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### MM Mathematical Modeling

- PC.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.
- PC.MM.1.1 Explain contextual, mathematical problems using a mathematical model.
- PC.MM.1.2 Create mathematical models to explain phenomena that exist in the natural sciences, social sciences, liberal arts, fine and performing arts, and/or humanities contexts.
- PC.MM.1.3 Using abstract and quantitative reasoning, make decisions about information and data from a contextual situation.
- PC.MM.1.4 Use various mathematical representations and structures with this information to represent and solve real-life problems.

### FGR Functional & Graphical Reasoning

- Functions and their Characteristics
- PC.FGR.2 Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
- Analyze piecewise-defined functions using different representations.
- PC.FGR.2.1 Graph piecewise-defined functions, including step functions and absolute value functions.
- PC.FGR.2.2 Describe characteristics by interpreting the algebraic form and graph of a piecewise-defined function.
- PC.FGR.2.3 Represent the limit of a function using both the informal definition and the graphical interpretation in the context of piecewise-defined functions; interpret limits expressed in analytic notation.

- Analyze rational functions using different representations.
- PC.FGR.2.4 Divide polynomials using various methods.
- PC.FGR.2.5 Graph rational functions and identify key characteristics.
- PC.FGR.2.6 Represent the behavior of a rational function using limit notation for vertical and horizontal asymptotes and end behavior.
- PC.FGR.2.7 Represent the limit of a function using both the informal definition and the graphical interpretation in the context of rational functions; interpret limits expressed in analytic notation.
- PC.FGR.2.8 Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
- PC.FGR.2.9 Perform partial fraction decomposition of rational functions using non-repeated linear factors.

- Analyze piecewise-defined functions using different representations.

- PC.FGR.2 Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
- Trigonometric Relationships and Functions
- PC.FGR.3 Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.
- Define and analyze trigonometric relationships.
- PC.FGR.3.1 Use the concept of a radian as the ratio of the arc length to the radius of a circle to establish the existence of 2? radians in one revolution.
- PC.FGR.3.2 Utilize right triangles on the unit circle to determine the values of the six trigonometric ratios for Π/6 , Π/4 , and Π/3 . Use reflections of the triangles as reference angles to establish known values in all four quadrants of the coordinate plane.
- PC.FGR.3.3 Define the six trigonometric ratios in terms of
*x*,*y*, and*r*using the unit circle centered at the origin of the coordinate plane. Interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle. - PC.FGR.3.4 Derive the fundamental trigonometric identities.
- PC.FGR.3.5 Determine the value(s) of trigonometric functions for a set of given conditions.

- Analyze trigonometric functions and their inverses.
- PC.FGR.3.6 Graph and write equations of trigonometric functions using period, phase shift, and amplitude in modeling contexts.
- PC.FGR.3.7 Classify the six trigonometric functions as even or odd and describe the symmetry.
- PC.FGR.3.8 Restrict the domain of a trigonometric function to create an invertible function and graph the inverse function. Evaluate inverse trigonometric expressions.

- Define and analyze trigonometric relationships.

- PC.FGR.3 Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.

### AGR Algebraic & Geometric Reasoning

- Trigonometric Identities and Equations
- PC.AGR.4 Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.
- Verify trigonometric identities and solve trigonometric equations.
- PC.AGR.4.1 Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
- PC.AGR.4.2 Use sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent to establish other identities and apply them to solve problems.
- PC.AGR.4.3 Solve trigonometric equations arising in modeling contexts.

- Apply trigonometry to general triangles.
- PC.AGR.4.4 Prove and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
- PC.AGR.4.5 Determine the area of an oblique triangle.

- Verify trigonometric identities and solve trigonometric equations.

- PC.AGR.4 Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.

### GSR Geometric & Spatial Reasoning

- Conic Sections and Polar Equations
- PC.GSR.5 Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.
- Analyze conic sections using different representations.
- PC.GSR.5.1 Identify and graph different conic sections given the equations in standard form.
- PC.GSR.5.2 Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.

- Extend trigonometry to the polar plane.
- PC.GSR.5.3 Define polar coordinates and relate polar coordinates to Cartesian coordinates.
- PC.GSR.5.4 Classify special polar equations and apply to contextual situations.
- PC.GSR.5.5 Graph equations in the polar coordinate plane with and without the use of technology.

- Analyze conic sections using different representations.

- PC.GSR.5 Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.

### AGR Algebraic & Graphical Reasoning

- Vectors and Parametric Equations
- PC.AGR.6 Represent and model vector quantities to solve problems in contextual situations.
- Perform operations with vectors in context.
- PC.AGR.6.1 Represent vector quantities as directed line segments; represent magnitude and direction of vectors in component form using appropriate mathematical notation.
- PC.AGR.6.2 Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
- PC.AGR.6.3 Add and subtract vectors on a coordinate plane using different methods.
- PC.AGR.6.4 Solve contextual vector problems, such as those involving velocity, force, and other quantities.

- Model situations with parametric equations.
- PC.AGR.6.5 Sketch the graph of a curve represented parametrically, indicating the direction of motion.
- PC.AGR.6.6 Apply parametric equations to contextual problems.

- Perform operations with vectors in context.

- PC.AGR.6 Represent and model vector quantities to solve problems in contextual situations.

### PAR Patterning & Algebraic Reasoning

- Sequences and Series
- PC.PAR.7 Demonstrate how sequences and series apply to mathematical models in real-life situations.
- Analyze sequences using multiple representations.
- PC.PAR.7.1 Demonstrate that sequences are functions whose domain is the set of natural numbers.
- PC.PAR.7.2 Represent sequences graphically, numerically, and symbolically.
- PC.PAR.7.3 Determine the limit of a sequence if it exists.

- Analyze series using multiple representations.
- PC.PAR.7.4 Demonstrate that a series is the sum of the sequence and represent series graphically, numerically, and symbolically.
- PC.PAR.7.5 Describe the behavior of a series in terms of the limit of its partial sums.
- PC.PAR.7.6 Derive and use the sum formula of a finite geometric series to solve contextual problems to model real-life situations.
- PC.PAR.7.7 Derive and use the sum formula of an infinite geometric series to solve contextual problems to model real-life situations.

- Analyze sequences using multiple representations.

- PC.PAR.7 Demonstrate how sequences and series apply to mathematical models in real-life situations.