One-Question Math Exams
Seven open-ended, one-question exams, one per course: non-Euclidean geometry, fractions between 5/7 and 5/8, mountain ranges from piecewise lines and polynomials, designing an experiment, 1-liter vases as solids of revolution, and the gnarliest trig identity.
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Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2016-08-31-one-question-math-exams/ (CC BY-NC 4.0)Transcript
[1] Geometry: "Assume the parallel line postulate is false. Prove as many new theorems as you can."
[2] Fractions: "Find as many fractions as you can that are between 5/7 and 5/8. (One bonus point for each fraction you find that no one else does.)"
[3] Algebra: "By graphing parts of lines, create a cool-looking mountain range. (Specify equations and x-values.)" [jagged piecewise-linear graph]
[4] Precalculus: "By graphing parts of polynomials, create a cool-looking mountain range." [rounded piecewise graph]
[5] Statistics: "Write your own statistics test, in two versions. Give each version to half of the class. Compare the scores. Is there a meaningful difference between your two versions?"
[6] Calculus: "Your boss at the vase company wants to create lots of differently shaped vases holding 1 liter each. Describe mathematically as many such vases as you can." [three solids of revolution]
[7] Trigonometry: "Create the gnarliest true trigonometric identity that you can." [(1 + tan²θ)(1 + cot²θ) = (tan(π/2 − θ) + cot(π/2 − θ))²]