My Favourite Problems


A set of six posters featuring interesting mathematical problems for students in key stage 4

The FMSP Central Team has chosen six mathematical problems to display as posters. The aim of the posters is to engage students in problem solving and extend the mathematical ideas and approaches they encounter at GCSE.

Hints and solutions

Problem 1

Hint: Label the area of each region. The areas required are combinations of triangles and semi-circles.

Solution to problem 1

Problem 2

Hint: Assume the ball is dropped from a specified height, say of 1 metre.
What is the height of the first rebound?

Solution to problem 2


Problem 3

Hint: Numbers with lots of factors need most connections.

Solution to problem 3


Problem 4

Hint: Introduce some algebra to label unknown lengths and use similar triangles.

Solution to problem 4


Problem 5

Hint: Use geometrical reasoning to consider the areas of triangles and parallelograms.

Solution to problem 5
Geogebra file: Feynman1
Geogebra file: Feynman2


Problem 6

Hint: A diagram will be very useful!


Solution to problem 6



Other Problems

You will also find other GCSE level problems along with prompts and worked solutions on the GCSE Problem Solving page.

The Year 10 Maths Feast Competition Materials provide a fantastic resource for developing problem solving skills in mathematics.

The NRICH website has an abundance of interesting mathematical problems at a range of different levels of challenge.