quadratic equations
graphically and
algebraically?
A2.A.4 Solve quadratic inequalities in
one and two variables, algebraically and
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.
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A2.N6 Write square roots of negative
numbers in terms of i
A2.N7 Simplify powers of i
A2.N8 Determine the conjugate of a
complex number
A2.N9 Perform arithmetic operations on
complex numbers and write the answer in
the form a+bi
A2.A47 Determine the equation of a
circle
A2.A48 Write the equation of a circle
given a point
A2.A49 Write the equation of a circle
from its graph
nature of the roots
simplify expressions containing
complex numbers (include
rationalizing the denominator)
solve quadratic inequalities
solve systems of quadratics
algebraically
Determine the equation of a circle
given the center and the radius, a
point and the radius, the center and
a point
Determine the equation of a circle
in center-radius form by
completing the square of the
equation in standard form
Dec 6th
– Dec
17th
Unit 7: 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
A2.A.26 Find the solution to polynomial
equations of higher degree that can be
solved using factoring and/or the
quadratic formula
Student will be able to
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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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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.
Divide polynomials by factoring,
long division or synthetic division
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
5-2 Polynomials, Linear
Factors and Zeros
5-3 Solving Polynomial
Equations
5-4 Dividing Polynomials
5-7 The Binomial Theorem
Jan 3rd
– Jan
15th
Unit 8: 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?
How do you perform
composition of
functions?
How do you find the
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
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
Find composition of functions
Find inverses of functions
Determine if a function is one to
one or onto or both
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Exponents
Conjugates
Radicals
Rationalize
the
denominato
r
Extraneous
roots
f- 1(x)
inverse of a
function
one to one
onto
Page 360 Properties of
exponents
6-1 Simplify radical
expressions
6-2 Multiply and divide
radical expressions
6-3 Binomial Radical
Expressions
6-4 Rational Exponents
6-5 Solve radical equations
6-6 Function operations
6-7 Inverse relations and
functions
(the text does not cover
“onto” so this will have to
be supplemented with
Ch 4-1 of AMSCO)
inverse of a function?
A2.A.22 Solve radical equations
How do you
determine if a
function is 1 to 1 or
onto?
A2.A.40 Write functions using function
notation
A2.A.41 Use function notation to
evaluate functions for given values in the
domain
A2.A.42 Find the composition of
functions
A2.A.43 Determine if a function is 1 to 1,
onto, or both
A2.A.44 Define the inverse of a function
A2.A.45 Determine the inverse of a
function and use composition to justify
the result
Jan 18th – Jan 24th MIDTERM REVIEW
Jan
31st –
Feb
19th
Unit 9: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?
Which type of
function models the
data best?
A2.A.6 Solve an application with results
in an exponential function.
A2.A.12 Evaluate exponential
expressions, including those with base e.
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Students will be able to:
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model exponential growth and
decay
explore the properties of functions
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
the form. y  b for positive values of b,
including b = e.
x
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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.
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.
A2.S.6 Determine from a scatter plot
whether a linear, logarithmic, exponential,
or power regression model is most
appropriate.
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asymptote
change of
base
formula
common
logarithm
exponential
equation
exponential
function
exponential
decay
exponential
growth
logarithm
logarithmic
equation
logarithmic
function
natural
logarithmic
function
7 -1 Exploring Exponential
Models
7 - 2 Properties of
Exponential functions
7 – 3 Logarithmic Functions
as Inverses
- Fitting Curves to Data
Page 459
7 - 4 Properties of
Logarithms
7 - 5 Exponential and
Logarithmic Equations
7 - 6 Natural Logarithms
NOTE- the text only does
problems compounding
interest continuously. You
will need to supplement to
do problems that compound
quarterly, monthly, etc.)
Ch 7-7 AMSCO
Feb
28th –
March
15th
Unit 10: 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?
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A2.A.17 Simplify complex fractional
expressions
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.
A2.A.23 Solve rational equations and
inequalities
Algebra 2 Topics
Students will be able to
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A2.A.5 Use direct and inverse variation
A2.A.16 Perform arithmetic operations
with rational expressions and rename to
lowest terms
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Identify from tables, graphs and
models direct and inverse variation
Solve algebraically and graph
inverse variation
Graph rational functions with
vertical and horizontal asymptotes
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
Solve rational inequalities
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Inverse
Variation
Asymptotes
Simplest
form
Rational
Expression
Common
factors
Reciprocal
Least
Common
Multiple
Lowest
Common
Denominato
r
Common
factors
Complex
Fraction
Rational
equation
8-1 Inverse Variation(omit
combined and joint
variation)
8-2 Reciprocal functions
and transformations
8-3 Rational functions and
their graphs
8-4 Rational Expressions
8-5 Adding and Subtracting
Rational Expressionsincludes simplifying
complex fractions
8-6 Solving Rational
Equations
NOTE: Teachers must
supplement for solving
rational inequalities
(Ch. 2-8 of AMSCO)
March
16th –
March
25th
Unit 11: Probability
How do you calculate
the probability of an
event?
A2.S.9 Differentiate between situations
requiring permutations and those
requiring combinations
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.11Calculate the number of possible
combinations (nCr) 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)
A2.S.13 Calculate theoretical
probabilities, including geometric
applications
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
Experimenta
l Probability
Dependent
events
Independent
events
Mutually
exclusive
11-1 Permutations and
Combinations
11-2 Probability
11-3 Probability of Multiple
Events
11-8 Binomial Distributions
You may wish to
supplement the text using
additional resources from
www.emathinstruction.com
March
28th –
April
8th
Unit 12: 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)
A2.S.2 Determine factors which may
affect the outcome of a survey
Students will be able to
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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
A2.S.16 Use the normal distribution as an
approximation for binomial probabilities
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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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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
11-6 Standard Deviation
11-7 Samples and Surveys
11-9 Normal Distributions
P 741 Approximating a
Binomial Distribution
April
11th –
April
15th
Unit 13: Sequences
and Series
What is the
difference between
arithmetic and a
geometric sequence?
How do you find an
explicit formula?
How do you write a
recursive definition
for a sequence?
How do you find the
common difference
and the nth term of
an arithmetic
sequence?
How do you find the
common ratio and the
nth term of a
geometric sequence?
How do you find the
sum of a finite series
using the formulas?
A2.A.29 Identify an arithmetic or
geometric sequence and find the formula
for its nth term
A2.A.30 Find the common difference in
an arithmetic sequence
Students will be able to
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A2.A.31 Determine the common ratio of
a geometric sequence
A2.A.32 Determine a specified term of
an arithmetic or a geometric sequence
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A2.A.33 Specify terms of a sequence
given its recursive definition
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A2.N.10 Know and apply sigma notation
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A2.A.34 Represent the sum of a series
using sigma notation
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A2.A.35 Determine the sum of the first n
terms of an arithmetic or a geometric
series
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Use patterns to find subsequent
terms of a sequence
Use explicit formulas to find terms
of sequences
Find a recursive definition for a
sequence
Find an explicit formula to define
a sequence
Tell whether a sequence is
arithmetic, geometric, or neither
Find the common difference of an
arithmetic sequence
Find the nth term of an arithmetic
sequence
Find the common ratio in a
geometric sequence
Find the nth term of a geometric
sequence
Find the sum of a finite arithmetic
series
Write a series using sigma notation
Find the sum of a finite geometric
series
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Sequence
Arithmetic
sequence
Geometric
sequence
Explicit
formula
Recursive
definition
Finite Series
Sigma
notation
9-1 Mathematical patterns
9-2 Arithmetic Sequences
9-3 Geometric Sequence
9-4 Arithmetic Series
9-5 Geometric series
April
25th –
May
13th
Unit 14: Solving
Trig Equations
How do you verify a
trigonometric
identity?
How do you solve
trigonometric
equations?
How do you use the
trigonometric angle
formulas to find
values for trig
functions?
A2.A.67 Justify the Pythagorean identities
A2.A.68 Solve trigonometric equations
for all values of the variable from 0º to
360º
A2.A.59 Use the reciprocal and cofunction relationships to find the value of
the secant, cosecant, and cotangent of 0º,
30º, 45º, 60º, 90º, 180º, and 270º angles
A2.A.76 Apply the angle sum and
difference formulas for trigonometric
functions
A2.A.77 Apply the double-angle and halfangle formulas for trigonometric functions
Students will be able to
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Identify reciprocal identities
Verify trig equations using trig
identities
Verify Pythagorean identities
Simplify trig expressions using
identities
Solve linear and quadratic trig
equations within the given domain
Verify an angle identity
Use the angle sum and difference
formulas to evaluate a trig
expression or verify a trig.
equation
Use the angle double angle and
half angle formulas to evaluate a
trig expression or verify a trig.
equation
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CATCH-UP, REVIEW AND FINALS
Trig.
Identities
Reciprocal
Trig.
Function
Pythagorea
n identities
Negative
angle
identity
Cofunction
identity
Angle sum
formula
Angle
difference
formula
Double
angle
formula
Half angle
formula
14-1 Trigonometric
Identities
14-6 Angle Identities
14-7 Double Angle and Half
Angle Identities
14-2 Solving Trigonometric
Equations