The alleged victim told Cardiff Crown Court that she was "too drunk" to agree to sex with Neilson Smith and that "he was old enough to be my dad".
It is claimed that the accused, a teacher at Willows High School in Tremorfa, met the woman at a Cardiff nightclub last December and took her home.
The 41-year-old denies rape.
The court has heard the alleged victim had downed wine and cocktails with friends and was "definitely drunk".
She told the jury that she remembered nothing of the evening until waking to find the defendant on top of her.
"She remembers going out to the bar but after that, next to nothing else," said prosecutor Matthew Cobbe.
"She went into a taxi but remembers nothing of being taken home. She remembers waking up in her bed with him raping her.
"She was in no condition to consent to any sexual activity."
The woman told the court: "I was paralysed with fear, I thought he was old enough to be my father and tried to push him off."
Mr Smith, from Pontypridd, Rhondda Cynon Taff, has claimed the woman wanted sex after he took her home.
The trial continues.
A PE teacher took advantage of a drunken woman and raped her, a jury has heard.