Yesterday, for some strange reason, I actually had more time than my usual 2 seconds to prepare for classes, and I was giving a test in precalculus, and I have a handful of very smart kids that are polite and bored in class because it's going too slow for them.
This all adds up to a differentiated test on vectors and polars. The bulk of the class just had the standard test that asked them to:
find the angle between 2 vectors,
convert a polar point to a rectangular point and visa versa,
plot r = 3 sin theta + 2, etc.
Without saying anything to them, I handed the super-smart kids a different version of the test and kept an eye on them throughout the period to see their reaction. They did fine. It took them the whole allotted time (whereas usually they're done in less than 1/2 the time of the other students). They're aware of this fact, so periodically, one of them would look up as another student handed in his test. I wonder what was going through their minds.
Their questions were more of the variety of (and maybe I could have made them harder, but ...) :
give me 2 vectors that are perpendicular to each other and neither lies on the axes or has equal components,
plot 4 points on the polar plane that when connected form a rectangle, none are on the axes. then give me their coordinates, each in 2 ways.
vector u is <6,> find me a vector in the same direction that is 1 unit long (and we did NOT cover this in our short time with vectors). I did give them a hint by making them answer a "similar triangle" type question right before this one.
Anyway, I'm glad I could "unbore" them briefly, and hopefully I can do this again.