There are some pitfalls to getting your iPhone to sync up with the calendars you'd like, but it is possible.
Navigate Safari to m.google.com/sync?hl=en. If Google complains, that your device is not supported, it's most likely because of your language settings. In that case, locate the link to change your language on the bottom of the page, and change it to
English (US). The link I've provided should do that automatically, but in case it doesn't, well, you know what to do.
Now you should see a list of mobile devices associated with your Google account. Pick the one whose settings you want to change.
You'll see a list with all your calendars. At the top of the page, you'll see how many calendars you'll be able to sync your phone with. Pick the calendars you'd like to sync, tap
Save, and you're done.