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Cogito

AP Calculus BC · Chapter 1 · Lesson 1

Practice Worksheet

Parametric Equations

Two functions of a third variable.

11 problems · about 25 minutes · AP Calculus BC 9.1, 9.2

NameDate

Figure — use these to answer the problems

A parametric point traces a path. Move it and read the coordinates.
-10-10-5-5551010
(3, 4)
x at this t3
y at this t4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. dx/dt = 3, dy/dt = 15. What is dy/dx?

    Answer

  2. x = 3t, y = t. What is x when t = 4?

    Answer

  3. dx/dt = 4, dy/dt = 12. What is dy/dx?

    Answer

  4. dx/dt = 5, dy/dt = 0. What is dy/dx?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x = t, y = t². Eliminating t gives y = x to what power?

    Answer

  2. Select every true statement about parametric curves.

    • They may cross themselves.
    • They must pass the vertical line test.
    • Eliminating the parameter loses the direction.
    • dy/dx is the same as dy/dt.
    • Tick every box that applies.

  3. x = t + 2, y = 3t. What is y when x = 5?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. dx/dt = 0 at a point. Is the tangent vertical there? 1 for yes, 0 for no.

    Answer

  2. Order the steps for eliminating the parameter.

    Write 1 to 3 in the boxes to put these in order.

    • Solve one equation for t
    • Substitute into the other
    • Simplify to a relation in x and y

  3. At a Moment

    x = 2t, y = t². What is x when t = 3?

    Answer

  4. The Slope

    dx/dt = 2 and dy/dt = 6. What is dy/dx?

    Answer