Reasoning, Justifying, Convincing and Proof - Advanced

Prime Sequences

Age 16 to 18
Challenge Level

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

Stats Statements

Age 16 to 18
Challenge Level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Integration Matcher

Age 16 to 18
Challenge Level

Can you match the charts of these functions to the charts of their integrals?

Impossible Square?

Age 16 to 18
Challenge Level

Can you make a square from these triangles?

Dodgy Proofs

Age 16 to 18
Challenge Level

These proofs are wrong. Can you see why?

Impossible Triangles?

Age 16 to 18
Challenge Level

Which of these triangular jigsaws are impossible to finish?

Polynomial Interpolation

Age 16 to 18
Challenge Level

Can you fit polynomials through these points?

What's a Group?

Age 16 to 18
Challenge Level

Explore the properties of some groups such as: The set of all real numbers excluding -1 together with the operation x*y = xy + x + y. Find the identity and the inverse of the element x.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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