Balneus

Australian Lefty on Politics, Governance, Science and Info Management

How to fail a maths student

Posted by Dave Bath on 2008-05-08


Here are a couple of questions I’d use to fail any year 11 maths student who got them wrong, or even looked horrified when given the questions.

I wonder if anybody else has questions with a similar attititude?

I’d give the students a pen, three sheets of paper, forbid use of calculators, slide rules and reference materials.  I’d tell them if they have five minutes per question, and if they don’t complete the task, any working on paper of the problem will be taken into account.  I wouldn’t tell them the two questions are related.

It’s shocking how many look at you as if the task was impossible!  Discussion over the fold.

Question 1: Attempt to calculate, to at least 6 decimal places, the natural logarithm of the square root of e.

Question 2: Given the base 10 log of 2 is 0.30, approximate, to two significant digits, the base 10 log of 7.  Indicate if the correct value is likely to be higher or lower.


Actually, both the questions are really at year 9 or 10 maths level.

Both of these are outrageously simple, but the second is an opportunity to show a little inventiveness.  With both, the pen, paper, and "five minutes per question" are distractors, designed to make them assume the questions are harder than they are.

Question 1 should take no time if they understand what logarithms are.  The answer is 0.500000 (exactly) by definition.  Anybody who complains at the end that they didn’t know the value of e should be taken out and shot.

Question 2, unless they just write down “0.85, with the real answer a little lower”, should have working similar to the following:

1-0.3=0.7;
1.7/2=0.85 because 49 is just a little bit under 50.

For those who don’t get that working:

  • 1-0.3 is calculating the log of 5.  :  (log 10)-(log 2)=(log 5)
     
  • If the log of 5 is 0.7, the log of 50 is 1.7  :  (log 10)+(log 5)=(log 50).
     
  • 49 is the square of 7, and a little under 50, so the square root of 50 is just a little bit more than 7.  :  (log 49)/2=(log 7).
     
  • 1.7/2=0.85, and therefore the log of 7 is just a little bit under.
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2 Responses to “How to fail a maths student”

  1. AAAAAAAAAAARGH! I don’t think I had to learn logarithms in GCSE (in the UK). I can’t even remember what e was or is. I think the teaching of logarithms is a lot less prominent than it was, because of the advent of calculators.

    I gave up maths in year 10. Rather embarrassing, because my mother is a maths teacher and a superb mathematician.

  2. Dave Bath said

    LE:
    (1) You said “I can’t even remember what e was or is”.
    The point is, you don’t have to. The only thing you need to know for that question is that “natural logarithm” is based on the number you are taking the square root of:

    log base x of (x^0.5) = 0.5 for any positive x. (Hmmm. Perhaps negative x as well.)

    (2) “Teaching of logarithms is a lot less prominent than it was because of the advent of calculators.”
    It’s not actually the ability to provide quick approximations that makes the teaching of logarithms useful: it is developing a feel for the way indices work – something important when trying to understand a number of physical (and economic) phenomena at a “gut level”.

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