Advanced Level Mathematics Examination, Vintage 1981

It’s been a while since I posted any of my old examination papers, but I wanted to put this one up before term starts in earnest. In the following you can find both papers (Paper I and Paper 2) of the Advanced Level Mathematics Examination that I sat in 1981.

Each paper is divided into two Sections: A covers pure mathematics while B encompasses applied mathematics (i.e. mechanics) and statistics. Students were generally taught only one of the two parts of Section B and in my case it was the mechanics bit that I answered in the examination. Paper I contains slightly shorter questions than Paper 2 and more of them..

Note that slide rules were allowed, but calculators had crept in by then. In fact I used my wonderful HP32-E, complete with Reverse Polish Notation. I loved it, not least because nobody ever asked to borrow it as they didn’t understand how it worked…

I also did Further Mathematics, and will post those papers in due course, but in the meantime I stress that this is just plain Mathematics.

If it looks a bit small you can use the viewer to zoom in.

I’ll be interested in comments from anyone who sat A-Level Mathematics more recently than 1981. Do you think these papers are harder than the ones you took? Is the subject matter significantly different?


40 Responses to “Advanced Level Mathematics Examination, Vintage 1981”

  1. Proof by induction, complex numbers and matrices(!) had all made the jump to Further Maths (although Further Maths AS) by 2005. It would be interesting to know how extensive you formula book was as well… Ours was huge, and still comes in handy now.

    • There was no formula book, but if you did the statistics bit you got a copy of the Cambridge statistical tables (which I still use from time to time).

  2. Ian Douglas Says:

    The HP 32-e might be dead, but you can get a 15c emulator for the iPhone:

    Just in case you feel the need for reverse polish again.

    My maths A-level (pure and mechanics only, no statistics) was in 1990 and I seem to remember it being quite similar to this. Apart from the last part of paper two, obviously.

  3. I sat in 1986, with Stats, not Mechs. Pretty sure complex algebra wasn’t in there – didn’t really get into that seriously until degree level. I’m curious to go and find them now…

    Did you keep yours or find these in an archive ?

    • I don’t know why but I kept all the examination papers I sat, from O-level through A-level, Cambridge Scholarship entry, and all my University exams from 1st year to finals.

      • The mists of time. I feel a bit cheated. Both by my memory and/or the exam board for leaving bits off the syllabus. Now I’m just off to rummage through the garage…
        … anybody out there with Cambridge 1986 A-level Maths Exam Papers ?

      • hI,
        Any chance you can scan all the A-level papers ie maths, physics & chemistry and email them?

      • telescoper Says:

        I’ve already posted the maths and physics ones on the blog; feel free to download if you like.

        I haven’t done the chemistry one yet though.

  4. I did JMB Maths with Mechanics in 1988. (Obviously) apart from the stats bits, this looks pretty similar. We did do complex algebra and plenty of calculus of this level (simple calculus having been introduced at O-Level back then of course). The Mechanics questions are almost identical (as they were every year from memory – there are only so many ways of asking about circular motion, friction etc. I guess).

    The one strange thing on our syllabus was there was no matrix algebra at all – and in fact I never saw a matrix until I got to university where everyone else seemed pretty familiar with them.

    Our school did not offer Further Maths – I assume matrices were on there.

  5. John Peacock Says:

    This paper doesn’t look very different from the one I recall taking in 1973. As for matrices, I recall them being a topic for one of the very first maths classes in secondary school. This radical approach was courtesy of the SMP revolution. Amazingly, from a current perspective, schools just allowed universities to tear up existing syllabuses and rewrite them in a way that better fitted students for university entrance. Hard to see that happening now.

    But although many of us in the university sector bemoan declining standards in our incoming undergraduates, concentrating on syllabuses and exams may be missing the point. I teach 1st-year maths for physics, and initially the lectures go over material that should be familiar: I’ve seen it in syllabuses and exam papers that I know these kids have passed and (in most cases) got A’s in. And yet very commonly they can’t do the things that they have allegedly passed with flying colours. It seems that ideas don’t stick in their heads in the way that once would have been the case. Too much modularisation? Too much time on short attention-span activities like tweeting? Not sure, but the problem (and I think it is one) is clearly there.

    • I agree with your main point, but don’t know enough about how maths is taught in schools nowadays to put my finger on what has changed.

      I went through a very old-fashioned style of teaching which involved doing exercise after exercise, rather like you would learn to play a musical instrument: the scales and arpeggios were undoubtedly quite boring, but essential for getting the required skills hard-wired to the extent that they became second nature.

      On theory I have – with, I might add, a complete lack of evidence to support it – is that we teach things in too many bits and pieces, wheras what is needed is something much more immersive.

  6. Looks very similar to the papers I took in 2005/6. I took 15 modules (6 modules = 1 A Level) in a pretty random order so I’m not sure how it splits up between Maths/Further Maths/Additional Maths unfortunately.

    I think my papers had less questions with more parts though, rather than the short ones in Section A. Those ones seem easier than what I did.

  7. Thanks very much for this – FYI, I am collating more O&C board mathematics papers and making them available here:

  8. Do you have any step or cambridge entrance papers in physics?
    I’ve been looking for them everywhere!
    I took both step maths and step physics in 2001.

  9. Do you mind sending me a copy of the physics paper? I would pay you.

  10. Thanks for the link.
    That is an A level paper – not a Entrance paper – i.s scholarship level paper, though it is about as difficult as the STEP paper in physics that I took in 2001!

  11. Stansfield Says:

    My husband has a small, mixed collection of ‘A’ and/or ‘S’ level papers 1960-1990s including a couple of Pure & Further Maths paper complete with his teaching calcualtions and solutions. If anyone would like them please contact asap as I am about to consign them to the tip!

  12. Rich Wainwright Says:

    I also have a hoard of past A level Oxford Delegacy of local examination papers, mainly in Maths and Further Maths (1978-86) … if anyone is interested

    • Andrew Bassom Says:

      Hi Rich

      If you still have your past papers I’d be interested.
      Took some of those papers myself in 79/80 — now am Head of Mathematics at University of Western Australia in Perth. Always on the lookout for historic A-level maths and f maths papers
      Look forward to hearing from you
      Andrew Bassom

    • I will be thankful if you can email those maths past papers to me

  13. Hello, it seems you have stopped replying recently but I hope you’re still there. I am interested in the books that were used to prepare for these sorts of exams and/or the usual O/A/S level exams back in the 80’s. In particular I am interested in the physics books that were used at this level.


    • My name is John Scholes (forgot to complete the form)

      • hitsuyonai Says:

        Not sure you are still interested in the answer eight years later, but: Whelan and Hodgson, Essential Pre-university Physics

      • I was looking for the 1967 JMB Pure Math A level exam.


      • Ed Arakelian Says:

        Can anyone get hold of the 1967 JMB A level Pure Math exam?

    • telescoper Says:

      I’m afraid I don’t remember which book(s) we used for physics at school!

      • KarenStansfield Says:

        Hello, Sorry for delays in replying. The store of A Level exam papers both Mathematics and Entrance went to a new home with Chris T. last year. I’m afraid I have no idea which books were used for preparation of candidates as my own academic subject is English Literature. I have looked to see if there are any more stashed around the place but my mission was successful, we are clear of ‘vintage papers’. K. Stansfield

  14. I have worked through both papers and as I now teach both Maths and further maths and I think I am in a position to compare then and now. There are some straightforward problems on the 1981 paper but lots of more complex ones that you just wouldn’t find on a 90 minute exam. In particular the geometry is harder and the layout of some of the questions less clear than at present – no diagrams for example are included on the paper

  15. Any mark scheme ? Thank you very much. This is very interesting indeed.

  16. Edward J Coad Says:

    Did you post an old S level paper at some point? Can you send link?


    • telescoper Says:

      I didn’t do S level Mathematics. I did the Special papers in Physics and Chemistry but I don’t think I posted them here.

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