Algebra 2 2020-2021

Prerequisites

Number Sets
  • Natural Numbers
  • Whole Numbers
  • Set of Integers
  • Rationals 
  • Irrationals
  • Real Numbers​
Notation and Abbreviations
  • Do you understand the shorthand used by advanced mathematics?
  • Can you translate verbal to symbolic?
  • Can you translate symbolic to verbal?
  • Can you describe specific portions of a graph, a function's domain, or a function's range using advanced notation?
Functions
  • Do you understand the notation, vocabulary, and abbreviations used to describe a function?
  • domain of a function
  • range of a function
  • end behavior of a function
  • asymptote of a function
  • vertex of a quadratic function
  • vertex of an absolute value function
  • composition of functions
  • inverse of a function
  • Can you perform and interpret the meaning of HLT and the VLT?
    • HLT = horizontal line test
    • VLT = vertical line test
  • Can you state the domain and range of a function using a variety of methods?
    • verbal
    • abbreviations
    • symbolic
  • Can you predict the integer or rational coordinates that lie on functions?
  • Can you perform operations with functions?
  • Can you perform composition with functions?
  • Do you understand the connection between a function and its inverse?
  • Can you write a piecewise function for an absolute value function or a quadratic function?
  • Can you determine a function's inverse when possible and be able to state when whether a singe inverse exists or not?
Exponent and Radical Laws
  • Do you know the exponent laws and definitions?
  • Do you know the radical laws and definitions?
  • Can you rewrite expressions that involve exponents?
  • Can you rewrite expressions that involve radicals? 
  • Can you rewrite an expression with negative exponents?
  • Can you convert an expression with fractional exponents to its related radical expression?
  • Can you convert an expression with a radical to its related  expression with  fractional exponents?
  • Can you convert an expression with fractional exponents to its related radical expression?
Factoring and Rewriting Expressions
  • Can you express a linear function in a variety of notations?
    • slope intercept
    • point slope
    • modified point slope
    • standard form
  • Can you express a quadratic function in a variety of notations?
    • standard form
    • vertex form
    • intercept form
  • ​Can you factor any quadratic expression?
  • Do you know the special patterns related to quadratic expressions?
    • DOTS-difference of two squares
    • PST-perfect square trinomials
    • missing constant quadratics​
Rational Expressions
  • Can you combine two rationals expressions into a single rational expression?
    • addition
    • subtraction
    • mutiplication
    • division
  • Can you determine the domain restrictions of a rational expression?
  • Can you determine the zeros of a rational expression?
  • Can you rewrite complex fractions
Graphs and Transformations
  • ​Can you graph each of the types of function or a relation regardless of form?
    • linear
    • quadratic
    • absolute value 
    • radical
  • Can you transform the parent function?
    • linear
    • quadratic
    • absolute value 
    • radical
    Do you understand the impact of type and signs related to coefficients, constants, bases, and other related parts on the graph of a function or a relation?
    • linear
    • quadratic
    • absolute value 
    • radical
  • Can you express the domain and range a function?
  • Can you determine the intercepts from a function algebraically or with the assistance of technology? 
  • Can you determine the "special" points from a function algebraically or with the assistance of technology?
    • ​intercepts
    • integer coordinates
    • rational coordinates
    • local extremes 
  • Can you determine the "specific" points from a function algebraically or with the assistance of technology?
    • ​given x find y
    • given y find x
    • tables that increment by a specific amount​
Solving Equations
  • Can you solve an equation algebraically?
    • linear
    • quadratic
    • absolute value 
  • Can you connect a graph of a system to its related equation's solutions?
  • Can you use tables and the location principle to find an estimate of a solution?
  • Can you use technology to confirm solutions to equations?
  • Can you use technology to find solutions to equations?
  • Do you understand what it means for an equation to not have a solution algebraically?
  • Do you understand what it means for an equation to not have a solution graphically?
Solving Inequalities
  • Can you use proper notation, vocabulary, and abbreviations associated with inequalities?
    • boundary lines
    • boundary points
    • disjoint sets of solutions
    • conjunction sets of solutions
    • conjunctions (AND inequalities)
    • disjunctions (OR inequalities)
  • Can you solve and represent the solution set of an inequality on the number line using a variety of methods
    • algebraically
    • graphically
    • verbally 
  • Can you distinguish the difference between the different types of lines and points used on the graph of number line, compound number line inequalities, absolute value inequalities, single line linear inequalities, and systems of linear inequalities.
  • Can you use technology to represent inequalities in two variables?
  • Can you apply inequalities in a real world setting
    • linear programming
Coordinate Geometry
  • Can you use proper notation, vocabulary, and abbreviations associated with the coordinate plane?
  • Can you use proper notation, vocabulary, and abbreviations associated with the coordinate plane in three dimensions?
  • Can you plot points in the 2-D coordinate plane as well as the 3-D coordinate plane?
  • Can you determine the slope of a line segment from two given points?
  • Can you find the distance between two points?
  • Can you determine the midpoint between two points?
Linear Functions
Lists of Points
  • Can you write a linear function based on two points?
    • slope intercept form
    • point slope form
      • modified point slope form
    • standard form
  • Can you write a piecewise linear function from a list of coordnates?
  • Can you determine if a list of points represents a linear relationship?
  • Can you use technology to perform linear repression?
  • Can I use technology to model behaviors of coordinates from a list of points?
Direct Variation 
  • Do you recognize direct variation line from a table of coordinates, the graph of the direct variation line, or the linear function that represents the linear function?
  • Can you use vocabulary that is associated with direct variation?
  • Can you determine the constant of variation of a direct variation line?
  • Can you use direct variation in a real life scenario?
  • Can I use technology to model behaviors of direct variation function?
Horizontal and Vertical Lines
  • Can you write an equation of a vertical line that passes through a given point?
  • Can you write the equation of a vertical line as a set of points?
  • Can you write an equation of a horizontal line that passes through a given point?
  • Can you write the equation of a horizontal line as a set of points?
  • Do you know the equations of the lines that are called the x axis or the y axis?
  • Can you distinguish slope of 0 and undefined slope
  • Do you know the only line that is NOT a linear function?
  • Can you perform the Vertical Line Test on a set of coordinates or a graph?
    • Can you explain it means to fail the VLT?
    • Can you explain it means to pass the VLT?
  • ​Can you perform the Horizontal Line Test on a set of coordinates or a graph?
    • Can you explain it means to fail the HLT?
    • Can you explain it means to pass the HLT?
  • Can you explain the mathematical implications of each of the four scenarios below?
    • Pass HLT and Pass VLT
    • Pass HLT and Fail VLT
    • Fail HLT and Pass VLT
    • Fail HLT and Fail VLT
Slope Intercept Form
  • Can you isolate each of the letters in y = mx+b?
  • Can you determine the slope of a linear function from slope intercept form?
  • Can you determine the y intercept of a linear function from slope intercept form?
  • Can you determine the x intercept of a linear function from slope intercept form?
  • Can you determine the integer coordinates of a linear function from slope intercept form?
  • Can you determine the inverse of a linear function from slope intercept form?
  • Can you determine if a pair of lines is parallel, perpendicular, or intersecting only from a given set of slope intercept form lines.
  • Can you apply linear functions to model real life scenarios?
  • Can you convert slope intercept lines into point slope form lines or standard form lines?
Point Slope Form
  • ​Can you isolate each of the letters in point slope form?
  • Can you isolate y in particular (this is a modified form of the point slope form of the line that is very helpful)
  • Can you determine the slope of a linear function from point slope form?
  • Can you determine the y intercept of a linear function from point slope form?
  • Can you determine the x intercept of a linear function from point slope form?
  • Can you determine the implied point of a linear function from point slope form?
  • Can you determine the integer coordinates of a linear function from point slope form?
  • Can you determine the inverse of a linear function from point slope form?
  • Can you determine if a pair of lines is parallel, perpendicular, or intersecting only from a given set of point slope form lines.
  • Can you apply linear functions to model real life scenarios?
  • Can you convert point slope lines into slope intercept form lines or standard form lines?
Standard Form of Line
  • Can you isolate each of the letters in standard form of the line?
  • Can you determine the slope of a linear function from standard form of the line?
  • Can you determine the y intercept of a linear function from standard form of the line?
  • Can you determine the x intercept of a linear function from standard form of the line?
  • Can you determine the integer coordinates of a linear function from standard form of the line?
  • Can you determine the inverse of a linear function from standard form of the line?
  • Can you determine if a pair of lines is parallel, perpendicular, or intersecting only from a given set of standard form lines.
  • Can you apply linear functions to model real life scenarios?
  • Can you convert standard form of the line into slope intercept form lines or point slope form lines?
Systems of Equations
  • ​Can you use proper notations, abbreviations, and vocabulary associated with linear systems of equations and inequality in two variables?
  • Can you graph a linear system regardless of lines within the system?
    • two horizontal lines
    • two vertical lines
    • one vertical line and one horizontal line
    • One vertical line and a slope intercept form line
    • One horizontal line and a slope intercept form line
    • One slope intercept form line and one standard form line
    • One slope intercept form line and one point slope form line
    • One point slope form line and one standard form line
    • two slope intercept form lines 
    • two standard form lines
    • two point slope form lines
  • Can you extend the graphing of linear systems of equations to the graphing of linear systems of inequalities
  • Do you understand the following classifications of linear systems 
    • Consistent & Dependent Linear System
    • Consistent & Independent Linear System
    • Inconsistent Linear System
  • Could you give an example of a system of lines that does not have any solutions?
  • Could you give an example of a system of lines that have infinitely many solutions?
  • Could you give an example of a system of lines that has a single solution?
  • Can you apply a linear system to model real-life scenarios?
  • Can you solve a linear system and confirm its solution using a variety of methods?
    • Elimination method
    • Substitution method
    • Graphing with and without the assistance of technology 
    • Matrix Equations & Inverses

Solving Three Variable Equations

  • Abbreviation, Notation, and Vocabulary associated with 3 x 3 Systems of Equations   
  • Can you use proper notations, abbreviations, and vocabulary associated with three variable systems?
    • consistent system
      • consistent and independent systems
      • consistent and independent systems
    • inconsistent system
    • solution to a system of equations of three variables
    • short hand or matrix notation for 3 x 3 matrices
    • entry of a matrix
    • address of an entry in a matrix
    • row of a matrix
    • column of a matrix 
    • diagonal of a matrix
    • square matrix
    • rectangular matrix
    • matrix equation
    • determinant of a matrix
    • identity matrix
    • inverse of a matrix
  • Could you locate each of the following in three dimensional space?
    • XY Plane
    • YZ Plane
    • XZ Plane
    • the eight octants of space
    • X axis
    • Y axis
    • Z axis
    • Origin
  • Can you use three dimensional coordinates effectively?
    • Using (x,y,z) coordinates
      • (x,y,0)
      • (x,y,n) for any real n
      • (0,y,z)
      • (n,y,z) for any real n
      • (x,0,z)
      • (x,n,z) for any real n​
  • Representation of 3 x 3 Systems in 3-D Space
  • Can you connect a three dimensional system of equations to a graph of three planes in space?
  • Can you connect a three dimensional system of equations to the number and type of solutions it has?
  • Can you use technology to represent three variable systems?
  • Can you sketch a three dimensional representation of a  three variable equation based on its intercepts? 
  • Types of 3 x 3 Systems and their Related Solution(s)
  • consistent system
    • consistent and independent systems
    • consistent and independent systems
  • inconsistent system
  • Systems that have a single point as its solution
  • Systems that have a line in three dimensions as its solution set
  • Systems that have no solutions
Solving Three Variable Systems through Elimination
  • Do you understand how to eliminate a variable in an equation using linear combinations of two equations in a 3 x 3 system?
  • Can you use notations related to matrices to facilitate elimination process?
  • Can you systematically perform the algebra required to solve a linear system of three variables using elimination?
Solving Three Variable Systems through Substitution
  • Do you understand how to isolate a variable in an equation in a 3 x 3 system?
  • After isolating a variable, can you use substitution to write a system of two variables?
  • Can you systematically perform the algebra required to solve a linear system of three variables using substitution?
Solving Three Variable Systems through Use of Matrices and Cramer's Rule.
  • Can you use the notations, abbreviations, and vocabulary related to matrices in the context to solve any 3x3 system?
  • Can you find a determinant of a matrix algebraically?
  • Can you find a determinant of a matrix with the assistance of technology?
  • Can you solve 2 x 2 and 3 x 3 systems using matrix determinants and Cramer's Rule? 
Solving Three Variable Systems through Use of Matrices and Inverse Matrices
  • Can you use the notations, abbreviations, and vocabulary related to matrices in the context to solve any 3x3 system?
  • Can you set up a matrix equation from a system of equations?
    • 2x2 systems
    • 3x3 systems
    • n x n systems
  • Can you deternine the inverse of a matrix algebraically?
    • 2x2 systems
    • 3x3 systems
  • Can you deternine the inverse of a matrix through the use of technology?
    • 2x2 systems
    • 3x3 systems
    • n x n systems

Quadratic Functions

Forms of the Quadratic Function
  • Can you use the notations, abbreviations, and vocabulary related to quadratic function?
    • parabola
    • vertex of a parabola
    • roots of a quadratic function
    • y intercept of a parabola
    • x intercept of a parabola
    • points on the parabola
    • axis of symmetry
    • focus coordinate
    • directrix line
  • Can you write each of the forms of a quadratic function from another?
    • vertex form
    • intercept form
    • standard form
    • general conic form
  • Can you connect the letters associated with parabolas to their respective parts?
    • a, b, c
    • h, k
    • p
  • Can you recognize a parabola's equation that is NOT a quadratic function?
Graphs and Transformations of the Quadratic Function and Relation
  • Can you graph and lable the parts of a parabola regardless of the form given with and without technology?
  • Can you determine the parts of the parabola based on the given form?
    • Can you determine the vertex and intercepts of a parabola?
    • Can you determine the axis of symmetry of a parabola?
    • Can determine the focus and directrix line of a parabola?
  • Can you determine the missing values in a table related to a given quadratic function?
  • Can you connect the properties of transformation of parabolas and absolute value functions?
  • Can you write a quadratic function as a piecewise function?
  • Can you graph quadratic inequalities?
  • Can you describe the domain and range of a parabola using a variety of methods?
Quadratic Models
  • Can you connect a quadratic model to a real life scenario?
    • Can you connect a quadratic model to a distance problem?
    • Can you connect a quadratic model to a falling object problem?
    • Can you connect a quadratic model to an area problem?
    • Can you connect a quadratic model to a business problem?
  • Can you determine critical points related to real life quadratic models?
  • Can you discuss feasible solutions to a quadratic model?
  • Can you use a matrix to build a matrix
Quadratic Equations and Theory
  • Can you construct a quadratic function from a variety of parts of a function?
    • vertex and y intercept
    • vertex and any point on parabola
    • any three points
    • two x intercepts and any additional point
    • focus and equation of directrix line
  • Can you determine the location of any point in relationship to a parabola?
    • on parabola
    • within a parabola's interior
    • outside a parabola
  • Can you solve a variety of quadratic equations using a variety of methods?
    • factoring
    • completing the square
    • use of a radical
    • quadratic formula
  • Do you understand the rate of change associated with a quadratic function?
  • Can you explain why a quadratic equation will have real or imaginary solutions?
  • Can you derive the quadratic formula?
  • Do you understand the role of the discriminant of the quadratic formula? 
  • Can you determine the number and type of solutions present?
    • 0 real (this means two imaginary)
    • 1 real (this means the parabola is tangent to x axis)
    • 2 real (this means the parabola crosses the x axis)
    • 1 rational (this means that the parabola 
  • Can you write a piecewise inverse for a parabola?

Complex Numbers

Fundamental Theorem of Algebra
  • Connect the Fundamental Theorem of Algebra to the number and type of solutions to a polynomial equation based on degree of polynomial and shape of related polynomial function graph
  • Connect Fundamental Theorem of Algebra to number and type of solutions to a quadratic equation.
Complex Number abbreviation, notations, and vocabulary
  • Can you use the notations, abbreviations, and vocabulary related to complex numbers?
    • real part of complex number
    • imaginary part of complex number
    • value of "i"
    • completely simplified radical
    • completely simplified radical coefficient
    • a+bi
    • real axis
    • imaginary axis
    • modulus of an imaginary number
    • complex conjugate
  • Can you draw and label the entire number set?
  • Can you describe the domain of a square root function?
  • Can you determine the real and imaginary parts of an imaginary number?
  • Can you determine the exact completely simplified version of a real solution to a quadratic equation that is a irrational solution?
  • Can you determine the exact completely simplified version of a real solution to a quadratic equation that is an imaginary solution?
  • Can you distinguish between pure imaginary numbers and imaginary numbers?
Operations with complex numbers
  • Can you perform basic operations with complex numbers?
    • addition 
    • subtraction
    • multiplication
  • Can you determine which power of i  is connected to each of the following numbers?
    • i
    • -1
    • -1i
    • 1
  • Can you expand and completely simplify a complex raised to a power?
    • Can you use Pascal's Triangle to perform binomial expansion?
  • Can you determine the absolute value of complex number?
    • Can you connect absolute values of imaginary numbers to the graph of a complex number in the complex number plane?
  • Can you use complex conjugates to rationalize expressions that have a complex number in the denominator of a rational expression?
Plotting in the imaginary number plane 
  • Can you describe the connections in appearance for the complex number plane to a real Cartesian coordinate plane?
  • Can you plot imaginary numbers in the imaginary plane?
  • Can you connect absolute values of imaginary numbers to the graph of a complex number in the complex number plane?
Connections of imaginary numbers to higher level mathematics 
  • Connect advanced mathematical representations to complex numbers
    • fractals 
  • Euler's Identity

Polynomials
  • Determine the domain and range of polynomial functions 
  • Be able to determine intercepts, integer coordinates, and rational coordinates that lie on the graph of a polynomial function
  • Be able to graph the polynomial function with and without technology
  • Be able to use proper vocabulary related to transformation of polynomial functions
  • Use polynomial functions in a real-life scenario 

Matrices

applications of matrices
  • Be able to set up and use matrices in an inventory scenario
  • Be able to use coordinates and determinants to find areas of triangles
  • Be able to use coordinates and matrices to build polynomials from their coordinates

Sequences and Series

sequence and series notation and vocabulary
  • Be able to use a sequence of no less than three values to write general rule for all terms in sequence
  • Be able to use proper notation, abbreviations, and vocabulary associated with sequences and  series
    • common difference
    • common ratio
    • first term in a sequence
    • last term in a finite sequence
    • nth term in a sequence
    • arithmetic sequence
    • geometric sequence
    • recursive sequence
    • sum of a finite sequence 
    • sum of an infinite sequence 
  • Be able to classify a sequence properly
arithmetic sequence and series
  • Be able to determine when a given sequence of no less than three terms is arithmetic
  • Be able to write an arithmetic sequence rule for a given arithmetic sequence
  • Be able to determine the number of terms are in a finite sum of an arithmetic sequence
geometric ​sequence and series
  • Be able to determine when a given sequence of no less than three terms is geometric
  • Be able to write a geometric sequence rule for a given geometric sequence
  • Be able to determine the number of terms are in a finite sum of an geometric sequence
  • Be able to determine the sum of a geometric sequence of infinite number of terms
recursive series and sequence
  • Be able to write a recursive rule for an arithmetic sequence 
  • Be able to write a recursive rule for an geometric sequence 
  • Be able to write a recursive rule for for a given sequence 
factorials, permutations, and combinations
  • Be able to use proper vocabulary and notations associated with factorials, permutations, and combinations
  • Be able to determine the value of factorials 
  • Interpret the meaning of a factorial in relation to arrangement of items
  • Understand and be able to use the algebraic definitions and notations associated with permutation
  • Understand and be able to use the algebraic definitions and notations associated with permutation
  • Be able to distinguish the difference between permutation of n items, permutation of n choose r items, and the combination of n choose r items
  • Connect permutation, combination, and factorial to probability
  • Be able to use technology to calculate permutations, combinations, and factorials 
summation
  • Be able to use summation notation to represent finite and infinite sums
  • Be able to use algebraic methods to determine finite and infinite sums
  • Be able to use technology to find given sums and general rule for a sequence​

Advanced Functions and Relations

Functions Revisited 
  • Do you understand the notation, vocabulary, and abbreviations used to describe more advanced function?
  • domain of a function
  • range of a function
  • end behavior of a function
  • asymptote of  a function
  • vertical asymptote of a function
  • horizontal asymptote of a function
  • slant asymptote of a function
  • oblique asymptote  of a function
  • reciprocal of a function​
  • local extremes
  • local minimums
  • local maximums
  • absolute extremes
  • absolute minimum
  • absolute maximum
  • inverse function
  • one to one function
  • even function
  • odd function
  • continuous function
  • constant function
  • piecewise function
  • step functions
  • floor function
  • ceiling function
  • composition of functions
  • index of a radical function
  • radicand of a radical function
  • base of a logarithmic function
  • base of an exponential function
Exponential Functions and their Transformations
  • Determine the domain and range of exponential functions
  • Be able to determine intercepts, integer coordinates, and rational coordinates that lie on the graph of an exponential function 
  • Be able to graph the parent exponential function related to a specific base with and without technology
  • Be able to use proper vocabulary related to transformation of exponential functions
  • Be able to distinguish the difference between exponential functions that have a base that is between 0 and 1 and exponential functions that have a base that is greater than 1
  • Connect exponential functions to logarithmic functions
  • Use exponential functions in a real-life scenario 
  • Be able to determine intercepts, integer coordinates, and rational coordinates that lie on the graph of a logarithmic function
Logarithmic Functions and their Transformations
  • Determine the domain and range of logarithmic functions 
  • Be able to determine intercepts, integer coordinates, and rational coordinates that lie on the graph of a logarithmic function
  • Be able to graph the parent logarithmic function related to a specific base with and without technology
  • Be able to use proper vocabulary related to transformation of logarithmic functions
  • Be able to distinguish the difference between logarithmic functions that have a base that is between 0 and 1 and logarithmic functions that have a base that is greater than 1
  • Connect exponential functions to logarithmic functions
  • Use logarithmic functions in a real-life scenario 
Polynomial ​Functions and their Transformations
Rational ​Functions and their Transformations
  • Determine the domain and range of rational functions 
  • Be able to determine intercepts, asymptotes, integer coordinates, and rational coordinates that lie on the graph of a rational function
  • Be able to graph the rational function with and without technology
  • Be able to use proper vocabulary related to transformation of rational functions
  • Use rational functions in a real-life scenario 
Piecewise Functions
  • Be able to describe the domain and range of a piecewise function
  • Be able to graph a piecewise function with and with out technology
  • Be able to classify a piecewise function as continuous or not continuous
  •  Be able to write a piecewise function from its graph
  • Be able to write a piecewise function for absolute value functions.
  • Be able to write a piecewise function for quadratic functions.
Conic Sections 
  • Be able to use proper notation and vocabulary related to a conic section
    • Center
    • points on graph
    • vertices
    • co-vertices
    • focus and foci
    • minor axis
    • major axis
    • conjugate axis
    • transverse axis 
  • Be able to write a standard form equation of a conic section based on its parts
  • Graph a conic section from its standard form
    • Parabola
    • Circle
    • Ellipse
    • Hyperbola
  • Graph a section from its general form
    • Parabola
    • Circle
    • Ellipse
    • Hyperbola
  • Apply conic sections in a real-lef scenario
  • Parabola
  • Circle
  • Ellipse
  • Hyperbola
    • Parabola
  • Circle
  • Ellipse
  • Hyperbola
    		•
    Polar Graphs
    • Be able to plot points on a polar grid
    • Be able to use proper notation and vocabulary related to polar graphs
      • circles with center at (0,0)
      • circles tangent to the x axis
      • circles tangent to the y axis
      • diagonal lines 
      • vertical lines
      • Limacons
      • Cardiods
      • Rose Curves
      • Lemniscates
    • Be able to plot a variety of polar graphs with and without technology

    ​Probability

    Probability
    • Be able to use proper notation and vocabulary related to single and multiple event probabilities​
      • ​single event probability
      • multiple event probability
      • conditional probability 
      • simple events
      • compound events
      • independent events
      • dependent events
      • mutually exclusive events 
      • complement of an event
      • sample space
      • Venn diagram
    • Be able to determine probabilities algebraically
    • Be able to determine probabilities with the assistance of technology
    • Be able to use regression to model data
    • Connect probability to permutations and combinations
    • Be able to use the Fundamental Counting Principle.
    • Be able to read and create Venn Diagrams to aid in the comprehension and determination of probabilities 

    Prerequisites

    • Number Sets
    • Notation and Abbreviations
    • ​Functions
    • ​Exponent and Radical Laws
    • ​Factoring and Rewriting Expressions​
    • Solving Equations​​
    • Solving Inequalities
      • ​On Number Line
      • In Coordinate Plane
    • Coordinate Geometry
    • Linear Functions 
      • ​​Lists of Points
      • Horizontal and Vertical Lines 
      • Direct Variation Lines
      • Slope Intercept Form Lines
      • Point Slope Form Lines
      • Standard Form Lines
      • Systems of Linear Equations
      • Piecewise Linear Functions
      • Inverses of Linear Functions

    Solving Three Variable Equations

    • Abbreviation, Notation, and Vocabulary associated with 3 x 3 Systems of Equations   
    • Representation of 3 x 3 Systems in 3-D Space
    • Types of 3 x 3 Systems and their Related Solution(s)
    • Solve 3 x 3 Systems through Elimination
    • Solve 3 x 3 Systems through Substitution
    • Solve 3 x 3 Systems ​Using Matrix Determinant (Cramer's Rules)
    • Solve Using Matrix Inverses

    Quadratic Functions

    • ​Forms of the Quadratic Function​
    • Graphs and Transformations of the Quadratic Function and Relation
    • ​Quadratic Models​
    • Quadratic Equations and Theory

    Complex Numbers

    • Fundamental Theorem of Algebra
    • Complex Number abbreviation, notations, and vocabulary
    • Operations with complex numbers
    • Plotting in the imaginary number plane
    • Connections of imaginary numbers to higher level mathematics 
    ​

    Polynomial Functions

    • Abbreviation, Notation, and Vocabulary associated with Polynomials
    • Polynomial Transformation
    • Addition, Subtraction, and Multiplication of Polynomials​
    • Division of Polynomials
      • ​Long Division
      • Synthetic Division
    • ​Expansion of binomials raised to a power
    • Modeling with Polynomials
    ​

    Rational Exponents and Radical Functions


    Rational Functions

    • Exponential Functions and their Transformations
    • ​Logarithmic Functions and their Transformations
    • ​Polynomial ​Functions and their Transformations
    • ​Rational ​Functions and their Transformations
    • ​​Piecewise Functions
    • Conic Sections 
    • ​Polar Graphs

    ​Sequences and Series

    • sequence and series notation and vocabulary
    • ​​arithmetic sequence and series
    • ​geometric ​sequence and series
    • ​recursive series and sequence
    • ​​factorials, permutations, and combinations
    • ​summation

           LARSON'S BIG IDEAS MATH
    Instructions for the use of this link
    1. Go to the link below
    2. Go to "Choose Your Program"
    3. Select Common Core High School
    4. Select Algebra 2 Book Link
    This link below should at least get you to the Big Ideas Math Easy Access Home Page if not the direct link to the text
    Algebra & Algebra 2
    Geometry
    ​
    ​

    Common Core Mathematics Standards

    Illinois Mathematics Standards