Oh, and knowing when to ‘round’ figures. Drives me loopy when people used rounded figures mid-way through a basic calculation.
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I don't know about you, but I always remember being told to only round when giving answers, and to use something like the Ans button on the calculator to do calculations using a particularly long previous answer (so that you get the exact answer rather than a truncated version).
I will also concur with those who did A Level Maths and found it a surprisingly huge jump from GCSE. I got a 7 (A) in GCSE Maths and a B in GCSE Further Maths, so I was somewhat bullish about my mathematical abilities and my aptitude for Maths A Levels, so I chose to do both A Level Maths and A Level Further Maths. I didn't
technically choose to do A Level Further Maths as a first choice, but I had to pick it because I was unable to do my 4th A Level choice due to a timetabling clash, and I ultimately agreed to do it as a substitute.
Picking Further Maths was a huge mistake in hindsight. I found it unbelievably hard, and it's comfortably one of the times in my academic life where I have felt the most out of my depth. Within weeks, possibly even days, of starting that A Level, I knew that I had made a massive mistake. In Further Maths, we delved into the horrifying world of things like imaginary numbers (which are just as confusing as they sound once you get beyond the basics), and I could never get my head around the things we covered no matter how hard I tried. Problems would sometimes take a whole lesson to dissect, I would often leave lessons with my head feeling completely fried, I could never understand the solutions to problems even after poring over the mark schemes for ages, and to put it simply, I
just didn't get it. It also didn't help that the 2 other boys I was in the class with (yes, only
3 people in our year, out of about 100 or so overall, did Further Maths...) were immeasurably more able mathematicians than me, so I was by far the weakest in the class and often felt left behind. I did two mocks, got Us in both of them (the limited part of the material within Further Maths that I could loosely grasp only covered the 1 mark tickbox questions at the beginning of the exam... all of the properly meaty questions went way over my head), and ultimately dropped it after about 4 or 5 months as I felt that it was likely to be a lost cause given that I didn't get it at all and my attainment had been woeful in every assessment we had done. I don't know if I gave up on it too soon, but in hindsight, I do feel like I made the right choice, and I certainly don't feel like I've been held back by not having completed Further Maths.
Maths was OK to begin with. Year 1 (AS Level) wasn't too bad; a lot of it seemed like it was simply a natural progression from similar topics at GCSE, and I could handle it perfectly fine. Although with that being said, it may simply have felt easy in the first few months due to the fact that I was doing Further Maths, and just about anything would have felt easy compared to that...
However, Year 2 (A2 Level) was another matter entirely... I was not prepared for just how difficult Maths would get in Year 13. It was a considerable step up from Year 12 in every way, and some topics were absolutely rock hard. Some topics in Year 13 Maths almost felt like Year 12 Further Maths in that I really struggled to get my head around them no matter how hard I tried... those Y13 differentiation and integration rules in particular stick out in my mind as being phenomenally hard to grasp, and there were plenty of other topics within the same category. I struggled through Year 13, got some rather poor mock results (I think I might have dipped as low as an E in one Y13 mock), and ultimately scraped a C at the end. While I was pretty disappointed with a C, as I was hoping for all As and above at A Level, I wasn't particularly surprised in my heart of hearts given that I had really struggled with the subject throughout Y13 and my final mini exams felt like they went quite poorly...
By Y13, I was comfortably one of the weakest mathematicians, if not the weakest mathematician, within my A Level Maths class of 6 boys (uptake of A Level Maths was remarkably low in our year, for some reason...), and I think both the Maths A Levels I did proved that I am not the brilliant mathematician I clearly thought I was before starting Sixth Form...
I did not give myself an easy ride at A Level, come to think of it. My A Level subjects were Maths, Physics and Computer Science, and Maths and Physics in particular were subjects that I actually found really hard... both were a real uphill struggle for me. By some absolute miracle, I managed an A in Physics, but I only managed a C in Maths. My final A Level results were an A* in Computer Science, an A in Physics and a C in Maths. With hindsight, I probably would have done a more varied selection of A Levels rather than putting all of my eggs into the STEM basket like I did, but the combination of A Levels I did is apparently very desirable for job opportunities, so it may well have been beneficial in the long term.
On a separate note, it's funny that a number of you should mention Geography, because Geography was actually the 4th A Level choice that I was unable to do. I loved Geography at GCSE, I got a 9 (A**) in it, and I couldn't wait to do it at A Level, but when I applied to sixth form, I had a subject clash when my choices were Maths, Physics, Computer Science and Geography. The interviewer struggled to hide their disdain for my choice to do Geography alongside Maths, Physics and Computer Science, so they strongly recommended that I ditch Geography and do Further Maths instead because "Further Maths is far more desirable to top universities, particularly given the other subjects you've picked, whereas Geography seems like an odd choice, and possibly a bit of a soft option for someone like you". As such, I took their advice and did Further Maths instead.
In many ways, I still regret that I was unable to do Geography A Level. I really enjoyed Geography, particularly Human Geography, and I would have loved to done the A Level. Given my 9 at GCSE, I also reckon that I could potentially have done quite well at it. To be honest, I would quite happily have done a degree in Human Geography had I not chosen a Computer Science degree.