As you may know, the Mathematics A and B modules are aimed at Physical Natural Scientists. The B course covers everything the A course does, but goes at a faster pace and therefore covers some additional topics. Both courses are examined by the same two (non-calculator) papers, but those who did the B course will have a couple more questions to choose from. Maths A-level is required for either course and Further Maths (at least to AS-level) is recommended. You do not need to do the B course to do the Part 1B (second year) Maths module.
Last year I took the Maths B option, along with Physics, Chemistry and Evolution and Behaviour. Although I enjoyed the Maths course, I’m not taking the second year Maths module. I chose the B course as I enjoyed A-level Maths and Further Maths and I wanted to take the gamble of learning extra content in order to have a wider choice of questions on the exam. This paid off to an extent as I answered one B course only question in my second paper. Transferring from the B course to the A course is possible at any point in Michaelmas term (after that the courses cover some topics in a different order), but going the other way (from A to B) is trickier. Therefore, if you are unsure which to choose I would recommend starting on the B course.
Some general advice for both courses would be to find a friend doing the other course to you and having a look at their lecture notes/practice questions, particularly for topics you’re struggling with. Different lecturers have different ways of explaining things so this may help you understand the topic from a new perspective. Supervisions are also an excellent opportunity to further your understanding. I didn’t really use books when revising (I preferred my annotated lecture notes and past exam papers) but one the one I found most useful was “Mathematical Methods in the Physical Sciences” by M. L. Boas. Another that I have heard follows the course well, but that I don’t have personal experience of, is “Mathematical Methods for Physics and Engineering” by Riley, Hobson and Bence. Both are available in Sidney Sussex College library.
The programme specification for Maths A and B is available below. If you have any further questions, please get in contact!
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Maths course website: http://www.maths.cam.ac.uk/undergradnst