Coordinates

problem
Favourite

Route to Infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?
problem
Favourite

Beelines

Age

14 to 16

Challenge level

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
problem
Favourite

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
Favourite

Parabella

Age

16 to 18

Challenge level

This is a beautiful result involving a parabola and parallels.
problem
Favourite

Cubestick

Age

16 to 18

Challenge level

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.
problem

Cushion Ball

Age

16 to 18

Challenge level

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
problem

Plane to See

Age

16 to 18

Challenge level

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.
problem

Four Points on a Cube

Age

16 to 18

Challenge level

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?
problem

What Are You Plotting?

Age

7 to 11

Challenge level

Investigate the positions of points which have particular x and y coordinates. What do you notice?
problem

Mesh

Age

16 to 18

Challenge level

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?