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problem

Just Opposite

14 to 16

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?

Placeholder: several colourful numbers

problem

Integral Arranging

16 to 18

How would you sort out these integrals?

problem

What Do Functions Do for Tiny X?

16 to 18

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.

problem

Pouring the Punch Drink

7 to 11

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

problem

Perspective Drawing

11 to 16

Explore the properties of perspective drawing.

problem

Grid Lockout

14 to 16

What remainders do you get when square numbers are divided by 4?

game

Phiddlywinks

7 to 18

Have a go at this version of John Conway's game. Do you have any good strategies for winning?

problem

Long Short

14 to 16

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

problem

Archimedes and Numerical Roots

14 to 16

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

problem

Folding Fractions

14 to 16

What fractions can you divide the diagonal of a square into by simple folding?