OK, so this question roughly equals ‘What do I REALLY need to learn about these fifteen (yes, FIFTEEN) poems that I’ve been given for this exam?’ My answer to you is that, actually, you do not need to know quotes for all the poems – but you do need to be strategic about which poems you learn quotes for.
Let’s break this down. As you’ll probably know (so forgive me, but just in case, right?), you’ll get one of the poems in the exam, along with a list of all fifteen, and a question focusing on the theme. This question will ask you how the poets present ideas about X (your theme) in the poems. Your job is then to select a suitable poem that addresses the same theme to compare to the poem on the paper. This means that a key revision task is to work out the main themes of the collection (i.e. what the exam questions could focus on) and which poems belong in each group.
If you then look at which poems appear in multiple groups, you will see which ones are the most helpful to get to know in the most depth. For example, I personally wouldn’t do much with Storm on the Island (sorry Heaney, much as I love your work, in terms of this collection, the poem is not multipurpose enough for our needs – and to those teachers reading, yes I know this is a terrible and functional approach, but why not seek to reduce the load of students where possible?) Clearly, you need to make sure that if you are reducing the number of poems you revise thoroughly in this way, that you have every theme covered, so do check this. Obviously, you might choose Storm on the Island as your ‘power of nature’ poem, and that’s fine – up to you. I’m just recommending that you try to narrow it down, and know why you’re doing it. You can’t just pick the ones you like best!
At the same time, you can’t just dump the ‘less useful’ ones entirely, because (of course) any of them could be the one that the question is about. Obviously, though, you will have that poem in front of you, so memorised quotes will be unnecessary. What you will need to know about is the context and meaning, so make sure that is known for ALL the poems (yes, sorry, all of them).