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)

(ii)

This is easiest to solve with fractions. Keep in mind that

We want real solutions only, so:

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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.

The large circle has radius

*2r*, the smaller circle

*r*.

Basic calculation here is

*A = SA*

_{ACD}- A_{EAF}- 1/2A_{B}Simple enough, right? So,

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

Last but not least:

So, let's lob it all in.

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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

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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!