My partner is a personal trainer and wrote me a list of exercises that works out into a 24 minute workout. It's 3 sets of exercises, so you could split in to 3 separate ones of 8 minutes each time. It's to the music of insanity which is like 30 seconds of one exercises, then the next, then back to the first.
Without the music, and for an 8-10 min exercise, I'd do a warm up for 2 minutes, probably 30 seconds alternating between the below. Then in the sets of exercises below, you do exercise 1 and 2 30 seconds each alternating 4 times, then do a power move for a full minute. Just do as many as you can in your 10 min window.
Warm up exercises:
Jumping jacks
High knees
Skipping
Exercise set 1:
Walking lunges
Kettlebell swings
Power move: split squats
If you don't have a kettle bell, use a handbag with something heavy in.
Exercise set 2:
Split squats, arms out (alternate on each leg)
Press ups
Power move: I don't know the name of it, but lie on your back and bring your left leg up to meet your right arm, then alternate.