## 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.

Notes:
– 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.

## Exdexcel Formula Sheet lays Pooh Traps for Further Mathematics Pupils

FP3 integration standard forms could lead unwary pupils and teachers into a Pooh Trap. The following issue arises each year as the finer points of this course get sharpened.

When consulting the Edexcel formula sheet to find the integral,

$\displaystyle \int \dfrac{1}{\sqrt{a^{2}+x^{2}}} \textnormal{d}x$

two anti-derivatives are given,

$\textnormal{arsinh}\left(\dfrac{x}{a}\right)\ \ \ \textnormal{and}\ \ \ \ln\{x+\sqrt{x^{2}+a^{2}}\}$

Some might be tempted to infer that these functions are equal, this is the Pooh Trap, because whilst they both differentiate to $\dfrac{1}{\sqrt{a^{2}+x^{2}}}$ they are not equal.

Play with exponential functions and quadratic equations give us the logarithmic form of $\textnormal{arsinh}\ x$ which is also represented in formula books.

$\textnormal{arsinh}\ x=\ln\{x+\sqrt{x^{2}+1}\}$

Then,
$\textnormal{arsinh} \left(\dfrac{x}{a}\right)=\ln\left\{\dfrac{x}{a}+\sqrt{\left(\dfrac{x}{a}\right)^{2}+1}\right\}=\\\ln\left\{\dfrac{x+\sqrt{x^{2}+a^{2}}}{a}\right\}=\ln\left\{x+\sqrt{x^{2}+a^{2}}\right\}-\ln a$
The two anti-derivatives differ by the constant $\ln a$.

In a definite integration, this constant is added and then taken away making no difference as to which anti-derivative the student uses. In a particular solution to a differential equation, the evaluation of the integral using boundary condition would lead to two different constant values.

The worse case is that a student takes the integration standard from and reads it as the logarithmic form of the inverse of $\sinh x$. I have seen this happen.

## support for school mathematics exams

I have developed a database driven website which shares past papers, markschemes and my own ‘write outs’ for most Edexcel modules in mathematics and further mathematics:

jped Exam Bucket

I use this mostly as a resource for my own teaching; using it I can lay my hands of exam questions and solutions of different types very quickly.  My students and pupils find it useful too because it shows how to do exam questions using the techniques taught in class; there is an important difference with mark schemes here.

The UK mathematics exam system is in a state of flux at the moment.  I see this is as a great opportunity to review and refresh all my teaching material.  I look forward to generating new material to support a revised school exam system.