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Paddy MacMahon @paddymacmahon.com · 01/10/2026

The normal approximation gives a value of 464.9... and the correct answer is n=465. Nice hidden quadratic to solve along the way too!

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Paddy MacMahon @paddymacmahon.com · 29/09/2026

#CoreMaths #MathsToday How are @netflix.com delivering more value by *increasing* their prices...? 🧐

An email from Netflix:

Thanks for letting us entertain you since 2014. Starting on 29 October, we're updating our prices to bring you even more exciting, new entertainment. Your monthly total will increase from £12.99 to £13.99.
Why are prices changing?
We're updating our prices to deliver even more value for your membership. Expect fresh, can't-miss films, series, live and exclusive content every week to keep you entertained. Next month alone, you can expect more than 87 new releases.

The sentence *We're updating our prices to deliver even more value for your membership* is highlighted

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Paddy MacMahon @paddymacmahon.com · 22/09/2026

Chi-squared tests in #CoreMaths #MathsToday. We used this resource yesterday: www.paddymacmahon.com/resources/a-... The presence of actual M&Ms is proving somewhat distracting...

A pupil sorting a packet of M&Ms into a 'bar chart'.

The final bar chart for a packet of M&Ms.

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Paddy MacMahon @paddymacmahon.com · 17/09/2026

Argand diagrams in #FurtherMaths #ALevelMaths #MathsToday, so I made a little completion table. drive.google.com/file/d/1aFK0...

A completion table for working with modulus and argument. Link to document in the post.

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Paddy MacMahon @paddymacmahon.com · 07/09/2026

A coordinate geometry question for discussion in #ALevelMaths #FurtherMaths #MathsToday. Most plumped for using perpendicular gradients, equations of lines and simultaneous equations. One went for a trig solution. I like this method (none of the class went for it... 😕): youtu.be/Df07cDPguPc?...

A coordinate geometry question: given points A(-1, 3), B(11, 0) and C(9, 9), what is the distance of C from the line through A and B? Students are required to discuss possible strategies.

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Paddy MacMahon @paddymacmahon.com · 20/08/2026

Doing further maths definitely seems to improve your single maths outcome. #MathsToday #ALevelMaths

A graph showing single maths A level score against IGCSE maths score for two cohorts: further mathematicians (in blue) and single mathematicians (in red). The trendline for the further mathematics cohort is noticeably higher than that for single mathematicians.

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Paddy MacMahon @paddymacmahon.com · 15/08/2026

Was there last month! Enjoy Zimbabwe - best country in the world!

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Paddy MacMahon @paddymacmahon.com · 27/07/2026

Without saying your age what is your favorite movie from the year you turned 18.

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Paddy MacMahon @paddymacmahon.com · 24/07/2026

If you see this, quote a pic of you in sunglasses

A man in a shirt and shorts wearing sunglasses standing next to a sign for Maramba High School

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Paddy MacMahon @paddymacmahon.com · 22/07/2026

Book number 31 of the year (I'm on track for my half century, I think...) and this was a corker. Beautiful, tense and devastating.

The cover of The Death of Us by Abigail Dean: a sunlit room with a single wooden chair and a woman's shadow on the wall behind it. Less clearly, a man's shadow next to it.

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Paddy MacMahon @paddymacmahon.com · 01/07/2026

It's King Edward VI Grammar School in Chelmsford, I think. They're a selective school, and have selective entry to their sixth form, so this is highlighting the criteria for entry. Here's the full entry from their GCSE choices booklet, link here: www.kegs.org.uk/wp-content/u...

An extract from the GCSE choices booklet for King Edward's Grammar School, Chelmsford, available at https://www.kegs.org.uk/wp-content/uploads/2025/02/GCSE-Options-Booklet-for-September-2026.pdf

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Paddy MacMahon @paddymacmahon.com · 04/06/2026

Probability Generating Functions (which are ace!) Or a cunning splitting of the series into other series:

A derivation of E(X²) for a geometric distribution.

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Paddy MacMahon @paddymacmahon.com · 04/06/2026

And \mathrm{N} will give an upright N for the normal distribution. Looks like latex commands work (as they do in desmos labels) but have to pasted in by hand...

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Paddy MacMahon @paddymacmahon.com · 04/06/2026

Here you go: I pasted the expression \bar{x} into the equation box. Can't type it in directly as \ is itself a shortcut for an expression.

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Paddy MacMahon @paddymacmahon.com · 11/05/2026

They've every right to feel aggrieved. What's that italic d supposed to mean...?!

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Paddy MacMahon @paddymacmahon.com · 06/05/2026

My 21st book of 2026 (I'm aiming for a half century this year...) and one of the best so far. A saga of three generations of women in Donegal and New York. Highly recommended!

The cover of "Confessions" by Catherine Airey, showing a b&w photo of a young woman holding a kitten on a city street.

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Paddy MacMahon @paddymacmahon.com · 05/05/2026

Maths timetable looking a lot sparser in #MathsToday since year 11 and upper sixth have left for study leave!

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Paddy MacMahon @paddymacmahon.com · 01/05/2026

Lovely message from one of my upper sixth in #MathsToday!

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Paddy MacMahon @paddymacmahon.com · 28/04/2026

It's been a little while... Find the exact value of the green area. #MathsToday #ALevelMathd #FurtherMaths

The graph of y=ke^(kx) is shown in red, together with the tangent to the curve that passes through the origin, in blue. The area enclosed by the curve, the tangent and the x-axis is shaded green.

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Paddy MacMahon @paddymacmahon.com · 25/04/2026

This is on a samsung phone. At some point I installed a Greek keyboard, and now I can press the little globe in the bottom left to switch between Greek and English.

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Paddy MacMahon @paddymacmahon.com · 13/04/2026

#MathsOnHoliday #MathsToday Circles and sectors in the desert in Egypt, seen from the plane. Presumably a crop of some sort, but I'm intrigued...!

A picture from an aircraft window of dark circles and sectors in the sand, west of the Nile in Egypt.

Circles and sectors in the sand, seen from an aircraft window.

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Paddy MacMahon @paddymacmahon.com · 12/04/2026

Art and maths in #MathsToday at the Hargeisa Cultural Centre, Somaliland.

A picture of a lion, camel (killed by the lion) and other animals under an acacia tree. There's a hyena with a geometric series spurting from his head.

An open book with mathematical formula rising from its pages.

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Paddy MacMahon @paddymacmahon.com · 11/04/2026

A shining sunbird in #WildlifeToday #birds #naturalists, seen in Sheikh, Somaliland.

A male shining sunbird calling from an acacia tree.

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Paddy MacMahon @paddymacmahon.com · 09/04/2026

A pair of Abyssinian white-eyes in #birds #WildlifeToday. Sheikh, Somaliland. Meanwhile, in #MathsToday, I've been seeing pupils for practice ahead of their IGCSE exams next month. Lots and lots of tree diagrams!

An Abyssinian white-eye grooming its mate on an acacia branch.

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Paddy MacMahon @paddymacmahon.com · 08/04/2026

A Speke's Gazelle in #WildlifeToday. An endangered species, pretty much restricted to Somalia. The school I'm staying at has a small herd which roams the (fenced) campus.

A Speke's Gazelle next to a small acacia bush.

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Paddy MacMahon @paddymacmahon.com · 07/04/2026

Remote Edexcel outpost in the middle of Somaliland.

A sign in Sheikh, Somaliland: Pearson Exam Centre

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Paddy MacMahon @paddymacmahon.com · 06/04/2026

Normal distributions in #ALevelMaths #MathsToday. Hadn't realised I'd be teaching first thing, but with 2 minutes to go was asked 'are you ready', so had to be! One of my favourite topics, and I really enjoyed meeting the pupils in Sheikh, Somaliland.

A whiteboard with some normal distribution graphs and questions.

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Paddy MacMahon @paddymacmahon.com · 04/04/2026

In #MathsToday this week, I'll be visiting Sheikh Pharo Secondary School in Somaliland, where I'll be leading some CPD with the maths department and working with pupils preparing for their IGCSEs and AS Levels. Might also manage to fit in a spot of birdwatching...

A pair of binoculars and a camera with two books: the Bradt guide to Somaliland and a field guide to the Birds of the Horn of Africa.

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Paddy MacMahon @paddymacmahon.com · 28/02/2026

Modelling. The other is American. From Chambers:

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Paddy MacMahon @paddymacmahon.com · 07/02/2026

I've split into 50 congruent triangles. 26 are shaded, so 13/25.

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Paddy MacMahon @paddymacmahon.com · 05/02/2026

We were using a template for the conclusion to hypothesis tests in #ALevelMaths #MathsToday. Too many straightforward marks lost on these questions.

A template for conclusion to a hypothesis test.

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Paddy MacMahon @paddymacmahon.com · 03/02/2026

In L6 #FurtherMaths #MathsToday we used this picture to start talking about hypothesis tests. Analysis and introduction to chi-squared goodness of fit tests using this @googlecolab.bsky.social notebook: colab.research.google.com/drive/1HU9yF...

A packet of M&Ms arranged as a bar chart by colour next to the empty bag. There are unusually (?) many orange M&Ms...

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Paddy MacMahon @paddymacmahon.com · 03/02/2026

Normal distributions in #CoreMaths this week. I like the approach of introducing calculations using the proportions within 1, 2 or 3 standard deviations of the mean to begin with. And thanks to @catrionaagg.bsky.social I always label inflection points. #MathsToday docs.google.com/document/d/1...

A sheet on the normal distribution using rules of thumb for proportions within 1, 2 or 3 standard deviations of the mean. There are three diagrams: one showing 68% of the distribution within 1 sd, a second showing 95% of the distribution within 2sd, and a third showing almost 100% within 3sd. Then there are 4 questions:

1. Masses of adult females of a species of dolphin are normally distributed with mean 220 kg and standard deviation 18 kg. What proportion of female dolphins of this species are between
202 kg and 256 kg in weight?
2. Heights of leprechauns are normally distributed with a mean of 1.2 m. 16 % of leprechauns are over 1.3 m tall. What proportion of leprechauns are under 1 m tall?
3. Harriet is studying a species of lizard. 2.5 % of them have masses under 20g, and 16 % of them have masses over 38 g. What is the mean mass of the lizards, assuming that their masses are normally distributed?
4. Harshant measures the heights of 400 sixteen year old boys. The tallest is 191 cm tall and the shortest is 158 cm tall. Estimate the probability that a randomly selected sixteen year old boy is between 169 cm and 180 cm tall. What assumptions are needed for this estimate to be valid?

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Paddy MacMahon @paddymacmahon.com · 16/01/2026

Normal probability plots using @desmos.com in #CoreMaths #MathsToday. www.desmos.com/calculator/2...

Screenshot of a normal probability plot created using desmos (link in post)

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