AP Calculus BC Unit 9 practice questions: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
8 original multiple-choice questions on AP Calc BC Unit 9, parametric equations, polar coordinates, and vector-valued functions. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
A curve is given by x = t², y = t³. What is dy/dx at t = 2?
Question 2 of 8
For a parametric curve, how do you find d²y/dx²?
Question 3 of 8
A particle moves with x′(t) = 3 and y′(t) = 4. What is its speed?
Question 4 of 8
Which integral gives the area enclosed by a polar curve r = f(θ) for α ≤ θ ≤ β?
Question 5 of 8
Which rectangular point matches the polar point r = 2, θ = π/3?
Question 6 of 8
A particle has position ⟨t², 3t⟩. What is its velocity vector at t = 1?
Question 7 of 8
Which integral gives the length of a parametric curve x(t), y(t) for a ≤ t ≤ b?
Question 8 of 8
What is the graph of the polar equation r = 2?
Key ideas in Unit 9
- For parametric curves, dy/dx = (dy/dt)/(dx/dt), and d²y/dx² = [d/dt (dy/dx)]/(dx/dt).
- Arc length of a parametric curve is ∫√((dx/dt)² + (dy/dt)²) dt.
- For vector-valued motion, velocity is ⟨x′(t), y′(t)⟩ and speed is its magnitude.
- Polar coordinates convert with x = r cos θ and y = r sin θ. The area of a polar region is (1/2)∫ r² dθ.
More AP Calc BC practice
← Unit 8: Applications of Integration
Unit 10: Infinite Sequences and Series →
The full AP Calculus BC practice test, all units
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