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    You can take the BMO round 1 even if you don't qualify for it through the SMC. If you don't qualify, then you have to pay to take it. If you do qualify, then you can take it for free. The details are somewhere on the UKMT's website.

    Your school maths teachers will probably be writing at least some of your UCAS reference, especially if you're thinking of applying to do maths at uni.

    I wouldn't move colleges, that would only disrupt your education.

    How to gain mathematical knowledge surrounding AS/A2 maths...? The typical answer, read around the subject. In other words, say you're really into differentiation, try to find books away from the standard C1-4 course books and try to learn about the subject, make links between areas of maths, set yourself questions which you don't think you can answer - then try to. Expand your confidence zone.

    Ask your teacher, if the school don't do Further Maths for example they may still have course books relating to it - have a look at them, study them yourself - even enter into the exam if you really wanted (doubt you'll have enough units to make up the further maths AS/A2 but it looks good to universities that you did more out of your own free will than the school normally allow). Further Pure units help out with the Pure Core units, and reading around the FP units will help you even more in understanding areas of maths you didn't previously know much about.
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