Court of Fives by Kate Elliot

• Jessamy is the daughter of a Commoner mother and a Patron father, a commander whose status is dependent on his rank in the army.  Jes and her sisters are mixed-race and are looked down on in her world, so they must be very careful in everything they do
  
• When disaster strikes and threatens to tear her family apart, Jes takes the opportunity to compete in the Fives, a complex athletic competition for which she has secretly been training for years.
  
• Jes hopes that the Fives will give her the chance to protect her mother and sisters, save her father’s reputation, and perhaps bring herself a little glory.
  

The author describes her book as "Little Women meets American Ninja Warrior in a setting inspired by Greco-Roman Egypt" while her publisher has pitched it as "Little Women meets Game of Thrones meets The Hunger Games" -- but I would just say it's a great adventure fantasy story set in a unique world.

Grades 7-12
Book 1 of Court of Fives Series