Case 1:

The apparent wind would shift aft and increase slightly.

I'd ease the fine trim on the jib and the main, and trim
back in as I headed up.

Case 2
I assume you mean the true wind direction does not
change. That would not be immediately "apparent".

My immediate reaction would be to wait a bit and coast
while I studied the water upwind for clues.

In this case, I'd have the option of coasting in the same
direction hoping for the wind to fill in again--powering
through the lull with the momentum of the boat. Or, if
I felt the original puff was not representative of the
typical conditions of the day, I'd bear away slightly to keep
the boat in the groove, which you might be forced to do,
if the wind did not pick up immediately. I'd try to get a
little bit of coast on my present track before bearing away
to power up. At that point I would want fuller sails for
more power and make adjustments accordingly--easing
the backstay for example.

Nav wrote

Lets say you are racing hard on the wind with no boats near you and the
wind strength changes from 10 to 15 knots with the same direction.

Q1) As helm what should you first do first:

1) Nothing and wait
2) Immmediately change course to keep apparent wind direction the same
3) Counter increased weather helm but keep course the same
4) Reduce helm and let boat round up more quickly
5) None of the above -explain.


Q2. The wind drops to 10 knots again with no change in direction.

Your immediate reaction is to...