How do I handle a pupil who won't speak?

In my S2 class (along with the four boys who barely shut up), I have two girls, both of whom are very quiet. They will whisper between themselves occasionally and one will give an answer to a question if asked directly. The other, however, will not. When asked a direct question, she will stare back at me like a rabbit in the headlights and then look down and say nothing, even if I know she knows the answer (because I've seen her do the sum correctly in her jotter). I've tried silence but all that happens is that eventually one of her friends will provide the answer. I don't feel comfortable pressing her, as I suspect that might end in tears (literally). It's not just me apparently, she's like that with her regular maths teacher and also her English teacher. So..... two questions:
1)how should I go about getting her to contribute vocally? Nothing has worked so far, even asking simple questions along the lines of “What's the answer to question 4? You can just read it out from your homework”, even though I know the answer is there on the page and it is correct.
2)should I be demanding more of her at all? If speaking in class is so uncomfortable for her, why would trying to force the issue be a good thing? Might it even be a bad thing?
On top of that is the assessment issue: how can I know if she is learning when she won't speak to me? I can know that the answers she is writing are correct – I've watched her work through some of them – but it's possible she might be collaborating on homework outside of class (though I hasten to add I have no evidence of that). I can watch her working by standing beside her but if I try to intervene one-to-one, she simply clams up again.