Your Solutions - Stage 4 & 5

Mediant Madness

Age 14 to 16 Challenge Level:

Kyle and his teacher disagree about his test score - who is right?

Farey Neighbours

Age 16 to 18 Challenge Level:

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

Triangle in a Triangle

Age 14 to 16 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Areas and Ratios

Age 16 to 18 Challenge Level:

Do you have enough information to work out the area of the shaded quadrilateral?

Another Triangle in a Triangle

Age 16 to 18 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the green triangle?

System Speak

Age 16 to 18 Challenge Level:

Five equations... five unknowns... can you solve the system?

Area L

Age 16 to 18 Challenge Level:

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?

Irrational Arithmagons

Age 16 to 18 Challenge Level:

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

Graphs of Changing Areas

Age 16 to 18 Challenge Level:

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

Mega Quadratic Equations

Age 16 to 18 Challenge Level:

What do you get when you raise a quadratic to the power of a quadratic?