Is a transponder needed to be turned on to operate above 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.
Generally, Class B airspace extends up to 10,000ft. That said, FAA states that:
All aircraft are required to be equipped with a Mode C transponder when flying at or above 10,000 feet msl, over the 48 contiguous states or the District of Columbia, excluding that airspace below 2,500 feet agl.