 Gwinnett County School District
 High School AKS Standards
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High School Mathematics

High School Mathematics  Accelerated Geometry: Concepts & Connections
A  Patterning & Algebraic Reasoning
 interpret the structure of and perform operations with polynomials within a geometric context
B  Geometric & Spatial Reasoning
 experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain reallife phenomena
 establish facts between angle relations and generate valid arguments to prove theorems and solve geometric problems involving lines and angles to model and explain reallife phenomena
 use center and scale factor to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion for triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain reallife phenomena
 examine side ratios of similar triangles; use the relationship between right triangles to develop an understanding of sine, cosine, and tangent to solve mathematically applicable geometric problems and to model and explain reallife phenomena
 explore the concept of a radian measure and special right triangles
 examine and apply theorems involving circles; describe and derive arc length and area of a sector; model and explain reallife frameworks involving circles
 develop informal arguments for geometric formulas using dissection arguments, limit arguments, and Cavalieri's principle; solve problems involving volume; explore and visualize relationships between twodimensional and threedimensional objects to model and explain reallife phenomena
C  Probabilistic Reasoning
 solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions
D  Data & Statistical Reasoning
 examine reallife situations presented in a twoway frequency table to calculate probabilities, to model categorical data, and to explain reallife phenomena
 communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting realworld data
E  Algebraic & Geometric Reasoning
 manipulate, prove, and apply trigonometric identities and equations to solve contextual, mathematical problems

High School Mathematics  Advanced Algebra: Concepts & Connections
A  Data & Statistical Reasoning
 communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting realworld data
B  Functional & Graphical Reasoning
 explore and analyze structures, patterns, and inverse relationships for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model reallife phenomena
 explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model reallife phenomena
 extend exploration of quadratic solutions to include real and nonreal numbers and explore how these numbers behave under familiar operations and within realworld situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model reallife phenomena
 analyze the behaviors of rational functions to model applicable, mathematical problems
F  Patterning & Algebraic Reasoning
 represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to realworld linear programming applications
G  Geometric & Spatial Reasoning
 develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle

High School Mathematics  Advanced Algebra: Concepts & Connections Strategies
A  Data & Statistical Reasoning
 communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting realworld data
B  Functional & Graphical Reasoning
 explore and analyze structures, patterns, and inverse relationships for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model reallife phenomena
 explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model reallife phenomena
 extend exploration of quadratic solutions to include real and nonreal numbers and explore how these numbers behave under familiar operations and within realworld situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model reallife phenomena
 analyze the behaviors of rational functions to model applicable, mathematical problems
C  Patterning & Algebraic Reasoning
 represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to realworld linear programming applications
D  Geometric & Spatial Reasoning
 develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle

High School Mathematics  Advanced Calculus II
A  Abstract & Quantitative Reasoning
 interpret integrals of functions of one independent variable to solve contextual situations and explain reallife phenomena
B  Geometric & Spatial Reasoning
 apply Calculus to polar and parametric equations within a geometric context to explain reallife phenomena
 express functional relationships with vectors in two dimensions and use these relationships to explain reallife phenomena
 express spatial relationships with vectors and planes in three dimensions and use these relationships to explain reallife phenomena
 interpret vector functions using contextual situations to explain reallife phenomena
C  Patterning & Algebraic Reasoning
 express spatial and functional relationships with infinite sequences
 express spatial and functional relationships with infinite series

High School Mathematics  Advanced Financial Algebra
A  Quantitative Reasoning
 utilize fractions, decimals, percents, and ratios to write and solve a variety of financial problems
B  Functional & Graphical Reasoning
 explore and apply functions (i.e., linear, exponential, quadratic, cubic, rational, square root, greatest integer, piecewise) to model and explain reallife phenomena and to solve complex problems in business and financial contexts
C  Patterning & Algebraic Reasoning
 explore, evaluate, and rearrange formulas applicable to business and financial contexts
 write and solve systems of equations and inequalities in context of financial applications
E  Geometric & Spatial Reasoning
 apply properties of polygons, circles, and trigonometry to model and explore realworld applications
F  Data & Statistical Reasoning
 collect, analyze, interpret, summarize, and construct displays of data to make predictions within realworld applications
 conduct investigative research to solve reallife problems and answer statistical questions involved in business and financial decisionmaking

High School Mathematics  Advanced Mathematical Decision Making
A  Quantitative and Proportional Reasoning
 make decisions and solve problems using ratios, rates, and percents in a variety of realworld applications
 predict potential outcomes by analyzing averages and indices of large data sets through investigations of realworld contexts
B  Patterning and Algebraic Reasoning
 develop methods or algorithms to analyze discrete situations
 create and analyze mathematical models to make decisions related to earning, investing, spending, and borrowing money
 use vectors and matrices to model and solve reallife situations
 make informed decisions and solve problems with a variety of network models in quantitative situations
C  Probabilistic Reasoning
 analyze the probability of success or failure in order to make decisions
 rationalize decisions based on probabilities and risk of loss and gain of reallife situations
D  Data and Statistical Reasoning
 conduct investigative research to solve reallife problems and answer statistical investigative questions involved in business and financial decisionmaking
E  Functional and Graphical Reasoning
 use functions to model problem situations in both discrete and continuous relationships
F  Geometric and Spatial Reasoning
 use functions to model trigonometric problems

High School Mathematics  Algebra: Concepts & Connections
A  Functional & Graphical Reasoning
 construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain reallife phenomena; use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and nonlinear functions using parent graphs
 construct and interpret quadratic functions from data points to model and explain reallife phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model
 construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions
B  Geometric & Spatial Reasoning
 solve problems involving distance, midpoint, slope, area, and perimeter to model and explain reallife phenomena
C  Patterning & Algebraic Reasoning
 create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model reallife phenomena
 build quadratic expressions and equations to represent and model reallife phenomena; solve quadratic equations in mathematically applicable situations
 create and analyze exponential expressions and equations to represent and model reallife phenomena; solve exponential equations in mathematically applicable situations
D  Numerical Reasoning
 investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots
E  Data & Statistical Reasoning
 collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve reallife problems; represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve reallife problems

High School Mathematics  Algebra: Concepts & Connections Strategies
A  Functional & Graphical Reasoning
 construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain reallife phenomena; use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and nonlinear functions using parent graphs
 construct and interpret quadratic functions from data points to model and explain reallife phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model
 construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions
B  Geometric & Spatial Reasoning
 solve problems involving distance, midpoint, slope, area, and perimeter to model and explain reallife phenomena
C  Patterning & Algebraic Reasoning
 create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model reallife phenomena
 build quadratic expressions and equations to represent and model reallife phenomena; solve quadratic equations in mathematically applicable situations
 create and analyze exponential expressions and equations to represent and model reallife phenomena; solve exponential equations in mathematically applicable situations
D  Numerical Reasoning
 investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots
E  Data & Statistical Reasoning
 collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve reallife problems; represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve reallife problems

High School Mathematics  Applications of Linear Algebra in Computer Science
A  Functions and Linear Equations
 review function notation, domain/codomain, identity/associativity, inverse/invertibility connecting to the computer science concept of perfect secrecy (i.e., encryption)
 review Python psuedo random number generation, calculating probability distribution and interpreting probability events through application of Caesar's Cypher and other examples of cryptosystems
B  Python Programming
 understand how to program and utilize modules and control statements (e.g., loops, conditionals, grouping) in Python
 utilize sets, lists, dictionaries, comprehensions, indexing, and tuples in Python
 program input and output features to read from and write to files in Python
C  The Complex Field
 perform operations of complex number numbers (e.g., absolute value, adding, multiplying) and understand how they produce different transformations
 understand how complex numbers connect to the unit circle and represent them in polar form; perform transformations in polar form and utilize Euler's formula/The First Law of Exponentiation to understand these transformations; connect to performing image transformation on a computer graphic program
 work with the Galois Field to understand further concepts in perfect secrecy and network coding (i.e., providing efficiency in streaming services)
D  The Vector
 connect use of vectors in Galois Field(2) by applying concepts of perfect secrecy, allornothing secret sharing, and programming/solving lights out games
 perform vector operations in R(n) including addition, scalar multiplication, and dot product; review concepts of convex and affine combinations; represent and perform these operations using dictionaries and the Vec.py class in Python
 find the distance, its unit vector in the same or opposite direction, the projection of a vector onto a given vector or vector space, dot product, inner product, cross product, and angle between two vectors in Euclidean space
 solve triangular systems of linear equations using uppertriangular systems, backward substitution, and other algorithms
 use the dot product to display the concept of simple authentication schemes and interacting with them, and performing a senator voting record analysis
E  Vector Spaces
 determine if a given set of vectors in a vector space is a spanning set for that vector space and if they are linearly independent
 define and discuss uses of linear combinations and understand how to solve for coefficients or linear combinations, connect to programmed/solved lights out game
 determine if a linear combination is an affine combination and determine if an affine space exists by translating a vector space, represent and affine space as a solution set to a linear system
 find whether a vector is a linear combination of a given finite set of vectors in a vector space and provide this linear combination
 determine whether a provided subset of a vector space is a subspace and find the dimension of a subspace
 define span and what it means for linear combinations to be a span of vectors; connect span to simple authentication schemes; understand the geometric depiction of the span of vectors over R and the geometry of solution sets of homogenous linear equations and systems; understand the geometric interpretations of R^2 and R^3
F  Matrices
 define and understand what the null space is by connecting to concepts of homogenous linear systems/matrix equations, and error correcting codes such as linear codes and Hamming's code
 factor a given matrix into the product of two elementary matrices, find the adjoint of a matrix and use it to find the inverse of the matrix (understanding the conditions for invertibility) or solve a system of linear equations
 generate an augmented coefficient matrix from a system of linear equations
 program transformations in 2D geometry using Python and concepts of matrix operations
 perform matrix operations including transpose, addition, scaler multiplication, dot product, and multiplication; compute the inner and outer product
 program error correcting code concepts such as Hamming's code using matrix operations
 review the structure of a matrix and composition of the identity matrix, determine the size, transpose, inverse, rank, and LUfactorization of a matrix; interpret matrices as vectors
G  The Basis and Dimension
 determine whether a given set of vectors in a vector space forms a basis for that vector space and recognize standards bases in the vector spaces nth dimensional Euclidean space, the set of all polynomials of degree greater than or equal to n
 understand if a linear function is invertible utilizing the concept of dimension and determine if a function is onto or onetoone; discuss in connection with KernalImage Theorem and Rank Nullity Theorem, demonstrate using checksums
 discuss rank theorem and demonstrate its use via the Simple Authentication Schema in computer science
 connect the Exchange Lemma to the concept of camera image perspective rendering in a Python lab
 define the coordinate representation of a basis and connect to lossy compression in computer science; find a basis for the column or row space of a matrix, and find a basis for and the dimension of the nullspace of a matrix
 define what it means for vectors to be linearly dependent and linearly independent and define the SuperfluousVector Lemma; perform tests of linear dependence
 utilize direct sum to add vector spaces and find the basis for the direct sum and understand if two subspaces are complementary
 review the minimum spanning forest problem in GF(2) in connection with the Grow and Shrink Algorithms and how to formulate the problem in linear algebra
 find the transition matrix from one basis to another (i.e., change of basis)
 define and determine the dimension and rank of a basis (and therefore vector space); use it to prove the Morphing Lemma and prove the SupersetBasis Lemma
 demonstrate that every vector space has a basis and any finite set of vectors contains a basis for its span (e.g., SubsetBasis Lemma)
H  Gaussian Elimination
 solve systems of linear equations and finding the basis for a Null space by use of Gaussian Elimination, GaussJordan Elimination, LU factorization, and Cramer's Rule; show how the simple authentication scheme can be attacked/improved over GF(2) using Guassian Elimination
 understand how Threshold Secret Sharing works in conjunction with Gaussian Elimination through a programming lab in Python
 understand how factoring integers can be performed using Euclid's algorithm and utilizing prime set factors in Python
 use elementary row operations to create matrices in rowechelon and reduced rowechelon form
I  Orthogonalization
 define and perform QR factorization of a matrix to compute solutions to the matrix equation Ax=b; use to perform the application of least squares to find the line or curve of best fit (linear/quadratic) to approximate data in the industrial espionage problem/sensor node problem/machine learning problem
 find an orthogonal basis for a given basis/subspace/inner product space by applying the Gram Schmidt orthonormalization process
 given the solution space of a homogenous system of linear equations, find an orthonormal basis
 determine if two given vectors/sets of vectors(complements)/subspaces are orthogonal, parallel, or neither; find the orthogonal component of a given subspace
 use orthogonalization to find the closest point in the span of many vectors, compute a basis/subset basis, direct sums of complements
J  Special Bases
 utilize compression by suppression to find the closest ksparse vector coordinate representation in terms of an orthogonal basis
 understand how images and sounds can be represented as wavelets and the bases representation of wavelets as well as wavelet transformation, implementation, and decomposition, perform Python lab on using wavelets to perform file compression
 define and demonstrate the Fourier transform connecting how a sound is stored as a sequence of amplitude samples and how the Fast Fourier Transform Algorithm is utilized/derived/coded
K  The Eigenvalue/Eigenvector
 connect use of the determinant and eigenvectors to code functionality of Google's PageRank search engine in Python
 discuss how Markov chains work to model various concepts such as population movement, dance patterns, literary documents, and Google's search engine PageRank
 utilize eigenvalues/vectors and single value decomposition to program face recognition software (Eigenfaces)
 determine an orthogonal matrix that diagonalizes a given matrix
 find a nonsingular matrix(D) for a given matrix (if one exists) such that D^1AD is diagonal; find a basis for the domain of a linear transformation such that the matrix of the linear transformation relative to the basis is diagonal
 find the determinant, minors, and cofactors of a given matrix and use the determinant to find whether a given matrix is singular/nonsingular; use determinant properties to characterize eigenvalues
 find the eigenvalues of a given symmetric matrix and find the dimension of the corresponding eigenspace
 find the characteristic equation and eigenvalues/corresponding eigenvectors of a given matrix and determine if the matrix is diagonizable/symmetric/orthogonal
 verify the eigenvalue/eigenvector of a given matrix while understanding the geometric interpretation and coordinate representation; connect to the Internet Worm case of 1988; perform eigen theorem proofs
L  Linear Programming
 perform a Python lab to explore concepts of linear programming
 explore samples of linear programming cases including the diet problem, the vertices of polyhedra (polyhedral combinatorics), the simplex algorithm, game theory, nonzerosum games, and compressed sensing for MRI imaging
 perform a machine learning lab on a large set of health care data that incorporates concepts of linear programming

High School Mathematics  Calculus (NonAP)
A  Functional & Graphical Reasoning
 apply limit notation and characteristics of continuity to analyze behaviors of functions
B  Algebraic & Graphical Reasoning
 relate limits and continuity to the derivative as a rate of change and apply it to a variety of situations including modeling contexts
 apply derivatives to situations in order to draw conclusions including curve analysis and modeling rates of change in applications
C  Geometric & Algebraic Reasoning
 analyze the relationship between the derivative and the integral using the Fundamental Theorem of Calculus
D  Patterning & Algebraic Reasoning
 apply the definite integral and indefinite integral to contextual situations

High School Mathematics  College Readiness Mathematics (Mathematics Capstone Course)
A  Numerical & Quantitative Reasoning
 utilize exact and approximate calculations to quantify realworld phenomena and solve problems
B  Patterning & Algebraic Reasoning
 construct expressions, equations, and inequalities, and use them to represent and solve problems by choosing appropriate procedures and interpreting solutions in context
C  Functional & Graphical Reasoning
 define, build, and interpret functions that arise in various contexts by applying knowledge of the characteristics of the different families of functions, and analyze the effects of parameters
D  Geometric & Spatial Reasoning
 reason deductively and inductively about figures and their properties and make sense of geometric situations using measurements in realworld contexts
E  Data & Statistical Reasoning
 make sense of and reason about variation in data using graphs, tables, and probability models to solve problems and draw appropriate conclusions from solutions

High School Mathematics  Differential Equations
A  Abstract Reasoning
 solve contextual, mathematical problems involving firstorder differential equations to explain reallife phenomena
 solve contextual, mathematical problems involving secondorder and higherorder differential equations to explain reallife phenomena
 solve contextual, mathematical problems involving systems of differential equations to explain reallife phenomena
 solve contextual, mathematical problems using Laplace transforms to explain reallife phenomena
 approximate solutions to differential equations using power series and apply the approximations to reallife phenomena

High School Mathematics  Engineering Calculus
A  Multidimensional Engineering Analysis
 learn to evaluate matrices and apply their properties to solve engineering problems; calculate determinants of matrices; express systems of linear equations in matrix equation form; use Gaussian elimination to compute solution sets of linear systems
 investigate functions of two and three independent variables to model engineering systems; compute limits of scalar and vectorvalued functions; identify, interpret and graph level curves of multivariate functions; calculate regions of continuity of such functions
 apply knowledge of mathematics, science, and engineering design to solve problems; determine the equations of lines and surfaces using vectors and 3D graphing; apply dot and cross products of vectors to express equations of planes, parallelism, perpendicularity, angles; describe the role of vectors in engineering applications, such as modeling the velocity of moving objects or static forces on structures and objects
 use visual and written communication to express basic design elements in the appropriate mathematics notation; demonstrate fundamentals of technical sketching using computer generated visuals by using the appropriate mathematics scale; present a technical design, using computergenerated model, for an assigned design project utilizing the appropriate scientific units (US standards and SI units)
B  Differentiation In Engineering
 evaluate and apply partial differentiation of multivariable functions with two or more independent variables; compute the first and second partial derivatives of a function; use the general chain rule to determine the partial derivatives of composite functions; compute and apply the gradient of multivariable functions; solve engineering optimization problems by applying partial differentiation or Lagrange multipliers; utilize partial derivatives in developing the appropriate system balances (e.g., mass balance) in engineering problems
C  Multidimensional Integration in Engineering Systems
 apply the techniques of double and triple integration to multivariable scalar and vectorvalued functions; manipulate integrals by changing the order of integration, introducing variable substitutions, or changing to curvilinear coordinates; evaluate and apply line integrals that are independent of path; apply properties of integrals to calculate and represent area, volume, or mass; use integrals of vectors to define and apply the gradient, divergence, or the curl e. Interpret the theorems of Green, Stokes, or Gauss and apply them to the study of realworld phenomena

High School Mathematics  Enhanced Advanced Algebra and Precalculus: Concepts and Connections
A  Data & Statistical Reasoning
 communicate descriptive and inferential statistics by collecting, critiquing, analyzing, and interpreting realworld data
B  Functional & Graphical Reasoning
 explore and analyze structures, patterns, and inverse relationships for exponential and logarithmic functions and use exponential and logarithmic expressions, equations, and functions to model reallife phenomena
 explore and analyze structures and patterns for radical functions and use radical expressions, equations, and functions to model reallife phenomena
 extend exploration of quadratic solutions to include real and nonreal numbers and explore how these numbers behave under familiar operations and within realworld situations; create polynomial expressions, solve polynomial equations, graph polynomial functions, and model reallife phenomena
 analyze the behaviors of rational functions to model applicable, mathematical problems
 analyze the behaviors of rational and piecewise functions to model contextual mathematical problems
 utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions
C  Patterning & Algebraic Reasoning
 represent data with matrices, perform mathematical operations, and solve systems of linear equations leading to realworld linear programming applications
 demonstrate how geometric sequences and series apply to mathematical models in reallife situations
D  Geometric & Spatial Reasoning
 develop an introductory understanding of the unit circle; solve trigonometric equations using the unit circle
 analyze the behaviors of conic sections and polar equations to model contextual, mathematical problems
E  Algebraic & Geometric Reasoning
 manipulate, prove, and apply trigonometric identities and equations to solve contextual, mathematical problems
 represent and model vector quantities to solve problems in contextual situations

High School Mathematics  Geometry: Concepts & Connections
A  Patterning & Algebraic Reasoning
 interpret the structure of and perform operations with polynomials within a geometric context
B  Geometric & Spatial Reasoning
 experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain reallife phenomena
 establish facts between angle relations and generate valid arguments to prove theorems and solve geometric problems involving lines and angles to model and explain reallife phenomena
 use center and scale factor to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion for triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain reallife phenomena
 examine side ratios of similar triangles; use the relationship between right triangles to develop an understanding of sine, cosine, and tangent to solve mathematically applicable geometric problems and to model and explain reallife phenomena
 explore the concept of a radian measure and special right triangles
 examine and apply theorems involving circles; describe and derive arc length and area of a sector; model and explain reallife frameworks involving circles
 develop informal arguments for geometric formulas using dissection arguments, limit arguments, and Cavalieri's principle; solve problems involving volume; explore and visualize relationships between twodimensional and threedimensional objects to model and explain reallife phenomena
C  Probabilistic Reasoning
 solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions
D  Data & Statistical Reasoning
 examine reallife situations presented in a twoway frequency table to calculate probabilities, to model categorical data, and to explain reallife phenomena

High School Mathematics  Geometry: Concepts & Connections Strategies
A  Patterning & Algebraic Reasoning
 interpret the structure of and perform operations with polynomials within a geometric context
B  Geometric & Spatial Reasoning
 experiment with transformations in the plane to develop precise definitions for translations, rotations, and reflections and use these to describe symmetries and congruence to model and explain reallife phenomena
 establish facts between angle relations and generate valid arguments to prove theorems and solve geometric problems involving lines and angles to model and explain reallife phenomena
 use center and scale factor to describe properties of dilations; use the precise definition of a dilation to describe similarity and establish the criterion for triangles to be similar; use these terms, definitions, and criterion to prove similarity, model, and explain reallife phenomena
 examine side ratios of similar triangles; use the relationship between right triangles to develop an understanding of sine, cosine, and tangent to solve mathematically applicable geometric problems and to model and explain reallife phenomena
 explore the concept of a radian measure and special right triangles
 examine and apply theorems involving circles; describe and derive arc length and area of a sector; model and explain reallife frameworks involving circles
 develop informal arguments for geometric formulas using dissection arguments, limit arguments, and Cavalieri's principle; solve problems involving volume; explore and visualize relationships between twodimensional and threedimensional objects to model and explain reallife phenomena
C  Probabilistic Reasoning
 solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions
D  Data & Statistical Reasoning
 examine reallife situations presented in a twoway frequency table to calculate probabilities, to model categorical data, and to explain reallife phenomena

High School Mathematics  Mathematics of Industry and Government
A  Abstract Reasoning & Deterministic DecisionMaking
 solve contextual, mathematical problems involving linear programming and use the mathematics as a model to make decisions about reallife phenomena
 solve contextual, mathematical problems involving optimal locations and use the mathematics as a model to make decisions about reallife phenomena
 solve contextual, mathematical problems involving optimal paths and use the mathematics as a model to make decisions about reallife phenomena
B  Abstract Reasoning & Probabilistic DecisionMaking
 solve contextual, mathematical problems with normal distributions to make appropriate decisions
 solve contextual, mathematical problems using other distributions (e.g., binomial, geometric, and Poisson) as well as simulations to make appropriate decisions
 use simulations to make appropriate decisions
 using quantitative reasoning, determine fair methods to reflect the wishes of a larger population with representatives
C  Probabilistic Reasoning
 use probabilistic models to make appropriate decisions

High School Mathematics  Multivariable Calculus
A  Patterning & Algebraic Reasoning
 express spatial and functional relationships with vectors and matrices, functions, and analytic geometry in three dimensions, and use these relationships to solve contextual, mathematical problems
B  Abstract & Quantitative Reasoning
 define, describe, and represent the differentiation of functions of two independent variables and differential vectors to solve contextual, mathematical problems and to explain reallife phenomena
C  Abstract & Quantitative Reasoning
 interpret integrals of functions of two independent variables and of vector functions to solve contextual, mathematical problems and to explain reallife phenomena

High School Mathematics  Number Theory
A  Logical Reasoning
 interpret, represent, and communicate logical arguments to explain reasoning and justify thinking when solving problems and to include reallife phenomena
 apply methods of proof to prove or disprove mathematical statements; explain reasoning and justify thinking through mathematical induction when formulating mathematical arguments
B  Abstract and Quantitative Reasoning
 use sets to describe relationships and equivalence when solving contextual, mathematical problems used to explain reallife phenomena
C  Numerical Reasoning
 apply properties of numbers to uncover mathematical patterns
 explore and solve problems using properties of integer divisibility
 explore and apply mathematical congruences in reallife phenomena
 explore and apply mathematical theorems and conjectures related to prime numbers in reallife phenomena

High School Mathematics  Precalculus
A  Functional & Graphical Reasoning
 analyze the behaviors of rational and piecewise functions to model contextual, mathematical problems
 utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions
B  Algebraic & Geometric Reasoning
 manipulate, prove, and apply trigonometric identities and equations to solve contextual, mathematical problems
C  Geometric & Spatial Reasoning
 analyze the behaviors of conic sections and polar equations to model contextual, mathematical problems
D  Algebraic & Graphical Reasoning
 represent and model vector quantities to solve problems in contextual situations
E  Patterning & Algebraic Reasoning
 demonstrate how geometric sequences and series apply to mathematical models in reallife situations

High School Mathematics  Statistical Reasoning
A  Data & Statistical Reasoning
 formulate statistical investigative questions of interest that can be answered with data
 collect data by designing and implementing a plan to address the formulated statistical investigative question
 analyze data by selecting and using appropriate graphical and numerical methods
 interpret the results of the analysis, making connections to the formulated statistical investigative question