Parametric Equations



Name ___________________________

AP Calculus AB 2015

Summer Assignment

Dear AP Calc Student,

Welcome to AP Calculus! I am looking forward to working with you this coming September. This is your first assignment – the summer review packet. It is a review from Chapter 1.

Neatly show the work and solution for each problem assigned using pencil. Please do not use pen. Correct work must be shown for full credit. Review the families of functions, in your function notebook, as part of this packet. You will have a quiz on this material within the first week of school. You should also know your unit circle.

Please make sure that your function notebook is up to date. You can check my Teacher Page on School Wires for this information. You should have the material from Chapter 1 and the first part of Chapter 2. There will be a Function Notebook check when we complete Chapter 2.

A graphing calculator that you can operate is required for this class. I will be using the TI 84 and TInspire. It is expected that you have a moderate proficiency skill level with your calculator.

Our goal is to be ready for the AP Test scheduled for early May. You will practice open ended questions and take practice tests to prepare your for this test. Also, I hope that you plan on competing in Math League, which will be held on Tuesdays after school.

If you have any questions, please contact Mrs. Brumberg email: mbrumberg@ or mbrumberg74@. I do check my school email from home.

See you in September.

Mrs. Brumberg

Parametric Equations

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Circles

Examples of Circles

Square both equations and add them together.

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Ellipses

Lines, line segments and many other curves can be defined parametrically.

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Parametrization for a line

Use the formulas [pic]

Assign t = 0 to your first point.

Assign t = 1 to your second point

(This choice is for convenience. Making it more complicated is okay too but unnecessary)

Let’s go through the steps to finding a parametrization for a line segment containing (-2, 1) and (3, 5)

1. Let t = 0, x = -2, and y = 1 and find [pic]

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2. Now use t = 1, x = 3, and y = 5 to find a and b

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3. Write the answer

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This is just one possible answer.

Try these!

Find a parametrization for a line segment containing the points.

a) (1,3) and (2,5)

b) (-2, 6) and (4,2)

Summer Assignment AP Calculus Name ______________

Quick Check Chapter 1

|x |- 2 |2 |4 |

|f(x) |4 |2 |1 |

Assessment Chapter 1

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* In applications, t often denotes time, an angle or the distance a particle has traveled along its path from a starting point.

* Parametric graphing can be used to simulate the motion of a particle.

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7. Write a piecewise formula for the function.

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