Archive for the ‘Formulae’ Category

FREE Olympic GCSE Maths lesson – archery and circles

Actually it’s a Paralympic Maths lesson: teach area and circumference of circles in the context of Paralympic Archery. 

Bull’s eye! A KS4 Maths lesson taken from Cisco’s Out of the blocks – Maths and Science series 2012. Click to download (5MB, so be patient…)

Like what you see?  More lessons like this are freely available on ActiveTeach – no login required.

Rugby World Cup Maths: FREE Activity to download

September 15, 2011 Leave a comment

The Rugby World Cup is upon us.  There’s a lot more mathematics to rugby than you might think, and we’ve created a bespoke Beast Index to prove it.

Keep your class on their toes with these AO1 and AO3 problem-solving questions on averages & range, and using formulae:

Not just a pretty face. Click to download and see how the world's most massive rugby player can help with GCSE Maths.

Fibonacci Sequences – the Golden Rule about the Golden Ratio, which we just found out…

November 18, 2010 Leave a comment

We just found out something new….

It turns out that if you take the first ten terms of any Fibonacci sequence, the sum of those 10 terms is equal to the 7th term multiplied by 11.  Got it?

OK, let’s unpack that.  Here’s the most basic Fibonacci sequence:


If you plug these into your head/calculator, you will find that the sum of these 10 terms is 143.

Much quicker: take the 7th term (in this case 13), multiply that by 11 and you get, as if by magic… 143.

And it works for any Fibonacci sequence.  Let’s imagine one with bigger numbers starting with (to pick a number completely at random) 42:

42, 42, 84, 126, 210, 336, 546, 882, 1428, 2310

So we add all the terms up on a calculator and get 6,006.

Now, much quicker, jot down the 7th term (here: 546), multiply it by 11 and, hey presto: 546×11=6,006

It’s a trick you can cheerfully teach to your maths students – get them to take it home and impress their parents.  Something along the lines: “hey, dad/mum, I bet I can add up a Fibonacci sequence faster in my head than you can using a calculator”. 

Our thanks to the Republic of Maths blog that brought this to our attention, via this video link.

One final note: the covers on our (as in: Longman’s) AQA GCSE Maths Student Books this year were inspired by spirals.  A spiral galaxy on our Foundation sets book, a spiral staircase on our Higher sets book, and a chameleon’s tail on our Middle sets book (someone must’ve been wondering what this image was?) –

Sherlock Holmes GCSE Maths Challenge – episode 4 solution

November 16, 2010 Leave a comment

Many congratulations to the Episode 4 winners of our Sherlock Holmes maths competition:

Jonathon Cox at The Littlehampton Academy

for successfully working out where Holmes and Watson must go next.

And the answer is:


We’ll be sending the winners a FREE Class set of Longman’s unique AQA A-A* and G-F Practice Books (15 copies of each) and a tin of Cadbury’s Heroes.

Coming up next… a spot of Christmas shopping in Episode 5 on Wednesday.

Here is the winning solution to episode 4:

The solution to how far away Moriarty is from the tunnel.

The path of the firework is y=300+44x-x^2. This is a quadratic so using the quadratic formula to find x when y=0

x= (-b +/- square root (b^2 – 4ac))/(2a)

where a=-1, b=44 and c=300

x = (-44 +/- square root (44^2 – 4X-1X300))/(2X-1)

x = (-44 +/- square root (1936 + 1200))/(-2)

x = (-44 +/- square root (3136))/(-2)

x = (-44 +/- 56)/(-2)

Either x = (-44 – 56)/(-2) = -100/-2 = +50 (where the tunnel is)

or x = (-44 + 56)/(-2) = 12/-2 = -6 (where Moriarty must have fired the firework from)

 So 50 – -6 = 56 metres away from the tunnel

 Moriarty is 56 metres away

 The Code.

 Using the Coordinates of the Tate Modern (34, 14) and the code FG DG.

Using a shifted substitution D=1, E=2, F=3 etc

The Coordinates generated from substitution of CK EE gives (08, 22) which give the coordinates for Oxford Circus

 Moriarty’s Target is Oxford Circus

EPISODE 4: Sherlock Holmes Maths Competition – FREE AO3 Maths challenge for 5th November

November 3, 2010 1 comment


Episode 4 – “G U N P O W D E R ,  T R E A S O N   A N D   P L O T”

The story so far… Called to investigate the disappearance from Harrods of the world’s largest ruby, the Devil’s Eye, Holmes and Watson follow a trail from there to the London Eye.  Further clues at the London Eye lead them into a Halloween, midnight chase through the tunnels under the Thames.  Ably assisted by two Maths teachers from Gloucestershire College, they solve the probability clues and arrive at…  B O R O U G H   M A R K E T!

Emerging from the tunnels, Holmes and Watson finally catch a glimpse of the thief in EPISODE 4:

"So that's who the thief is!" Click to download PDF.

And here’s the accompanying worksheet:

Watson's Worksheet. Click to download PDF.




The winning entry will be drawn at random from all correct answers, and will receive a FREE Class set of Longman’s unique AQA A-A* and G-F Practice Books (15 copies of each) and a tin of Cadbury’s Heroes. 

If you’re NEW to this competition…

View this page of our blog to keep up to date with all the action.  The competition is free to enter, and you can join in any Round/Episode.  All the page references in the Episode point to maths support in our AQA GCSE Middle sets Student Book.  All new and existing subscribers are entitled to receive a single free copy of this book – request your copy by leaving a comment on this post.

GOT ANY QUESTIONS?  Just leave a comment on this post and we’ll get straight back to you.

Quick reminder…

October 25, 2010 Leave a comment

Don’t forget our Halloween Maths Challenge remains open until this Sunday, 31st October.

Episode 3 of our Sherlock Holmes Maths competition: solve the mathematical clues and let us know where Holmes should go next to track down the thief of the world’s largest ruby!

Since many schools are on half-term this week, we actively encourage teachers to have a go on their own behalf – no need to enter on behalf of their class.  All details of the competition can be found here.

This episode’s winner will receive: a FREE Sherlock Holmes DVD (the 2009 Guy Ritchie movie) and a tin of Cadbury’s heroes.

Sherlock Holmes Episode 1 solution…

September 29, 2010 Leave a comment

Our thanks to everyone who’s taken part in Episode 1 of our Sherlock Holmes competition: The Mystery of the Devil’s Eye!

In Episode 1, Holmes and Watson are called to Harrods by a frantic Inspector Lestrade: the world’s largest Ruby, the Devil’s Eye, has been stolen and he doesn’t know where to go next.  There are just a few cryptic clues that only a master of deduction, and mathematics, could solve…


Are Holmes and Watson being led around by the nose? Click to download updated map.


Our congratulations to this week’s winners: CLASS 10 Set 3 from Sutton Grammar School in Surrey.

Here’s their answer:

If you work out the volume of the ruby; (area of rectangle + area of trapezium) x length

((10 x 3.5) + (7 x 2.5)) x 11 = 577.5 cubic cm.

The Mass is density x volume;     so 4 x 577.5 = 2310 g

If we split the answer 2310 in to 2 parts we got the co-ordinate (23, 10)


{and the thief keeps talking about eyes at the start of the note}

[We also worked out the thief got through Door B;   if you draw the lasers as lines on the graph, all the doors are blocked except B]

We’ll be sending the winners a Sherlock Holmes DVD and a tin of Cadbury’s Heroes in the post! 



And remember, you can join this competition at any time.  There will be six Episodes in total, with a prize to the winner of each one.  You can keep up-to-date with all details of the competition on this page of our blog.