Archive for the ‘Quadratics’ Category

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.

World Cup Round-up: Summary of our FREE Maths Classroom activities

As we come to terms with England’s defeat at the weekend to Germany (or rejoice at it, depending on your point of view), we thought this would provide an appropriate moment briefly to re-cap the football-themed resources we’ve produced in recent weeks.

In chronological order, with the most recent posts first:

World Cup Maths: The Curse of the Jabulani – 3D shapes and nets

(Seriously, was this prophetic on some level?  Two days after we posted it, England’s crucial 2nd half goal against Germany is disallowed…)

World Cup Maths: The Mathematician’s Guide to Penalty Shoot-outs – Pythagoras, trigonometry, quadratics, probability

UPDATED World Cup Wall Chart: Free to download – Averages, probability, relative frequency

World Cup maths: the route to the Final! – Number skills, distance-speed-time, scatter graphs

(This activity has been the biggest hit with teachers…)

Cup Final Maths – Free resource! – fractions, decimals, percentages

Countdown to the World Cup! – fractions

(…and this one has been the second biggest hit.)

World Cup Maths: The Mathematician’s Guide to Penalty Shoot-outs

June 24, 2010 4 comments

With England.v.Germany looming on Sunday, we thought we’d give you a sneak preview of how England are preparing for another of their famous penalty shoot-outs!

We have produced a new World Cup Maths activity.  To advise Steven Gerrard and the boys on their penalty strategy, your students will need to use a combination of trigonometry, quadratics and distance-speed-time.  We’ve also thrown in some probability questions for good measure.  GCSE grades have been applied to all the questions to give an indication of difficulty level.

This activity spread is free for our subscribers.  The good news for maths teachers is that subscribing to this blog is cost-free, spam-free and hassle-free.  Just enter your school email address in the box on the top right of the screen.

World Cup Maths activity: penalty shoot-out. Click to view. Full pdf available to subscribers.

Click here to download the accompanying worksheet.

How exactly do I subscribe to this blog and when do I get the Penalty shoot-out activity?

Just enter your school email address in the box top right.  You’ll then receive an email asking you to confirm your subscription.  Once you’ve accepted that, we’ll email the activity out to you as a pdf, along with the accompanying worksheet.

Why should I subscribe to this blog?

You will receive each of our posts by email, about 2-4 per week.  We never spam our subscribers, and we never share details with any third parties.  Oh, and subscription to this blog is free, has always been free and will always be free. 

Our subscribers are part of our community of maths teachers, we value them and they will continue to receive free resources not available to all browsers of this blog.

A-A* Practice Book: free sample chapters


Some rivers are easier to cross than others... Sample question on the Millau Suspension Bridge from A-A* book. Click to enlarge.

We published our A-A* Practice Book last week. It’s the only book in the market we can find, which targets top grade candidates and future A-Level stars.  And it’s our answer to anyone who says Maths GCSE is being dumbed down.  The book is full of engaging, colourful questions – all of them clearly graded and labelled like the AO2 sample above on the Millau Suspension bridge (Chapter 4 on Accuracy in calculations).  

And here’s a Challenge Yourself question from the Proportionality chapter:

Challenge Yourself... Or better still, challenge your students. Sample question on proportionality. Click to enlarge.

Challenge Yourself questions in every section offer some fun and danger to the brightest students – the questions go beyond GCSE but the underlying maths doesn’t.  We blogged some other samples a few months back – Mean, Meaner, Meanest – as well as answers

Click here to download free sample Chapter 3, Proportionality, or Chapter 4, Accuracy in calculations

The A-A* Practice Book can be ordered here.

Answers to “Challenge Yourself” questions

Last week we posted three of the “Challenge Yourself” questions from our forthcoming AQA GCSE Maths A-A* Practice Book.  Labelling them “mean”, “meaner” and “meanest”, we picked a selection that should test the full gamut of ability in a top maths set.  

You’ll find the questions at this link, and here are the answers: 


Answer to probability/tree diagram question about the basketball player: 

Click to enlarge


Answer to quadratics question on the Golden Ratio: 

Click to enlarge


Answer to the question on cones: 

Click to enlarge

Mean, Meaner, Meanest: “Challenge Yourself” questions in our A-A* Practice Book

March 5, 2010 2 comments
Try some “Challenge Yourself” questions from our forthcoming A-A* Practice Book!  We’re very excited about this book (as far as we know, there’s nothing else like it on the market?), and these challenges are the most fun part of it.  There’s one at the end of every section in every chapter. 

The questions are tougher than anything in a GCSE exam, but don’t actually require knowledge beyond the GCSE curriculum.  Well, that’s the theory anyway.  In case you find them a bit hairy,  answers can be found at this link.  Have a go at the questions:


Here’s one on tree diagrams.  It’s taken from the Probability chapter in Unit 1 (Statistics and Number).  We know this one wasn’t too bad, because we could all do it (well, most of us…):

Question on tree diagrams from our AQA GCSE A-A* Practice Book. Click to enlarge.


Now one on the golden ratio.  This is from the quadratics chapter in Unit 2 (Number and Algebra). Familiar territory, and an interesting subject – but can you actually come up with a proof?

The golden ratio - Maths problem-solving challenge

Question on the golden ratio from our AQA GCSE A-A* Practice Book. Click to enlarge.


And now the crunch.  You’ll find this one in the shapes chapter in Unit 3 (Geometry and Algebra).  A tricky question on cones, disguised beneath a humble egg-timer:

Question on cones from our AQA GCSE A-A* Practice Book. Click to enlarge.

A final note:

Our whole AQA GCSE Maths 2010 series is about differentiation.  We’ve had just as much fun putting together a dedicated Practice Book for G-F grades, as well as a whole tier of resources for Middle sets / borderline C.  Click here for a full chart of all the components in the GCSE series.  And click here for a free evaluation pack.  Any comments or suggestions, let us know!