Creating and manipulating expressions and formulae

problem
Multiplication square

Age

14 to 16

Challenge level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
problem
Diagonal sums

Age

7 to 14

Challenge level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
problem
Triangles within pentagons

Age

14 to 16

Challenge level

Show that all pentagonal numbers are one third of a triangular number.
problem
Triangles within squares

Age

14 to 16

Challenge level

Can you find a rule which relates triangular numbers to square numbers?
problem
Triangles within triangles

Age

14 to 16

Challenge level

Can you find a rule which connects consecutive triangular numbers?
problem
Nine, ten and one

Age

11 to 14

Challenge level

Can you find the value of t in these equations?
problem
No matter

Age

11 to 14

Challenge level

After performing some operations, what number is your answer always a multiple of?
problem
Salinon

Age

14 to 16

Challenge level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
problem
And so on - and on - and on

Age

16 to 18

Challenge level

Can you find the value of this function involving algebraic fractions for x=2000?
$Complex partial fractions$

problem
Complex partial fractions

Age

16 to 18

Challenge level

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.