Download Algebra II

Teacher: CORE Algebra II
Year: 2014-15
Month: All
Months
Course: Algebra II
UNIT 1A: SOLVING EQUATIONS AND INEQUALITIES (PART A) ~ 1-1: Expressions and Formulas
1-2: Properties of Real Numbers
1-3: Solving Equations
Standards
A-SSE.1a-Interpret parts of an expression, such as terms,
factors, and coefficients.
A-SSE.1b-Interpret complicated expressions by viewing one
or more of their parts as a single entity.
Essential
Questions
Assessments
How are
Quiz 1-1
algebraic
10/1/2014
expressions and
formulas used in
real-life?
A-SSE.2-Use the structure of an expression to identify ways How are the
Quiz 1-2
to rewrite it.
properties of real
numbers useful
in working with
money?
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.
How can creating Test 1A
and solving
equations be
used to simplify
everyday
activities?
Skills
Content
Lessons
Resources
use the order of operations to
simplify expressions.
order of operations
variable
algebraic expression
formula
1-1: Expressions and
Formulas
Textbook - Glencoe,
Algebra 2 pgs. 6-10
use the order of operations to
evaluate expressions.
use formulas.
classify real numbers.
real
rational
use properties of real numbers to irrational
evaluate expressions.
natural
whole
use the distributive property to integer
solve problems.
commutative
associative
identity
inverse
distributive
translate verbal expressions into equation
algebraic expressions and
solution
equations, and vice versa.
reflexive
symmetric
solve equations using the
transitive
properties of equality.
substitution
1-1: Expressions and
Formulas
1-2: Properties of Real
Numbers
Glencoe pgs. 11-18
1-2: Properties of Real
Numbers
1-3: Solving Equations
Glencoe pgs. 20-27
1-3: Solving Equations
solve for specific variables in a
formula.
UNIT 1B: SOLVING EQUATIONS AND INEQUALITIES (PART B) ~ 1-4: Solving Absolute Value Equations
1-5: Solving Inequalities
1-6: Solving Compound and Absolute Value Inequalities
Standards
Essential
Questions
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.
A-SSE.1b-Interpret complicated expressions by viewing one
or more of their parts as a single entity.
How can
Quiz 1-4
absolute value be
used to show
maximum and
minimum values
for an event?
Assessments
Skills
Content
Lessons
Resources
evaluate expressions involving
absolute value.
absolute value
empty set
1-4: Solving Absolute
Value Equations
Glencoe pgs. 28-32
solve absolute value equations.
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.
A-CED.3-Represent constraints by equations or inequalities,
and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a
modeling context.
A-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.
A-CED.3-Represent constraints by equations or inequalities,
and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a
modeling context.
How can
inequalities be
used to make
economic
comparisons?
Quiz 1-5
solve inequalities.
solve real-world problems
involving inequalities.
How can
Test 1B
inequalities be
used to show an
acceptable range
of values for a
given situation?
inequality
set notation
interval notation
solve compound inequalities.
compound inequality
intersection
solve absolute value inequalities. union
1-5: Solving Inequalities
Glencoe pgs. 33-39
1-6: Solving Compound
and Absolute Value
Inequalities
Glencoe pgs. 40-46
UNIT 2A: LINEAR RELATIONS AND FUNCTIONS (PART A) ~ 2-1: Relations and Functions
2-2: Linear Equations
2-3: Slope
Standards
Essential
Assessments Skills
Questions
F-IF.4-For a function that models a relationship between two quantities,
How can
Quiz 2-1
interpret key features of graphs and tables in terms of the quantities, and
relations and 10/31/2014
sketch graphs showing key features given a verbal description of the
functions be
relationship. Key features include: intercepts; intervals where the function is
used to help
increasing, decreasing, positive, or negative; relative maximums and
analyze
minimums; symmetries; end behavior; and periodicity.
collected
F-IF.5-Relate the domain of a function to its graph and, where applicable, to the data?
quantitative relationship it describes.
F-IF.4-For a function that models a relationship between two quantities,
How can
Quiz 2-2
interpret key features of graphs and tables in terms of the quantities, and
linear
sketch graphs showing key features given a verbal description of the
equations be
relationship. Key features include: intercepts; intervals where the function is
used to model
increasing, decreasing, positive, or negative; relative maximums and
real-life
minimums; symmetries; end behavior; and periodicity.
variable
F-IF.9-Compare properties of two functions each represented in a different way relationships?
(algebraically, graphically, numerically in tables, or by verbal descriptions).
F-IF.4-For a function that models a relationship between two quantities,
How does
Test 2A
interpret key features of graphs and tables in terms of the quantities, and
slope apply to 10/31/2014
sketch graphs showing key features given a verbal description of the
rate of
relationship. Key features include: intercepts; intervals where the function is
change?
increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.
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.
Content
Lessons
Resources
ordered pair
coordinate plane
find functional values.
quadrant
relation
domain
range
function
mapping
vertical line test
independent variable
dependent variable
function notation
identify linear equations and
linear equation
functions.
linear function
standard form
write linear equations in standard y-intercept
form and graph them.
x-intercept
2-1: Relations and
Functions
Glencoe pgs. 56-62
find and use the slope of a line.
2-3: Slope
analyze and graph relations.
slope
rate of change
graph parallel and perpendicular family of graphs
lines.
2-2: Linear Equations Glencoe pgs. 63-67
Glencoe pgs. 68-74
UNIT 2B: LINEAR RELATIONS AND FUNCTIONS (PART B) ~ 2-4: Writing Linear Equations
2-5: Using Scatter Plots
2-6: Special Functions
Essential
Assessments Skills
Questions
Standards
A-CED.2-Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
A-SSE.1b-Interpret complicated expressions by viewing one or more of their
parts as a single entity.
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.
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.
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.
How can
linear
equations
apply to
various
business
models?
Quiz 2-4
Content
write an equation of a line given slope-intercept form
the slope and a point on the line. point-slope form
Lessons
Resources
2-4: Writing Linear
Equations
Glencoe pgs. 75-80
2-5: Using Scatter
Plots
Glencoe pgs. 81-86
write an equation of a line given
two points on the line.
How can a
Quiz 2-5
scatter plot be
used to
predict future
occurrences?
How do
special
functions
apply to
various reallife
situations?
Test 2B
write an equation of a line
parallel or perpendicular to a
given line.
draw scatter plots.
find and use prediction
equations.
bivariate data
scatter plot
line of best-fit
prediction equation
identify and graph step, constant, step function
2-6: Special Functions Glencoe pgs. 89-95
and identity functions.
greatest integer
function
identify and graph absolute value constant function
and piecewise functions.
identity function
absolute value function
piecewise function
UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES ~ 3-1: Solving Systems of Equations By Graphing
3-2: Solving Systems of Equations Algebraically
3-3: Solving Systems of Inequalities By Graphing
Standards
Essential Questions Assessments Skills
A-REI.6-Solve systems of linear equations
exactly and approximately (e.g., with
graphs), focusing on pairs of linear
equations in two variables.
How can a system of
equations be used to
predict sales?
Quiz 3-1
12/1/2014
A-CED.3-Represent constraints by
How can systems of
Quiz 3-2
equations or inequalities, and by systems of equations be used to make 12/1/2014
equations and/or inequalities, and interpret consumer decisions?
solutions as viable or nonviable options in a
modeling context.
A-CED.3-Represent constraints by
How can a system of
Test 3A
equations or inequalities, and by systems of inequalities be used to
12/1/2014
equations and/or inequalities, and interpret help in maximizing profit?
solutions as viable or nonviable options in a
modeling context.
Content
solve systems of linear equations by graphing.
Lessons
Resources
system of equations
graphing method
determine whether a system of linear equations is
consistent
consistent and independent, consistent and dependent, inconsistent
or inconsistent.
independent
dependent
solve systems of linear equations by using substitution. substitution method
elimination method
solve systems of linear equations by using elimination.
3-1: Solving Systems of Glencoe pgs. 110Equations By Graphing 115
solve systems of inequalities by graphing.
3-3: Solving Systems of Glencoe pgs. 123Inequalities By
128
Graphing
determine the coordinates of the vertices of a region
formed by the graph of a system of inequalities.
system of
inequalities
3-2: Solving Systems of Glencoe pgs. 116Equations
122
Algebraically
UNIT 5A: POLYNOMIALS (PART A) ~ 5-1: Monomials
5-2: Polynomials
5-3: Dividing Polynomials
Standards
Essential Questions
Assessments
Skills
Content
Lessons
Resources
A-APR.1-Understand that polynomials form How is scientific notation Quiz 5-1
a system analogous to the integers, namely, useful in working with
they are closed under the operations of
extremely large and small
addition, subtraction, and multiplication; numbers?
add, subtract, and multiply polynomials.
multiply and divide monomials.
5-1: Monomials
Glencoe pgs. 222228
A-APR.1-Understand that polynomials form How can polynomials be
a system analogous to the integers, namely, applied to financial
they are closed under the operations of
situations?
addition, subtraction, and multiplication;
add, subtract, and multiply polynomials.
Quiz 5-2
add and subtract polynomials.
5-2: Polynomials
Glencoe pgs. 229232
A-APR.6-Rewrite simple rational
How can division of
expressions in different forms; write
polynomials be used in
a(x)/b(x) in the form q(x) + r(x)/b(x), where manufacturing?
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.
Test 5A
monomial
constant
coefficient
degree
power
simplify
standard notation
scientific notation
polynomial
terms
like terms
binomial
trinomial
FOIL method
long division
synthetic division
5-3: Dividing
Polynomials
Glencoe pgs. 233238
use expressions written in scientific notation.
multiply polynomials.
divide polynomials using long division.
divide polynomials using synthetic division.
UNIT 5B: POLYNOMIALS (PART B) ~ 5-4: Factoring Polynomials
5-5: Roots of Real Numbers
5-6: Radical Expressions
Standards
Essential
Questions
Assessments
Skills
Content
Lessons
A-APR.6-Rewrite simple rational expressions in How does
Quiz 5-4
different forms; write a(x)/b(x) in the form q(x) factoring apply to
+ r(x)/b(x), where a(x), b(x), q(x), and r(x) are geometry?
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.
factor polynomials.
5-4: Factoring Polynomials Glencoe pgs. 239-244
N-RN.2-Rewrite expressions involving radicals How can square
and rational exponents using the properties of roots be used in
exponents.
formulas?
simplify radicals.
factor
GCF
grouping
difference of two squares
sum of two cubes
difference of two cubes
X-method
T-method
square root
nth root
principal root
5-5: Roots of Real
Numbers
Glencoe pgs. 245-249
rationalizing the denominator
like radical expressions
conjugates
5-6: Radical Expressions
Glencoe pgs. 250-256
Quiz 5-5
A-SSE.2-Use the structure of an expression to How do radical
Test 5B
identify ways to rewrite it.
expressions apply
to the velocity of
objects?
simplify polynomial quotients by
factoring.
use a calculator to approximate
radicals.
simplify radical expressions.
add, subtract, multiply, and divide
radical expressions.
Resources
UNIT 5C: POLYNOMIALS (PART C) ~ 5-7: Rational Exponents
5-8: Radical Equations and Inequalities
5-9: Complex Numbers
Standards
Essential
Questions
A-SSE.2-Use the structure of an expression to How do rational
identify ways to rewrite it.
exponents apply
to formulas in
science?
Assessments
Skills
Content
Quiz 5-7
write expressions with rational
rational exponent
exponents in radical form, and vice
versa.
simplify expressions in exponential
or radical form.
solve equations containing radicals. radical equation
extraneous solution
A-REI.2-Solve simple rational and radical
How do radical
Quiz 5-8
equations in one variable, and give examples equations apply to
showing how extraneous solutions may arise. physics and
engineering?
N-CN.1-Know there is a complex number I
How do complex Test 5C
such that i2 = –1, and every complex number numbers apply to
has the form a + bi with a and b real.
polynomial
N-CN.2-Use the relation i2 = –1 and the
equations?
commutative, associative, and distributive
properties to add, subtract, and multiply
complex numbers.
add and subtract complex numbers. imaginary unit
complex number
multiply and divide complex
complex conjugates
numbers.
Lessons
Resources
5-7: Rational Exponents
Glencoe pgs. 257-262
5-8: Radical Equations
and Inequalities
Glencoe pgs. 263-267
5-9: Complex Numbers
Glencoe pgs. 270-275
UNIT 6: QUADRATIC FUNCTIONS ~ 6-1: Graphing Quadratic Functions
6-2: Solving Quadratic Equations By Graphing
6-3: Solving Quadratic Equations By Factoring
6-5: The Quadratic Formula
6-6: Analyzing Graphs of Quadratic Functions
Standards
A-SSE.1a-Interpret parts of an expression, such as terms,
factors, and coefficients.
F-IF.9-Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
Essential
Questions
Assessments Skills
How can
Quiz 6-1
quadratic
functions help
to show
maximum and
minimum
values?
A-CED.2-Create equations in two or more variables to
How can a
Quiz 6represent relationships between quantities; graph equations quadratic
on coordinate axes with labels and scales.
equation be
F-IF.4-For a function that models a relationship between two used to model
quantities, interpret key features of graphs and tables in terms the motion of a
of the quantities, and sketch graphs showing key features given moving object?
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.
graph quadratic functions.
Content
quadratic function
quadratic term
find and interpret the maximum
linear term
and minimum values of a quadratic constant term
function.
parabola
axis of symmetry
vertex
maximum value
minimum value
solve quadratic equations by
quadratic equation
graphing.
root
zero
estimate solutions of quadratic
equations by graphing.
Lessons
Resources
6-1: Graphing
Quadratic Functions
Glencoe pgs. 286-293
6-2: Solving Quadratic Glencoe pgs. 294-299
Equations By Graphing
A-SSE.2-Use the structure of an expression to identify ways to
rewrite it.
F-IF.8a-Use the process of factoring and completing the square
in a quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a
context.
N-CN.7-Solve quadratic equations with real coefficients that
have complex solutions.
A-SSE.1b-Interpret complicated expressions by viewing one or
more of their parts as a single entity.
How is the Zero Quiz 6-3
Product
Property used
in geometry?
How can the
Quiz 6-5
Quadratic
Formula help in
understanding
gravity's effect
on objects?
F-IF.8a-Use the process of factoring and completing the square How can the
Test 6A
in a quadratic function to show zeros, extreme values, and
graph of y = x2
symmetry of the graph, and interpret these in terms of a
be used to
context.
graph any
F-BF.3-Identify the effect on the graph of replacing f(x) by f(x) + quadratic
k, k f(x), f(kx), and f(x + k) for specific values of k (both positive function?
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.
solve quadratic equations by
factoring.
Zero Product Property
6-3: Solving Quadratic Glencoe pgs. 301-305
Equations By
Factoring
write a quadratic equation with
given roots.
solve quadratic equations by using Quadratic Formula
the Quadratic Formula.
discriminant
use the discriminant to determine
the number and type of roots of a
quadratic equation.
analyze quadratic functions of the vertex form
form y = a(x - h)2 + k.
family of graphs
write a quadratic function in the
form y = a(x - h)2 + k.
6-5: The Quadratic
Formula
Glencoe pgs. 313-319
6-6: Analyzing the
Graphs of Quadratic
Functions
Glencoe pgs. 322-328
Content
Lessons
Resources
polynomial in one variable
7-1: Polynomial
Functions
Glencoe pgs. 346-352
UNIT 7: POLYNOMIAL FUNCTIONS ~ 7-1: Polynomial Functions
7-2: Graphing Polynomial Functions
7-8: Inverse Functions and Relations
Standards
Essential
Questions
Assessments Skills
F-IF.4-For a function that models a relationship between two Where are
Quiz 7-1
quantities, interpret key features of graphs and tables in terms polynomial
of the quantities, and sketch graphs showing key features given functions found
a verbal description of the relationship. Key features include: in nature?
intercepts; intervals where the function is increasing,
decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.
evaluate polynomial functions.
F-IF.7c-Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end
behavior.
graph polynomial functions and
locate their real zeroes.
F-BF.4-Find inverse functions.
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, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ? 1.
How can graphs Quiz 7-2
of polynomial
functions show
trends in data?
How are inverse Test 7A
functions
related to
measurement
conversions?
identify general shapes of graphs of degree of a polynomial
polynomial functions.
leading coefficient
polynomial function
end behavior
Location Principle
7-2: Graphing
Glencoe pgs. 353-358
Polynomial Functions
relative maximum
find the maxima and minima of
polynomial functions.
find the inverse of a function or
relation.
relative minimum
inverse relation
inverse function
determine whether two functions
or relations are inverses.
identity function
one-to-one
7-8: Inverse Functions Glencoe pgs. 390-394
and Relations
UNIT 9A: RATIONAL EXPRESSIONS AND EQUATIONS (PART A) ~ 9-1: Multiplying and Dividing Rational Expressions
9-2: Adding and Subtracting Rational Expressions
9-3: Graphing Rational Functions
Standards
A-APR.7-(+) Understand that rational expressions form a
system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero
rational expression; add, subtract, multiply, and divide rational
expressions.
A-APR.7-(+) Understand that rational expressions form a
system analogous to the rational numbers, closed under
addition, subtraction, multiplication, and division by a nonzero
rational expression; add, subtract, multiply, and divide rational
expressions.
A-CED.2-Create equations in two or more variables to
represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
F-IF.9-Compare properties of two functions each represented
in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
Essential
Questions
How are
rational
expressions
used in
mixtures?
How can
complex
fractions be
used in
coordinate
geometry?
How can the
graphs of
rational
functions be
used to help
solve real-life
problems?
Assessments
Skills
Content
Lessons
Resources
Quiz 9-1
simplify rational expressions.
simplify complex fractions.
rational expression
complex fraction
9-1: Multiplying and
Dividing Rational
Expressions
Glencoe pgs. 472-478
Quiz 9-2
determine the LCM of polynomials. LCM of polynomials
add and subtract rational
expressions.
9-2: Adding and
Subtracting Rational
Expressions
Glencoe pgs. 479-484
Test 9A
determine the vertical asymptotes
and the point discontinuity for the
graphs of rational functions.
rational function
continuity
asymptote
point discontinuity
9-3: Graphing Rational Glencoe pgs. 485-490
Functions
Content
Lessons
graph rational functions.
UNIT 9B: RATIONAL EXPRESSIONS AND EQUATIONS (PART B) ~ 9-4: Direct, Joint, and Inverse Variation
9-5: Classes of Functions
9-6: Solving Rational Equations
Standards
A-CED.2-Create equations in two or more variables to
represent relationships between quantities; graph equations
on coordinate axes with labels and scales.
Essential
Questions
Assessments
How is variation Quiz 9-4
used in
different
branches of
science?
F-BF.3-Identify the effect on the graph of replacing f(x) by f(x) + How can the
Quiz 9-5
k, k f(x), f(kx), and f(x + k) for specific values of k (both positive graphs of
and negative); find the value of k given the graphs. Experiment special
with cases and illustrate an explanation of the effects on the functions relate
graph using technology. Include recognizing even and odd
to real-life
functions from their graphs and algebraic expressions for them. situations?
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.
Skills
recognize and solve direct and joint direct variation
variation problems.
constant of variation
recognize and solve inverse variation
problems.
joint variation
inverse variation
identify graphs as different types of special functions
functions.
identify equations as different types
of functions.
Resources
9-4: Direct, Joint, and Glencoe pgs. 492-498
Inverse Variation
9-5: Classes of
Functions
Glencoe pgs. 499-504
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.
A-REI.2-Solve simple rational and radical equations in one
variable, and give examples showing how extraneous solutions
may arise.
How are
Test 9B
rational
equations used
to solve
problems
dealing with
work and rate?
solve rational equations.
rational equation
9-6: Solving Rational
Equations
Glencoe pgs. 505-511
eliminate extraneous solutions to
rational equations.
extraneous solution
Content
Lessons
Resources
Glencoe pgs. 523-530
UNIT 10A: EXPONENTIAL AND LOGARITHMIC RELATIONS (PART A) ~ 10-1: Exponential Functions
10-2: Logarithms and Logarithmic Functions
10-3: Properties of Logarithms
Standards
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.
F-IF.8-Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function.
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.
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.
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.
Essential
Questions
Assessments Skills
How does
Quiz 10-1
exponential growth
and decay relate to
topics like
population and
money?
How is a
Quiz 10-2
logarithmic scale
used to measure
things?
graph exponential functions.
solve exponential equations and
inequalities.
exponential function
exponential growth
exponential decay
exponential equation
exponential inequality
10-1: Exponential
Functions
evaluate logarithmic expressions.
solve logarithmic equations and
inequalities.
logarithm
logarithmic function
logarithmic equation
logarithmic inequality
10-2: Logarithms and Glencoe pgs. 531-538
Logarithmic Functions
How are the
Test 10A
properties of
exponents and
logarithms related?
simplify and evaluate expressions using Properties of Logarithms
the properties of logarithms.
solve logarithmic equations using the
properties of logarithms.
10-3: Properties of
Logarithms
Glencoe pgs. 541-546
Lessons
Resources
10-4: Common
Logarithms
Glencoe pgs. 547-551
10-5: Base e and
Natural Logarithms
Glencoe pgs. 554-559
UNIT 10B: EXPONENTIAL AND LOGARITHMIC RELATIONS (PART B) ~ 10-4: Common Logarithms
10-5: Base e and Natural Logarithms
10-6: Exponential Growth and Decay
Standards
Essential
Questions
Assessments Skills
A-CED.1-Create equations and inequalities in one variable How are common Quiz 10-4
and use them to solve problems. Include equations arising logarithms used in
from linear and quadratic functions, and simple rational and science?
exponential functions.
A-SSE.2-Use the structure of an expression to identify ways How is the natural Quiz 10-5
to rewrite it.
base e used in
working with
money?
Content
solve exponential equations and
common logarithm
inequalities using common logarithms. Change of Base Formula
evaluate logarithmic expressions using
the Change of Base Formula.
evaluate expressions involving the
natural base e
natural base and natural logarithms. natural base exponential
function
solve exponential equations and
natural logarithm
inequalities using natural logarithms. natural logarithmic
function
F-IF.8-Write a function defined by an expression in different
but equivalent forms to reveal and explain different
properties of the function.
F-LE.4-For exponential models, express as a logarithm the
solution to abct = d where a, c, and d are numbers and the
base b is 2, 10, or e; evaluate the logarithm using
technology.
How can you
determine the
current value of a
house or car?
Test 10B
use logarithms to solve problems
involving exponential decay.
rate of decay
10-6: Exponential
Growth and Decay
Glencoe pgs. 560-565
rate of growth
use logarithms to solve problems
involving exponential growth.
UNIT 11: SEQUENCES AND SERIES ~ 11-1: Arithmetic Sequences
11-2: Arithmetic Series
11-3: Geometric Sequences
11-4: Geometric Series
Standards
Essential Questions Assessments Skills
Content
Lessons
Resources
F-IF.4-For a function that models a relationship between How can an arithmetic
Quiz 11-1
two quantities, interpret key features of graphs and
sequence be used to make
tables in terms of the quantities, and sketch graphs
predictions?
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.
A-CED.4-Rearrange formulas to highlight a quantity of How do arithmetic series Quiz 11-2
interest, using the same reasoning as in solving
apply to construction?
equations.
use arithmetic sequences.
find arithmetic means.
sequence
term
arithmetic sequence
common difference
arithmetic means
11-1: Arithmetic
Sequences
Glencoe pgs. 578-582
find sums of arithmetic series.
use sigma notation.
11-2: Arithmetic
Series
Glencoe pgs. 583-587
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.
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.
use geometric sequences.
find geometric means.
series
arithmetic series
sigma notation
index of summation
geometric sequence
common ratio
geometric means
geometric series
11-3: Geometric
Sequences
Glencoe pgs. 588-592
11-4: Geometric
Series
Glencoe pgs. 594-598
How can geometric
Quiz 11-3
sequences apply to salaries
and investing?
How can a geometric
Test 11A
series be used in the study
of health and disease?
find sums of geometric series.
find specific terms of geometric
series.
UNIT 12: PROBABILITY AND STATISTICS ~ 12-1: The Counting Principal
12-2: Permutations and Combinations
12-3: Probability
12-4: Multiplying Probabilities
12-5: Adding Probabilities
Standards
Essential Questions
Assessments Skills
S-CP.1-(+) Define a random variable for a quantity of How can the Counting
interest by assigning a numerical value to each event in Principle be used to
a sample space; graph the corresponding probability determine the number of
distribution using the same graphical displays as for
possible outcomes for an
data distributions.
event?
Quiz 12-1
S-CP.9-(+) Use permutations and combinations to
compute probabilities of compound events and solve
problems.
Quiz 12-2
How can permutations and
combinations apply to
sports?
Content
solve problems involving independent outcomes
events.
sample space
event
solve problems involving dependent
independent events
events.
Fundamental Counting
Principle
dependent events
solve problems involving linear
permutation
permutations.
linear permutation
combination
solve problems involving
combinations.
Lessons
Resources
12-1: The Counting
Principle
Glencoe pgs. 632637
12-2: Permutations
and Combinations
Glencoe pgs. 638643
S-CP.5a-Find the expected payoff for a game of
chance.
What do probability and
odds tell you about life's
risks?
Quiz 12-3
find the probability and odds of events. probability
12-3: Probability
success
create and use graphs of probability
failure
distributions.
random
odds
random variable
probability distribution
uniform distribution
relative-frequency histogram
Glencoe pgs. 644650
S-CP.8-(+) Apply the general Multiplication Rule in a
uniform probability model, P(A and B) = P(A)P(B|A) =
P(B)P(A|B), and interpret the answer in terms of the
model.
How does probability apply
to games of chance?
Quiz 12-4
find the probability of two
independent events.
12-4: Multiplying
Probabilities
Glencoe pgs. 651657
12-5: Adding
Probabilities
Glencoe pgs. 658663
S-CP.5b-Evaluate and compare strategies on the basis How does probability apply
of expected values.
to your personal habits?
Test 12A
area diagram
find the probability of two dependent
events.
find the probability of mutually
simple event
exclusive events.
compound event
find the probability of inclusive events. mutually exclusive events
inclusive events