ALGEBRA I & II
 NUMBER AND OPERATIONS
- Understanding of very large and very small numbers
- Representations of very large and very small numbers
- Properties of numbers and number systems
- Rational and real numbers
- Complex numbers as solutions to quadratic equations
- Vectors and matrices as systems that have some of the properties of the real-number system
- Relationships involving whole numbers
- Multiplication, division, computing powers and roots on the magnitudes of quantities
- Addition and multiplication of vectors and matrices
- Permutations and combinations as counting techniques
- Operations with real numbers, vectors, and matrices
- Numerical computations
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ALGEBRA
- Explicitly defined and recursively defined functions
- Relations and functions
- Functions of one variable
- Transformations such as arithmetically combining, composing, and inverting commonly used functions
- Properties of classes of functions
- Representations of functions of two variables
- Equivalent forms of expressions, equations, inequalities, and relations
- Symbolic algebra
- Recursive and parametric equations for functions and relations
- Identify essential quantitative relationships
- Iterative and recursive forms of symbolic expressions
- Conclusions about a situation being modeled
- Interpret rates of change from graphical and numerical data
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DATA ANALYSIS AND PROBABILITY
- Differences among various kinds of studies and inferences that can be drawn from them
- Characteristics of well-designed studies
- Measurement data and categorical data
- Univariate and bivariate data
- Histograms, parallel box plots, and scatter plots
- Understanding basic statistics
- Distinction between a statistic and a parameter
- Univariate and bivariate measurement data
- Bivariate data where at least one variable is categorical
- Linear transformations of univariate data and their affects
- Trends in bivariate data
- Simulations to explore the variability of sample statistics from a known population
- Sampling distributions
- Understand how sample statistics reflect the values of population parameters
- Sampling distributions as the basis for informal inference;
- Statistical techniques used to monitor process characteristics
- Sample space and probability distribution
- Simulations to construct empirical probability distributions
- Expected value of random variables
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MEASUREMENT
- Units and scales
- Precision, accuracy, and approximate error in measurement
- Formulas for the area, surface area, and volume of geometric figures
- Successive approximation, upper and lower bounds, and limits in measurement
- Unit analysis to check measurement computations
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GEOMETRY
- Properties and attributes of two- and three-dimensional objects
- Congruence and similarity among classes of two- and three-dimensional geometric objects
- Establish the validity of geometric conjectures
- Angles and Lines
- Triangles and Quadrilaterals
- Coordinate systems - navigational, polar, or spherical
- Two- and three-dimensional objects represented with Cartesian coordinates
- Circles and three-dimensional figures
- Translations, reflections, rotations, and dilations of objects
- Simple transformations and their compositions
- Similar triangles and transformations
- Advanced triangle applications
- Representations of two- and three-dimensional geometric objects
- Visualize three-dimensional objects and spaces
- Cross sections of three-dimensional objects
- Vertex-edge graphs
- Geometric models in other areas of mathematics
- Inductive and deductive reasoning
- Writing proofs
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TRIGONOMETRY
- Trigonometric Functions
- Graphing Trigonometric Functions
- Right Angle Trigonometry and Basic Identities
- Trigonometric Identities
- Inverse Trigonometric Functions
- Oblique triangles
- Exponential and Logarithmic functions
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PRE-CALCULUS
- Sets, series, sequences, number systems, factoring, exponents
- Linear and non-linear equations & inequalities
- Linear, quadratic, polynomial and rational functions
- Cartesian coordinate system
- Logarithms and exponential functions
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