Mathematics examination paper from 1970

Scroll to see replies

Reply 60

DFranklin

Q4:

first bit

(a)

(b)

(c)

Reply 61

Scipio90

DFranklin

Q4:

first bit

(a)

(b)

(c)

For b, is it not sufficient to note that |z + i| + |z - i| = constant => distance from (0,-1) + distance from (0,1) is constant, which defines an ellipse with foci at those points?

Reply 62

kayjay

Generally looks alright, i.e there is nothing which stands out as completely undoable, having said this i haven't done maths for a year and therefore probably would actually struggle to get a solution to the question, and i am comparing it to the advanced higher course so i don't know what current A level is actually like

Reply 63

OrmondDrone

Mr M

yes s level was used for cambridge (and oxford) entry

I was talking to my dad about this. He said that many schools, especially state sector, didn't enter candidates for S level papers - I suppose in the same way as many now don't enter for STEP or AEA papers.

At my dad's school entering S level papers were optional, there was no additional tuition for them, and they were taken by any students who wanted to stretch themselves. It wasn't exclusively about Oxbridge admission though I suppose many who entered for S levels applied for Oxbridge. S levels were around til 1990 apparently.

Reply 64

DFranklin

first bit

(a)

(b)

Reply 65

DFranklin

Scipio90

For b, is it not sufficient to note that |z + i| + |z - i| = constant => distance from (0,-1) + distance from (0,1) is constant, which defines an ellipse with foci at those points?

Yeah, except I think you'd be still be expected to get to an actual equation, or at least values for major/minor axes (since you're expected to sketch each locus). And I couldn't be bothered to look up the ellipse equations to do that from the "sum of distance from focii" starting point.

Reply 66

JoshJGordon

jj193

taylor/maclauren series aren't on A-Level...

Pretty sure I did them for A-Level. Not sure what module, but was not that long ago, 2005/6.

The paper does not seem that bad, I am just very much out of practice with maths.

I am a physicist, don't need to do that complicated stuff too often.

Reply 67

DFranklin

Mr M

I have the other six (count 'em) 1970 A Level papers too. This is the hardest one. Graham at Edexcel has a library of old papers.

Would be interesting to see the other ones - I think the S-level/AEA/etc. has actually seen a smaller drop off in difficulty than the bog standard A-level.

I took my A Levels in 1986 and this is more difficult than my papers. I think the time pressure is the problem. I can answer most of the questions but I couldn't knock out 8 good answers in 3 hours!

Yeah, but don't forget you probably only needed 6 questions for a distinction. 8 in 3 hours looks tough, but not impossible; main problem for current generation is relative lack of coord geometry, since the last 4 questions all lean that way.

Reply 68

conroe-killed-the-k8-star

JoshJGordon

Did Taylor/Maclaurin expansions in FP3 last year ,not sure if it's been taken out of the spec since then.

Pretty enlightening post seeing these questions , I could probably manage most of them but only by the fact I've finished my first year reading Mathematical Physics (we do a lot of the same maths modules as the maths students).I'd have definitely needed hints to finish most of those questions if I'd done them a year ago.

Reply 69

red_roses

It says "special" A-level, which equivalent to today's AEA. My dad did one in Chemistry.

EDIT: looks like someone else beat me to it :p:

Reply 70

OrmondDrone

red_roses

It says "special" A-level, which equivalent to today's AEA. My dad did one in Chemistry.

EDIT: looks like someone else beat me to it :p:

In fairness, the OP said it in the very first post but most people didn't bother reading it

Reply 71

red_roses

OrmondDrone

In fairness, the OP said it in the very first post but most people didn't bother reading it

Ahh I read the third post thinking it was still the OP's about it saying how the A-level syllabus had obviously been dumbed down. I fail at speed reading :p:

Reply 72

AsakuraMinamiFan

I have quite a few questions from Oxford + Cambridge scholarship papers dated at the very latest 1963. Only problem is that I have no idea how many of them are per paper or what the time limit is. Here's one for now that I have wrote down:

1. (Oxford.) By means of the substitutions

x \pm x^{-1} = t

, or otherwise, find:

\displaystyle \int \frac{x^2 + 1}{(x^4+x^2+1)^2} \, \mathrm{d}x \qquad \int \frac{x^2 - 1}{(x^4+x^2+1)^2} \, \mathrm{d}x \qquad \int \frac{1}{x^4+x^2+1} \, \mathrm{d}x.

I'll try and bring some more later today. :p:

Reply 73

Mr M

Study Forum Helper

DFranklin

Would be interesting to see the other ones - I think the S-level/AEA/etc. has actually seen a smaller drop off in difficulty than the bog standard A-level.

I will put some more up later.

Reply 74

Mr Nonsense

-G-a-v-

Looking at some of those questions makes me feel incredibly bad at maths :p:

that said, i've not actually got a pen and paper out and tried to do them ... yet. lol

Anyone got access to any typical 'normal' A-level papers from back then?

i have a set of 1970s physics papers that are also a massive shock compared to current A-level papers.... I mean, they are a lot, lot harder

Reply 75

Mr M

Study Forum Helper

Mr Nonsense

i have a set of 1970s physics papers that are also a massive shock compared to current A-level papers.... I mean, they are a lot, lot harder

A Level physics is simply embarrassing these days. The problem comes from not requiring A Level physicists to study any mathematics beyond GCSE. I understand and accept the reason (the low number of candidates is a concern) but it means no topic can be examined in any meaningful depth.