The Student Room Group

Old A-level Pure Maths exams

With one day to go to Results Day, I thought I'd scan in the three old A-level Pure Maths exams that a relative gave me - hopefully some of you will be able to use up some of the remaining time looking at these papers, and perhaps doing some of the questions, rather than worrying about results. :smile:

Plus, in the next few days the media will probably claim that exams have become easier than ever, so it would perhaps interest some of you to see the Maths exams from a few decades ago.

Enjoy. :biggrin:

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Reply 1

Reply 2

Excellent - more entertaining Maths. :smile: The 1970's question difficulty seems somewhere between the current A-level questions and the STEP questions, don't you think?

Reply 3

Indeed, the style of many of them reminds me more of STEP questions (although not as difficult) - the parts leading into one another, application of previous parts, that sort of thing.

I did also find applied maths papers from '71, but I didn't scan them because they aren't as interesting - entirely mechanics.

Reply 4

fatuous_philomath
Excellent - more entertaining Maths. :smile: The 1970's question difficulty seems somewhere between the current A-level questions and the STEP questions, don't you think?

It's hard not to be... :confused:

Reply 5

If you think the 1970s were hard... try these from 1960!!

Reply 6

A Levels were taken by a very small percentage of students, ones who were highly educated and almost certainly going on to university, in 1960 and as only the top 10% would receive an A, with the bottom 20% given a U, it is hardly surprising that the exams themselves were more difficult.

Reply 7

Indeed - but by no means are the questions out of people's depth for the brighter students nowadays - it's just that A-levels are now more accessible. And with that sort of timing, plus an element of choice, I think that it's the fact that the style is different that makes the biggest distinction between the papers then and now.

Reply 8

i love it. gravity in feet per second. god the 60s were a riot!

Reply 9

how would you do question 9 on the 68 paper?

centroid?

can do the rest on that paper.

also note, it's 3 hours.

compared to modern day 1 and a half hour maths exams...

plus you don't even have to finish the paper, it only asks for 8 questions to be answered.

Reply 10

I think the centroid is sort of like... where the centre of mass would be if it were a uniform lamina.

Reply 11

Adje
I think the centroid is sort of like... where the centre of mass would be if it were a uniform lamina.

helping helping...

and isn't there an integral you can find which will give u the x coordinate of the centroid?

do i need to integrate it then, half that value, then find limits which match?

Reply 12

I don't know how to find the centre of mass of an object by integration, but if it's like the way we do it in M2... which is cx=ΣmixiΣmi, \displaystyle c_x = \frac{\Sigma m_ix_i}{\Sigma m_i} \, , \, \displaystyle

it'd be something like:

cx=abxf(x)dxabf(x)dx \displaystyle c_x = \frac{\int_{a}^{b} x f(x) \, dx}{\int_{a}^{b}f(x) \, dx}

I have no idea if that's right. Don't hold me to it!

Reply 13

Dystopia: not for a simple area. f(x)^2 for the solid you get by revolving around the x-axis.

Reply 14

DFranklin
Dystopia: not for a simple area. f(x)^2 for the solid you get by revolving around the x-axis.

Oops.

Reply 15

Is what I posted anywhere close to the proper method?

Reply 16

Yes, it's the standard method for finding the centroid of a uniform lamina.

Reply 17

Ah, that's nice. Thank you. I can't see what to do for the y-coordinate, though :s-smilie:. I shan't take up any more of your time.

Reply 18

Adje
Ah, that's nice. Thank you. I can't see what to do for the y-coordinate, though :s-smilie:. I shan't take up any more of your time.


Rearrange it to make x the subject of the formula, so you have x = f(y) instead, and then try
cy=abyf(y)dyabf(y)dy \displaystyle c_y = \frac{\int_{a}^{b} y f(y) \, dy}{\int_{a}^{b}f(y) \, dy} ? That looks like a logical thing to try but it might be horribly difficult or not possible to integrate?

Reply 19

The question doesn't actually ask for the y-coordinate, I think. But by symmetry it's going to be 0.