Maths papers for the modern British State – this one is for the smarter 16-year-olds

UPDATE”:- Here’s a link to some Americans, who also like me object to the deliberate obscuring of how to to “math”.

UPDATE1:- WE talk about the A-level maths papers here.

David Davis

This is “module 1” (you do it in bite-size, topic-related bytes now.)


And the mark scheme is…



And this is “module 3”:-


And here’s the answers as directed that you should give them:-


Do you want to see  _2  papers_  for the poor individuals who are perhaps not so smart? here it is: remember, these people are usually 16:-



Oh, I forgot: if you do rubbish in it, you can “retake” that modile as many times as you want to. (But it will of course have different questions in it the next time around.)

I will not waste time putting up the answers for these as you will all do them in about 3 minutes.


I have to say that nothing was this bad even in 2001, let alone in 1997 when the Nazis came to power here. Using text books from the 1990s spooks today’s students, even some of the brighter ones, for the books contain topics and concepts with which they are entirely unfamiliar. Like, for example, the graphs of y=sin x, y=cos x, y=tan x, and transformations of the same. The concept of angular velocity, as a property of trig functions and the units of radians, are now only dealt with in the second or third modules of A-level maths. I’m not sire they even properly understand it even then. I can do it with the bright ones, That’s merely what came to mind on the spur of the moment.

Oh and they don’t know what a logarithm is until at least halfway through their first year of A-level maths. They have no clue who computed logarithms first, or why, or which logs he calculated and on what base: they are not really told what these things are for, economically.

Those of you of 60 or over will know that we all did differentiation and integration for O-level. These are now “advanced” concepts in “AS” and “A2”.


  1. “Those of you of 60 or over will know that we all did differentiation and integration for O-level.”

    A-hem. I’m forty-two and seven days and I remember doing differentiation and integration for O-level. I think. It might have been a paper called “Additional Mathematics” that those of us who took the O Level a year early did, perhaps. It might have been called an “AO” level. But it was “pre-17” at least.

    Do they still make slide rules and do they ever have to take such things and log tables into exams?

  2. None of my students, and mane teachers, have never seem a slide rule. I produce one, and the general reaction is “what the f*** is _that_?”

    They don’t know what logs are. Not til A-level at least.

    They are allowed “scientific calculators” (£9.99 iin Smiths) to be able to do elementary trig, for the advanced students. Also to do standard form calcs. They are never told what most of the finction buttons do.

  3. I’m forty-five and we definitely didn’t do calculus till A-Level. If the higher level paper challenges you you’re five years behind doing calculus.

    The root problem is shown by question 2 in the higher paper.

    For 3 marks you have to calculate a mean of a pile of data. It’s not utterly trivial like most of the paper, I could do it when I was 11, you can use a calculator, but it is an actual maths question.

    However, part 2, for two marks, requires you to write a question to find out which days people will car share, and add a response section.

    What has this to do with Mathematics ? Why is it 40% of the marks for this question ?

    If you think this is bad, have a look at

    – 21st Century Science aka Science for the pub
    – Information and Communication Technology
    – Citizenship.

    The first two are rubbish, the second is just Labour propaganda – in some cases literally – in a way that is way beyond the endless power station questions and so on.

    This is a quote from AQA Citizenship 2006.

    “The United Kingdom Government takes equal opportunity very seriously and has set up special agencies to promote people’s rights. The Commission for Racial Equality provides advice on racial matters while the Equal Opportunities Commission promotes equal opportunities for men and women. More recently, the Disability Rights Commission started work to promote the rights of disabled people. In spite of this, discrimination sometimes takes place.”

  4. The other point which no-one has mentioned is how piddlingly short these exams are.

    2 x 25 minutes with a 5 minute break ?

    The only exams I recall being short were those that had a specific reason for doing so. For example, language multiple choice where you answered questions from a tape recording as you went along was the same length as the tape recording.

    But most exams were between 2 and 3 hours long, probably 2 1/2 was the most common.

  5. Jock, I’m 43 (you young whippersnapper you!) and did Additional Math and A-Level Pure and Applied Maths (failed the A Level, lolz). I’m pretty certain we didn’t start calculus until A-Level, and I can’t for the life of me remember what was in the Add. Math exam or what extra study it entailed, though I think it must have involved some. I do know I sat Bog-Standard Math and Add. Math the same year (spring 82, I guess, not sure, never was very good with numbers) and Add. Math was IIRC just presented as another paper you did if you were going to do O-Level.

    FWIW, my feeble excuse for failing Pure Maths A Level was the teacher- the first day of calculus he said, I remember this very distinctly, “When I was at school, we were taught why all this works, I’m not going to teach you that, you don’t need to know it for the exam, I’m just going to teach you how to do it”. Since I’m very much one of those people who needs to understand underlying principles in order to maintain my interest and learn a skill, that pretty much damned me from day one. I came out of two years of integrating and differentiating with a few vague ideas of increasing the power by one or something but no ability at calculus at all. A few years later I bought a book on calculus that explained what calculus actually is and does and understood it in a couple of weeks. Should have done that at the time of course, but then one of the disadvantages IMV of “schooling” as a means of education is its authoritarian structure. You presume you’re being taught the right way and it stifles students’ initiative to learn on their own.

    Which might probably some kind of insight into statism as a whole, if I had the brains to integrate my thoughts coherently. I blame the schools.

  6. I’m 20, but I went to a “British” school abroad. I did Maths GCSE in Year 9, A-Levels in Year 11 and Further Maths in Year 12. My dad showed me his O-level books which covered all the Further stuff and more.

  7. Bm is broadly right.

    I still have a collection of native British maths text books covering the last 50-60 years, plus my early-60s roneoed exams and tests from prep school, and I find I was factorising cubic equations aged 11 by both the factor- and remainder-theorems, plus ordinary long-division of polynomials, and doing basic calculus at 12/13. At 14, I was doing trig identities including all the usual double-angle series (all those Co-Cos + or – Sin-Sin etc etc etc). (I now remember not having understood it very well at the time, but the A-level teachers helped.)

    There has clearly been some long-term-agenda to dis-educate the indigenous British population. I can’t of course begin to be able to suspect why this has been so: can you people suggest something?

    The science papers I have supplied speak for themselves.

  8. Dave:

    Jim Slater (Tory Wet, Slater Walker) summed the whole deal up in the ‘Seventies when he appeared on TV to say this:

    “In Britain toaday, there are “thing-makers” and there are “money-makers.”

    The “thing-makers” don’t make any money.

    The “money-makers” don’t make any things.”

    Edward Heath got a million-pound tax-free, interest-free, non-repayable ‘loan’ from Merchant Bankers Morgan Grenfell.

    With this money, he purchased “Morning Cloud”, an ocean-going luxury racing yacht, and covered its (considerable) operating expenses. So he’s a sailor, yeah?

    Imagine Ted Heath building a superb ocean-going yacht… (laugh)

    Naturally, the men and women who custom-build the yachts don’t get to have one for themselves. On the money the bosses pay them, they couldn’t even cover the upkeep.

    This is “Crony-Capitalism” par excellence…

    All my life, I loved imagining, designing, prototyping and tooling and producing stuff I dream into reality.

    Among the projects I hove underway right now, are these:

    “Lenticular Aerodynes”, three metre diameter UCAVs fitted with .50 caliber semiauto sniper rifles. Stealthy, invisible in camo, fast, manoeuverable and deadly. Kills at 2,500 metres… Working with Ryan McMillan in Phoenix, builders of the top-flight “Tac-50” sniper rifles, which hold the records for long-range targeted kills in Afghanistan. I work with Lockheed-Martin Palmdale, who built the Lockheed ‘Blackbirds’, the SR-71s…

    “Golden Arrows”: road-going combat planes; fully enclosed motorcycles with rear engines: you sit in an armoured fighter-plane fuselage with retractable polycarbonate cockpit canopy and windscreen, with full roll-cage.

    200+ mph; air conditioning; retractable stabilizer wheels for low speeds and parking. 36 inches across the flats fuselage, with hexagonal cross-section bodywork with ‘chisel-pointed’ forward section.

    Some toffee-nosed snotty asshole pulls out in front of you, you can drive straight through his goddamn car…. Super-stealthy — no radar ‘returns’… LCD programmable number-plates from China; you phone them up with your mobile, and key in your ‘preferred’ number plate in yellow and black…

    SAT NAV: Hub-centre steering; Race-tuned suspension. Exhilarating acceleration… ABS disk brakes… (all this ‘off-the-shelf’ now with CAD/CAM.

    We’ll sell them on eBay and Web Sites. 50% cash with order, balance payable on on collection or delivery.

    Justus Schneider, VP Marketing with Mercedes in Stuttgart will accompany us to the Nurburgring, with a view to Mercedes licencing the design to go head-to-head with BMW in the world motorcycle markets…

    You can trail half-round wingsa and a ducted-fan and spars. Fit these to the chassis and you accelerate using motorcycle power, switch on the Ducted Fan at the back, and you get to fly… Cool!

    etc. etc, etc…


    Lightweight, compact rotary cannons, with spherical tungsten ammo, fed via Teflon-lined armoured hoses connecting the backpack ammo store to the breech. NATO Technical Section love them!

    *The Rheinmetall smoothbore 120mm. Leopard II main gun is now fitted to all the Abrams tanks. The British military still have rifled guns. The Abrams can stay out of range, and take Challenger IIs out with DY or tungsten flechettes at 50% more range…*

    RadarVision — phased arrray readar on a chip, enabling blind people and warfighters to ‘see’ their surroindings via a Dolby 5.1 3-D enhanced sound-field remapped by digital signal processors from the radar returns,..

    And more, much more…

    Am I in this for the money?

    You gotta be kidding, right???

  9. At 62 I certainly didn’t do calculus at O Level, although I did do co-ordinate geometry, which doesn’t make A level these days I believe. I recall my Physics A Level also included stuff like the flow of gases in a pipe, including all the factors like friction, turbulence etc (although I freely admit that was the beginning of the end for me and physics)

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