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AP Precalculus centers on functions modeling dynamic phenomena. Research indicates that deep understanding of functions and their graphs as embodying dynamic covariation of quantities best supports student preparation for calculus.
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Learning Progression 19: Conic Sections
Include how variables covary. Conic sections introduced implicitly but also explore parametrically making the trigonometric connection. Conic sections are limited to those whose graphs have vertical and horizontal lines of symmetry. The implicitly-defined functions study of conic sections does not include all of the characteristics found in a full analytical treatment of conic sections. It is limited to quantities found in the equations involving two variables that are needed to sketch graphs of the functions.
Learning Intention 4.6.A: I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Learning Intention 4.6.A: I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Success Criteria:
Learning Intention 4.6.A: Optional Day - I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Learning Intention 4.6.A: Optional Day - I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Success Criteria:
Learning Intention 4.6.A: Optional Day - I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Learning Intention 4.6.A: Optional Day - I am learning to represent conic sections with horizontal or vertical symmetry analytically.
Success Criteria:
Learning Progression 20: Vectors
Including Law of Sines and Law of Cosines. The course framework limits matrices, vectors, and lineartransformations to R^2, but R^n can be explored if desired.
Learning Intention 4.8.D: I am learning to determine angles between vectors and magnitudes of vectors involved in vector addition.
Learning Intention 4.8.D: I am learning to determine angles between vectors and magnitudes of vectors involved in vector addition.
Success Criteria:
Learning Progression 21: Matrices & Linear Transformations
Building understanding needed to have matrices act as (linear transformation) functions on vectors including inverse functions. Solving systems are an instance of solving matrix-vector equations. Light version of Markov models with real numbers in 2 dimensions with input vectors and output vectors. Discussion on the basis of a vector space is bypassed but can be developed if time allows since determining if vectors are linearly independent reinforces multiple topics such as determinants and inverses.
Success Criteria:
Success Criteria:
Success Criteria:
Learning Intention 4.11.B: I am learning to apply the value of the determinant to invertibility and vectors.
Learning Intention 4.11.B: I am learning to apply the value of the determinant to invertibility and vectors.
Success Criteria:
Learning Intention 4.12.A: I am learning to determine the output vectors of a linear transformation using a 2x2 matrix.
Learning Intention 4.12.A: I am learning to determine the output vectors of a linear transformation using a 2x2 matrix.
Success Criteria:
Learning Intention 4.13.A: I am learning to determine the association between a linear transformation and a matrix.
Learning Intention 4.13.A: I am learning to determine the association between a linear transformation and a matrix.
Success Criteria:
Learning Intention 4.13.B: I am learning to determine the composition of two linear transformations.
Learning Intention 4.13.B: I am learning to determine the composition of two linear transformations.
Success Criteria:
Success Criteria:
Success Criteria:
Learning Intention 4.14.B: I am learning to apply matrix models to predict future and past states for n transition steps.
Learning Intention 4.14.B: I am learning to apply matrix models to predict future and past states for n transition steps.
Success Criteria:
Learning Intention 4.14.B: Optional Day - I am learning to apply matrix models to predict future and past states for n transition steps.
Learning Intention 4.14.B: Optional Day - I am learning to apply matrix models to predict future and past states for n transition steps.
Success Criteria:
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