Post-AP Calculus Projects
Requirements:
Must be done in pairs. There will be one group of three (which means I will be more critical of your work since there were more
brains put toward it). During our regularly scheduled class days, you must work on the project in the classroom. You will not be
dismissed to go elsewhere.
Graded Components:
The project is worth a test grade and will be assessed on the following pieces.
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Written Solution (Couple of pages) with Diagrams/Visual Aids. This must be able to stand alone by itself and not be
dependent on a verbal explanation. Clarity of supporting work/evidence and explanations is critical. (Assume that someone
will be reading this that hasn’t seen the presentation). How professionally it is put together counts!
Oral Presentation with visual aids [10-15 minutes]
Movie, Power-point, or Website typed with diagrams/mathematical steps either computer generated or handwritten nicely
(with colors) and scanned in.
Bibliography of sources (including source of initial problem)
Self/Team Assessment of Contributions to the Project
Due Date:
ALL written Solution and Powerpoint/Movie/Website must be submitted to me by hand or via email by
8 am on May 25 [M510b] or by 8 am May 26 [M510a/c]
to be considered “on-time” regardless of what day you are selected to give the presentation.
Presentations will be given on:
May 25/27th (and perhaps June 1 if needed) – M510b
May 26/27th (and perhaps May 31 if needed) – M510a and M510c
Note: A lottery will be drawn to determine when you will be presenting. If you are not in class for the time slot you have been
assigned, your grade will be marked down and your partner will have to do the presentation by themselves.
Possible Problems/Topics:
Teach Yourself More Complex Topics that were beyond the scope of the course, then teach the class:
o Parametrics and Calculus (Check Index of our text. Spread over multiple chapters)
o Polar Coordinates and Calculus (Check Index of our text. Spread over multiple chapters)
o More Complex Integration Methods (7.2 – 7.5)
o L’Hopital, Arc Length and Improper Integrals (4.7, 7.7, 7.8, 8.2, 8.3, Gabriel’s Horn App)
o Sequences and Series (Chapters 9 & 10)
o Density, Center of Mass, and Other Physics Apps (8.4 & 8.5)
o Applications to Econ (8.6)
o Probability (8.7 & 8.8)
o Other integration techniques (parts, partial fractions, trig substitution, and Simpsons) (7.4 & 7.5)
o Hyperbolic Functions (Check Index. Spread over multiple chapters. Starts in 3.8)
o More Complex Differential Equations (Second Order, etc & SARS project) (Ch 11)
 There are possible projects at the end of each of the chapters of our book.
 Build high quality 3-D models of some of the volume problems we examined…allowing students to be able to visualize not
only the whole object internally and externally, but the cross-sections as well. Must include the actual solution of the
problems that you’ve modeled.
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Problems/Projects from James Stewart’s text “Single Variable Calculus”
o “Where to Sit at the Movies?” [p. 476]
o “Where Should a Pilot Start Descent?” [p. 237]
o Applications to Economics and Biology [Section 6.6]
o Applications of Integration – Focus on Problem Solving [p.502-505]
o Calculus and Baseball [p. 540-1]
o Predator-Prey Systems [Section 7.6]
o Applications of Differential Equations – Focus on Problem Solving [p.560-561]
o Probability [Section 6.7]
Do some research! Find a cool problem/project that isn’t listed.
Some other possibilities:
CALC I Projects - Caustic Rain, Profitable Production, Pest Control, Legality of Stock Market, Drag, Water Contamination, Drug
Absorption, Art and Decay:
http://www.math.lsa.umich.edu/~glarose/courseinfo/calc/calcprojects.html
Arc Length, Volumes, Infinite Series:
http://www3.wheatoncollege.edu/tratliff/writing/calculus_II.html
“Writing Projects for Mathematics Courses: Crushed Clowns, Cars & Coffee to Go” by Crannell, LaRose, and Ratliff (Can be found on
Amazon.com)
Bridge Building: (Background info needed: Hyperbolic Functions)
http://www.math.unl.edu/~jorr/calculus/projects/spr95proj2.html
CALCULUS PROJECT RUBRIC
Level of Difficulty
Problem Included (if applicable)
Written Work
Mathematically Clear Explanations/Sufficient Details
Supporting Diagrams
Put together in a professional manner
Accuracy of mathematics
Presentation
Did presentation come off well prepared?
Well done technological support
Accurate/clear explanation
Bibliography of sources
Team Assessment
TOTAL POINTS
Points
Possible
5
3
10
4
5
10
3
5
5
2
3
55
FINE-PRINT:
If you finish your problem in one or two class periods, then it probably was too easy. You should choose something else to do as a
second problem to supplement this.
The teacher reserves the right to deny your project proposal if it is thought to be “below your capabilities” and not rigorous
enough for your brilliance. If your project takes very little time, you can select a second to supplement.
**Projects will be STRONGLY GRADED ON DIFFICULTY LEVEL. Easy projects will have a maximum grade of a B-.**