http://ib.berkeley.edu/undergrad/major/freshman.php indicates that the IB major does not accept AP credit to waive lower division requirements.
It does say that if you want to choose some other math sequence besides 10A and 10B (which are specialized for biology majors) to ask the department what may be accepted. It is possible that AP calculus may allow you to start in a more advanced course in such an alternate sequence, but you need to ask the department about that.
AP US history can fulfill the American history and institutions requirement, although such a requirement can be fulfilled by having just a high school US history course on your record. AP US government can fulfill the American institutions part. http://registrar.berkeley.edu/?PageID=ahi.html
The College of Letters and Science does not accept AP credit for the seven course breadth requirement.