1. When I leave school, I'll go on to study. (WRONG) You need to say what subject you will go on to study. The meaning is that after you finish school you will later attend another school where you will study a different subject. When I leave school, I'll go on studying. This sentence is correct. It implies that you will not go to more school. It means that you will continue studying on your own (just as you did in school), even though you will no longer be in school. 2. I wish people would stop talking This means I wish people would not talk anymore or cease talking. I wish people would stop to talk This means I wish people would stop by for a chat. This could be said while on the street and many people are going by and you are trying to talk to them, but nobody is stopping to talk to you. They continue to go on their way. 3. I think I should try to give up smoking This means I think I should quit smoking. I think I should try cycling to college instead of driving This means I think I should start cycling (riding a bicycle) to college and see how I like it instead of driving. 4. I'll always remember to send my mother a card. This means I will never forget to send my mother a card. I'll always remember going on a plane for the first time This means I will never forget the time I went on a plane for the first time. This is the only one where they mean the same thing.

1.1 to study: I will continue my learning. 1.2 studying: (to study, or) I will start my learning again. 3.1 smoking: I want to stop using cigarettes. 3.2 of driving: I want to stop using hard transport, I want to use transport which is more easy 4.1 to send: I never forget to drop a postcard into a mailbox for my mum 4.2 going on: I never forget my first trip on a plane

1. It seems the first one implies that you weren't studying before, but after you leave school, you will study later. The second one implies that you are currently studying and even when you leave school, you'll continue studying. 2. The first one means that you want people to not talk (they are talking and you want them to stop). The second one means that you want people to stop (as in: stop walking or stop what they're doing) and talk to you. 3. These two sentences are the same kind of structure, just a difference in what you think you should try. Maybe you're confused by the (to give up vs. cycling) being different forms? 4. The first one means that you'll always remember to do something in the future (send your mother a card). The second one means you'll always remember something that happened to you in the past (the first time you went on a plane). "Send my mother a card" is something in the future you haven't done yet. "Going on a plane for the first time" is a specific thing that you did in the past. I hope these help somewhat!