Public Schools in Kanton Geneva or Vaud

Family, Education, Health and Pets
1
How do kids get into kurz gymnasiums in the French speaking part of Switzerland?

There is an entry exam to get into a kurz gymi in Zurich. What happens if a family moves from Zurich to kanton Vaud?

Is there an exam to enter a kurz gymi, in case the child in 13 years old and is currently in the 2nd Sek A class (has not done kurz gymi Prufung yet)?

2
Short gymnasium doesn’t really exist as a concept in Romandie.

I’m not in Vaud so I will leave others who know the system there better than I do to give you all the details.