subdomains on slave only?

[Mooky Mooksgill]

i have a domain.com.

i have specified my isp's two nameservers to handle dns for domain.com
and www.domain.com with my registrar.

i have also specified two nameservers from a free dns place. 

i'd like to use the free dns interface to point subdomains.domain.com
to other IPs addresses. i've done so, but it only works when i use
this free nameserver as my nameserver, to query the subdomain (e.g.,
goose.domain.com), and then the regular domain.com doesn't resolve -
should i add the primary's a records to  the slave (e.g.
www.domain.com)?

do these subdomains need to be in the primary as well. the whole idea
is for me to manage the subdomains w/o having to call the isp, who own
the primary dns machines.


do i need to ask the isp to specify somewhere that this free
nameserver is the slave? is it ok if the primary doesn't know about
the subdomains, but delegates/lets the slave handle them?

thanks!

-m