Unit 09 Honors / Extended Practice

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Honors / Extended pathway

Parametric Curves & Vector-Valued Motion

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

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?

13. For r(t)=⟨10t,20t−4.9t²⟩, when does the projectile return to height 0?

14. Which statement best describes the central reasoning in Projectile, Cycloid & Trajectory Modelling?

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