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For younger learners

  • Early Years Foundation Stage

STEP on Up

A picture of old stairsIn this feature there are 4 problems based on STEP questions, all of which involve number theory.  You can find more number theory questions here.  

STEP is a mathematics admissions test taken at the end of Year 13 (June before starting university in September).  It is compulsory for Mathematics places at Cambridge, and many other UK universities recommend students work through past papers, or give reduced offers for students who take STEP and do well in it.

For more information on STEP, and help in preparing for the tests, see the STEP Support Programme.  The last day for sending in solutions to the live problems on this page is Monday 10th July 2023.

 

Square Difference

Age 16 to 18
Challenge Level Yellow starYellow star
Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?

Divisible Factorisations

Age 16 to 18
Challenge Level Yellow star
Can you show that $n^5-n^3$ is always divisible by $24$?

Proper Factors

Age 16 to 18
Challenge Level Yellow starYellow star
Can you find the smallest integer which has exactly 426 proper factors?

Square Remainders

Age 16 to 18
Challenge Level Yellow star
What is the remainder if you divide a square number by $8$?

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Patterns in Number Sequences

These resources are designed to get you thinking about number sequences and patterns.

Reasoning Geometrically

These resources are designed to get you thinking about geometrical reasoning.

Reasoning with Numbers

These resources are designed to get you thinking about reasoning with numbers.

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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