The topictree endpoint has all of this information, and you can use the kind
filter to show exercises (and topics). http://www.khanacademy.org/api/v1/topictree?kind=Exercise
You can also load individual topics to navigate the entire tree (not just videos and exercises). For example, this URL gets direct information about the "combining-functions" topic:
http://www.khanacademy.org/api/v1/topic/combining-functions?format=pretty
From there, you can see that there's a child article with ID "xd2620963". You can load JSON information about that article using the /api/v1/articles
endpoint (which unfortunately isn't documented):
http://www.khanacademy.org/api/v1/articles/xd2620963?format=pretty
Or, with many topics, they will have child topics that you can navigate to.
(That format=pretty
at the end just makes the JSON response a little more human-readable; you should leave it off when accessing the JSON programmatically.)