To begin with, to pursue a career of engineering, you will need to take Mathematics, Physics and preferably Chemistry.
Simply having Chemistry and Mathematics, you will be allowed to pursue a medical career, however I must ask you which country you wish to study in, so that I can give you a more accurate evaluation of the acceptance.
Edexcel Biology is a VERY long syllabus, and is often not worth the trouble, if you want to make do with 3 A levels, which is a very minimal undertaking, then Physics, Mathematics and Chemistry should be the answer.
For Business, I believe simply having a Mathematics A Level is suffice, however, a business studies A Level will make the new material more friendly to learn.
Now, with regard to abuyusef, the chances of doing well in that subject is actually quite well, so I would encourage you to think twice before condemning a subject, although, the subject itself has few applications, it should give you a knowledge of how business works, and if you do want to seriously consider taking a business career, then taking it would be a good idea.
And hard work is necessary to achieve desired grades, often having a good number of A Levels gives you a better chance at stronger and more prominent universities.
