# 759: 3x9

 3x9 Title text: Handy exam trick: when you know the answer but not the correct derivation, derive blindly forward from the givens and backward from the answer, and join the chains once the equations start looking similar. Sometimes the graders don't notice the seam.

## Explanation

In college courses with a very large number of students (picture the huge, tiered, amphitheater-style lecture halls shown in any movie or TV show about college), teaching assistants are employed to help the professors grade student work. In math and science courses, students are expected to solve the problems and show their work as supporting evidence. Due to the high volume of work to grade, whether it's being done by the professor or a TA, the grader will get lazy and look for correct answers and the existence of work without checking that the work is accurate.

The math switches from β being square root notation to it being division notation midway. That is an illegal operation. But the correct answer is reached anyway, because 27 is the correct answer to 3 × 9, 3β81, and 81 ÷ 3.

More generally, this pattern holds true for any number and its square; namely, π₯π¦ = π¦² ÷ π₯ whenever π¦ = x²   (... namely, x*y = y^2/x whenever y=x^2) .

## Transcript

[A problem is given on an arithmetic test: "4) 3x9=?". In handwriting, the student's work follows. The student has accurately reformatted the question as 3 times the square root of 81, which visually resembles the long division problem of 3 divided into 81, and then solved the latter to get 27 β the correct answer to both.]

# Discussion

In the middle of a Physics I exam, I forgot one of the equations of motion. Using my basic working knowledge of Calculus and the relationship between acceleration, velocity, and position, I managed to derive an equation which I used to solve the problem. When I got my exam back, I was given only partial credit because I got the right answer using the wrong formula.Smperron (talk)