Good A-Level choices?

Maths and History are fantastic subjects to have at A Level - universities view them highly, and I do History and can vouch the course is great. I don't know about Psychology and Engineering, but have you considered doing more core sciences? Universities tend to prefer more core subjects. However, if you're passionate about all your subjects and don't see yourself doing any others, then do what you enjoy

I would not recommend engineering. If you intend to pursue engineering at university, Maths is an absolute requirement and depending on the specific area of engineering you apply for, Physics is almost universally required. If you absolutely don't want to take Physics, but want to keep your options open, I would recommend Further Maths, as this opens up opportunities in Computer Science and similar areas.

History and Maths are both good subjects, although the combination may seem a little odd, unless applying to e.g. Economics or PPE - in which case Maths is required/highly recommended, and a strong essay subject like History is very useful. Psychology is a reasonable choice; it's not necessary to apply for psychology courses at uni, but can give you some idea if it's something you want to pursue. Beyond that, it's a generally accepted essay based subject and has some quantitative element which is useful as well.

Thank you for responding! I know that in normal maths A-Level you now have to do all of it, including the Mechanics side. My maths teacher says this greatly helps anyone wanting to do engineering so will it?

The engineering teacher has told me engineering will be great to take if I wish to do engineering as it's basically maths and physic being applied to create things.
My sister took Maths and Physics as two of her A-Levels and then did engineering in yr 13 and she said that's what it's like; all the maths and physics you need minus the physics things you don't need to know. Again, is this correct?

Engineering is the subject I'm most concerned about so any other information you have about it will be great!!

I'm speaking specifically about continuing on to engineering at university - in this case Physics is required for almost all courses. Taking Engineering as a third/fourth A-level in addition to Maths and Physics would be acceptable for continuing to study engineering at uni, although Further Maths with as many mechanics options as possible would be the next best choice (or for chemical//biomedical/materials engineering, Chemistry).

Additionally most aspects of A-level Physics will be relevant for parts of most engineering courses; for example the quantum phenomena is relevant for semiconductor physics, underpinning all kinds of computing and electronic engineering topics, the wave topics are relevant both for electromagnetic wave propagation in electrical/electronic engineering and also aspects of mechanical or civil engineering (acoustics, vibrations etc). The materials elements will crop up anywhere in various guises. There aren't really any "non required" elements other than that in theory they could just teach you the whole thing from scratch in a mathematically rigorous fashion, ala the Russian (and to an extent, French) style - this has it's downsides and more relevantly isn't how engineering is taught in the UK

In general, if you intend to continue to higher education, it's most useful during A-level selection to consider first if you intend to pursue a STEM subject or not. STEM subjects usually are best prepared for by, and usually prefer, to have a full set of science/maths A-levels. If you decide you do not wish to pursue STEM areas, but are not entirely sure otherwise, it's fairly reasonable and not too difficult to build up a broader portfolio of A-level subjects to prepare for multiple possibilities. For example, History and Maths would provide excellent preparation to any number of social science or humanities courses, including more quantitative ones such as economics.

While mixing "arts" and science subjects is suitable for continuing to "arts" subjects (i.e. social sciences and humanities of various "flavours" including some slightly more quantitative such as economics, or more scientific such as human sciences or some psychology courses), it's usually less helpful for enabling you to continue to the sciences; certainly at e.g. Cambridge or Imperial, you will limit the courses you could apply to significantly and potentially weaken your application for those courses.

This is an unfortunate truth but it's best to be aware of before you move into A-levels, than after. That said, if you do take a mixed set, or even purely "arts" subjects, there are many science/engineering foundation years available which will allow you to follow this route. Some examples include Manchester, Lougborough, and Southampton.

It's also worth noting 4 A-levels is unusual if one of them isn't Further Maths in a purely STEM A-level portfolio, and isn't actually required for any university. This is also a larger work commitment than it would usually be and should be carefully considered before continuing with; while taking e.g. 3 science subjects and say, History would prepare you for all manner of courses, it's a signifcant workload. Additionally many quantitative social science subjects or more analytical essay based subjects such as Law will accept science A-levels as suitable preparation. not doing subjects such as History or English literature usually only limits you from pursuing those specific subjects, and most humanities or social science subjects otherwise aren't assumed to have been previously encountered and usually have no specific requirements beyond a rigorous academic preparation (which a science subject portfolio provides).

I'm aware the above may seem biased in favour of STEM subjects, but that wasn't the intention; this is just my experience as my background has been in these areas. I had the misfortune of doing IB so I have some background in "arts" areas however so I've hopefully provided at least some insight into that side as well the main thing is, think about what you may want to do after school, generally. Pretty much, consider if you intend to continue to uni (which isn't by any means required and there are an increasing number of degree apprenticeships that allow you to earn a degree in many areas, including law or engineering for example) and then consider if you want to continue in STEM, or otherwise. This will be a good first step to take

On one hand I like the look of Forensic Psychology, but on the other Engineering sounds great, and on the other I love love love maths but hate the sound of courses like economics and jobs like being an accountant, but then I also love History, and then a part of me just wants to do everything that's offered and just want to do every job out there! So I have no idea what I want to do, which worries me as my lack of science subject can impact me down the line but my choice of a science subject might turn out to be a waste of time and can affect my mental health (which I'd greatly rather avoid). Also, there's always apprenticeships or going to work in the army which don't require a science (as my teacher who was in the navy and son who's now in the marines as an engineer has told me along with many others).

The only university I'm looking at is University of Liverpool due to money and other reasons.

Thank you so much for your response! It's been a great help!!