Summer Math for incoming AP® Calc AB & BC Students

For ALL AP Calc Students (AB & BC):

Veritas (honor policy): Each student is to work individually. Students may discuss the general nature of each project with others but not the specific values being calculated. Each student’s submission is to contain there own originally-derived calculations, observations, and conclusions.

Questions may be emailed to Mr. Rick Aaron at raaron@montgomerycatholic.org 

(Printing issues: Some students have had problems printing the project files from a web browser. It is recommended to download each file to the student's computer and printing the downloaded file.)

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Students starting  Calculus AB in the fall will complete the 4 assigned projects attached below. Students who wait until the end of the summer will have difficulty completing all at once and will not benefit in class from the ideas within each project.

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Students starting Calculus BC in the fall who have:

• Completed Calc AB:  Must complete the following summer math:

  • Parametric Equations:

8.6 Precalculus (OpenStax)

• • • Read "Parameterizing a Curve" (p. 708)

    • Review Ex. 1 & 2

    • Review Ex. 3 (note that it is entails simply finding the equation of a line starting with computing a slope but where x(t) is also the "rise")

    • Read "Eliminating the Parameter"

    • Review Ex. 4, 5, 6, 7

    • Visualize ("see") parametric equations like composite functions; then "see" Ex. 8 & 9 as decompositions of functions

    • DO (for turn-in on first class day): (p. 717) 7, 11, 19, 23, 31, 33, 35, 37, 39, 41, 43, 47, 49

8.7 Precalculus (OpenStax)

• • • Read "How To..." (p. 719)

    • Review Ex. 1 & 2

    • DO (for turn-in on first class day):  (p.726): 13, 15, 17, 23, 25, 27

    • (* for additional parametric help see: Parametric Equations: https://www.khanacademy.org/math/algebra-home/alg-trig-functions/alg-parametric/v/parametric-equations-1 )

  • Polar Equations:

8.3 Precalculus (OpenStax)

• • • Read "Plotting Points Using Polar Coordinates..."

    • Review Ex. 1 & 2

    • Read the blue box of formulas on p. 674 ("Converting from Rectangular to Polar...")

    • Review Ex. 3, 4, 5, 6, 7, 8

    • Read "Identify and graph polar equations..." (p. 676)

    • Review Ex. 9 & 11

     8.4 Polar Coordinates: Graphs (OpenStax) 

• • • Read "Graphing Polar Equations by Plotting Points" (p. 683)

    • Review of Ex. 2

    • Review the Summary of Curves (p. 694) at the end of section 8.4

    • DO (before the first day of class): DeltaMath "Calc BC - Summer Math (Polar Coordinates)"

      1. Create a DeltaMath account (if you don't have one) & register for our Calc BC class at this link: https://www.deltamath.com/students?code=2U45-KH7S 

      2. Click this link to this Summer Math assignment: https://www.deltamath.com/app/assignment/19335121 

• NOT completed Calc AB: Must complete BOTH the 4 projects for summer math for Calc AB and the summer math for Calc BC.