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Oxford Maths Test - HSN forum

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Oxford Maths Test


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#1 Vixus

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Posted 24 November 2005 - 04:47 PM

Yaaagh! I just got invited for an interview at Oxford. As happy as this makes me feel, I just saw the Maths for Physicists exam.

http://www.admissions.ox.ac.uk/interviews/tests/MathPhy.pdf

The stuff covered here I haven't even learnt in school yet (I only just finished Unit 1 of AH Maths!) The only thing I can do however, is the differentiation. There could be topics covered that aren't in this sample paper and I haven't gone over at school! Help!

So what do you suggest I do? Go over these questions with my Maths teacher? -Well, I did... got loads of help. This test isn't so bad after all.


Solutions

1 Laws of logs and indices.
(i)
ln(x^3) - ln(5) = ln(200)

ln(x^3 /5) = ln(200)

x^3 / 5 = 200

x^3 = 1000

x = 10

(ii)
x^4 = 0.0081

This is easiest to solve with fractions. Keep in mind that
9/100 = 0.09

x^4 = 0.09^2

x^4 = (x^2)^2 = 0.09^2

x = \pm0.3

We want real solutions only, so:
x = 0.3

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2 I haven't actually done this yet, so I guess I'll have to read the textbook notes on this, but at least they're in there!

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3 Ah, fun fun number juggling. I edited the diagram a little bit.
user posted image

The large circle has radius 2r, the smaller circle r.

Basic calculation here is
A = SAACD - AEAF - 1/2AB

Simple enough, right? So,

SA = \theta /360 \times \pi (2r)^2

SA = 90/360 4\pi r^2

SA = (4\pi r^2)/4

SA = \pi r^2

Then I seperate the triangle into two smaller ones cuz I rock:

A_{EAF} = 2 x \frac{1}{2} r \times r

A_{EAF} = r^2

Last but not least:

A_{B} = \pi r^2

So, let's lob it all in.

Area = SA - A_{EAF} - A_{B}

Area = \pi r^2 - (\frac{1}{2}(\pi r^2) + r^2)

Area = (2\pi r^2)/2 - ((\pi r^2)/2 + r^2)

Area = \pi r^2 - r^2

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4 Easy peasy, just write out the numbers involved.
(i) Total must be 6 => combinations are:
1,5 / 2,4 / 3,3 / 4,2 / 5,1 (5 in all)

36 combinations are available in total (6x6)

=> 5/36

(ii) Draw out a grid of first numbers (1-6) against second number (1-6) and tick of all the ones where 2nd > 1st. It forms a nice little triangle and you'll find their are 15 such combos.

=> 15/36 (or 5/12 to be pedantic)

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5 Everyone can do this.
(i) Differentiate for f'(x), do f'(x) = 0... careful about that range!
(ii) Use the double derivative f''(x). Remember, if it's +ve it's a minimum, if it's -ve it's a max... if you get 0 have fun with the nature table!

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6 Solve graphically. Very important and easy.
The trick here is not to find the numerical solutions as that's impossible without a calculator. It just asks how many solutions there are. You'll find there are two. One when both sinx and tanx are +ve and one where they are both -ve. (+0.001)

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7 Straight lines and circles. Perpendicular gradients.... Higher stuff wink.gif

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8
a) Simple integration methinks.
b) Haven't done by parts yet, need to read textbook.

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9 Still thinking about this one, I'm afraid. If anyone has any ideas, SCREAM!

#2 dfx

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Posted 24 November 2005 - 05:44 PM

You have PM.

It seems easier (to relate to) than the Cambridge STEP papers.

#3 Bridget

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Posted 24 November 2005 - 06:09 PM

I wouldn't be fooled by the Oxford maths exam called "Mathematics for Physicists" - although the specimen paper looks fairly easy the actual exam is almost impossible (sorry!). I sat it last year and it asked the most obscure questions possible... the majority of which were not covered in the AH syllabus. Then you'll have at least 2 interviews - one involves the usual "Why did you choose Oxford?" type questions and a couple of questions on topics you've covered recently in maths and physics at school. The second will be mainly deriving formula (some things you won't have seen before) on a white-board for the interviewer which was easier.
Good Luck ! smile.gif

#4 dfx

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Posted 24 November 2005 - 06:13 PM

Ah.. no wonder.. it isn't the pure math exam - I was kinda surprised. That's what you get for not reading the title!

#5 broughy

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Posted 24 November 2005 - 09:23 PM

er, i'm in 2nd year studying physics (at strathclyde - not quite oxford, but hey, it'll do me fine!) & i've only seen about 3/4 of that paper before!
when i'm dancin' with you,
tomorrow doesn't matter,
turn that music up,
till the windows start to shatter,
cos you're the only one who can get me on my feet,
& i can't even dance

No Tomorrow - Orson

#6 Vixus

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Posted 25 November 2005 - 06:52 PM

Well... does this mean I'm doomed or do you still have a chance even if you fail the test? biggrin.gif

#7 Bridget

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Posted 25 November 2005 - 09:56 PM

It depends on lots of factors. However, remember that last year, Oxford's total intake of scottish students dropped from around 7% to about 1.2% ohmy.gif Even then, the majority of those applicants came from the best schools in Scotland...

#8 Vixus

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Posted 26 November 2005 - 10:43 AM

Ha! Probably won't get in anyway... but I've got offers from London and HW so far... so no big deal, I guess. I'm lucky just to be called for the interview, methinks.

#9 dfx

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Posted 26 November 2005 - 01:00 PM

What London one? And inviting you for interview means that they are considering you seriously. Well they are givin you the chance to shine at the interview and test.

#10 Vixus

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Posted 26 November 2005 - 03:00 PM

QUOTE(dfx @ Nov 26 2005, 01:00 PM)
What London one? And inviting you for interview means that they are considering you seriously. Well they are givin you the chance to shine at the interview and test.

View Post


University College London. As for the interview, that should be ok... but it's the test I'm worried about, y'see?


#11 dfx

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Posted 26 November 2005 - 09:11 PM

Ah.. cool.. had my UCL interview two weeks back and I'm awaiting a reply.

#12 Vixus

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Posted 26 November 2005 - 11:40 PM

They took me without an interview, said it would be too inconvenient getting me down to London. smile.gif
Damn that test!

#13 Vixus

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Posted 28 November 2005 - 06:58 PM

*Bump!

Got you all! This is actually easier than it looks. Got some help from my maths teacher.
I'll post solutions in the first post.

#14 Bridget

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Posted 29 November 2005 - 12:11 AM

QUOTE(Bridget @ Nov 24 2005, 07:09 PM)
although the specimen paper looks fairly easy the actual exam is almost impossible

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Wait until you see the real thing before saying it's easier than it looks tongue.gif !

#15 Vixus

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Posted 29 November 2005 - 05:37 PM

QUOTE(Bridget @ Nov 29 2005, 12:11 AM)
QUOTE(Bridget @ Nov 24 2005, 07:09 PM)
although the specimen paper looks fairly easy the actual exam is almost impossible

View Post



Wait until you see the real thing before saying it's easier than it looks tongue.gif !

View Post


Yeah, I know, but I'm counting on finding a logical answer to stuff (yeah right.) Bet my brain wimps out. XD
Anyway, better making a good impression at the interview than being one of those nerdy kids that has no life skills. smile.gif





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