Last updated: 2/12/2024

Algebra 2 Next Gen

9 days, 1 Quiz and 1 Test

Unit 1 Algebraic Essentials Review
(2) 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.
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(3) AII.A.REI.11 Given the equations y = f(x) and y = g(x):
  1. recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
  2. find the solutions approximately using technology to graph the functions or make tables of values;
  3. find the solution of f(x) < g(x) or f(x) <= g(x) graphically; and
  4. interpret the solution in context. ★
(1) AII.A.REI.1b Explain each step when solving rational or radical equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
(5) AII.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Write complex solutions in a + bi form.
(4) AII.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(3) AII.A.SSE.3a Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
(4) AII.A.SSE.3c Use the properties of exponents to rewrite exponential expressions.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(3) AII.N.RN.2 Convert between radical expressions and expressions with rational exponents using the properties of exponents.
(2) N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

1. Can you solve an equation?

2. Can you combine like terms and manipulate exponents?

3. Can you multiply polynomials?

#1 – Variables, Terms and Expressions

#2 – Solving Linear Equations 

#3 – Common Algebraic Expressions

#4 – Basic Exponent Manipulation

#5 – Multiplying Polynomials

#6 – Using Tables on Your Calculator

Algebraic Expression

Associative Property

Bimodal

Commutative Property

Distributive Property

Equivalent Expressions

Evaluate

Expression

Identity

Inconsistent

Integer

Justify

Like Terms

Monomial

Polynomial

Quadratics Expression

Rational Expressions

Standard form of a Polynomial

Terms

Trinomial

Variable

I can...

  • Evaluate algebraic expressions
  • Combine like terms
  • Solve linear equations
  • use and manipulate exponent rules for multiplying polynomials
  • use the STORE function in the calculator and finding values from tables 

Unit 1 Cover Sheet.docx
CC Algebra Spiral Review One.docx
A2 Unit 1 review.docx
CC-Algebra-II.Unit-1-Review.docx
Store Feature Directions.notebook
Unit 1 Note pages..docx
emathinstruction.com

 

 

11 days, 1 Quiz and 1 Test

Unit 2: Functions As The Cornerstones Of Algebra
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(3) AII.A.REI.11 Given the equations y = f(x) and y = g(x):
  1. recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
  2. find the solutions approximately using technology to graph the functions or make tables of values;
  3. find the solution of f(x) < g(x) or f(x) <= g(x) graphically; and
  4. interpret the solution in context. ★
(3) AII.A.REI.7b Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
(3) AII.F.BF.1 Write a function that describes a relationship between two quantities.
(4) AII.F.BF.1a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(3) AII.F.BF.4a Find the inverse of a one-to-one function both algebraically and graphically.
(5) AII.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities;
  2. sketch graphs showing key features given a verbal description of the relationship.
(3) AII.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
(4) AII.F.IF.7e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(1) F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
(1) F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
(1) 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) 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.★
(1) 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.

1. Can you define a function and a one-to-one function?

2. Can you use and understand function notation and inverse function notation?

3. Can you use composition of function to simplify or solve expressions?

4. Can you find the domain and range of a function?

#1 – Introduction to Functions 

#2 – Function Notation

#3 – Function Composition

#4 – The Domain and Range of a Function

#5 – One to One Functions

#6 – Inverse Functions

#7 – Key Features of Functions

Composition of functions

Constant

Decreasing Function

Dependent Variable

Domain

Function

f(g(x))

(f◦ g)(x)

f-1(x)

Horizontal Line Test

Increasing Function

Interval Notation

Input

Inverse of a Function

Maximum

Minimum

One-to-one

Output

Range

Set Builder Notation

Vertical Line Test

X-intercepts

Zeros

I can...

  • Evaluate functions algebraically and from a graph
  • Determine domain and range
  • identify and define one to one functions
  • use and create inverse functions
  • identify and use the vocabulary of functions

CCAlgII-U2L2-Function-Notation.pdf
CCAlgII-U2L3-Function-Composition.pdf
Composition of Functions Word problems (Electrical Circuits).docx
CC-Algebra-II.Unit-2-Review.docx
Algebra 2 Unit 2 vocabulary.docx
Quiz Function Notation and Composition of Functions.docx
Unit 2 Cover Sheet.docx
Unit 2 Note Pages.docx
Unit 2 Outline.docx

12 days, 1 Quiz and 1 Test

Unit 3: Linear Functions, Equations, And Their Algebra
(1) (+).F.BF.4b Verify by composition that one function is the inverse of another.
(1) (+).F.BF.4c Given the graph or table of an invertible function, determine coordinates of its inverse.
(1) (+).F.BF.4d Determine an invertible function from a non-invertible function by restricting the domain.
(3) AII.A.REI.11 Given the equations y = f(x) and y = g(x):
  1. recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x);
  2. find the solutions approximately using technology to graph the functions or make tables of values;
  3. find the solution of f(x) < g(x) or f(x) <= g(x) graphically; and
  4. interpret the solution in context. ★
(3) AII.F.BF.1 Write a function that describes a relationship between two quantities.
(4) AII.F.BF.1a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(3) AII.F.BF.4a Find the inverse of a one-to-one function both algebraically and graphically.
(5) AII.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities;
  2. sketch graphs showing key features given a verbal description of the relationship.
(2) AII.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(1) A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
(2) F-LE.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).

1. Can you find the average rate of change of a function?

2. Can you use and write equations of lines in various forms?

3. Can you graph a piecwise function?

4. Can you solve a system of equations?

#1 – Direct Variation

#2 – Average Rate of Change

#3 – Forms of a Line

#4 – Linear Modeling

#5 – Inverses of Linear Functions

#6 – Piecewise Linear Functions

#7 - Systems of Linear Equations (Primarily 3 by 3)

Constant of Variation            

Direct Variation                                 

Parallel Lines                          

Perpendicular Lines

Piecewise Functions

Proportional Relationship

Rate of Change

Slope-Intercept of a Line

Solving Systems of Equations

Step Function

I can...

  • Write and solve proportions
  • use the average rate of change formula
  • determine the slope between two points
  • Write the equation of a line using slope/intercept and point/slope form
  • Writing/graphing an inverse function 
  • graphing peicewise functions
  • solve systems of equations with 3 equations and 3 unknowns

Graphing Piecewise functions Page 2.docx
Graphing Piecewise functions Page 1.docx
Equations of Lines.docx
Unit 3 Homework Packet ALL.pdf
End of Unit 3 Packet.pdf
Piecewise Functions.pdf
Piecewise functions-linear.pdf
SYSTEMS OF EQUATIONS.docx
Word Problems Systems 3 equations 3 variables.docx
CC-Algebra-II.Unit-3-Review.docx
Unit 3 Note Pages.docx
Unit 3 Outline.docx
Unit 3 Vocabulary.docx

30 days, 2 Quizzes and 1 Test

Unit 4: Exponential And Logarithmic Functions
(1) A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(2) AII.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(4) AII.A.SSE.3c Use the properties of exponents to rewrite exponential expressions.
(3) AII.F.BF.4a Find the inverse of a one-to-one function both algebraically and graphically.
(5) AII.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities;
  2. sketch graphs showing key features given a verbal description of the relationship.
(2) AII.F.IF.6 Calculate and interpret the average rate of change of a function over a specified interval.
(4) AII.F.IF.7e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(2) AII.N.RN.1 Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
(3) AII.N.RN.2 Convert between radical expressions and expressions with rational exponents using the properties of exponents.
(1) F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
(1) F-BF.1.b 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.
(2) F-LE.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).
(1) N-RN.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.
(2) N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

1. Can you use the law of exponents and logs?

2. Can you solve exponential and logarithmic equations?

3. Can you graph logarithmic functions?

4. Can you use and solve equations with "e" and the natural log?

5. Can you solve word problems using exponents and logs?

#1 – Integer Exponents

#2 – Rational Exponents

#3 – Exponential Function Basics

#4 – Finding Equations of Exponentials

#5 – The Method of Common Bases

#6 – Exponential Modeling with Percent Growth and Decay

#7 – Mindful Percent Manipulations

#8 – Introduction to Logarithms

#9 – Graphs of Logarithms

#10 – Logarithm Laws

#11 – Solving Exponential Equations Using Logarithms

#12 – The Number e and the Natural Logarithm

#13 – Compound Interest

#14 – Newton's Law of Cooling

Common Base

e

 

Exponential Function

Logarithmic Function

Natural Log

Rational Exponents

Roots

I can...

  • Use the calculator to find the regression equation for an exponential function
  • work with exponents that are negative and rational
  • understand basic parts of an exponential function
  • Use the method for changing the base to solve exponential equations
  • graph logarithms 
  • use logarithms to solve equations

A2 exp function review.docx
Jmap Pages Exponential Functions.notebook
Lesson 4 Exponential Equations Worksheet.docx
Log And Exponent review - Lori.docx
Logarithm Worksheet -Review.doc
Regents Exponential Equations A=Pert.doc
CC-Algebra-II.Unit-4-Review.docx
A.SSE.B.3.ModelingExponentialFunctions2.doc
Algebra_2Exponents Problem Attic.pdf
Jmap Pages Exponential Functions.notebook
Unit 4 Note Pages.docx
Unit 4 Outline.docx

10 days, 1 Quiz and 1 Test

Unit 5: Sequences And Series 
(4) AII.F.BF.1a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(1) AII.F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
(1) AII.F.IF.3 Recognize that a sequence is a function whose domain is a subset of the integers.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(1) 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. For example, calculate mortgage payments.
(1) F-IF.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) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

1. Can you identify Arithmetic and Geometric Sequences?

2. Can you use summation notation?

3. Can you use Arithmetic and Geometric Series?

#1 – Sequences

#2 – Arithmetic and Geometric Sequences

#3 – Summation Notation

#4 – Arithmetic Series

#5 – Geometric Series

#6 – Mortgage Payments

an term

Arithmetic Sequence

Common Difference

Common Ratio

Explicit Definition

Geometric Sequence

Index

Recursive Definition

Sequence

Series

Sigma Notation

Summation

I can...

  • find common different or common ratio
  • Match a formula to a series of numbers
  • find a specific term of a sequence given a formula
  • Evaluate sums given Sigma notation
  • Find sums of arithmetic and geometric series

Sequences- Arithemtic and Geometric.docx
Christmas Bonus.docx
DO Now Sequences.docx
Sequences and Arithmetic Sequences Extra Practice.docx
Series and Sequences Practice (half page).docx
A2 cc Unit 5 review 201`7.docx
CC-Algebra-II.Unit-5-Review.docx
Notes Unit 5.docx
Unit 5 Note Page Formulas and Vocab.docx

22 days, 2 Quiz and 1 Test

Unit 6: Quadratic Functions And Their Algebra
(2) 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.
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(5) AII.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Write complex solutions in a + bi form.
(3) AII.A.REI.7b Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
(4) AII.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(3) AII.A.SSE.3a Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
(3) AII.F.BF.3b Using f(x) + k, k f(x), f(kx), and f(x + k):
  1. identify the effect on the graph when 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);
  2. find the value of k given the graphs;
  3. write a new function using the value of k; and
  4. use technology to experiment with cases and explore the effects on the graph.


Include recognizing even and odd functions from their graphs.
(2) A-REI.4 Solve quadratic equations in one variable.
(1) A-REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
(2) A-REI.4.b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
(1) A-REI.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.
(1) 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).
(1) 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.★
(1) G-GPE.2 Derive the equation of a parabola given a focus and directrix.

1. Can you factor polynomials by factoring completely and by grouping?

2. Can you use the zero product law?

3. Can you solve quadratic inequalities?

4. Can you use completeing the square to find the vertex form of a parabola?

5. Can you write and interpret equations of circles?

6. Can you determine the equation of a parabola using the focus and directrix?

5. 

#1 – Quadratic Function Review

#2 – Factoring

#3 – Factoring Trinomials

#4 – Complete Factoring

#5 – Factoring by Grouping

#6 – The Zero Product Law

#7 – Quadratic Inequalities in One Variable

#8 – Completing the Square and Shifting Parabolas

#9 – Modeling with Quadratic Functions

#10 – Equations of Circles

#11 – The Locus Definition of a Parabola

Axis of Symmetry

Completing the Square

Conjugates

Difference of Perfect Squares

Directrix

Equidistant

Factor (noun)

Factor (verb)

Factoring by Grouping

Focus

Locus Definition of a Parabola

Parabola

Quadratic Function

Turning Point

Vertex

x – intercepts

y – intercepts

Zero Product Law

I can...

  • Factor Quadratic Trinomials
  • Factor by grouping
  • Completing the square
  • solve quadratic equations
  • use interval noatation to write solutions of quadratic inequalities
  • write and equation of a circle

A2_Quadratic_Functions_and_Their.pdf
Factor Completely.docx
Problem-Attic Unit 6 Quadratic Functions and Their Algebra.notebook
Quadratic Functions and Their Algebra.docx
CC-Algebra-II.Unit-6-Review.docx
Unit 6 Cover Sheet.docx

10 days and 1 Test

Unit 7: Transformations Of Functions
(2) (+).F.BF.3c Determine algebraically whether or not a function is even or odd.
(3) AII.F.BF.3b Using f(x) + k, k f(x), f(kx), and f(x + k):
  1. identify the effect on the graph when 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);
  2. find the value of k given the graphs;
  3. write a new function using the value of k; and
  4. use technology to experiment with cases and explore the effects on the graph.


Include recognizing even and odd functions from their graphs.
(4) AII.F.IF.7e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

1. Can you shift, reflect and stretch functions?

2. Can you identify even and odd functions?

3. Can you use transformations to write and interpret equations of logs and radical functions?

#1 – Shifting Functions

#2 – Reflecting Parabolas

#3 – Vertically Stretching of Functions

#4 – Horizontal Stretching of Functions

#5 – Even and Odd Functions

Even Function

Horizontal

Odd Function

Reflection

Shift

Shrink

Stretch

Vertical

I can...

  • Understand function notation
  • graph various functions
  • shift functions up, down, left and right
  • reflect functions
  • Horizontally/Vertically stretch and compress functions

Transformations of Logarithmic Functions.docx
Transformations of Radical Functions.doc
CC-Algebra-II.Unit-7-Review.docx
Unit 7 Cover Sheet.docx
Unit 7 Note Pages.docx
Unit 7 Review.notebook
Unit 7 Title Page.docx

9 days and 1 Quiz...Test is given with Unit 9

Unit 8: Radicals And The Quadratic Formula
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(2) AII.A.REI.2 Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
(5) AII.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Write complex solutions in a + bi form.
(4) AII.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(4) AII.A.SSE.3c Use the properties of exponents to rewrite exponential expressions.
(3) AII.F.BF.3b Using f(x) + k, k f(x), f(kx), and f(x + k):
  1. identify the effect on the graph when 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);
  2. find the value of k given the graphs;
  3. write a new function using the value of k; and
  4. use technology to experiment with cases and explore the effects on the graph.


Include recognizing even and odd functions from their graphs.
(5) AII.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities;
  2. sketch graphs showing key features given a verbal description of the relationship.
(3) AII.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(2) AII.N.RN.1 Explore how the meaning of rational exponents follows from extending the properties of integer exponents.
(3) AII.N.RN.2 Convert between radical expressions and expressions with rational exponents using the properties of exponents.
(1) A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
(2) A-REI.4.b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

1. Can you simplify radicals with various indexes?

2. Can you use exponent properties to simplify radicals?

3. Can you solve equations with radicals?

4. Can you solve quadratic equations using the quadratic formula?

#1 – Square Root Functions

#2 – Solving Square Root Equations

#3 – The Basic Exponent Properties

#4 – Fractional Exponents Revisited

#5 – More Exponent Practice

#6 – The Quadratic Formula

#7 – More Work with the Quadratic Formula

Extraneous Roots

Quadratic Formula

I can...

  • graph square root functions
  • simplify square roots
  • solve square root equations
  • Basic exponent properties
  • Use the quadratic formula

CC-Algebra-II.Unit-8-Review.docx
Unit 8 Cover Sheet.docx
Unit 8 Notes.docx

9 days, 1 Quiz and 1 Test on Units 8  and 9

Unit 9: Complex Numbers
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(5) AII.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Write complex solutions in a + bi form.
(3) AII.A.REI.7b Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
(1) AII.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.
(1) AII.N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
(2) A-REI.4 Solve quadratic equations in one variable.
(1) N-CN.7 Solve quadratic equations with real coefficients that have complex solutions.

1. Can you use the powers of "i"?

2. Can you add, subtract and multiply complex numbers?

3. Can you solve quadrtic equations with complex solutions?

4. Can you use the discriminant to determine types of roots?

#1 – Imaginary Numbers

#2 – Complex Numbers

#3 – Solving Quadratic Equations with Complex Solutions

#4 - The Discriminant of a Quadratic

Complex Numbers (closed)

Complex Roots

Discriminant

i

Imaginary Numbers

Irrational Roots

Tangent ( to the x-axis)

I can...

  • Simplify square roots
  • multiply binomials
  • use the quadratic formula
  • use the discriminant

A2 Unit 9 Review.docx
CC-Algebra-II.Unit-9-Review.docx
Unit 9 Cover Sheet.docx
Unit 9 Imaginary Numbers Note Pages.docx

17 days, 1 Quiz and 1 Test

Unit 10: Polynomial And Rational Functions
(2) (+).F.BF.3c Determine algebraically whether or not a function is even or odd.
(1) A-APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.
(1) AII.A.APR.2 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).
(7) AII.A.APR.3 Identify zeros of polynomial functions when suitable factorizations are available.
(1) AII.A.APR.6 Rewrite 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).
(2) AII.A.CED.1 Create equations and inequalities in one variable to represent a real-world context.
(2) AII.A.REI.2 Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.
(5) AII.A.REI.4b Solve quadratic equations by:
  1. inspection,
  2. taking square roots,
  3. factoring,
  4. completing the square,
  5. the quadratic formula, and
  6. graphing.


Write complex solutions in a + bi form.
(4) AII.A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.
(3) AII.A.SSE.3a Factor quadratic expressions including leading coefficients other than 1 to reveal the zeros of the function it defines.
(4) AII.A.SSE.3c Use the properties of exponents to rewrite exponential expressions.
(3) AII.F.BF.1 Write a function that describes a relationship between two quantities.
(4) AII.F.BF.1a Determine a function from context. Determine an explicit expression, a recursive process, or steps for calculation from a context.
(3) AII.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
(6) AII.F.IF.8b Use the properties of exponents to interpret exponential functions, and classify them as representing exponential growth or decay.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(1) A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

1. Can you add, subtract, multiply, divide and simplify rational expressions?

2. Can you solve rational equations?

3. Can you solve rational inequalities?

4. Can you identify the zeros of a polynomial?

5. Can you use the zeros to create polynomial equations?

6. Can you determine if an equation is an identity? 

7. Can you use long division?

8. Can you use the remainder theorem to determine roots/factors?

#1 – Power Functions

#2 – Graphs and Zeroes of a Polynomial

#3 – Creating Polynomial Equations

#4 – Polynomial Identities

#5 – Introduction to Rational Functions

#6 – Simplifying Rational Expressions

#7 – Multiplying and Dividing Rational Expressions

#8 – Combining Rational Expressions Using Addition and Subtraction

#9 – Complex Fractions

#10 – Polynomial Long Division

#11 – The Remainder Theorem

#12 – Solving Rational Equations

#13 – Solving Rational Inequalities

#14 - Reasoning About Radical and Rational Equations

Common Denominator

Common Factors

Complex Fraction

Critical Values

End Behavior

Extaneous Roots

Identity

Opposites

Power Functions

Reciprocal

Remainder Theorem

Quotient

Undefined

x-> infinity, x-> negative infinity

I can...

  • determine zeros of polynomial functions
  • understanding of x-intercepts and y-intercepts
  • factor polynomials
  • find common denominator using polynomials
  • long division of polynomials
  • Solve rational equations and inequalities

CC-Algebra-II.Unit-10-Review.docx
Unit 10 Notes.docx
Unit 10 Review for Test.docx

13 days and 1 Test(Take-Home)

Unit 11: The Circular Functions
(1) AI.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities; and
  2. sketch graphs showing key features given a verbal description of the relationship.
(1) AI.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(5) AII.F.IF.4 For a function that models a relationship between two quantities:
  1. interpret key features of graphs and tables in terms of the quantities;
  2. sketch graphs showing key features given a verbal description of the relationship.
(1) AII.F.IF.7 Graph functions and show key features of the graph by hand and using technology when appropriate. ★
(4) AII.F.IF.7e Graph cube root, exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.
(7) AII.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
(1) AII.F.TF.2 Apply concepts of the unit circle in the coordinate plane to calculate the values of the six trigonometric functions given angles in radian measure.
(1) AII.F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift, and midline.
(1) AII.F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1. Find the value of any of the six trigonometric functions given any other trigonometric function value and when necessary find the quadrant of the angle.
(1) F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

1. Can you convert from degrees to radians and radians to degrees?

2. Can you find the exact value of special angles in both degrees and radians using sine, cosine, tangent and reciprocal functions?

3. Can you graph sine and cosine functions?

4. Can you shift and stretch sine and cosine functions?

#1 – Rotations and Angle Terminology

#2 – Radian Angle Measurement

#3 – The Unit Circle

#4 – The Definition of the Sine and Cosine Functions

#5 – More Work with the Sine and Cosine Functions

#6 – Basic Graphs of Sine and Cosine

#7 – Vertical Shifting of Sinusoidal Graphs

#8 – The Frequency and Period of a Sinusoidal Graph

#9 – Sinusoidal Modeling

#10 – The Tangent Function

#11 - The Reciprocal Functions

30 – 60 – 90 Right Triangle

45 – 45 – 90 Right Triangle

Amplitude

Arc Length

Circular Functions

Cosecant

Cosine

Cotangent

Coterminal Angles

Degrees

Exact Values!

Frequency

Initial Ray

Midline (Average Value)

Negative/ Positive Rotation

Period

Periodic

Pythagorean Identity

Quadrantal Angles

Quadrants

Radian

Rationalize the Denominator

Reciprocal Function

Reference Angle

Secant

Sine

Sinusoidal Function

Standard Position            

Tangent

Terminal Ray

Trigonometric Functions

Unit Circle

I can...

  • draw and determine reference angles
  • convert degrees to radians and visa versa
  • work with the unit circle
  • understand Sine and Cosine as it relates to the unit circle

A2 1.5 11 review.docx
CC-Algebra-II.Unit-11-Review.docx
Unit 11 Circular Functions Notes.docx
Unit 11 Cover Sheet.docx
Unit 11 Review Smartboard.notebook

8 days

Unit 12: Probability
(1) S-CP.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").
(1) S-CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object 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 the student is in tenth grade. Do the same for other subjects and compare the results.
(1) S-CP.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.

1. Can you add and multiply probabilities? 

2. Can you use conditional probability?

3.  Can you use probability with independent and dependent events?

#1 – Introduction to Probability

#2 – Sets and Probability

#3 – Adding Probabilities

#4 – Conditional Probability

#5 – Independent Events

#6 – Multiplying Probabilities

Complement

Conditional Probability

Dependent

Elements

Empirical Probability

Event

Experiment

Fair

Intersection

Multi-Stage Experiments

Not Dependent (Independent)

Outcome

Product Test for Independence

Random

Sample Space

Set

Single-Stage Experiment

Subset

Theoretical Probability

Tree Diagram

Union

Venn Diagram

With Replacement

Without Replacement

I can...

  • understand basic probability, boith experimental and theoretical
  • Finding probabilities using addition (union and intersection)
  • Finding conditional probabilities
  • Finding probabilities based on independent events
  • Finding probabilities using multiplication (Multi-stage events with and without replacement)

Algebra-2Unit-12-Review2017.docx
CC-Algebra-II.Unit-12-Review.docx
Unit 12 Cover Sheet.docx
Unit 12 Probability Lessons and Homework.docx

7 days

Unit 13: Statistics
(1) AII.S.IC.6a Use the tools of statistics to draw conclusions from numerical summaries.
(1) AII.S.IC.6b Use the language of statistics to critique claims from informational texts. For example, causation vs correlation, bias, measures of center and spread.
(1) AII.S.ID.4a Recognize whether or not a normal curve is appropriate for a given data set.
(1) AII.S.ID.4b If appropriate, determine population percentages using a graphing calculator for an appropriate normal curve.
(1) AII.S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables’ values are related.
(1) AII.S.ID.6a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.
(1) S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
(1) S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
(1) S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

1. Can you explain situations involving variability and sampling?

2. Can you use and explain normal distribution and z-scores?

3. Can you use sample means and proportions?

4. Can you use data and find the regression?

#1 – Variability and Sampling

#2 – Population Parameters

#3 – The Normal Distributions

#4 – The Normal Distribution and Z-Scores

#5 – Sample Means

#6 – Sample Proportions

#7 – The Difference in Samples Means

#8 - The Distribution of Sample Means

#9 - The Distribution of Sample Proportions

#10 - Margin of Error

#11 – Linear Regression and Lines of Best Fit

#12 – Other Types of Regression

95% Confidence Interval

Bell Curve

Bias

Central Limit Theorem

Distribution of Sample Proportions

Experimental Studies

Exponential Regression

Induced Variability

Inferential

Inter-Individual Variability

Linear Regression

Margin of Error

Mean

Measurement Variability

Natural Variability

Normal Distribution

Observational Studies

Observational Variability

Percentile

Placebo

Population

Population Parameters

Randomization

Sample Variability

Sampling Bias

Standard Deviation

Survey

Variability

Z-Scores

I can...

  • Understand population parameters (box/whisker, standard deviation and mean)
  • Answer questions about Normal Distribution and standard deviations
  • Calculate z-scores
  • Reading and interpreting data
  • Interpreting computer simulations using margin of error and 95% confidence interval
  • Find regressions and correlations 

Calculator Regression.docx
Calculator Standard Deviation.docx
CC-Algebra-II.Unit-13-Review.docx
A2 Unit 13 test review 1.5 2017.docx
Unit 13 Cover Sheet.docx
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