AP Exam Weight: 10-15% | Multiple Choice: 4-6 questions | Free Response: Parts of several questions

📚 Table of Contents

1. [Parametric Functions]
2. [Polar Coordinates]
3. [Vector Functions]
4. [Motion in Space]
5. [Applications]

1. Parametric Functions 📊

Understanding Parametric Functions

A way to describe curves using parameter t. Think of it as:

• Motion over time
• Coordinated x and y movement
• Path tracing
• Indirect curve description

Basic Form

x = f(t), y = g(t)

Key Concepts

1. Parameter t:
   • Independent variable
   • Often represents time
   • Controls both x and y
   • Defines curve position
2. Elimination of t:
   • Find rectangular form
   • Solve for relationship
   • Identify curve type
   • Check domain restrictions

Derivatives

First Derivative

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

Process

1. Find dy/dt and dx/dt:
   • Differentiate y = g(t)
   • Differentiate x = f(t)
   • Keep in terms of t
   • Watch chain rule