Is it normal for parents to treat their daughter like this?

I wondered if what i went through when i was a young is normal? From the age of 3 i have memories of my mum hitting me and screaming at me. I'll share some of the occasions i remember clearly, just to give an idea of what was going on. Age 3, being smacked across the face with a rolled up magazine. Age 4, being repeatedly hit with a metal spoon, leaving bruises. Age 5, mum throwing a plate at me for getting upset about not being able to tie my shoe laces. 7, being made to sleep on the hallway floor because i got into a fight with another kid at school. 9, i was doing my homework and eating dinner at the same time, she pulled me off my chair by my hair, kicked and punched me repeatedly, pulled me up by the hair, punched the back of my head so hard that my face connected with the wall in front of me. Through my teens i was beaten for so much as using her bath salts. I was thrown out my home constantly, being too scared to go to family in case they asked questions, i would always go to a friends house. She pushed me into the garden shed at night time and locked me inside once, leaving me there in my pjs for a long time. Another time i was thrown outside in the winter, i started to freeze, she eventually asked my step dad to pick me up and thaw me out in the bath when she realised she would have to take me to hospital if she left me any longer. I have numerous scars (reminders) on my body from her nails. I've been given a few black eyes as well. My step dads even had a turn at punching my face, he used to laugh at me when i screamed for help. I wasn't the best behaved child, like all my friends i got up to my fair share of mischief, i sometimes had the police at the door if i got caught, it was only ever stupid things like stealing turnips from a farmers field, climbing on roofs, exploring abandoned buildings etc. My father was never around, my step fathers been there since i was 5, my brother was born when i was 13, hes 8 now. Mum hit him once when he was small and my step dad slapped her, its never happened again thankfully. She told me she hates me, wishes i was never born and that id ruined her life. She had me when she was 17 and raised me alone. I always wondered if she took her anger out on me because she resented me for fucking her younger years up, her behaviour towards me and my brother are completely different, which i'm grateful for as i love my brother and never want him to feel the way i felt. Whenever i brought up the fact that she beat me, she always played it down and claimed she got it worse from my grandparents, this always made me think it was normal and that it wasn't worth speaking about. I haven't felt any affection or love from her coming up on 10 years now. Theres so much more to tell but this is long enough already. I don't get the physical abuse any more, but the verbal and emotional abuse is worse than ever. I have no confidence in myself at all, she mocks and down plays my achievements all the time. I'm 21, i feel like i shouldn't feel this weak at this age. Is what i'm crudely explaining normal behaviour for a mother? I think i could happily cut my ties to her, but would that make me selfish and ungrateful for keeping me and raising me? Please don't take the piss, i've never talked about this properly. Apologies for the novel. Lana x