A-Level Further Mathematics Examination, 1981
I’ve been forcibly evicted from my office this afternoon while a highly-trained operative of Cardiff University’s esteemed Estates Department replaces a broken window. It’s been broken since I moved into the office, about four years ago, by the way, but you can’t rush these things. Anyway, having been forced to change location I took the opportunity to decamp to the upstairs computer room wherein our departmental scanner resides and occupied myself with the task of scanning in yet another of the old examinations I took when I was in school. This one is the Further Mathematics examination, consisting of two papers each of three hours’ duration: Paper 1 is entirely Pure Mathematics; Paper 2 contains a mixture of Pure and Applied Mathematics, and Statistics.
Looking back on the paper now, thirty years after I first saw it, it seems to me that the Applied Mathematics questions (6-11 on Paper 2) actually look quite tough by the standard of 1st year undergraduate examinations in mechanics. However, I’ll leave it to you to comment on whether you think it’s harder, or easier, or about the same, compared to current A-levels in Further Mathematics. I’d also be interested in knowing whether there’s anything on these papers that isn’t on the syllabus nowadays.
The comments box awaits…
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In the Dark 
October 24, 2011 at 2:58 pm
One thing that strongly strikes me is that it asks for knowledge of Cardano’s formula from the outset, which I don’t think I was ever taught (and which I have had to use exactly once)…but then the calculus is pretty trivial. I suspect much of the difference from today’s exams comes from the pedagogy of 1981 not even thinking about calculators but instead on applying tomes like Abramowitz & Stegun.
October 24, 2011 at 7:43 pm
What is really worrying is that 44 years ago, when I did Further Maths A level (and S level) I could have done these questions, but now I have no chance….
October 25, 2011 at 9:00 am
These papers seem about as hard as the ones I sat in 1974. Looking back, further maths in those days seems an amazingly ambitious course, both in terms of its broad content and the challenging nature of its exams. Objectively, this material was too hard for schoolkids, even filtering down to those who were likely to go to university to read maths or physics. But of course we didn’t realise this: we assumed that we ought to be able to do it and just got on with things.
I don’t have a basis for comparison with current English exams, but this is certainly more challenging than the Scottish “Advanced Highers”, which is as far as you can take school maths North of the border. There’s no way we could contemplate setting questions this hard to our pre-honours undergraduates, and indeed I think many of our honours students would consider these papers tough.
So who’s right? Are we too undemanding of our students, or were these old papers ridiculously overambitious? All I know is that I’m very grateful that I went through the old system: it really gave a great foundation for university study, and I think I feel the benefit to this day.
October 25, 2011 at 11:19 am
I certainly found this A-level quite tough, as a 4th A-level alongside Maths, Physics and Chemistry but I think the benefit of doing it wasn’t so much learning extra bits of mathematics that were on the syllabus. It was more about developing a sort of determination not to be dismayed when faced with a tough problem. The effect of making the A-levels easier is that undergraduates are less battle-hardened than we were, and many seem to just give up when they can’t see how to do a problem immediately. Unless the problems you tackle are at the very limit of what you can do you never really grow.
October 25, 2011 at 12:05 pm
“Unless the problems you tackle are at the very limit of what you can do you never really grow.”
Well said! The better public schools, where the money is, now teach to well above the standard of current A-levels, so as to stretch their pupils in this way.
The other vital thing is post-mortem analysis. It’s no use telling someone he got only 40% if you don’t explain in some detail where he personally went wrong, so that he can learn from his mistakes. Otherwise, since learning is cumulative, there is a risk that potentially good people might trip up once and never be able to catch up, losing heart and becoming lost to the subject. This is the great strength of the Oxbridge supervision system that backs up lectures. It costs, but it is worth it.
October 25, 2011 at 8:32 pm
What was the difference in England between Further Maths & “normal” A-level Maths? In Wales, if one did the WJEC (Welsh Joint Education Comittee) board exams, they offered “Pure & Applied Maths”, “Pure Maths” and “Applied Maths”, there wasn’t a Further Maths. P&A was a 2-year course, as were Pure and Applied as separate subjects, so the syllabi for Pure and Applied as separate subjects were each twice as long/in depth as the “P&A” done as a single A-level.
October 25, 2011 at 8:41 pm
This link has the current WJEC Maths and Further Maths syllabi
Click to access 3665.pdf
March 18, 2012 at 1:20 am
Not a comment but a request really.
I sat my WJEC A levels, Pure Maths and also Applied Maths in 1974.
Would anyone have or know where copies of these could be acquired?
April 19, 2012 at 4:58 pm
I sat the same board and exam about 4 years later, and this reminds me just how tough it was … lucky to scrape an E!
I actually remember throughout the whole sixth form schools/colleges in Rugby, only about 7/8 people passed the exam out of the 20 odd! that took it
June 22, 2021 at 12:05 pm
[…] Special Paper in the afternoon. I’ve actually posted the first of these on this blog, here, along with quite a few of the papers I took way back […]
October 22, 2021 at 12:55 pm
I went to a secondary modern and was one of only two people studying Further Mathematics. My friend was the clever one and got straight A’s, I managed an A in mathematics, but only a D in Further Mathematics. I did these exact1981 papers as practice before sitting my A level in 1981. Since then I have been a senior engineer and for the last twenty years a Mathematics teacher in a grammar school, so I am well versed in what the demands of the current A levels are. However, I realise that I am trying to compare something I tried aged 18 with something I have been doing for the last 40 years, so who better to ask than some 18 year olds… My Further Mathematics students can cope with the questions that overlap in the current curriculum, though they find the style (particularly in Mechanics questions) challenging. Their judgement was that they are all generally harder than what they are faced with today
October 22, 2021 at 12:56 pm
Sorry I meant I sat my A levels in 1982!