Hi, 10th grader here. I did this for you (I schedule this way all the time for myself! It seems like too much effort into scheduling [it's actually not, i got used to this xD], but giving myself a timeframe helps me be organized and get things done on time.) However, it looks like you might have to "stack" some tasks on top of the other to get more sleep. I'll make some comments in bold on the schedule...
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• 5:30a (i recommend app Sleep Cycle if you struggle to get up on time, it really helps! ik this sounds like an advertisement but i swear i just like answering questions xD)
- 10 min wash up sleep in workout clothes so you don't need to get dressed
- 2 min eat small snack for energy
- 30 min workout
- 10 min get ready
- 10 min breakfast on the go
• 7:00a
- private coaching
• 10:00a
- 1 hr 30 min studying
• 11:30a
- commute to school
- school
• 5:50p
- get to house
• 6:00p
- 20 min shower
- 20 min dinner
• 6:45p
- 2 hours PC stuff (can you eat dinner while being on the computer? I know it's not good but it saves time. Keep in mind how your family might feel about this.)
• 8:45p
- 2 hrs 30 min studying (or if you can eat a smaller and therefore faster dinner, then eat a healthy snack while studying to serve as the rest of the dinner.)
• 11:15p
- 5 min brush teeth
• 11:25p
- bed
- 6 hr 5 min sleep :s
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There is also an app that does this schedule thing, it's called "Routinist". It really helps you go one task to the other without wasting time. I'm also sure there's a subReddit for this, but i forgot what it was called.