Are you in the UK? If so, you need to decide which exams you wish to do and which exam board you're going to use. If you're thinking of doing GCSEs, know that home educated kids will almost all do IGCSEs (as do many private schools and some grammar schools). It's now pretty much impossible to do bog standard GCSEs if you're home educated, hence the switch to IGCSEs, provided by Edexcel and Cambridge (CIE) exam boards.
You'll have to find yourself a place at an exam centre somewhere. Have you tried your local private schools? Colleges? Often private schools (especially those that have charitable status) and colleges of further education are a lot more helpful than state schools when it comes to finding an exam centre as a private candidate. If all else fails, and there really is nowhere close to your home that will take private candidates, you're just going to have to find one in another part of the country and travel there to do your exams. There is no way around that (sorry!).
Your other option now is to go to college now and study for your GCSEs there -- home educated kids can now go to college to study for GCSEs for free (only free if you do the whole course with the college, you still have to pay if you just want to sit the exam as a private candidate).
If you happen to be in London and the South East I can definitely give you the details of some exam centres around here. If you give some idea of where else you are (just the region like SW or NE or better still, your closest city) I have a list of exam centres I'll share with you that say they accept private candidates.
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Oh, yep, lIncolnshire does seem to be in a no-man's land all of its own when it comes to exam centres. The only *possibilities* I could find were :
King Edward VI Academy, Spilsby ( http://www.king-edward.lincs.sch.uk )
The Priory Academies ( http://www.prioryacademies.co.uk/page/default.asp?title=Home&pid=1 )
Lincoln Minster School ( http://www.lincolnminsterschool.co.uk )
They're exam centres that home educators have used in the past and which have told at least one exam board that they will consider applications from private candidates, on a case by case basis, in the future. Of course it'll all depend on you doing your exams through the same exam board as the exam centre uses ; if the exam centre is not registered with your chosen exam board then you won't be able to do your exams with them.
Have you asked your local authority if they can help? Some keep their own lists of exam centres that will take private candidates and some will let you do your exams in the local Referral Unit. Another thing, if you haven't done already, is to ask other home educators in your town where they went to do exams. I'm not kidding but I iterally found my exam centre by talking to a boy at a bus stop! We were in town, both waiting for the same bus, in the middle of a school day and he was clutching a copy of an IGCSE Physics book, so I just asked him if he was home educated and where he was planning to do his exams.
Don't wish to put you off but I heard of someone today who had to try over 200 schools and colleges before she eventually found an exam centre for her son! You just have to keep plugging away until you find someone that says 'yes'. Mid Kent College ( http://www.midkent.ac.uk/about-us/new-medway-campus ) is the exam centre I used (£80 per subject) but that's a way away from you, but if you find you've got to travel outside of Lincolnshire anyway, they're a definite option for home educators to do exams.
A few other definites, depending on your chosen exam board, are :
Cambridge Independent 6th Form Centre, Cambridge ( http://www.ccss.co.uk/exam-centre.htm )
Oxford International College Oxford ( http://www.oxcoll.com/external-exam-candidates.html )
Greene's Tutorial College, Oxford ( http://www.greenes.org.uk/examinations )
London Brookes College in Hendon, North London ( http://www.londonbrookescollege.co.uk/private-candidates-examination-centre-hendon-london )
Pascalls College in Beckenham, Kent ( http://www.pascalscollege.co.uk/untitled.html )
The Tutorial Foundation, Bromley, Kent ( http://www.thetutorialfoundation.co.uk/examination-centre )