Whilst it would be correct to say that most Computer Science degrees have a requirement for Maths A level, that don't all have such a requirement.
Your phrase "something business-related" is a tad vague, but I'm not sure where you got the impression that A level Maths was required for such a course. It is not generally required for Business Management, if that's the sort of course you mean.
The two BTECs you have (in IT and Applied Science) - are they BTEC Level 3 National
Extended Certificates? If your overall grades were impacted by poor
exam performance (rather than poor
coursework performance), then you can absolutely resit the exams. See the resit rules
here:
"
Resit Rules for BTEC Nationals:Learners are permitted to resit the external assessment twice. This equates to
THREE attempts in total - one inclusive of registration, the remaining two attempts as re-sits."
I'm not sure what you mean by "so I can carry those grades over to my new uni application". You are required to enter
all your qualifications from secondary education onward on your UCAS form. You don't get to pick and choose. So you will need to list both BTECs. (You will also need to list the original Psychology grade, as well as then adding Psychology a second time with a grade of "Pending").
Right now, it sounds like you have the equivalent of three A levels:
• A Level in Psychology (which you're currently re-taking)
• BTEC Level 3 National Extended Certificate in IT
• BTEC Level 3 National Extended Certificate in Applied Science
What benefit to you expect to gain form taking a
4th A level-equivalent?
Finally, you mention "my new uni application". Does this mean that you applied last year, but didn't manage to secure a place? What are your target universities this time around?