The Old Entrance Examination

Original post by Gregorius

I know this is resurrecting an old thread, but I wonder if anyone would be interested in seeing an example from Autumn 1976 of these maths entrance papers. I have scans of 501-4 and of 801 (Physics) and 998 (general paper) that I sat in this year. I'm quite happy to post them.

Yes!

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Reply 22

Doones

Original post by Gregorius

Here we go.

I took these in November of 1976 as a seventh term candidate. It was possible to sit these exams in the fourth term of sixth form; but this was not recommended for mathematicians. As I was applying for Mathematics with Physics, I had the additional pleasure of a physics paper.

https://dl.dropboxusercontent.com/u/81755552/Maths_501_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_502_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_503_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_504_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_801_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_998_1976.pdf

Brilliant
And you got in.... ? :wink:

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Reply 23

Gregorius

14

Original post by jneill

Brilliant
And you got in.... ? :wink:

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I did, rapidly dropping the "with Physics" option when advised against it by our Directors of Study, went on to do Part III and then off to Warwick for a PhD and then off into the big wide world...

It's been fascinating comparing the entrance process of my day with what my daughter has just (successfully) gone through (NatSci, not Maths, though!) We turned up for our interviews (post A-level) to be met with "...well you're clearly a clever chap, but we don't take any notice of A-levels, we have our own entrance exam..."

Reply 24

Original post by Gregorius

Here we go.

I took these in November of 1976 as a seventh term candidate. It was possible to sit these exams in the fourth term of sixth form; but this was not recommended for mathematicians. As I was applying for Mathematics with Physics, I had the additional pleasure of a physics paper.

https://dl.dropboxusercontent.com/u/81755552/Maths_501_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_502_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_503_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_504_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_801_1976.pdf
https://dl.dropboxusercontent.com/u/81755552/Maths_998_1976.pdf

Thanks for these, I've never seen a 504 paper before. The questions are certainly harder than STEP. I actually want to try some of these now!

Reply 25

tiny hobbit

15

I must have some upstairs somewhere. I took 501 - 503 in 1972 as a 4th term candidate. I also taught some candidates in 1977 onwards, though I think the only Maths candidates were for Oxford. I certainly have some Cambridge Maths for Scientists papers.

I remember one wonderful projectile question about Harold (he of the Battle of Hastings). It told you facts about his eye height, how far behind a wall he was standing, how fast the arrow left the Norman's bow, etc and then asked you whether he could be shot in the eye (or something along those lines).

I'll see what I can find.

Reply 26

nulli tertius

OP

Original post by Gregorius

I did, rapidly dropping the "with Physics" option when advised against it by our Directors of Study, went on to do Part III and then off to Warwick for a PhD and then off into the big wide world...

It's been fascinating comparing the entrance process of my day with what my daughter has just (successfully) gone through (NatSci, not Maths, though!) We turned up for our interviews (post A-level) to be met with "...well you're clearly a clever chap, but we don't take any notice of A-levels, we have our own entrance exam..."

Thank you.

Knowing what we know now, it is a pity you didn't answer General Paper question 3 (i) (i) by offering a dialogue on the subject of Jim'll Fix It

"You do not have to say anything but anything you do say may be taken down and used in evidence"

Reply 27

Original post by tiny hobbit

I must have some upstairs somewhere. I took 501 - 503 in 1972 as a 4th term candidate. I also taught some candidates in 1977 onwards, though I think the only Maths candidates were for Oxford. I certainly have some Cambridge Maths for Scientists papers.

I remember one wonderful projectile question about Harold (he of the Battle of Hastings). It told you facts about his eye height, how far behind a wall he was standing, how fast the arrow left the Norman's bow, etc and then asked you whether he could be shot in the eye (or something along those lines).

I'll see what I can find.

Very nosey, but did you get in? Taking these as a 4th term student is mightily impressive!

Also, how did the Oxford system compare to Cambridge? Was it another set of entrance exams of similar difficulty?

Reply 28

tiny hobbit

15

Original post by shamika

Very nosey, but did you get in? Taking these as a 4th term student is mightily impressive!

Also, how did the Oxford system compare to Cambridge? Was it another set of entrance exams of similar difficulty?

Yes I got in. Most female applicants were 4th term candidates. I don't remember having any choice as to which exams I took.

From what I remember, the Oxford system was similar, with 3 exams for Mathematicians and a separate Maths for scientists paper, but I'll have a look this afternoon.

Reply 29

Gregorius

14

Original post by shamika

Also, how did the Oxford system compare to Cambridge? Was it another set of entrance exams of similar difficulty?

I'd be interested in Tiny Hobbit's take on this too. From my memory, we used past Oxford entrance papers to practice for the Cambridge exams (in addition, of course, to Cambridge past papers) and my memory of them was that they were of similar difficulty to 501-3 at least.

Reply 30

lai812matthew

10

Out of curiosity . after the reform of a levels next year would entrance examination used again for Cambridge. (consider 2x years ago the a level system are linear)

Reply 31

Doones

Original post by lai812matthew

Out of curiosity . after the reform of a levels next year would entrance examination used again for Cambridge. (consider 2x years ago the a level system are linear)

See Christ's AT thread (started today) for the answer to that.

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Reply 32

nulli tertius

OP

Original post by Gregorius

I'd be interested in Tiny Hobbit's take on this too. From my memory, we used past Oxford entrance papers to practice for the Cambridge exams (in addition, of course, to Cambridge past papers) and my memory of them was that they were of similar difficulty to 501-3 at least.

One difference is that at Oxford there wasn't a separate general paper for scientists. Everyone did the same General Paper 1 other than mathematicians who (at least by the end) were exempt.

Reply 33

DFranklin

18

Original post by shamika

Thanks for these, I've never seen a 504 paper before. The questions are certainly harder than STEP. I actually want to try some of these now!

One thing I notice about the older papers is that the difficulty seems to be all over the map.

For that 504 paper, looking at it I'd say that

Q4, 8 and 9 are obviously approachable to someone doing STEP III now, and Q16 would have been reasonably straightforward to someone "doing STEP III with the typical syllabus from back then". Q15 is a bit borderline.

And these are exactly the questions circled, so I assume whoever owned the paper felt the same way.

Edit: on the flip side, I have absolutely NO IDEA how you would even begin Q6 on that paper. I don't think it's just syllabus divergence, either.

(edited 8 years ago)

Reply 34

Original post by DFranklin

One thing I notice about the older papers is that the difficulty seems to be all over the map.

For that 504 paper, looking at it I'd say that

Q4, 8 and 9 are obviously approachable to someone doing STEP III now, and Q16 would have been reasonably straightforward to someone "doing STEP III with the typical syllabus from back then". Q15 is a bit borderline.

And these are exactly the questions circled, so I assume whoever owned the paper felt the same way.

Edit: on the flip side, I have absolutely NO IDEA how you would even begin Q6 on that paper. I don't think it's just syllabus divergence, either.

Thought Q3 looked OK and Q16 looks approachable.

Didn't think Q8 looks that easy, unless I'm missing something obvious. I liked Q2 (which unless I've done something wrong in my head, is fairly straightforward for someone who has done some uni maths).

Reply 35

Gregorius

14

Original post by DFranklin

For that 504 paper, looking at it I'd say that

Q4, 8 and 9 are obviously approachable to someone doing STEP III now, and Q16 would have been reasonably straightforward to someone "doing STEP III with the typical syllabus from back then". Q15 is a bit borderline.

And these are exactly the questions circled, so I assume whoever owned the paper felt the same way.

Very perceptive observations! My school had adopted the SMP (School Mathematics Project) syllabus, which one might identify as one of the precursors of syllabuses today. So my choice of questions on this paper does reflect a "modern" syllabus bias.

I was cross with myself at the time for not getting Q1 out, as a question in similar style had been set on the "S"-level exam paper in the previous summer and I'd done that fully. It's the sort of question that would quite happily come up in Tripos IA these days, if a probablity theorist was feeling mean.

Edit: on the flip side, I have absolutely NO IDEA how you would even begin Q6 on that paper. I don't think it's just syllabus divergence, either.

Similarly, question 6 is an example of a question absolutely bang-spot-on aimed at the previous generation syllabus when a considerable amount of attention was aimed at classical conic sections and projective geometry.

(edited 8 years ago)

Reply 36

DFranklin

18

Original post by shamika

Thought Q3 looked OK and Q16 looks approachable.

Q3 looks like it's either OK (most likely) or horrible and without doing it it's hard to be sure which.

Q16 is easy enough if you've seen something like it before. I think people prepping for 503/504 back then would have found it one of the easier questions (I was aware of the concepts involved when I did my exams), but I think most people now aren't very comfortable with cross products.

Didn't think Q8 looks that easy, unless I'm missing something obvious. I liked Q2 (which unless I've done something wrong in my head, is fairly straightforward for someone who has done some uni maths).

Q8 spoiler

It took me a few minutes to get through the verbiage of Q2 but other than that I also think it's straightforward - more a matter of bookkeeping than anything else. Like you I might be missing something though.

Q11 looks surprisingly "routine". I can believe it gets a little messy, but to be honest my feeling is it doesn't get that bad.

The first result in Q12 looks like it falls to just "bashing through" without too much difficulty. (i.e. form the obvious area integral and split out terms). Given that result I assume the last bit will fall to parallel + perpendicular axes theorems without too much pain.

Q13 + Q14 look fairly hideous.

Would be interested in your thoughts on Q10. Feels that's definitely one where finding a correct method is a huge part of the battle.

Reply 37

Original post by jneill

See Christ's AT thread (started today) for the answer to that.

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Do you mind posting the precise link to the AT's answer on this? It's already got 80+ posts!

Reply 38

DFranklin

18

Original post by Gregorius

Similarly, question 6 is an example of a question absolutely bang-spot-on aimed at the previous generation syllabus when a considerable amount of attention was aimed at classical conic sections and projective geometry.

Would that have been true even for "non-CCE" applicants?

FWIW I think the earliest non-CCE questions I did were some FM S-level questions from 1980 and although conics were covered it was very much a cartesian approach. (It also always seemed to me that the conics questions were by far the hardest in the normal FM A-level. So it made no sense for people to attempt them in the exams).

Reply 39