1) Two mathematicians (A and B) are taking a walk and chatting.
A: I have 3 children.
B: How old are they?
A: The product of their ages is 36.
B: I can't figure out how old they are.
A: The number on the house that we are passing is the sum of their ages.
B: I still can't figure it out.
A: My oldest child is having a soccer match tomorrow.
B: Now I can figure it out!
How old are the children?

2) One line is defined by the equation y=ax+b,
the other -- by y=cx+d.
How can you tell if they are perpendicular to each other?

3) You have 2 identical ropes, a scissors and a box of matches.
Each rope, when ignited at one of its ends, burns for 1 hour.
Fugure out how to measure off 45 minutes by burning these ropes.
Notice: the ropes may be not uniform, so they can burn in starts
and stops, not at a constant speed.

4) Do integration exercises from the handouts I gave you.
Check your answers by differentiation. 

5) Try to work out the leaky bucket problem (page 19 of my writeup)
for a conical bucket instead of a cylindrical one.