Unit 09 Core Practice

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Core pathway

Parametric Curves & Vector-Valued Motion

College-level fluency, interpretation, and verification.

1. Eliminate t from x=2t+1, y=t².

2. Which statement best describes the central reasoning in Parametric Representation, Elimination & Orientation?

3. For x=t²+1,y=t³, find dy/dx.

4. Which statement best describes the central reasoning in First Derivatives & Tangent Lines?

5. For x=t,y=t³, find d²y/dx².

6. Which statement best describes the central reasoning in Second Derivatives & Concavity?

7. Find area under x=t²,y=t³ for 0≤t≤1.

8. Which statement best describes the central reasoning in Area from Parametric Curves?

9. Find length of x=3t,y=4t,0≤t≤2.

10. Which statement best describes the central reasoning in Parametric Arc Length?

11. For r(t)=⟨t²,3t⟩, find v and a.

12. Which statement best describes the central reasoning in Vector-Valued Position, Velocity & Acceleration?

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