Visualising and representing

problem
Areas and ratios

Age

16 to 18

Challenge level

Do you have enough information to work out the area of the shaded quadrilateral?
problem
Days and dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
Wrapping gifts

Age

16 to 18

Challenge level

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
problem
Ladder and cube

Age

14 to 16

Challenge level

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
problem
Set square

Age

16 to 18

Challenge level

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?
problem
Building tetrahedra

Age

14 to 16

Challenge level

Can you make a tetrahedron whose faces all have the same perimeter?
problem
Just opposite

Age

14 to 16

Challenge level

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
problem
Coke machine

Age

14 to 16

Challenge level

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
problem
Just rolling round

Age

14 to 16

Challenge level

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
problem
Circles ad infinitum

Age

16 to 18

Challenge level

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?