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Math
- Number and Quantity – The Real Number System (N-RN)
- Number and Quantity – Quantities (N-Q)
- Algebra – Seeing Structure in Expressions (A-SSE)
- Algebra – Arithmetic with Polynomials and Rational Expressions (A-APR)
- Algebra – Creating Equations (A-CED)
- Algebra – Reasoning with Equations and Inequalities (A-REI)
- Functions – Interpreting Functions (F-IF)
- Functions – Building Functions (F-BF)
- Functions – Linear, Quadratic, and Exponential Models (F-LE)
- Statistics and Probability – Summarize, represent, and interpret data on a single count or measurement variable. (S-ID)
- Statistics and Probability – Conditional Probability and the rules of Probability (S-CP)
- Number and Quantity – Quantities (N-Q)
- Geometry – Congruence (G-CO)
- Geometry – Similarity, Right Triangles, and Trigonometry (G-SRT)
- Geometry – Circles (G-C)
- Geometry – Expressing Geometric Properties with Equations (G-GPE)
- Geometry – Geometric Measurement and Dimension (G-GMD)
- Geometry – Modeling with Geometry (G-MG)
- Number and Quantity – The Real Number System (N-RN)
- Number and Quantity – Quantities (N-Q)
- Number and Quantity – The Complex Number System (N–CN)
- Algebra – Seeing Structure in Expressions (A-SSE)
- Algebra – Arithmetic with Polynomials and Rational Expressions (A-APR)
- Algebra – Creating Equations (A-CED)
- Algebra – Reasoning with Equations and Inequalities (A-REI)
- Functions – Interpreting Functions (F-IF)
- Functions – Building Functions (F-BF)
- Functions – Linear, Quadratic, and Exponential Models (F-LE)
- Functions – Trigonometric Functions (F-TF)
- Statistics and Probability – Interpreting Categorical and Quantitative Data (S-ID)
- Statistics and Probability – Making Inferences and Justifying Conclusions (S-IC)
- Statistics and Probability – Conditional Probability and the Rules of Probability (S-CP)
- Number and Quantity – The Complex Number System (N–CN)
- Number and Quantity – Vector and Matrix Quantities (N–VM)
- Algebra – Arithmetic with Polynomials and Rational Expressions (A–APR)
- Algebra – Reasoning with Equations and Inequalities (A-REI)
- Functions – Interpreting Functions (F–IF)
- Functions – Building Functions (F-BF)
- Functions – Trigonometric Functions (F–TF)
- Geometry – Similarity, Right Triangles, and Trigonometry (G-SRT)
- Geometry – Circles (G-C)
- Geometry – Expressing Geometric Properties with Equations (G-GPE)
- Geometry – Geometric Measurement and Dimension (G-GMD)
- Statistics and Probability – Making Inferences and Justifying Conclusions (S-IC)
- Statistics and Probability – Conditional Probability and the Rules of Probability (S-CP)
- Statistics and Probability – Using Probability to Make Decisions (S-MD)
- Contemporary Mathematics – Discrete Mathematics (CM-DM)
Arizona Math
Precalculus: Reasoning with Functions and Relations (RFR)
Interpret parameters of a function defined by an expression in the context of the situation.
- Comparing features of quadratic functions
- Comparing linear functions word problem: climb
- Comparing linear functions word problems
- Comparing maximum points of quadratic functions
- Exponential vs. linear growth over time
- Function notation word problems
- Interpret exponential expressions word problems
- Interpret quadratic models
- Interpret quadratic models: Factored form
- Interpret quadratic models: Vertex form
- Linear equations word problems
- Linear models word problems
- Worked example: domain & range of piecewise linear functions
- Worked examples: Forms & features of quadratic functions
Sketch the graph of a function that models a relationship between two quantities, identifying key features.
- Interpret change in exponential models
- Interpret change in exponential models: changing units
- Interpret change in exponential models: with manipulation
- Interpret time in exponential models
- Interpreting change in exponential models
- Interpreting change in exponential models: changing units
- Interpreting change in exponential models: with manipulation
- Interpreting time in exponential models
- Worked example: domain and range from graph
Interpret key features of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.
- Interpret change in exponential models
- Interpret change in exponential models: changing units
- Interpret change in exponential models: with manipulation
- Interpret time in exponential models
- Interpreting change in exponential models
- Interpreting change in exponential models: changing units
- Interpreting change in exponential models: with manipulation
- Interpreting time in exponential models
Use limits to describe long-range behavior, asymptotic behavior, and points of discontinuity.
- Divide polynomials by linear expressions
- Divide polynomials by x (no remainders)
- Divide polynomials by x (with remainders)
- Divide polynomials by x (with remainders)
- Divide quadratics by linear expressions (no remainders)
- Divide quadratics by linear expressions (with remainders)
- Dividing polynomials by linear expressions
- Dividing polynomials by linear expressions: missing term
- Dividing polynomials by x (no remainders)
- Dividing quadratics by linear expressions (no remainders)
- Dividing quadratics by linear expressions with remainders
- Dividing quadratics by linear expressions with remainders: missing x-term
- Factor using polynomial division
- Factoring using polynomial division
- Factoring using polynomial division: missing term
- Intro to long division of polynomials
- Polynomial division introduction
- Reduce rational expressions to lowest terms
- Reduce rational expressions to lowest terms: Error analysis
- Reducing rational expressions to lowest terms
- Reducing rational expressions to lowest terms
Sketch the graph of all six trigonometric functions, identifying key features.
- Amplitude & period of sinusoidal functions from equation
- Amplitude of sinusoidal functions from equation
- Amplitude of sinusoidal functions from graph
- Construct sinusoidal functions
- Example: Graphing y=-cos(π⋅x)+1.5
- Example: Graphing y=3⋅sin(½⋅x)-2
- Features of sinusoidal functions
- Graph of y=sin(x)
- Graph of y=tan(x)
- Graph sinusoidal functions
- Graph sinusoidal functions: phase shift
- Graphical relationship between 2ˣ and log₂(x)
- Graphing exponential functions
- Graphing logarithmic functions (example 1)
- Graphing logarithmic functions (example 2)
- Graphs of exponential functions
- Graphs of logarithmic functions
- Interpreting trigonometric graphs in context
- Intersection points of y=sin(x) and y=cos(x)
- Midline of sinusoidal functions from equation
- Midline of sinusoidal functions from graph
- Midline, amplitude, and period review
- Modeling with sinusoidal functions
- Modeling with sinusoidal functions: phase shift
- Period of sinusoidal functions from equation
- Period of sinusoidal functions from graph
- Sinusoidal function from graph
- Transforming exponential graphs
- Transforming exponential graphs (example 2)
- Transforming sinusoidal graphs: vertical & horizontal stretches
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection
- Trig word problem: length of day (phase shift)
- Trig word problem: modeling annual temperature
- Trig word problem: modeling daily temperature
Model relationships between quantities that require adding, subtracting, multiplying, and/or dividing functions
Model relationships through composition and attend to the restrictions of the domain.
- Composing functions
- Determine the domain of functions
- Determining whether values are in domain of function
- Domain and range from graph
- Evaluate composite functions
- Evaluate composite functions: graphs & tables
- Evaluating composite functions
- Evaluating composite functions (advanced)
- Evaluating composite functions: using graphs
- Evaluating composite functions: using tables
- Examples finding the domain of functions
- Find composite functions
- Finding composite functions
- Function domain word problems
- Function notation word problem: bank
- Identifying values in the domain
- Intro to composing functions
- Intro to composing functions
- Meaningfully composing functions
- Model with composite functions
- Modeling with composite functions
- Modeling with composite functions: skydiving
- What is the domain of a function?
- Worked example: determining domain word problem (all integers)
- Worked example: determining domain word problem (positive integers)
- Worked example: determining domain word problem (real numbers)
- Worked example: domain and range from graph
Rewrite a function as a composition of functions.
- Composing functions
- Evaluate composite functions
- Evaluate composite functions: graphs & tables
- Evaluating composite functions
- Evaluating composite functions (advanced)
- Evaluating composite functions: using graphs
- Evaluating composite functions: using tables
- Find composite functions
- Finding composite functions
- Function notation word problem: bank
- Intro to composing functions
- Intro to composing functions
- Meaningfully composing functions
- Model with composite functions
- Modeling with composite functions
- Modeling with composite functions: skydiving
Determine if a function has an inverse. If so, find the inverse. If not, define a restriction on the domain that meets the requirement for invertibility and find the inverse on the restricted domain.
- Determine if a function is invertible
- Determining if a function is invertible
- Evaluate inverse functions
- Find inverses of rational functions
- Finding inverse functions: linear
- Finding inverses of linear functions
- Finding inverses of rational functions
- Graphing the inverse of a linear function
- Inputs & outputs of inverse functions
- Intro to inverse functions
- Intro to inverse functions
- Intro to invertible functions
- Restrict domains of functions to make them invertible
- Restricting domains of functions to make them invertible
- Verify inverse functions
- Verifying inverse functions by composition
- Verifying inverse functions by composition
- Verifying inverse functions by composition: not inverse
- Verifying inverse functions from tables
Interpret the meanings of quantities involving functions and their inverses.
- Determine if a function is invertible
- Determining if a function is invertible
- Evaluate inverse functions
- Find inverses of rational functions
- Finding inverse functions: linear
- Finding inverses of linear functions
- Finding inverses of rational functions
- Graphing the inverse of a linear function
- Inputs & outputs of inverse functions
- Intro to inverse functions
- Intro to inverse functions
- Intro to invertible functions
- Restrict domains of functions to make them invertible
- Restricting domains of functions to make them invertible
- Verify inverse functions
- Verifying inverse functions by composition
- Verifying inverse functions by composition
- Verifying inverse functions by composition: not inverse
- Verifying inverse functions from tables
Verify by analytical methods that one function is the inverse of another.
Model real-world situations which involve conic sections.
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Identify key features of conic sections (foci, directrix, radii, axes, asymptotes, center) graphically and algebraically.
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Sketch a graph of a conic section using its key features.
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Use the key features of a conic section to write its equation.
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Given a quadratic equation of the form ax2+ by2 + cx + dy + e = 0, determine if the equation is a circle, ellipse, parabola, or hyperbola.
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Model real-world situations involving sequences or series using recursive and/or explicit definitions.
- Arithmetic sequences review
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of geometric sequences
- Converting recursive & explicit forms of geometric sequences
- Evaluate sequences in recursive form
- Evaluating sequences in recursive form
- Explicit & recursive formulas for geometric sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for geometric sequences
- Geometric sequences review
- Intro to arithmetic sequence formulas
- Intro to arithmetic sequences
- Linear functions word problem: iceberg
- Linear functions word problem: paint
- Linear models word problems
- Recursive formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for geometric sequences
- Sequences and domain
- Sequences and domain
- Sequences intro
- Use arithmetic sequence formulas
- Use geometric sequence formulas
- Using arithmetic sequences formulas
- Using explicit formulas of geometric sequences
- Using recursive formulas of geometric sequences
- Worked example: using recursive formula for arithmetic sequence
Use covariational reasoning to describe sequences and series.
- Arithmetic sequence problem
- Arithmetic sequences review
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of arithmetic sequences
- Converting recursive & explicit forms of geometric sequences
- Converting recursive & explicit forms of geometric sequences
- Evaluate sequences in recursive form
- Explicit & recursive formulas for geometric sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for arithmetic sequences
- Explicit formulas for geometric sequences
- Extend arithmetic sequences
- Extend geometric sequences
- Intro to arithmetic sequence formulas
- Intro to arithmetic sequences
- Intro to arithmetic sequences
- Intro to geometric sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Recursive formulas for geometric sequences
- Sequences intro
- Sequences word problems
- Sequences word problems
- Use arithmetic sequence formulas
- Use geometric sequence formulas
Represent finite or infinite series using sigma notation.
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Find the sums of finite or infinite series, if they exist.
- Evaluate sequences in recursive form
- Finite geometric series
- Finite geometric series formula
- Finite geometric series word problem: mortgage
- Finite geometric series word problem: social media
- Finite geometric series word problems
- Geometric series intro
- Geometric series introduction
- Geometric series with sigma notation
- Geometric series word problems: hike
- Geometric series word problems: swing
- Worked example: finite geometric series (sigma notation)
- Worked examples: finite geometric series