Mike Ollerton’s Problems

RF, DSE and AG went to a session on a Saturday morninng by Mike Ollerton, to get stuck into some problems. Here is one, that DSE and AG presented back to the team.

Bh-eqWQzTLMbJvzR2PcXgq8CNSMoRd5cv66rlsYswtYTdkAQqp9WqSkUT-TAbB5S-7SEXW2xda9KW9tt9ZA-gnhoEwRttsmY5U1TJiUhMqUsUayUFF4lSct_Qldb6gb5w5yC2jG0-28Untitled picture

Untitled picture2
Answers handed out promptly – ensures that you could discreetly check your own, and importantly, that everyone now has the same labels for each triangle
Untitled picture3
Linking to collecting like terms
Untitled picture4
Order through intuitive reasoning – no need to get bogged down in surds. Good application of telescoping sums in the extension.
Untitled picture5
A level extensions

To solve the question on the left…

  • Alberto dived into trigonometry, using double angle formula for tangent.IMG_6082.JPG
  • I dived into analytic geometry (after first “cheating” and finding the answer on geogebra), working out the equation of each line, the intersection of the lines, and then using the shoelace formula to work out the area

There surely must be a simpler way to work out the area, but nobody could find it yet.


An excellently stretchy task – plenty of further questions:

  • How many triangles in a 4 by 4 grid?
  • What about an m by n grid?
  • Explore areas? Angles?

Sphinx: other example of stretchy problem


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s