In "The Rocking Horse Winner" how is Paul considered determined?
The definition of determined is to be stubborn, persistent, and to not give up. Think of that definition in terms of Paul's determination to "be lucky," and to win money at the races, all in a sad attempt to win his mother's love. He is incredibly persistent; he thinks about it all of the time, and rides his horse for hours on end, even through the night sometimes. That shows a fierce determination to attain his goal--money, on the surface, but, love from his mother in the end. In fact, it is his sheer determination in the end that leads to his death. He is so ferverishly focused on finding the winning name for the Derby that he rides into the late hours of the evening. His mother gets home at "one o'clock in the morning" to find
"her son, in his green pyjamas, madly surging on the rocking-horse."
He rides himself into the ground, literally, and "collapses" on the floor in a fevered state, before triumphantly declaring that the winning horse is "Malabar!" He had ridden for so long, with such intense and unhealthy focus, that he wore himself thin, giving himself a fever, and in the end, dying. He was determined, no matter what, to figure out the winning horses.
I hope that those thoughts helped a bit; Paul's determination was a powerful force in his life, that was unfortunately focused on a losing battle: the battle for money to bring happiness. Good luck!