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UNCERTAINTIES AND OTHER MATHEMATICAL PRACTICE

Here are some resources I've produced over the years to cover some general skills or types of questions that textbooks and exam boards often don't explain clearly or specifically, perhaps assuming that pupils' Maths skills will encompass it, or perhaps that teachers will decide whether to cover it separately or as it crops up in lessons. I usually find pupils appreciate specific lessons about these sorts of things, followed up by use in context:

UNCERTAINTIES

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I've seen this come and go from specifications over the years, sometimes implied and sometimes explicit. What I've seen cause teachers particular concern is that a new specification will sometimes make a general statement about analysis of uncertainties being expected, but no further detail is given about exactly what methods of combining uncertainties will or won't be accepted.

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Below is a document which I wrote to explain this whole area to pupils in the later school years. There are also some practice questions at the end. Of course, I can't make any claims that the techniques described will or won't be accepted by any given exam board - and it's also worth noting that this issue becomes more involved at undergraduate level and beyond - but it's a reasonable way of dealing with the issue without overcomplicating it:

Uncertainties
Factor and Percentage change questions

FACTOR AND PERCENTAGE CHANGE QUESTIONS

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Your more naturally mathematical thinkers will probably be able to cope with these without much specific training, but others may not. Here are some practice questions and a worked example of how the logic should go:

Log-log graphs

LOG-LOG GRAPHS

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Some syllabuses ignore this technique completely, so this might not be relevant to you. However, it's a great technique if you're analysing some data and are having trouble finding a relationship that they fit. This sheet explains the theory and has some example data to analyse:

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Estimating (Fermi Questions)

ESTIMATING (a.k.a. FERMI QUESTIONS)

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Some syllabuses list this explicitly as a skill that will be tested, some don't. It's also known to be a favourite of some university interviewers. Again, some pupils will be entirely happy with this without specific training, but many will find the inherent ideas very intimidating compared to the comfort of a more precisely-answerable Physics question that they can just throw an equation at. Here's a presentation I use when teaching this to Year 12 (first year of A-level) pupils:

© 2019 by Mark Harrison. Spotted a mistake? Found this information useful? Like to know more? Please leave feedback!

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