I suggest you to combine suggestions of aegis and compass.

Try to motivate the whole team in the best possible way taking into account psychologies of each individual. Assign tasks to members based on their skills and core comptencies keeping in mind relevance to your specific task.

A good leader leads by example. Show belief in your team, make them realise they are good enough for this work. Listen to their problems/issues. ( What is distracting them?) Then try to solve or suggest possible solutions. Just do not give up till the job is finished. If you have to do most of the work, so be it. A team only succeeds when you do not care who gets the credit. In future other members will perform better. At least prepare them for next task. And when you do it yourself and try to alter or modify what they have already done, do it in a subtle way giving them enough credit for what they have already done. Do not tell them now that they are not doing good as you do not have enough time. Arguing will create more problem. You can explain things to them later in perspective. Now your top priority should be to finish task and finish it well.

Good luck!

This is a complicated situation and it's difficult to give advice on what to do because I don't know you, your teammates or even your school's culture. I can only say what I would do if it happened to me.

I'd tell the Group 1 people that their behavior is unacceptable and that I'm not going to be responsible for turning in work that they copied from the internet. If they promised to stop copying stuff from the internet, I'd still double check their work by doing a few Google searches of the text from their work.

The Group 2 people could be more difficult to work with because it sounds like they're honestly trying to do their best. Since it's a team project, you might want to work directly with them and help them raise their work to a higher level instead of waiting for them to turn in substandard work. This could be the actual test of your leadership abilities.

Actually, I'd talk to the other team leaders before I did anything else. They're probably dealing with similar issues and you could get some good advice from them. If all else fails, you could talk to the teacher about all of this. If I had to talk to the teacher about it, I'd probably avoid naming exactly who was in Group 1 and Group 2.

You may be a chinese. So am I.
1. As a team leader, it's part of your responsibility to motive you teammates, to make them understand that GPA is something really important for them. People cannot do something they aren't interested. So try to push them, to encourage them. Try your best first before complaining.

2. Help your teammates with their works. But be careful, please don't get across the bottom line. Your teammates have to done their works by their own. 

3. Take it easy. Things are going to be done in their way.

Sounds like a small, short-term group, so I'd try the following:

Group 1 - these guys are almost worthless, so have them download relevent information and do grunt work to support Groups 2 & 3. They could also cook, give massages, do laundry, etc for the people who are doing the real work.

Group 2 - have them produce work, to their best effort, but let them know it will be treated as a rough draft, and they will be asked to make corrections later.

Group 3 - have them do a share of the work, and mark-up the work of Group 2.

You - make sure everything is running smoothly, and the final product comes together well. If you have additional time, do a share of the work yourself.

你可以用中文发的，Allen。但是，这样就很不合理啊，难道没有办法来解决吗？