Creating and manipulating expressions and formulae

problem
Number rules - OK

Age

14 to 16

Challenge level

Can you produce convincing arguments that a selection of statements about numbers are true?
problem
Really Mr. Bond

Age

14 to 16

Challenge level

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?
problem
eNRICHing experience

Age

14 to 16

Challenge level

Find the five distinct digits N, R, I, C and H in the following nomogram
problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

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
Lens angle

Age

14 to 16

Challenge level

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
problem
Mediant madness

Age

14 to 16

Challenge level

Kyle and his teacher disagree about his test score - who is right?
problem
Lap times

Age

14 to 16

Challenge level

Can you find the lap times of the two cyclists travelling at constant speeds?
problem
Even so

Age

11 to 14

Challenge level

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
problem
Chocolate maths

Age

11 to 14

Challenge level

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it works?
problem
Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?