Download 2016 Algebra 2 - KY and QC Standards based

ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 1: Solving Linear and Absolute Value Equations and Inequalities
Textbook Sections:
1-4 Solving Equations and formulas
1-5 Solving Inequalities
1-6 Absolute Value Equations and Inequalities
Kentucky’s Common Core Standards:
A.CED.A.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.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
A.SSE.A.2
Use the structure of an expression to identify ways to rewrite it.
Quality Core Standards:
D.1. Expressions, Equations, and Inequalities
A. Solve linear inequalities containing absolute value
B. Solve compound inequalities containing “and” and “or” and graph the solution set
I Can Statements:
Section 1.4
I can…
 Create and solve linear equations.
Section 1.5
I can…
 Create and solve inequalities.
 Create and solve compound inequalities (containing “and” or “or”).
 Graph the solution set for an inequality.
 Describe a solution set in both set notation and interval notation.
Section 1.6
I can…
 Create and solve absolute value equations and inequalities.
 Graph the solution set for an inequality.
 Describe a solution set in both set notation and interval notation.
PAGE 1 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 2: Systems and Linear Programming
Textbook Sections:
3-1/3-2 Solving Systems of Equations
2-8 Linear Inequalities (REVIEW to help with Systems of Inequalities)
3-3 Systems of Inequalities
3-4 Linear Programming
Kentucky’s Common Core Standards:
A.CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A.CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
A.REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection
between the line y = –3x and the circle x2 + y2 = 3.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include
reading these from a table).
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f (x ) and y = g(x ) intersect are the solutions of the equation f (x ) = g(x ); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x ) and/or g(x )
are linear, polynomial, rational, absolute value, exponential, and logarithmic functions
F.BF.B.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.
Quality Core Standards:
D.1. Expressions, Equations, and Inequalities
c. Solve algebraically a system containing three variables
D.2. Graphs, Relations, and Functions
a. Graph a system of linear inequalities in two variables with and without technology to find the solution set to the system
b. Solve linear programming problems by finding maximum and minimum values of a function over a region defined by linear inequalities
I Can Statements:
Sections 3.1 & 3.2
I can…
 Solve a system of linear equations both graphically and algebraically.
PAGE 2 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Sections 3.5, 2.8, & 3.3
I can…
 Solve a system of equations with three unknowns. Do in Unit 3 Matrices.
 Graph inequalities. (REVIEW from Algebra 1 to help with solving systems of inequalities)
 Solve systems of inequalities with and without technology.
Section 3.4
I can…
 Create and solve linear programming models by creating and graphing constraints, then finding maximum and minimum values of an objective function over a
region defined by linear inequalities.
PAGE 3 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 3: Matrices
Textbook Sections:
12-1 Adding and Subtracting Matrices
12-2 Matrix Multiplication
12-3 Determinants and Inverses
12-4 Inverse Matrices and Systems
3-6 Systems with Three Variables
Kentucky’s Common Core Standards:
N.VM.C.6
Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
N.VM.C.7
Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N.VM.C.8
Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.C.9
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and
distributive properties.
N.VM.C.10
Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a
square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Quality Core Standards:
D.1. Expressions, Equations, and Inequalities
c. Solve algebraically a system containing three variables
I.1. Matrices
a. Add, subtract, and multiply matrices
b. Use addition, subtraction, and multiplication of matrices to solve real-world problems
c. Calculate the determinant of 2 × 2 and 3 × 3 matrices
d. Find the inverse of a 2 × 2 matrix
e. Solve systems of equations by using inverses of matrices and determinants
f. Use technology to perform operations on matrices, find determinants, and find inverses
I Can Statements:
Sections 12-1 & 12-2
I can…
 Represent data as a matrix.
 Add, subtract, and multiply matrices.
 Use technology to perform operations on matrices, find determinants, and find inverses.
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ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Section 12-3
I can…
 Calculate the determinant of 2x2 and 3x3 matrices.
 Find the inverse of 2x2 matrices.
 Use technology to perform operations on matrices, find determinants, and find inverses.
Sections 12-4 & 3-6
I can…
 Solve matrix equations by using inverses of matrices and determinants.
 Solve a system of equations with three variables using matrices.
 Use technology to perform operations on matrices, find determinants, and find inverses.
PAGE 5 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 4: Functions and Introduction to Quadratics
Textbook Sections:
2-1 Relations of Functions
6-6 Function Operations
4-1 Quadratic Functions and Transformations
4-2 Standard Form of a Quadratic Function
4-3 Modeling with Quadratic Functions
Kentucky’s Common Core Standards:
A.CED.A.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.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A.CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
A.APR.A.1
Understand that polynomials (quadratics) form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and
multiplication; add, subtract, and multiply polynomials
F.IF.B.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.B.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) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F.IF.C.7.b
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square
root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Write a function
that describes a relationship between two quantities. (Transformations of Functions)
A.SSE.A.1a
Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.A.1b
Interpret expressions that represent a quantity in terms of its context.*(Modeling standard) b. Interpret complicated expressions by viewing one or more of their parts as
a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
PAGE 6 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f (x ) and y = g(x ) intersect are the solutions of the equation f (x ) = g(x ); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x ) and/or g(x )
are linear, polynomial, rational, absolute value, exponential, and logarithmic functions
F.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context
F.BF.B.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.
Quality Core Standards:
C.1. Foundations
d. Perform operations on functions, including function composition, and determine domain and range for each of the given functions
E.2. Graphs, Relations, and Functions
a. Determine the domain and range of a quadratic function; graph the function with and without technology
b. Use transformations (e.g., translation, reflection) to draw the graph of a relation and determine a relation that fits a graph
I Can Statements:
Sections 2-1 & 6-6
I can…
 Determine the domain and range of a given function.
 Evaluate functions.
 Add, subtract, multiply, and divide functions.
 Find the composite of two functions.
Section 4-1
I can…
 Use transformations to (e.g. translations and reflections) to draw the graph of a relation and determine a relation that fits the graph.
 Graph quadratic functions written in vertex form.
Section 4-2
I can…
 Graph quadratic functions written in standard form.
 Convert equations in standard form to vertex form and vice versa.
Section 4-3
I can…
 Model data with quadratic functions.
 Apply quadratic functions to solve real world problems.
PAGE 7 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 5: Solving Quadratic Equations and Quadratic Systems
Textbook Sections:
4-4 Factoring Quadratic Expressions
** Simplifying Radicals & Rationalizing Denominators **
4-5 Solving Quadratic Equations
4-7 Quadratic Formula and Discriminants
4-8 Complex Numbers
4-6 Completing the Square
4-9 Quadratic Systems
Kentucky’s Common Core Standards:
A.CED.A.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.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A.CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling
context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
F.IF.B.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.B.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) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
A.SSE.B.3a
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function defines.***
N.CN.A.2
Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers
N.CN.C.7
Solve quadratic equations with real coefficients that have complex solutions.
A.APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.**Write
functions given the zeros
A.REI.C.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection
between the line y = –3x and the circle x2 + y 2 = 3.
PAGE 8 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f (x ) and y = g(x ) intersect are the solutions of the equation f (x ) = g(x ); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x ) and/or g(x )
are linear, polynomial, rational, absolute value, exponential, and logarithmic functions
N.CN.A.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.
F.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context
F.BF.B.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.
Quality Core Standards:
C.1. Foundations
a. Identify complex numbers and write their conjugates
b. Add, subtract, and multiply complex numbers
c. Simplify quotients of complex numbers
E.1. Equations and Inequalities
a. Solve quadratic equations and inequalities using various techniques, including completing the square and using the quadratic formula
b. Use the discriminant to determine the number and type of roots for a given quadratic equation
c. Solve quadratic equations with complex number solutions
d. Solve quadratic systems graphically and algebraically with and without technology
c. Graph a system of quadratic inequalities with and without technology to find the solution set to the system
E.2. Graphs, Relations, and Functions
c. Graph a system of quadratic inequalities with and without technology to find the solution set to the system
I Can Statements:
Lesson 4.4
I can…
 Factor quadratic expressions for 𝑎 = 1 and 𝑎 ≠ 1. (Assessed on DCA as part of solving quadratic equations.)
Lesson 4.5
I can…
 Simplify radical expressions (NOT assessed on DCAs)
 Solve quadratic equations by graphing.
 Solve quadratic equations by factoring.
 Solve quadratic equations by finding the square root.
 Apply quadratic equations to solve real world problems.
Lesson 4.7
I can…
 Solve quadratic equations using the quadratic formula.
PAGE 9 OF 24
ALGEBRA 2 UNIT SCHEDULE

Last revised: 7/13/16
Apply quadratic equations to solve real world problems.
Lesson 4.8
I can…
 Perform operations with complex numbers.
 Find complex number solutions of quadratic equations.
Lesson 4.6
I can…
 Solve quadratic equations by completing the square.
Lesson 4.9
I can…
 Solve quadratic systems of equations and/or inequalities.
Concept Byte
I can…
 Solve a one variable quadratic inequality.
PAGE 10 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 6: Polynomials
Textbook Sections:
5-1 Polynomial Functions
5-2 Polynomials, Linear Functions, and Zeros
5-3 Solving Polynomial Equations
5-4 Dividing Polynomials
5-5 Theorems about Roots of Polynomial Equations
5-6 Fundamental Theorem of Algebra
Kentucky’s Common Core Standards:
A.CED.A.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.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.B.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.B.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) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Write a function
that describes a relationship between two quantities.
(Transformations of Functions)
A.SSE.3a
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function defines.***
A.APR.A.1
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
A.APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.**Write
functions given the zeros.
A.APR.B.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.D.6
Rewrite simple rational expressions in different forms; write a(x )/b(x ) in the form q(x ) + r (x )/b(x ), where 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.
PAGE 11 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f (x ) and y = g(x ) intersect are the solutions of the equation f (x ) = g(x ); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x) and/or g(x ) are
linear, polynomial, rational, absolute value, exponential, and logarithmic functions
F.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context
F.IF.C.7c
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. c. Graph
polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F.BF.B.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.
N.CN.C.8 (+ )
***(not covered in ACT Course Standards) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
Quality Core Standards:
F.1. Expressions and Equations
a. Evaluate and simplify polynomial expressions and equations
b. Factor polynomials using a variety of methods (e.g., factor theorem, synthetic division, long division, sums and differences of cubes, grouping)
F.2. Functions
a. Determine the number and type of rational zeros for a polynomial function
b. Find all rational zeros of a polynomial function
c. Recognize the connection among zeros of a polynomial function, x-intercepts, factors of polynomials, and solutions of polynomial equations
d. Use technology to graph a polynomial function and approximate the zeros, minimum, and maximum; determine domain and range of the polynomial function
I Can Statements:
Section 5-1
I can…
 Simplify polynomial expressions.
 Graph and identify key features of polynomial functions.
Section 5-2
I can…
 Analyze the factored form of a polynomial.
 Write a polynomial function from its zeros.
Section 5-3
I can…
 Solve equations by factoring.
 Identify real roots by graphing.
PAGE 12 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Section 5-4
I can…
 Divide polynomials using long division.
 Divide polynomials using synthetic division.
Sections 5-5 and 5-6
I can…
 Solve equations using the Rational Root Theorem.
 Use the Conjugate Root Theorem.
 Use the Fundamental Theorem of Algebra to identify all roots of a polynomial to describe zeros of a polynomial function.
PAGE 13 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 7: Radical Expressions and Unit 8: Rational Expressions
Textbook Sections:
6-1 Roots and Radical Expressions
6-2 Multiplying and Dividing Radical Expressions
6-3 Binomial Radical Expressions
6-4 Rational Exponents
6-5 Solving Radical Equations
6-8 Graphing Radical Functions
8-4 Rational Expressions
8-5 Add and Subtract Rational Expressions
8-6 Solving Rational Equations
Kentucky’s Common Core Standards:
A.CED.A.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.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
N.RN.A.1
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
N.RN.A.2
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
A.REI.A.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
F.IF.B.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.B.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) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F.IF.C.7.B
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F.IF.C.7.D
(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given
a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
F.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
PAGE 14 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
A.BF.A.1
Combine standard function types using arithmetic operations. 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.B.3
Identify the effect on the graph of replacing f(x) by f(x) + k, kff(x), f(kx), and f(x + k) for special 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.BF.B.4a
Solve an equation of the form f(x) =x for a simple function f that has an inverse and write an expression for the inverse. For example:
𝑓(𝑥) = 2𝑥 3 𝑓𝑜𝑟 𝑥 > 0 𝑜𝑟 𝑓(𝑥) =
𝑥+1
𝑓𝑜𝑟 𝑥 ≠ 1.
𝑥−1
Quality Core Standards:
C.1. Foundations
d. Perform operations on functions, including function composition, and determine domain and range for each of the given functions
G.1. Rational and Radical Expressions, Equations, and Functions
a. Solve mathematical and real-world rational equation problems (e.g., work or rate problems)
b. Simplify radicals that have various indices
c. Use properties of roots and rational exponents to evaluate and simplify expressions
d. Add, subtract, multiply, and divide expressions containing radicals
e. Rationalize denominators containing radicals and find the simplest common denominator
f. Evaluate expressions and solve equations containing nth roots or rational exponents
g. Evaluate and solve radical equations given a formula for a real-world situation
I Can Statements:
Chapter 6 Sections 1 and 2
I can…
 Apply properties of exponents to simplify an expression.
 Find nth roots.
 Multiply, divide, & simplify radical expressions.
Chapter 6 Sections 3 and 4
I can…
 Add and subtract binomial radical expressions.
 Multiply binomial radical expressions.
 Rationalize expressions with radicals in the denominator.
 Convert radicals to rational exponents, and vice versa.
 Simplify radical expressions by converting radicals to exponents.
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ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Chapter 6 Section 5
I can…
 Solve equations involving one or more radicals.
Chapter 6 Section 8
I can…
 Graph radical functions.
 Translate radical functions.
Sections 8-5 & 8-6
I can…
 Determine the least common multiple for a pair of polynomials. (NOT assessed directly on DCAs).
 Solve rational equations.
 Use rational equations to solve real world problems.
Section 8-2
I can…
 Graph rational functions and identify the key features.
PAGE 16 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 9: Exponential and Log Functions
Textbook Sections:
7-1 Exploring Exponential Functions
7-2 Properties of Exponential Functions
7-3 Logarithmic Functions as Inverses
7-4 Properties of Logs
7-5 Exponential and Logarithmic Equations
7-6 Natural Logarithms
Kentucky’s Common Core Standards:
F.IF.C.7e
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph
exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Write a function
that describes a relationship between two quantities. (Transformations of Functions)
F.BF.B.5
(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
F.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F.BF.B.4a
Find inverse functions. 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.
A.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f (x ) and y = g(x ) intersect are the solutions of the equation f (x ) = g(x ); find the
solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f (x ) and/or g(x )
are linear, polynomial, rational, absolute value, exponential, and logarithmic functions
F.BF.B.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.
Quality Core Standards:
C.1. Foundations
d. Perform operations on functions, including function composition, and determine domain and range for each of the given functions
G.2. Exponential and Logarithmic Functions
a. Graph exponential and logarithmic functions with and without technology
b. Convert exponential equations to logarithmic form and logarithmic equations to exponential form
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ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
I Can Statements:
Chapter 7 Sections 3, 4 & 6
I can…
 Convert from logarithmic form to exponential form and vice versa.
 Evaluate logarithmic functions of different bases (use change of base formula).
 Use the properties of logarithms to expand and condense logarithm and natural logarithm expressions.
Chapter 7 Sections 5 & 6
I can…
 Solve exponential equations.
 Solve logarithmic equations.
 Solve equations using natural logarithms.
Chapter 7 Sections 1, 2, & 3
I can…
 Graph exponential and logarithmic functions.
 Model and solve real world problems using exponential and logarithmic functions.
PAGE 18 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 10: Sequences and Series
Textbook Sections:
9-2 Arithmetic Sequences
9-4 Arithmetic Series
9-3 Geometric Sequences
9-5 Geometric Series
Kentucky’s Common Core Standards:
A.SSE.B.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. For example, calculate mortgage
payments
F.LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F.IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined
recursively by f(0) = f(1), f(n + 1) = f(n) + f(n-1) for n ≥ 1.
F.IF.B.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) gives the number of
person hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
A.CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.BF.A.1a
Determine an explicit expression, a recursive process, or steps for calculation from a context.
F.BF.A.2
Write arithmetic and geometric sequences, both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
F.IF.B.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) gives the number of
person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Quality Core Standards:
H.2. Sequences and Series
a. Find the nth term of an arithmetic or geometric sequence
b. Find the position of a given term of an arithmetic or geometric sequence
c. Find sums of a finite arithmetic or geometric series
d. Use sequences and series to solve real-world problems
e. Use sigma notation to express sums
I Can Statements:
Sections 9-2 & 9-4
PAGE 19 OF 24
ALGEBRA 2 UNIT SCHEDULE
I can…




Last revised: 7/13/16
Find the nth term of an arithmetic sequence.
Find the position of a specified term of an arithmetic sequence.
Solve real world problems involving sequences and series.
Find the sum of an arithmetic sequence.
Sections 9-3 & 9-5
I can…
 Solve real world problems involving sequences and series.
 Find the nth term of a geometric sequence.
 Find the position of a specified term of a geometric sequence.
 Find the sum of a geometric sequence.
 Write a sum using sigma notation.
PAGE 20 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 11: Probability
Textbook Sections:
11-1 Permutations and Combinations
11-3 Probability of Multiple Events
11-4 Conditional Probability
Kentucky’s Common Core Standards:
S.CP.B.6
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
S.CP.B.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
S.CP.B.9
Use permutations and combinations to compute probabilities of compound events and solve problems.
S.CP.A.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of
other events ("or," "and," "not").
S.CP.A.2
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterizations to
determine if they are independent.
S.CP.A.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is
the same as the probability of A, and the conditional probability of B given A is the same as probability of B.
S.CP.A.4
Construct and interpret two-way frequency tables of data when two categories are associated with each other being classified. Use the two-way table as a sample space
to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their
favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that a student is in
10th grade. Do the same for other subjects and compare results.
S.CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of
having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Quality Core Standards:
H.1. Data Relations, Probability, and Statistics
a. Use the fundamental counting principle to count the number of ways an event can happen
b. Use counting techniques, like combinations and permutations, to solve problems (e.g., to calculate probabilities)
c. Find the probability of mutually exclusive and non-mutually exclusive events
d. Find the probability of independent and dependent events
e. Use unions, intersections, and complements to find probabilities
f. Solve problems involving conditional probability
PAGE 21 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
I Can Statements:
Probability
I can…
 Use the fundamental counting principle in real-world scenarios.
 Use permutations and combinations to solve problems.
 Calculate the probability of event A AND B and A OR B (for mutually and non-mutually exclusive events).
 Find conditional probability.
 Use tables and diagrams to determine conditional probability.
PAGE 22 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 12: Trigonometry
Textbook Sections:
13-2 Angles and the Unit Circle
13-3 Radian Measure
14-4 Area and Law of Sines
14-5 Law of Cosines
Kentucky’s Common Core Standards:
F.IF.C.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.IF.B.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.B.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) gives the
number of person hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
F.TF.B.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
F.TF.B.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of
angles traversed counterclockwise around the unit circle.
F.BF.B.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.TF.A.1: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
A.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quality Core Standards:
G.3. Trigonometric and Periodic Functions
a. Use the law of cosines and the law of sines to find the lengths of sides and measures of angles of triangles in mathematical and real-world problems
b. Use the unit-circle definition of the trigonometric functions and trigonometric relationships to find trigonometric values for general angles
c. Measure angles in standard position using degree or radian measure and convert a measure from one unit to the other
d. Graph the sine and cosine functions with and without technology
e. Determine the domain and range of the sine and cosine functions, given a graph
f. Find the period and amplitude of the sine and cosine functions, given a graph
g. Use sine, cosine, and tangent functions, including their domains and ranges, periodic nature, and graphs, to interpret and analyze relations
I Can Statements:
Trigonometry
I can…
 Use right triangle trigonometry to find an unknown side or angle measure. (NOT assessed on DCAs)
 Apply Law of Sines and Law of Cosines to find an unknown side or angle measure.
 Convert angle measures from radians to degrees and vice versa.
 Use the unit circle definition to evaluate trigonometry functions for general angles.
 Graph and interpret key features of cosine, sine, and tangent functions.
PAGE 23 OF 24
ALGEBRA 2 UNIT SCHEDULE
Last revised: 7/13/16
Unit 13: Conic Sections
Textbook Sections:
10-1 Exploring Conic Sections
10-2 Parabolas
10-3 Circles
10-4/10-5 Ellipses and Hyperbolas
Kentucky’s Common Core Standards:
F.IF.B.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.
G.GPE.A.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle
given by an equation. (Note: Algebra 2 completing the square problems)
G.GPE.A.2: Derive the equation of a parabola given a focus and directrix.
F.BF.B.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.
Quality Core Standards:
E.2. Graphs, Relations, and Functions
b. Use transformations (e.g., translation, reflection) to draw the graph of a relation and determine a relation that fits a graph
E.3. Conic Sections
a. Identify conic sections (e.g., parabola, circle, ellipse, hyperbola) from their equations in standard form
b. Graph circles and parabolas and their translations from given equations or characteristics with and without technology
c. Determine characteristics of circles and parabolas from their equations and graphs
d. Identify and write equations for circles and parabolas from given characteristics and graphs
I Can Statements:
Conic Sections
I can
 Identify conic sections from their standard form (parabolas, circles, ellipses, and hyperbolas).
 Graph conic sections (parabolas and circles).
 Write an equation for a conic section from its given characteristics (parabolas and circles).
 Determine various characteristics (center, vertex, focus, directrix) of a conic section given its equation (parabolas and circles).
PAGE 24 OF 24