Okay well I checked the syllabus for IB Analysis and Approaches Maths and well the SL is largely similar to the A-level maths course. There are differences as these differences are due to the SL course not covering the those topics that the A-level maths course does. The HL course on the other hand do cover those missed topics, but it should not be much of a difference.
If you want to sit the A-level exam you will have to teach yourself some pure topics and some from stats. You only need to teach yourself hypothesis testing and data collection for the stats bit, surprisingly your course covers nearly all of the compulsory statistics and probability topics from A-level. Imo it would have been better to focus on the pure stuff than stats, oh well I prefer pure anyway haha. You will also need to teach yourself the Mechanics part of A-level Maths, which is just Physics Mechanis but very mathematical, if you're good at Maths and Physics then you shouldn't need any teaching and can jump straight into doing the past paper questions/book questions.
You'll be able to cope with their courses, but you may find a shock as to the rigour of the extra maths you learn at uni. Also those extra maths you learn for engineering will include the stuff other people learn in the HL course and more, such as matrices which is not even covered by the HL course but is covered the Further Maths course in A-level.
Anyway I'm only saying this because it's not like you won't learn the HL stuff later on haha, such as vectors which is not even in the SL but is in A-level maths and is important for engineering.
You will be find at university, do not worry. But I do not how hard the SL exam questions are but if they are too easy then you may find the maths at university hard at first but with a good work ethic you will overcome it. I'm saying this because some of my friends did IB HL Maths and they said that the HL questions are much harder than the SL questions for the same topics. Whereas at A-level the the difficulty for both Further Maths and Alevel Maths are the same, it'a just at Further Maths you learn more maths hence the name lol. Although that's just my experience, someone else might disagree. When I was applying for universities for Physics, I saw that unis will ask for A-level Maths but for IB they want Math HL, which I found quite hard to understand as at HL Maths is harder and you learn more advanced topics for a normal 16-17 year old. Maybe the reason for this is that SL Maths has questions that are too easy? I don't know but that's my speculation. In this paragraph towards the end, I was talking about the old spec HL Maths in IB btw.
Anyway I waffled alot there at the end but that's my opinion as to how you'll cope without me knowing how good you are at maths. You are learning basically the same maths as an A-level Maths student, with some minor differences.
Hope this helped. I did Physics, Maths, Further Maths and Maths for A-level.
Btw HL AA has stuff that my Further Maths course did not have and my Further Maths stuff had topics that HL AA does not have. If you are wondering that is.
Final advice would be, if you are still worrying, do the research yourself. Look at the specification of A-level maths for a board and then compare the specification for your course. Then you'll know.
Hope this helped. My opinion after all, so take it what you will haha. Good luck and have fun