1. Presentation: Uma Quizizz: Anna 5n1: Emma
P a r a m e t r i c s & V E C T O R S
Presentation: Uma
Quizizz: Anna
5n1: Emma

2. What will be Covered Parametrics Vectors Graphing
Eliminating the Parameter
Finding the derivative
Finding the second derivative
Arc length in parametric
Vectors
PVA
Speed of a particle
Total distance traveled

3. P A R A M E T R I C S

4. Graphing Parametric Equations
Create a table of values for x, y, and t and insert selected values of t
Plug t values into given x and y equations and put solved x and y values into table
Use x and y values to graph the parametric

5. In the Calculator
Mode → Parametric Y=
Type in x and y equations

6. Eliminating the Parameter
Use the x equation to solve for t
Plug the expression equal to t in for t in y equation

7. Finding Divide the derivative of y by the derivative of x
Find the line tangent to the graph at

8. Finding 12 Determine concavity at ( 2 , 3 )
The second derivative of y over the first derivative of x 12

9. Arc Length
Find the length of the curve from
~1.317

10. V E C T O R S

11. Position < x(t) , y(t) >
Usually the first equations given in a question which can be derived to find velocity

12. Velocity < x’(t) , y’(t) >
The derivative of position, used to find:
Total distance traveled
Speed of the particle (magnitude of velocity vector)
Acceleration (derivative)

13. Acceleration < x”(t) , y”(t) > The derivative of velocity
Most commonly used to determine if the particle is speeding up or slowing down at a given point (whether velocity and acceleration have the same sign or not)

14. PVA Practice The position of a particle at any time Is given by
Find the magnitude of the velocity vector at time t = 5
Find the total distance traveled by the particle from t = 0 to t = 5
Find dy/dx as a function of x

15. Resources apcentral.collegeboard.org Barron’s
Panther Creek AP Calculus website
Past tests