Sale Prices: Fifty Seven Point Five Percent Off on Streets of Canterbury!

Whilst wandering through the streets of Canterbury this sign caught my eye. With the mathematics department’s favourite coffee shop in the back-ground, the sign promises a further drop of prices for outdoor enthusiasts.

‘Half price’ and ‘15%’ are both eye catching figures which are immediately understandable to the shopper, but the sign promises something else.

Will anyone think this is a ‘65% off’ sale and that bargains can be picked up for 35% of their recommended retail price(RRP)?

In fact a 15% reduction applied to a 50% sale is compound percentage problem best dealt with by percentage multipliers:

0.5 \times 0.85 =0.425

that is, half price with a further 15% applied amounts to a reduction of 57.5% with shoppers paying 42.5% of the RRP rather than 35%. Are the marketeers messing with our heads?

Perhaps nicer for the maths teachers in the coffee shop to see calculate in fractioons without electronic assistance:

\dfrac{50}{100} \times \dfrac{85}{100}= \dfrac{1}{2} \times \dfrac{17}{20}=\dfrac{17}{40}

Much nicer perhaps, but a ‘\frac{23}{40} off’ sale doesn’t have the same ring about it I suppose.

Edexcel Practice Paper G – Statistics and Mechanics

This paper felt a little rough around the edges as a finished product but good revision practice nevertheless. Only Word versions available with the parsing of symbols and format presenting small problems.

– Statistics section seemed very chatty, had to write a lot for the marks on offer.
-Q4, not sure whether ‘p-value’ is defined anywhere for pupils who have done this course, context makes it clear what it is I think but could be confusing.
-Q3, as an ex-weather forecaster I didn’t like the premise of this question. It doesn’t seem at reasonable that same pressure ranges would relate to same weather at different locations. Use of the term hurricane could trouble the pedantic – Hurricanes in US, Typhoons in China.
-A lot of marks came very quickly in the Mechanics section, easy?
-I didn’t like the premise of Q7, two see-saws ‘joined’ seems to me to make one long rod. In any case the question assumes that they can move independently and that no moment is transferred through the ‘join’. They have to be side by side but able to move freely.

Edexcel Mathematics Practice Paper A

Practice Paper A – Questions

Practice Paper A – Mark Scheme

Practice Paper A – JPED Write Out

My write out included to show students how I would have answered the questions using the style of mathematics taught in my lessons.

This paper was one of a number of revision and preparation resources published by the board.  I could only find Word originals which did not handle the typesetting of the mathematical symbols; pdf versions of these Word documents are added here.

I wonder if this paper would have passed the quality tests of the real exams.

Notes on the paper in no particular order:

  • Q6 – initially confusing.  The figure is bounded by ‘arcs’, would have preferred ‘circular arcs’, there are, after all, many types of arcs and this one looks like an ellipse.  At first sight it looks like an integration questions, but once you have figured that the arcs are circular together with the presence of \pi it has to be all about radians and sector area.
  • Q11 – there must be an error in the mark scheme here, I am happier with my answers than Edexcel’s.