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Library AP Precalculus Unit 4: Functions Involving Parameters, Vectors, and Matrices
⁂   AP Precalculus · Unit 4

4. Functions Involving Parameters, Vectors, and Matrices

0–0% of the AP exam. Key topics: Parametric Functions (parametric equations; tracing curves; eliminating the parameter), Implicitly Defined Functions and Conic Sections (circles, ellipses, parabolas, hyperbolas), Vectors in Two Dimensions (magnitude, direction, component form), Vectors in Three Dimensions (3D component form; distance), Vector Operations (addition, scalar multiplication, linear combinations), The Dot Product of Two Vectors (formula; geometric interpretation; angle between vectors), Matrix Operations (addition, subtraction, scalar multiplication), Matrix Multiplication, Matrices as Functions (linear transformations; mapping vectors), Matrices Modeling Contexts, Inverses and Determinants (2×2 inverse; determinant; solving matrix equations), Linear Systems and Matrices (augmented matrices; row reduction), Vectors in Motion (velocity vectors; parametric motion models), Matrix Composition and Transformations (composing transformations).

0–0% exam weight standard track

Unit 4: Functions Involving Parameters, Vectors, and Matrices

Study guide content for this unit is being prepared. Check back soon for complete lesson notes, formula sheets, and worked examples.

Topics in this unit

  • Parametric Functions (parametric equations; tracing curves; eliminating the parameter)
  • Implicitly Defined Functions and Conic Sections (circles, ellipses, parabolas, hyperbolas)
  • Vectors in Two Dimensions (magnitude, direction, component form)
  • Vectors in Three Dimensions (3D component form; distance)
  • Vector Operations (addition, scalar multiplication, linear combinations)
  • The Dot Product of Two Vectors (formula; geometric interpretation; angle between vectors)
  • Matrix Operations (addition, subtraction, scalar multiplication)
  • Matrix Multiplication
  • Matrices as Functions (linear transformations; mapping vectors)
  • Matrices Modeling Contexts
  • Inverses and Determinants (2×2 inverse; determinant; solving matrix equations)
  • Linear Systems and Matrices (augmented matrices; row reduction)
  • Vectors in Motion (velocity vectors; parametric motion models)
  • Matrix Composition and Transformations (composing transformations)