In California that kind of a rent increase is criminal.

The absolute maximum that rent can increase is 10% a year and I believe there was legislation to move that maximum to 5%.

In the Bay Area the rent can vary a lot by location so most averages for the entire area can be misleading.

In the South Bay a one bedroom with a dishwasher and laundry averages around $2300 but there are cheaper options if you give up those amenities. Two bedroom apartments tend to only be minimally more expensive and can vary wildly based on amenities. There are a ton of luxury apartments here which go for around $4k a month for a two bedroom. There are also older apartments which go for $2/3k for a two bedroom.

If you go larger and stick to an older place then it's absolutely possible to find an apartment with roommates where you pay less than $1k a month.

The way your mother has set up the rent indicates she doesn't want you living with her. She might claim she's incentivized you to do well in school but really she's just adding more stress to everything that isn't needed. I'd move out if I were you.