Exploring and noticing

problem

Turning to Calculus

Age

16 to 18

Challenge level

1 out of 3

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.
problem

Cubic Roots

Age

16 to 18

Challenge level

1 out of 3

Find the location of the point of inflection of this cubic.
problem

Simply Graphs

Age

16 to 18

Challenge level

1 out of 3

Look for the common features in these graphs. Which graphs belong together?
problem

Proving the Laws of Logarithms

Age

16 to 18

Challenge level

1 out of 3

Here you have an opportunity to explore the proofs of the laws of logarithms.
problem

Inequalities

Age

16 to 18

Challenge level

1 out of 3

Which of the statements must be true?
problem

The Koch Snowflake

Age

16 to 18

Challenge level

1 out of 3

Explore the strange geometrical properties of the Koch Snowflake.
problem

Polite Numbers

Age

16 to 18

Challenge level

2 out of 3

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?
problem

What Do Functions Do for Tiny X?

Age

16 to 18

Challenge level

2 out of 3

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

Impossible Triangles?

Age

16 to 18

Challenge level

2 out of 3

Which of these triangular jigsaws are impossible to finish?
problem

Farey Neighbours

Age

16 to 18

Challenge level

2 out of 3

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?