Impossible Final Exams

The end of the semester is approaching. If you still haven’t prepared a final exam for your students, consider using the MJ4MF Final Exam (PDF). Those teaching in online college classes can send this exam to their students.

Alternatively, here are some questions you could use, depending on what course you’re teaching:

Geometry: Provide one real-life application of Ceva’s theorem that’s useful.

Algebra: From the real world, provide one example of a quadratic equation with integer coefficients that has integer solutions.

Analysis: Derive the Euler-Cauchy equation using only a straightedge and compass.

Biology: Create life.

Computer Science: Write a fifth-generation computer language. Using this language, write a computer program to finish the rest of this exam for you.

And here’s a mathy joke about final exams…

A mathematician, who had earned his PhD nearly 30 years ago, returned to the school from which he matriculated. He visited with the faculty in the math department, and they shared their exams with him. “Why, the questions on these tests are the same ones I answered when I was a student here!” he said.

“That’s true,” said one of the professors, “but the answers are all different.”