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Weren't logarithms once included in O-levels/GCSE's?

Discussion in 'Mathematics' started by o8, Oct 26, 2014.

  1. o8

    o8 New commenter

    I have a feeling that logs used to be part of the GCSE (or O-level) at one time - is that right? If so - when did they get dropped? I checked the latest Singapore Maths spec and it's not even included there.

    I know they were included in the Additional Maths (which is now defunct isn't it? [unfortunately imho]) only a couple of years ago. I teach maths, physics and chemistry (to A-level) as a tutor - I would like to see logs included - certainly I find it helps when explaining the shape of the graph showing the change in pH during a titration and in radioactive decay.
  2. I did the SMP Modern Maths O level in the 1980s and I can't quite remember whether logs were included or not - I was aware of them personally, but I did a lot of reading outside the curriculum when I was a teenager! I have vague memories of the class being shown a slide rule in one lesson, but I'm not sure whether that was introduced as a 'curiosity' or whether it was linked to something being taught in the lesson i.e. logs.

    Certainly logarithms would have been included in a traditional O level course - 50 or 60 years ago every child in Britain needed to know logs because before the widespread introduction of calculators, log tables were the only method available of estimating the result of mutliplication or division of "large" numbers. I'm pretty sure my mother saw logarithms at school and she left at the age of 15 back in the 1950s when she had the option of staying on a year to sit O levels or not!

    You're absolutely right about their utility - logarithms and exponential growth underpin all sorts of physical and biological laws.

    I'm pretty sure they've never been included in GCSEs - the topic doesn't really fit in with the culture of low expectations that forms the basis of the GCSE system!
  3. I can remember logs at O level, but only used them as a short way of doing long multiplication, looking up the log values of 2 numbers then adding the logs and using anti-logs to undo the process. Never understood what I was doing or what a log was but could got through the process and get the right answer, not sure in the real value od being able to do that! Logs were taken out in 1985ish at the end of O levels and the introduction of 16+ course just before GCSE came mainstream. The use and availability of calculators made the whole process of logs for multiplication rather pointless.
  4. blue117

    blue117 New commenter

    I taught slide rule multiplication in mid-70s. I wasn't teaching logs then. GCSEs' first assessment year was 1988.
  5. examsolutions

    examsolutions New commenter

    Gosh, this will date me but I used logarithms at school back in 1969 when I did what was called CSE's.(Certificate in Secondary Education). Get a grade 1 and that was said to be equivalent to an O level grade C. Went onto a grammar school and did A-levels and then used a slide rule. Log tables were out by 1970 as far as I was aware.
  6. Piranha

    Piranha Star commenter

    I used them for my O levels, in 1973. Not only were there log tables, there were also log trig tables to that we could avoid looking up (say) a sine and them finding its log. I don't think we learned any teory, althoug it did make the more abstract use of logs in A level a lot easier to take understand, as we were already using the rules.
  7. EcoLady

    EcoLady New commenter

    I was taught to use 4 figure tables. I did my O levels in 1985 but honestly cannot recall whether logs were part of that or whether I'd been taught them just as a curiosity.
  8. I did my O level in 1978 (JMB) and we definitely had questions that asked us to use logs. It was a crazy system because two years earlier the first Sinclair calculator came in. So we used our calculator to look up the logs so we could answer the question that required logs for multiplication, powers, division etc. I think logs were dropped very soon after that at O level. I taught the first year of GCSE and there were no logs there (NEAB) but it did include the inverse of a matix under multiplication (I think I remember teaching the inverse of a 3x3 matrix), matrix transformations, inverse functions and composite functions. All of which are now FP1 or C3 (MEI)
  9. o8

    o8 New commenter

    I certainly remember using 4-fig log books which also had sin/cos/tan tables (& natural logs, square & cube roots and possibly e^x tables?) and we didn't do any more than add or subtract them although I think we also found nth roots - I took my O-level in 1978 but did modern maths in 77 and additional maths in 79. I did wonder if more work was done with logs at O-level/GCSE after 78.

    I found some old exam papers on scribd - e.g.


    but there were no logs in this particular paper. Is there another source of papers this old? One where (without fiddling with browser add-ons) I can download the papers easily - I find it interesting looking at the difficulty of these old papers - it's surprising that given the improvements in the standards of teaching (imho - more atuned these days to the difficulties learners face when learning instead of a more "broadcast oriented" style of teaching I had) and the ready availability of good course materials (books/internet) that some of the content in these old papers could not be tackled by students today given the curriculum they have to work from.

    Like you jeremyb66 I also taught myself a lot of material that was outside and beyond what was required - I'm pretty sure I wasn't even aware of such a thing as the curriculum at that time and there were virtually no text books tailored for students other than study guides for English Literature and a book for A-level chemistry - I remember it seeming very odd that the school was suggesting that we buy a copy of this chemistry book. By year 10 I was regularly skipping school to go to a local library to teach myself whatever I wanted - depth-wise I just went as far as my interest and time would allow.
  10. ian60

    ian60 New commenter

    I am another one who remembers using log tables at school.

    However I think my cohort (summer 1976) were the first to be allowed to use calculators in the exam. This was O&C board.

    I think they were very nervous about this innovation, every time you used a calculator in the exam you were meant to write (CALC) next to your answer.

    Change is so hard...
  11. Ruthie66

    Ruthie66 New commenter

    I used log tables in my JMB O Level in 1982, I used them purely mechanically, didn't know what I was doing at all.
  12. I've gone all nostalgic now! I took O level Maths and Add Maths in 1967 and we used both slide rules (mainly for long multiplication and division where allowed) and our personal book of maths tables (for calculating using logs to base 10 and trig tables for sin, cos, tan). For A level Maths in 1969 we also used these but for the stats paper we also used the Multivo Mentor calculating machine (google it) to do all the number crunching. They were very noisy and I can remember how it upset the history students who were doing their A level paper in the hall at the same time. We also used the maths tables for Binomial, Poisson, Normal and Student's t distributions, all of which were covered in the basic Maths A level syllabus then (if you chose the stats option rather than mechanics - you weren't allowed to do both).

    It's also reminded me of my first job in 1972 in an accounting office where my boss regularly used a Fuller's spiral slide rule (google that as well) which was the equivalent of a straight slide rule 42 feet in length! But by then the rest of us were using the very basic calculators that were available.

    I retired from teaching Maths this year but always managed to squeeze a lesson on all this into my A level and GCSE classes somewhere. The students loved it.
  13. sarahtaylor999

    sarahtaylor999 New commenter

    Love it you have just made me feel 10 years younger ( I have CSE's but not in maths)!! Thanks
  14. PaulDG

    PaulDG Occasional commenter

    Logs were expected to be used to solve compound interest problems at the time. I don't recall there being numeracy questions specifically requiring logs though. Just wording in the question that allowed the use of log tables.

    Are you sure? 2D matrices and inverses of 2x2, transformations, etc. were common in the late 70s/early 80s. Don't think 3x3 were ever in O level.

    I've only recently begun to appreciate "Further Maths" is has become the "dumping ground" for everything that has been squeezed out of all the other courses. Perhaps it always was.
  15. markuss

    markuss Occasional commenter

    "O" Levels 1960. Yes, we had the booklets of log tables.

    Slide rules featured somewhere, as I recall but not compulsory.

    Those really good at maths did calculus and hard stuff.

    Those (such as me) not quite so good simply did Arithmetic, Geometry, Algebra, and Trigonometry.
    Lara mfl 05 likes this.
  16. PaulDG

    PaulDG Occasional commenter

    We know they were allowed.

    What no one seems to be certain of was "were they ever compulsory"? i.e. were there ever questions requiring evidence in the answer that log tables were used?

    I'm siding with "not".

    Not least because papers in those days didn't tend to specify methods. I think that's a relatively new thing designed to test if a particular part of the exam spec has been covered and not "can the candidate solve this problem?" which was the old thinking.
  17. I've just looked at 3 random past O level papers from 1968, 1962 and 1957. The 1968 paper required the candidate to use logarithms to find the cube root of 0.03791 and log tables were provided. The 1962 paper did not have a question requiring the use of logarithms even though mathematical tables were provided were provided. The 1957 algebra paper required the candidate to use logarithms as follows

    (i) Use logarithms to find the value of (0 ? 3818 × 216 ? 8) / ( 0? 0777× 5? 691)

    (ii) If V^2 = (a^3 + b^3) / 36? ,find the value of V when a = 2?671, b = 0?9343 and ? = 3?142.

    The link to the 1957 paper is below. Have a look at the standard required compared to current GCSE papers; I leave it to you to draw your conclusions, especially given that there was no distinction between foundation and higher students then.

  18. Logs were expected to be used to solve compound interest problems at the time. I don't recall there being numeracy questions specifically requiring logs though. Just wording in the question that allowed the use of log tables.

    I remember constructing the log/antilog table then using my calculator to look up the logs etc then filling in the table, even using the calculator to perform the simple additions/subtractions etc. I know I was a bit dim then but I don't remember being that dim
  19. armandine2

    armandine2 Established commenter

    may be your time has now come
  20. Lara mfl 05

    Lara mfl 05 Star commenter

    I was part of what i was told was the trial for the 'new SMP course way back in 1965 and we definitely had to use logarithms.
    Slide rules were just being introduced but we were provided with booklets for sine/ cosines & logs.

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