May need to do core maths :( Please give advice

Okay, so I had my College Tester day a few days ago, and I talked to my chemistry and biology teacher about my maths. Before i took my GCSE exams I was on a 5, however I don't think the exams went very well. I however need a 6 to get into my sciences, the teachers suggested that I may need to do core maths alongside my alevels (if they even let me on the course).However I really don't want to do that, so my question is if i can learn core maths this summer and do past papers, proving to them I can do it, they may let me on the course?
(Sorry about my bad writing)

It's difficult to understand why random strangers on the internet (of which I am one!) will have any idea what some random college will think with regards to you doing past papers for Core Maths over summer - as a substitute for getting a grade 6 in GCSE Maths.
If I were working at that college I wouldn't be convinced at all by any claim you might be able to make regarding having learned the whole of Core Maths (which is the equivalent in size to an AS level) over the summer break and taken paper papers at home.
There are currently four qualifications which sit under the "Core Maths" umbrella:
• AQA Certificate Level 3 Mathematical Studies
• Pearson Edexcel Mathematics in Context
• OCR Core Maths A (MEI) Level 3 Certificate
• OCR Core Maths B (MEI) Level 3 Certificate
Do you know which the college want you do to alongside you A levels? Have you looked at the specification to see whether or not you think it's viable?

It's the AQA Level 3, with Paper 2A. It's not that I'm bad at maths, I just missed a lot of school so I didn't have time to catch up on all of my subjects.

OK. So have a read of the specification here, or download a past paper or two from here on the AQA web site. Try to get a sense of how easy it would be to cover in the next two months or alongside your A levels.
Why are you so against doing it alongside your A levels? It provides UCAS points, if you'll be applying to universities will state their entry requirements in those terms, and some other unis will lower their entry requirements if you have Core Maths (in the same way as they sometimes do for those taking the EPQ).

I'm already planning to do 3 Alevels and a BTEC Extended Certificate, so If I do core maths I would have to drop one of them

Agreed. Three A levels, plus a BTEC Extended Certificate, plus Core Maths would be too much. (Although Core Maths is the size of an AS level, spread across two years - so it's not the size of an additional A level.)
It's usual for someone to do a BTEC Extended Certificate alongside three A levels. Do you mind me asking what the BTEC subject would be, and why you'd be doing it - given that most unis would ignore it and make you an offer based upon your three A levels?