Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Can you produce convincing arguments that a selection of statements about numbers are true?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?
Here are two games you can play. Which offers the better chance of winning?
Can you match each graph to one of the statements?
This problem challenges you to sketch curves with different properties.
This problem challenges you to find cubic equations which satisfy different conditions.
Quadratic graphs are very familiar, but what patterns can you explore with cubics?
This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.