Does the transponder need to be on in the upper limit of Class B airspace?
Yes:
If you combine the two sections provided by SMSvonder Tann and Raaj Tram you get: 


  14 CFR 91.215 - ATC transponder and altitude reporting equipment and use:
  
  
    (b)(4) All aircraft in all airspace above the ceiling and within the lateral boundaries of a Class B or Class C airspace area designated for an airport upward to 10,000 feet MSL; and
    
    (b)(5)(I) airspace of the 48 contiguous states and the District of Columbia at and above 10,000 feet MSL, excluding the airspace at and below 2,500 feet above the surface; and
  


You can't fly over B or C without a transponder. 

There are some specific exceptions for aircraft not originally equipped with an electrical system.