AP Calculus AB/BC
Final Project Options
Name _____________________________________
1. Mathematics Interest Project (maximum 2 participants per project)

“Research” a topic that interests you that pertains to any mathematical concept. (It does not
necessarily have to be a high-level math concept…sometimes the simplest connections are the most
interesting!).

Write a synopsis of your interest topic to be submitted. (31 points––see attached rubric)

Present your interest project to the class, including audio/visual aids. (19 points––see attached
rubric)
2. Calculus Video (maximum 4 participants per project)

Create a calculus music video/skit to help students remember an important concept or theme
from calculus. An explanation of the concept(s) MUST be part of the script, simply mentioning
the concept(s) is NOT sufficient.

Write a script for the video that includes calculus concept(s) and appropriate supporting material to
help students to learn and remember the concept(s). (40 points—see attached rubric)

Create a calculus music video/skit that shows the calculus concept to be played for the class.
(10 points—see attached rubric)
3. Bead Project (individual project)

See project sheet for details & scoring rubric.
4. Cooking with Calculus (maximum 2 participants per project)

See project sheet for details.
5. Matching Game (maximum 2 participants per project)

Create a matching card game for students where they must match 3-4 cards. (We did similar
activities with derivatives, graphical analysis, and slope fields…see examples and topic list for
ideas).

Use PowerPoint or the TI-nspire to create the individual cards (it will be helpful to map everything
out by hand first). There is also a lot of free online software available to create graphs and type out
mathematical notation.
o Use similar equations for some of the cards to make it more complex.

You must make 36 cards (this will be between 9 and 12 sets depending on the format of your game).
The cards must make connections among VERBAL, GRAPHICAL, and ANALYTICAL
representations of the topic. (36 points = 1 point per card).

You must include worked out, correct solutions. NO SOLUTIONS = NO CREDIT. (14 points, with
deductions for each incorrect solution)
PRESENTATIONS MUST BE GIVEN NO LATER THAN FRIDAY MAY 23RD FOR SENIORS,
AND NO LATER THAN FRIDAY MAY 30TH FOR JUNIORS.
AP Calculus
Post-AP Exam
Interest Topic Rubric
Synopsis (31 points):
Name _________________________________________________
Name _________________________________________________
Formatting
o
o
o
o
o
2
Typed
12 point Times New Roman font
Double-spaced
Standard 1” margins
2–3 pages
Sources
o
2
1
0
must have 2 credible sources listed on a Works Cited page, and cite each
source at least once in your paper
Citations
o
0
2
1
0
properly included in MLA format in body of paper
Mathematical Relevancy
5
4
3
2
1
0
Knowledge of Topic
5
4
3
2
1
0
Ability to Explain Topic
5
4
3
2
1
0
Ability to Explain Math
5
4
3
2
1
0
Mechanics/Grammar
5
4
3
2
1
0
o
o
o
o
o
no personal pronouns (I, me, you, us, we, etc.)
must include an introduction and conclusion
standard requirements for en essay
1 point deduction per spelling error
1 point deduction per punctuation/capitalization error
Subtotal: __________/ 31
Presentation (19 points):
Eye Contact
3
2
1
0
Speaking Clearly
3
2
1
0
Enthusiasm
3
2
1
0
Comprehensibility
5
4
3
2
1
0
Audio/Visual Aid
5
4
3
2
1
0
Subtotal: __________/ 19
TOTAL ____________/ 50
NOTE:
If you choose to work with a partner, the collaboration efforts must be clear! Both individuals need to
be involved in the research, synopsis, and presentation.
Possible Interest Project Topics
 Fractals
 Tessellations (and MC Escher)
 Mobius strip
 The geometry of Tetris
 Rubik’s Cube
 Logic Problems (Lewis Carroll)
 Sudoku
 Card counting
 Casino games
 Origami
 Optical illusions
 Card tricks
 Fibonacci Sequence/The Golden Ratio (math in nature)
 Cryptography and codes
 Numerology
 Board games
 Alternative numbering systems/the history of numbers and numbering systems
 Abacus/slide rule (calculating before the calculator)
AP Calculus
Name _____________________________________
Video Project Grade Sheet
Name _____________________________________
Name _____________________________________
Name _____________________________________
PART 1:
Must be submitted and approved by no later than Friday, May 16th .
Must be approved before you begin filming your video.
SCRIPT (10 points)
____________/10
o Song and script content must be appropriate for school
STORY BOARD (5 points)
____________/5
o Includes a “slide” for each scene, explaining/detailing what will be seen/heard
PART 2: Must be completed for viewing by May 23rd for seniors, and May 30th for juniors.
MATHEMATICAL CONTENT AND ACCURACY (25 points)
____________/25
o Script clearly explains the concept(s). Simply mentioning the concept is not sufficient.
o 50% of the script/storyboard must pertain to the featured mathematical content.
o Deductions will be made for each mathematical inaccuracy.
VIDEO (10 points)
o Audio/visual clarity and quality
____________/10
(2 points)
o Video must be at least 3 minutes in length, but no more than 6 minutes
(2 points)
o Group participation (all members must be visible & contributing)
(3 points)
o Matches script/storyboard
(2 points)
TOTAL________ / 50
AP Calculus
Name _____________________________________
Bead Manufacturing Project
Date _______________________ Period ________
For this project you are going to play the part of a fashion bead designer, manufacturer, and distributor. A local
bead store, Boddy’’s Bead Emporium TM , has a machine that allows you to create a bead by entering
the correct calculus-based specifications into a computer (much like we do with our graphing calculators), and
the machine will produce the actual bead. The manufacturer will charge you one dollar for every 100 beads
made with this machine. You will use your knowledge of volumes of solids of revolution to design a bead
using algebraic and/or transcendental functions. Your objective will then be to calculate the cost per unit for
your bead to be manufactured as well as determine a price per unit for your bead to be sold. Obviously, you
want to make a profit from this venture, but the price must be reasonable enough that consumers will buy your
product, so design and price carefully.
Everybody will be operating with the following constraints and criteria:
 start with 1,000 cm3 of raw material that costs $100
 the hole of each bead must be 2 mm in diameter
 the material consumed by drilling the hole is not reusable (and we will assume that no other material is
lost during the rest of the manufacturing process)
 the bead design must contain at least 2 different functions
 each increment of the Zoom 4:Decimal View x- and y-axes on the graphing calculator will be equivalent
to 1 mm
Your final report will contain the following:

an accurate sketch, to scale, of the functions used that, when revolved around the x-axis, will determine
the design of your bead (label each function)

an accompanying sketch of the 3-dimensional bead

the volume of material needed per bead

the volume per bead of unusable material due to drilling the hole

the number of whole beads that you will be able to manufacture from the provided material

the production cost per bead (rounded to the nearest half-cent) and the total cost of the entire stock
(don’t forget about the manufacturers cost for using the machine).

the price for which you intend to sell your product, and the profit you will make from selling all of your
beads
You should consider your final report a business proposal to the owner and proprietor of Boddy’’s
Emporium
TM
, with whom you will be manufacturing the beads.
thorough, and presentable.
The report needs to be accurate,
Bead
AP Calculus
Name _____________________________________
Bead Project Rubric
BE SURE TO SHOW ALL WORK!!!
Sketches of silhouette & bead (10 points)
____________/10
The volume of material needed per bead (15 points)
____________/15
The volume per bead of unusable material (5 points)
____________/5
The number of beads manufactured (5 points)
____________/5
The production cost per bead (5 points)
____________/5
The price per bead and total profit made (5 points)
____________/5
Overall presentation (5 points)
____________/5
TOTAL ________ / 50
Instructions:
Each student or group will find a recipe with at least 10 numerical values in the recipe (ingredients
amount, cooking temperature, baking time, serving size, etc.). You must re-write all numerical values in
the recipe using calculus problems that represent the correct amounts in the recipe.
For example:
Old Recipe

New Recipe
2 eggs

3x eggs
lim 16x
8x2 5
yields 8 dozen

yields
2
x
 3x dx dozen
2
2
0
All students must include each of the following
types of problems once:
○
○
○
○
○
○
Limit evaluation
Definite Integral
Average Value
Slope of a Tangent Line
Higher Order Derivative Value
Volume of a Solid (by cross-sections OR
revolution)
BC Students also have the following types of
problems from which to choose, and must
choose 3:
○
○
○
○
○
Speed of a parametric particle
Arc Length (in any coordinate system)
Converging Improper Integral Value
Radius of Convergence for an Infinite Power
Series
Converging Infinite Series Value (geometric
series, power series, etc.)
Here are some other options for all students:
o
o
o
o
o
o
o
Relative Minimum/Maximum Value
Absolute Minimum/Maximum Value
Inflection Point
Area bounded by curves
Volume of a Solid with Known Cross-Sections
Volume of a Solid of Revolution
Related Rates
Here are some other options for BC students:
Limit evaluation using Euler’s Method
Polar area
Approximation using Euler’s Method
Values corresponding to Logistic Models
(carrying capacity, population at greatest
growth rate, etc.)
o Error Bound
o
o
o
o
You may use any other type of calculus problem, so that when you solve it, it gives you the number that is
represented in the recipe.
ADDITIONAL CRITERIA:

You must include a copy of the original recipe, separate from your typed calculus version of the
recipe.

Your group must also hand in an answer sheet that shows FULL SOLUTIONS for every value. Your
work does not need to be typed, but it must be neat and organized.

You are not required to actually make the recipe…but it definitely sweetens the deal! 
This project is worth 50 points. The points will be divided among the individual problems you create and
graded for accuracy. If you have a recipe that has the minimum 10 problems, each will be worth 5 points.
AP Calculus
Matching Game Topic Ideas
AB & BC Topics:
 Limits
 Continuity
 Position/velocity/acceleration
 Riemann/Trapezoidal sums
 Analysis of graphs
 Volume of a Solid
Additional BC Topics
 Infinite Series Tests for Convergence & Divergence
 Taylor Polynomials & Error Bound
 Taylor/Maclaurin Series
Please get teacher permission if you’d like to choose a different topic.