How to Get an A* in A-Level Maths

From the previous post, the possible answers were:

a) 4π cm²
b) 8π cm²
c) 16 cm²
d) 16π cm²
e) 32π cm²

Did you figure it out? Here's the correct answer:

A good multiple choice exam question is written with plausible wrong answers in mind - so that the question can identify people who don't have a full understanding of the subject.

Even this tiny bit of knowledge can be used to our advantage.

So - here are the answers to a multiple choice question... which is right?

a) 4π cm²
b) 8π cm²
c) 16 cm²
d) 16π cm²
e) 32π cm²

(π means pi by the way)

* I must admit that this problem is taken from The Art of Strategy - a book I'm reading applying Game Theory to real world situations. Recommended for those who want to apply maths to economics, business or politics!

Did you know there's a Ham Sandwich Theorem?

The Ham Sandwich Theorem states that if you have up to n objects in n-dimensional space, you can cut them all in half with a single (n-1)-dimensional cut

In other words...
if you have a ham + cheese sandwich (ham, cheese and bread in 3D), you can make a cut with the knife (a 2D cut) so that each half has exactly the same amount of ham, cheese, and bread.

Weird! I can't quite see how that's possible! Going to check it out with my lunch. :)

Good luck to everyone taking the Edexcel C4 exam today and to everyone else doing A-level maths this year!

Roll on the results on August 20!!

Just back from the cinema - went to see Spanish film 'La habitación de Fermat' (Fermat's Room)
Best described as Saw vs Maths, it's a thriller whereby the main characters have to use their maths skills to get themselves out of a sticky situation.

I should say that all the maths is correct and presented very well - it's easily accessible and should be interesting to an A-level student, say. The protaganists are occasionally a little bit slower at solving the puzzles than you might expect, but not very much so - I won't spoil the puzzles for you!

The key bit of maths in the plot is Goldbach's Conjecture (GBC)
Every even number (greater than 2) can be written as the sum of two prime numbers

e.g.
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
100 = 53 + 47
1528 = 599 + 929
and so on

GBC illustrates an important idea of proof in mathematics:
It would be easy to disprove GBC. We'd just need to find a number which doesn't work - a counterexample. Easy - if there is one we can easily find, anyway.
Proving GBC is more difficult - we have to be able to show mathematically that GBC will be true for EVERY number, even ones that we will never test.

You can tell that checking every number is not good enough... even if we check all the numbers up to 10¹⁸, it might be that bigger numbers don't work but we haven't checked them yet. Especially in this field of maths (number theory), this unexpected disproof does occasionally happen to conjectures... and mathematicians aren't satisfied until there's a clear proof.
So, a Conjecture is some important mathematical idea that is believable but nobody's managed to prove yet - after a proof is found the conjecture is upgraded to a Theorem (or if we disprove it, it's downgraded to a failed conjecture).

Goldbach's Conjecture is at least 267 years old and still mathematicians are trying to find a proof.

Good luck!

Welcome to maths.ronaldx.com

This is really a test post, I haven't got a name for the site or anything yet.
My goal is to publish a guide to getting an A* at A-level Maths.

Everything you need to know will be here, I'll publish a content page for every little piece of the AQA, Edexcel and OCR syllabuses. They'll be linked to questions in the style of the exams
I plan to publish this in Summer 2009 -- in good time for the 2010 exams and your first chance to get an A*.

I'm gonna use this blog to post interesting maths websites and things I've discovered
And we'll have a forum so you can discuss how you're doing or ask specific questions.

That's it for now, I'm not expecting anyone to read this but leave me a comment if you do!:
maths@treasurelondon.com

All the best,
Ronald Stewart