Advanced GCSE Masterclasses

Thursday 30th June 2022

This year, we've been piloting a series of Saturday morning masterclasses aimed at students in Year 10 and 11. We've been delighted to see so many students taking up the offer to attend these classes, giving up their Saturday mornings to work alongside other gifted mathematicians on various advanced topics and challenging problems. Our first class focused on polynomials, and involved activities designed to highlight why these are so important in maths. Here's an example for you to consider:

I am thinking of a polynomial P\((x)\). The coefficients are all single-digit non-negative integers. If you give me a number, \(x\), I will tell you the value of P\((x)\) for your number. What is the least number of times you’ll need to do this in order to work out what my polynomial is?

An answer to this problem is given at the end of the article!

The masterclasses are intended to stretch and challenge students who are likely to achieve high grades in GCSE Mathematics and who may be considering A level Mathematics or Further Mathematics. The classes also form part of a drive to encourage schools to offer additional qualifications such as the AQA Level 2 Certificate in Further Maths. With this in mind, our second session focused on matrices, a topic which is included in the Level 2 Further Maths course, and attempted to build a basic intuitive understanding of matrix transformations.

We intend to continue running these masterclasses next year, approximately once per half term. If you haven’t already, we'd strongly encourage you to send your students along! Keep an eye on the North East regional events page for these events.

You can do this with just one number: \(x=10\). As the coefficients are non-negative single digits, the value of \(P(10)\) will be a number whose digits are the coefficients of the polynomial.

By Michael Gibson

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