Yes, Gymspastics was the term for the mandatory class. Males and females had to pass. Everyone had to do stuff on the floor like handstands, cartwheels, somersaults, etc. Women also had elements on the balance beam, uneven bars and vault (same as Olympic apparatus). I don't know if the guys had to do all remaining 5 Olympic apparatus but certainly had to do most.
Increasing skill difficulty was required for a higher grade. For example, on the floor a somersault or a cartwheel would get you a D, whereas a handspring might be A material. Ditto with the other events. The biggest hurdle for women was doing a "hip circle" on the uneven parallel bars which was required to pass the course. It's harder than it looks if you've never tried it. I couldn't do it. Not once. Until the day of the test. Somehow, I did it that one time -- never could do it again. I'm sure the guys had their own challenges -- most likely with some of the strength moves.
In those days, most "girls" had taken at least some tumbling or gymnastics, so had a bit of a head start. Most guys had not. So watching guys who'd never done a cartwheel try to do one was quite comical and often looked rather spasmodic. Ditto with most of us on my of the apparatus. Hence the term "gymspastics."
Not sure when they did away with this as a mandatory PE element. The reason was almost certainly lack of skilled instructors. In addition, with the passage of Title IX, girls had a lot more options and my sense is that the number taking tumbling/gymnastics decreased.
When I attended, males had to do exercises on 10 different apparatuses (appurati?) which were the standard olympic stuff like Floor, Rings, Parallel bars, High Bar, Pommel Horse as well as rope (climbing rope), trampoline and a few others. For each apparatus, you had to do the first 4 exercises to pass and then there were four more to get higher grades.
To give an idea of how some of these worked, the first four of rope were something like this.
1. Climb rope using regular leglock on rope, touch ceiling, come down
2. Climb rope hands & arms only (no legs) to ceiling, come down
3. Climb Rope to ceiling, lower yourself halfway, do a "chin up" on the rope and then come down
4. Climb Rope to ceiling, come down a few feet, with legs locked in on rope, secure rope under armpit and show your palms to the coach/grader
Doing just those 4 was a low "D" (60%). I don't know what the more advanced exercises were because in each case, the four mandatory were a real struggle to do just by themselves.
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I'm not positive but I THINK that the mandatory floor exercises for men were something like this:
1. From Standing do a forward roll (somersault)
2. From Standing, sit into a back somersault
3. Headstand
4. Handstand