1. It's hard to explain the correct speed, because it's different for every horse. You don't want to be crawling along because it will a) look painful b)won't get you to the correct distances or steps in the line c) won't help your horse jump very round, but you don't want to be galloping either. You want a working walk, trot, and canter so it looks like your horse is taking you some place, but you're relaxed & have time to get there. It takes a while to figure out a certain horses "correct pace," you need something that gives them power to get over the jump round, and if you truly are on the correct pace & maintain it, you'll get the distance 90% of the time. Lines help figure out what pace you need because most horses, especially at a rated show, should be getting the step in the line.
2. Lead changes vs. refusals are really a judges disgression, I would always score lead problems higher than a refusal, but that's my opinion. Hunters is really just a persons opinion.
3. You want to go deep in your corners, but your turn needs to look easy & balanced, and put you going straight towards the center of the fence. I would avoid sharp turns in the hunters until you are in a handy class & very experienced & able to make a balanced, pretty, sharp turn.
4. The first round of a hunter derby round is normally a normal hunter course, unless otherwise stated. You should ride it like a normal class, although some riders do ride derbies with a little more forward & bold of a step, especially in big fields, to better stimulate foxhunting, which is where the hunters originated from. Hunter derbies are normally quite competitive, so without a lead change I wouldn't expect you to get called back. It also depends on how round, square & "correct" of a jump your horse has, how fancy & floaty of a mover he is, and how your distances & corners & a million other things were vs. everyone else in the class.
5. Again, judges disgression since coats were waived. I would always ride equitation classes with a coat, unless they have asked riders to refrain from wearing costs because it's gotten that hot. If the waive jackets, go ahead & don't worry about wearing it in the hunters, but I would always wear it in eq.
I hope this helps, let me know if you have any more questions & I will try to share what I know & have learned. Good luck!
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