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Another "impossible" A Level question

Discussion in 'Mathematics' started by DM, Jan 17, 2012.

  1. DM

    DM New commenter

    Well not exactly impossible but ambiguous. However I don't think this one is worthy of another media frenzy.
    Today's OCR MEI Core 2 paper asks:
    log_a (a^3)^6 =
    I think most of you will agree the expected answer is 18. However a significant number of people have given 729 as the answer as they believe the logarithm takes precedence over the final index.
    Try on your calculator:
    log (10^3)^6 =
    or ln (e^3)^6 =
    Oh dear.
  2. tbh I agree with your students.
  3. DM

    DM New commenter

    Not my students but you would think OCR MEI would have checked everything with a fine-toothed comb after the previous exams season fiasco.
  4. Karvol

    Karvol Occasional commenter

    Why would the logarithm take precedence? Unless I am misreading the question ( quite possible as I have just returned from a school function involving copious amounts of alcoholic substances), there is a world of difference between
    log_a (a^3)^6 and (log_a (a^3))^6.

  5. DM

    DM New commenter

    As I said, if you have the necessary coordination, prod the buttons of your calculator.
    MathCAD also agrees with the log first rule.
    Wolfram doesn't.
    Edit: Who would believe that adults are banned from using the word prod?
  6. I guess this is a good example of why we like cos^2(x) rather than cos(x)^2
    Maybe it should have been log_a^6( a^3)
  7. DM

    DM New commenter

    Indeed. And we also say ln^2 x for the same reason so an unambiguous notation does already exist.
    Edit: You edited and now my remark looks redundant!
  8. My Casio gives an answer of 18.
    I must admit that given all the possible questions to test their understanding of logs, it seems odd to create one like this. Ours sat the paper today but I haven't had my copy yet. Students seemed happy enough.
  9. DM

    DM New commenter

    My Casio (fx83) gives 729.
  10. davidmu

    davidmu Occasional commenter

    Why is anyone considering using a calculator? The answer is instant by inspection of 18.
  11. Piranha

    Piranha Star commenter

    Modern Casios insert brackets on functions such as Log, so the user decides the order calculations are done in. I would have interpreted it as intended.
    This all begs the question about why a question should be set which can be done on a calculator with little understanding of the underlying concepts. I assume some sort of working will be expected to get the marks. I would also think that candidates misinterpreting the question will get something.
  12. scraggy55

    scraggy55 New commenter

    Agreed. If a student needs a calculator for this question, then they don't understand the concept of logarithms; and the concept is being tested here, not the (correct) use of a calculator.
  13. DM: 'My Casio (fx83) gives 729'
    My fx83MS gives 18, but my fx83ES gives 729.
  14. DM

    DM New commenter

    That really is interesting. You would expect consistency in the same model.
  15. DM

    DM New commenter

    I don't think it is as simple as some of you appear to think. I'm not suggesting that candidates reached for a calculator at all. I am suggesting that there is a debate to be had about the "correct" order of operations here. I fully expect both answers to be accepted in the end.
  16. Polecat: 'My fx83MS gives 18, but my fx83ES gives 729.
    ...and my fx-85MS gives 1.800000000 x 10^1.

  17. DM

    DM New commenter

    Is your fx-85MS in Sci mode?
    And is this the calculator equivalent of philately?
  18. 'Is your fx-85MS in Sci mode?'
    Yes, just to illustrate the many faces of calculator output.
    'And is this the calculator equivalent of philately?'
    My album is rather chunky.
  19. how did you get tes to allow that word? long since banned from many a toxic argument in 'opinion' wrt n ireland.
  20. Totally agree with davidmu. That's why we have exams. Any pupil who thinks it's 729 by inspection or calculator will get a lower grade, as they should.

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