Explaining, convincing and proving

problem

Cyclic Quad Jigsaw

Age

14 to 16

Challenge level

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
problem

AMGM

Age

14 to 16

Challenge level

Can you use the diagram to prove the AM-GM inequality?
problem

Square LCM

Age

14 to 16

Challenge level

Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?
problem

Close to Triangular

Age

14 to 16

Challenge level

Drawing a triangle is not always as easy as you might think!
problem

Geometric Parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
problem

Dalmatians

Age

14 to 18

Challenge level

Investigate the sequences obtained by starting with any positive 2 digit number (10a+b) and repeatedly using the rule 10a+b maps to 10b-a to get the next number in the sequence.
problem

Road Maker

Age

14 to 18

Challenge level

Which of these roads will satisfy a Munchkin builder?
problem

IFFY Triangles

Age

14 to 18

Challenge level

Can you prove these triangle theorems both ways?
problem

Common Divisor

Age

14 to 18

Challenge level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
problem

Network Trees

Age

14 to 18

Challenge level

Explore some of the different types of network, and prove a result about network trees.