A Level Enrichment

Enrichment Material

Numberphile

Numberphile is an amazing youtube channel with loads of amazing videos, it's well worth having a look here. Below are some videos that Mr Fletcher recommends, and please inform him of any other videos that you find particularly interesting and worthy of being on this list for future students.

Euler's Number (e)

The Golden Ratio

Problem with dividing by 0

What's so special about the Mandelbrot Set?

The Riemann Hypothesis

Transcendental Numbers

Godel's Incompleteness Theorem

How to fill a Klein Bottle

Tau vs Pi

Fundamental Theorem of Algebra

The bridges to Fermat's Last Theorem

Maths and Movies (Pixar)

Fantastic Quaternions

BlackPenRedPen

BlackPenRedPen is the Youtube name of a great teacher in America, so you might find the terminology a bit different, but it well worth a look if you would like some extension questions. There's loads on his Youtube page, some of which have been recommended by Mr Fletcher below:

100 (hard) integrals

100 (hard) derivatives

Introduction to Hyperbolic Trigonometry

Integration by Parts - The DI Method

Derivative of x^x

Trinomial Expansion (a+b+c)^n

A Taste of Real Analysis (adult calculus)

Harder Trigonometric Integrals

Harder Integration by Parts

Lectures from Oxford University

Find here the youtube channel for Oxford University Mathematical Institute - they have loads of excellent lectures on all sorts of different areas of mathematics. Some are examples of university lectures, but the majority are for public viewing. Below are some of Mr Fletcher's favourites:

Productive Generalization - Timothy Gowers

1st Year Lecture on Converging Sequences - Vicki Neale

How to prepare for the OxMat

Andrew Wiles talks to Hannah Fry

Adams Integration Bee Resources (MIT Style)

In February, the upper 6th take part in the annual Adams Integration Bee. This is a non-house event where serious integrators compete to become the grand integrator. In preparation, the MIT Integration Bee website here. Scroll to the bottom of their page for resources.

MIT 2006 Integration Bee Video

MIT 2015 Integration Bee Video

MIT Integration Bee Qualification Test 2013 - Video Solutions

MIT Integration Bee Qualification Test 2019 - Video Solutions

MIT Integration Bee Qualification Test 2020 - Video Solutions