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Unit: Parametric equations, polar coordinates, and vector-valued functions
AP Calc:
CHA (BI)
, CHA‑3 (EU)
, CHA‑5 (EU)
, CHA‑6 (EU)
, FUN (BI)
, FUN‑3 (EU)
, FUN‑8 (EU)
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AP Calc:
CHA (BI)
, CHA‑3 (EU)
, CHA‑3.G (LO)
, CHA‑3.G.1 (EK)
Practice
- Parametric equations differentiationGet 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑3 (EU)
, CHA‑3.G (LO)
, CHA‑3.G.3 (EK)
Practice
- Second derivatives (parametric functions)Get 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑6 (EU)
, CHA‑6.B (LO)
, CHA‑6.B.1 (EK)
Learn
Practice
- Parametric curve arc lengthGet 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑3 (EU)
, CHA‑3.H (LO)
, CHA‑3.H.1 (EK)
Learn
Practice
- Vector-valued functions differentiationGet 3 of 4 questions to level up!
- Second derivatives (vector-valued functions)Get 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑8 (EU)
, FUN‑8.B (LO)
, FUN‑8.B.1 (EK)
, FUN‑8.B.2 (EK)
Learn
Practice
- Planar motion (differential calc)Get 3 of 4 questions to level up!
- Motion along a curve (differential calc)Get 3 of 4 questions to level up!
- Planar motion (with integrals)Get 3 of 4 questions to level up!
AP Calc:
FUN (BI)
, FUN‑3 (EU)
, FUN‑3.G (LO)
, FUN‑3.G.1 (EK)
, FUN‑3.G.2 (EK)
Learn
Practice
- Differentiate polar functionsGet 3 of 4 questions to level up!
- Tangents to polar curvesGet 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑5 (EU)
, CHA‑5.D (LO)
, CHA‑5.D.1 (EK)
, CHA‑5.D.2 (EK)
Learn
Practice
- Area bounded by polar curves introGet 3 of 4 questions to level up!
- Area bounded by polar curvesGet 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑5 (EU)
, CHA‑5.D (LO)
, CHA‑5.D.1 (EK)
, CHA‑5.D.2 (EK)
Practice
- Area between two polar curvesGet 3 of 4 questions to level up!
AP Calc:
CHA (BI)
, CHA‑5 (EU)
, CHA‑5.D (LO)
, CHA‑5.D.1 (EK)
, CHA‑5.D.2 (EK)
Practice
- Area with polar functions (calculator-active)Get 3 of 4 questions to level up!
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About this unit
While we're often familiar with functions that output just one variable and are graphed with Cartesian coordinates, there are other possibilities! Vector-valued functions, for example, can output multiple variables. Polar functions, too, differ, using polar coordinates for graphing. We can still explore these functions with derivatives and integrals.AP® is a registered trademark of the College Board, which has not reviewed this resource.