# Why the Mathematical Ninja hopes for a hard exam

The Mathematical Ninja sighs. “Say that again?”

“I hope it’s an easy paper!” says the student, brightly.

Wearily, the Mathematical Ninja goes to the board and sketches two curves. They look a little like boa constrictors that have swallowed elephants. “You’re above average, correct?” he asks.

The student doesn’t look quite so bright now. “… Yes? Not by much, but…”

“Above average, yes. This curve over here is the theoretical distribution of grades for an easy paper.”

“The who to the what now?” The bright smile is most definitely becoming a frown.

“If you have an easy paper,” says the Mathematical Ninja, “the grades will be spread out something like this: a whole bunch of Cs in the middle, then Bs out here, and As out here… and on the other side, Ds, Es and (heaven forfend) Us.”

The student nods.

“So if you get just slightly above an average mark - which is already higher, because it’s an easy paper, you probably end up with a C. Maybe a B.”

“Right!”

“However, over here,” continues the Mathematical Ninja, “is what happens for a hard paper. You’ll see: the average mark is lower and - here’s the good thing - if you do slightly better than average, it’s much more likely to tip you over into a B, or even an A.”

“So you’re saying I could get less marks in a hard paper, but a better grade?” Smile to frown to eyebrows raised.

“Fewer marks, my dear,” says the Mathematical Ninja. “Fewer marks.”