Jump lesson - big oxer to a tight right hand turn

We warmed up with Christa and Alina, then jumped with Christa.
Duke was a little stiff in warm up, he kept wanting to pop his head up instead of going round (mostly whenever we went past John), and he was hard to bend around my leg.  John had us go from trot to halt, and Duke halted square, but not round.  John said for now, to be happy with square, that it will just make Duke more anxious to then mess with the round.
We started with a cross rail, turned it into a vertical, then changed directions.
Then we went over an oxer, right hand turn to a vertical, left hand turn to another vertical.  I completely screwed up the first line, and went from the oxer on a hard right straight to the vertical, instead of looping around.
From there, then we did the second vertical on a very hard right turn to the first vertical.  The first time, I just had to halt in the wall, back up four steps, turn right, and then trot over it.  The second time, Duke did it perfectly.  The third time we made the turn, but only barely.
John said that it is being able to expect a 10 meter circle at any moment you want on show jumping.  If you can do a 10 meter circle in a dressage test, which is 320 mpm ish, you should also be able to ride a 10 meter circle at 350 mpm.  He said same thing in cross country, if you lift your chest, the horse should immediately go fro 550 mpm to 450 mpm, so you could make a 20 meter circle.
The tricky part was riding from the forward oxer (it was big, with a lot of space down the long side) to the very hard right turn; you couldn't ride that turn as forward as you rode the oxer, so you had to adjust to a more controlled (but impulse) stride, and you had to ride the line very precisely (John walked it out and showed us).
It was a great lesson in the importance of precision, being aware of the questions being tested, and riding every step.  Duke did ok.  I was really happy with the second ride through the line, but disappointed that we didn't keep it, and the third time through we were just on the edge of the fence again.