MO: Matrix Operations

MO.1.AIII: Students will perform operations with matrices and use them to solve systems of equations.

MO.1.AIII.2: Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).

Dilations

MO.1.AIII.7: Work with 2 𝑋 2 matrices as transformations of the plane; interpret the absolute value of the determinant in terms of area.

Dilations
Translations

MO.1.AIII.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

MO.1.AIII.9: Find the inverse of a matrix if it exists; use the inverse to solve systems of linear equations using technology for matrices of dimension 3 𝑋 3 or greater.

Solving Linear Systems (Matrices and Special Solutions)

CS: Conic Sections

CS.2.AIII: Students will identify, analyze, and sketch the graphs of the conic sections and relate the equations and graphs.

CS.2.AIII.1: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

CS.2.AIII.2: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant; find the equations for the asymptotes of a hyperbola.

Ellipses
Hyperbolas
Rational Functions

CS.2.AIII.3: Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section.

Circles

CS.2.AIII.4: Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas
Rational Functions

CS.2.AIII.5: Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology.

Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

FOP: Function Operations and Properties

FOP.3.AIII: Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses.

FOP.3.AIII.1: Compose functions (e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time).

Function Machines 1 (Functions and Tables)

FOP.3.AIII.2: Verify, by composition, that one function is the inverse of another.

Logarithmic Functions

FOP.3.AIII.3: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

FOP.3.AIII.5: Combine standard function types using arithmetic operations (e.g., 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).

Addition and Subtraction of Functions

FOP.3.AIII.6: Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

FOP.3.AIII.7: Graph transformations of functions including quadratic, absolute value, square root, cube root, cubic, and step functions; graph piece-wise defined functions including these transformations.

Absolute Value with Linear Functions
Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translations
Zap It! Game

IF: Interpreting Functions

IF.4.AIII: Students will be able to interpret different types of functions and key characteristics including polynomial, exponential, logarithmic, and rational functions.

IF.4.AIII.1: Graph rational functions identifying zeros and asymptotes when suitable factorizations are available; show end behavior.

General Form of a Rational Function
Rational Functions

IF.4.AIII.2: Analyze and interpret polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form

IF.4.AIII.3: Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), end behavior, point discontinuities, intercepts, and domain and range.

General Form of a Rational Function
Rational Functions

IF.4.AIII.4: Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

IF.4.AIII.5: Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, end behavior, intercepts, and domain and range.

Logarithmic Functions

SS: Sequences and Series

SS.5.AIII: Students will use sequences and series to represent and analyze mathematical situations.

SS.5.AIII.1: Write arithmetic and geometric sequences both recursively and with an explicit formula; translate between the two forms.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

SS.5.AIII.2: Use arithmetic and geometric sequences both recursively and with an explicit formula to model situations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences