I used to work in China till June this year but now work in Singapore. I still have a valid residence permit for China till April 2015. Can I travel to China for business using the residence permit for re-entry or do I need to apply for a business visa?
Yes, you can. Nobody is going to check whether you work in China or not.
Changing Educational Institution or Employer
If you want to study at a different educational institution or work for another employer, it is permitted to do this without having to start from the absolute beginning and get a new visa. The first criterion is that you must do this while the existing Temporary Residency Permit is valid...