Download Algebra 2 - Boone County Schools

2015-2016
Larry A. Ryle High School
Algebra 2 Curriculum Map
Unit Title
Unit 1 – Linear Equations and
Inequalities
Unit 2 – Intro to Functions
Unit 3 – Linear Systems
Duration
2 weeks
1 week
3 weeks
Primary Standards
Essential Question(s)
A.CED.1 – Create equations and inequalities in one
variable and use them to solve problems.
QC:D.1.b-Solve compound inequalities containing and/or
and graph the solution set
QC: D.1.a.-Solve linear inequalities containing absolute
value.
How can you use the
properties of real numbers to
simplify algebraic expressions,
equations and inequalities?
F.IF.1 – Understand that a function assigns to each
element of the domain exactly one element of the range.
F.IF.2 – Evaluate functions for inputs in their domain and
interpret statements.
F.IF.4 – For a function that models a relationship between
two quantities, interpret key features of graphs and tables
in terms of 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 of negative, relative
minimum and maximums, symmetries, end behavior and
periodicity.
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.CED.3 – Represent constraints by equations or
inequalities and by systems of equations or
inequalities and interpret solutions as viable or nonviable options in a modeling context, For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.
A.CED.4 Rearrange formulas to highlight a quantity
of interest, using the same reasoning as in solving
How do you solve an equation
or inequality?
What is the advantage of
writing a relation in function
form?
How do you analyze and
interpret the characteristics of
linear, quadratic, cubic,
absolute value, square root,
and rational functions using
graphs, tables, and simple
algebraic techniques?
How does representing
functions graphically help you
solve a system of equations?
How does writing equivalent
equations help you solve a
system of equations?
In real-world situations, how
do you find a
maximized/minimized a
quantity?
2015-2016
Larry A. Ryle High School
equations. For example, rearrange Ohm’s law V=IR
to highlight resistance R.
F.IF.5 – Relate the domain of a function to its graph
and where applicable to the quantitative relationship
it describes. For example, if the function h(n) give
the number of person hours it takes to assemble n
engines in a factory, then the positive integers would
be an appropriate domain.
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.CED.3 – Represent constraints by equations or
inequalities and by systems of equations or
inequalities and interpret solutions as viable or nonviable options in a modeling context, For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.
A.REI.6 – Solve a system of linear equations exactly
and approximately focusing on pairs of linear
equations in two variables.
A.REI.12 – Graph the solutions to a linear inequality
in two variables as a half plane and graph the
solution set to a system of linear inequalities in two
variables as the intersection of the corresponding
half - plane
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.2 – Create equations in two or more
variables to represent relationships between
quantities; graph equations on coordinate axes with
labels and scales
A.CED.3 – Represent constraints by equations or
inequalities and by systems of equations or
2015-2016
Unit 4 – Square Roots, Imaginary,
Complex, and Factoring
Unit 5 – Solving Quadratics
Larry A. Ryle High School
2-3 weeks
5 weeks
inequalities and interpret solutions as viable or nonviable options in a modeling context, For example,
represent inequalities describing nutritional and cost
constraints on combinations of different foods.
N.CN.1 – Know there is a complex number I such that
i2=-1 and every complex number has the form a + bi with
a and b real
N.CN.2 – Use the relation i2=-1 and the commutative
associative and distributive properties to add, subtract, and
multiply complex numbers.
N.CN.3-(+)Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex
numbers
QC:C.1.a.-Simplify quotients of complex numbers
G.1.d.-Add, subtract, multiply, and divide expressions
containing radicals.
G.1.e.-Rationalize denominators containing radicals and
find the simplest common denominator.
F.IF.8 – Write a function defined by an expression in
different but equivalent form.
A.CED.2 – Create equations in two or more variables to
represent relationships between quantities; graph
equations on coordinate axes with labels and scales
N.CN.7 – Solve quadratic equations with real coefficients
that have complex solutions
F.IF.5 – Relate the domain of a function to its graph and
where applicable to the quantitative relationship it
describes. For example, if the function h(n) give the
number of person hours it takes to assemble n engines in a
factory, then the positive integers would be an appropriate
domain.
QC:
E.1.a.-Solve quadratic equations and inequalities using
various techniques including completing the square and
using the quadratic formula.
E.1.b.-Use the discriminant to determine the number and
How are real, imaginary and
complex numbers related?
What are complex numbers?
How do you represent and
operate using them?
How can you write equivalent
forms of an expressions using
factoring?
What are the advantages of a
quadratic function in vertex
form? in standard form?
How is any quadratic function
related to the parent quadratic
function y=x2?
2015-2016
Unit 6 – Graphing Quadratics
Larry A. Ryle High School
3-4 weeks
type of roots for a given quadratic equation.
E.1.c.-Solve quadratic equations with complex number
solutions.
F.IF.8 – Write a function defined by an expression in
different but equivalent form.
F.IF.9 – Compare properties of two functions each
represented in a different way.
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.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.
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.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.
F.IF.5 – Relate the domain of a function to its graph and
where applicable to the quantitative relationship it
describes. For example, if the function h(n) give the
number of person hours it takes to assemble n engines in a
factory, then the positive integers would be an appropriate
domain.
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.IF.9 – Compare properties to two functions each
functions each represented in a different way
(algebraically, graphically, numerically in tables or by
verbal descriptions). For examples, given a graph of one
quadratic function and an algebraic expression for another,
say which has the larger maximum.
E.1.d.-Solve quadratic systems algebraically and
What are the advantages of a
quadratic function in vertex
form? in standard form?
How is any quadratic function
related to the parent quadratic
function y=x2?
How are the real solutions of a
quadratic equation related to
the graph of the related
quadratic function?
2015-2016
Larry A. Ryle High School
graphically with technology and without techonology.
Unit 7 – Polynomial
5 weeks
A.REI.7-Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically.
QC:
E.2.a.-Determine the domain and range of quadratic
function; graph the function with and without technology
E.2.b.-Use transformations to draw the graph of a relation
and determine a relation that fits a graph.
E.2.c.-Graph a system of quadratic inequality systems
with and without technology to find the solution set to the
system.
F.IF.9 – Compare properties of two functions each
represented in a different way.
N.CN.8 – Extend polynomial identities to the complex
numbers (i.e. factoring/Foiling, etc.)
N.CN.9 – Know the Fundamental Theorem of Algebra;
Show that it is true for quadratic polynomials.
F.IF.4 – For a function that models a relationship between
two quantities, interpret key features of graphs and tables
in terms of 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 of negative, relative
minimum and maximums, symmetries, end behavior and
periodicity.
A.SSE.2 – Use the structure of an expression to identify
ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2
thus recognizing it as a difference of squares that can be
factored as (x2 – y2)(x2 + y2)
A.APR.3 – Identify zeroes of polynomials when suitable
factors are available, and use the zeroes to construct a
rough graph of the function defined by the polynomial.
N.CN.7 – Solve quadratic equations with real coefficients
that have complex solutions
N.CN.8 – Extend polynomial identities to the complex
What does the degree of a
polynomial tell you about its
related polynomial?
For a polynomial function,
how are factors, zeros, and xintercepts related?
For a polynomial equation,
how are ractors and roots
related?
2015-2016
Unit 8 – Rational Exponents and
Radicals
Larry A. Ryle High School
3 weeks
numbers (i.e. factoring/Foiling, etc.)
N.CN.9 – Know the Fundamental Theorem of Algebra;
Show that it is true for quadratic polynomials.
F.IF.5 – Relate the domain of a function to its graph and
where applicable to the quantitative relationship it
describes. For example, if the function h(n) give the
number of person hours it takes to assemble n engines in a
factory, then the positive integers would be an appropriate
domain.
F.IF.7.c – Graph functions expressed symbolically and
show key features of the graph, by hand in some cases and
using technology for more complicated cases: Graph
polynomial functions identifying zeros when suitable
factorizations are available and showing end behavior.
A.APR.1 – Understand that polynomials for a system
analogous to the integers, namely, that they are closed
under the operations of addition, subtraction and
multiplication: add, subtract and multiply polynomials.
A.APR.2 – Know and apply the remainder theorem: For a
polynomial p(x) and a number a, the remainder on
division by x-a is p(a), so p(a) – 0 if and only if (x-a) is a
factor of p(x)
A.APR.3 – Identify zeroes of polynomials when suitable
factors are available, and use the zeroes to construct a
rough
QC:
F.1.b.-Factor polynomials using a variety of methods (eg:
factor theorem, synthetic division, long division, sum and
difference of cubes, and grouping)
F.2.a-Determine the number and type of rational zeros for
a polynomial function
F.2.b.-Find all rational zeros of a polynomial function.
F.2.c.- Recognize the connection among zeros of a
polynomial function, x-intercepts, factors of polynomials,
and solutions of polynomial equations.
A.REI.2 – Solve simple rational and radical equations in
one variable and give examples showing how extraneous
To simplify the nth root of an
expression, what must be true
2015-2016
Unit 9 – Function Operations and
Inverses
Unit 10 – Sequences and Series
Larry A. Ryle High School
1 week
1-2 weeks
solutions may arise.
QC:
G.1.b.-Simplify radicals that have various indices.
G.1.c.-Use properties of roots and rational exponents to
evaluate and simplify expressions.
G.1.d.-Add, subtract, multiply, and divide expressions
containing radicals.
G.1.e.-Rationalize denominators containing radicals and
find the simplest common denominator.
G.1.f.-Evaluate expressions and solve equations
containing nth roots or rational exponents.
G.1.g.-Evaluate and solve radical equations given a
formula for a real-world situation.
F.BF.1.b – Write a function that describes a relationship
between two quantities: Combine standard function types
using arithmetic operation. For example, build a function
that models the temperature of a cooling body by adding a
constant function to a decaying exponential, and relate
these functions to the model.
F.BF.4.a – 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.
QC:
C.1.d.-Perform operations on functions, including function
composition, and determine domain and range for each of
the given functions.
QC:
H.2.a.-Find the nth term of an arithmetic or geometric
sequence.
H.2.b.-Find the position of a given term of an arithmetic
or geometric sequence.
H.2.c.-Find sums of a finite arithmetic or geometric series.
H.2.d.-Use sequences and series to solve real-world
problems.
H.2.e.-Use sigma notation to express sums.
about the expression?
When you square each side of
an equation, is the resulting
equation equivalent to the
original?
How are a function and its
inverse related?
How are a function and its
inverse function related?
How are composition of
functions and inverse
functions used in our lives?
How can you represent the
terms of a sequence explicitly?
What are explicit
representations of arithmetic
and geometric sequences?
How do you write and
algebraic representation of an
arithmetic series or a
geometric series?
2015-2016
Larry A. Ryle High School