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Trinity Admissions Test Solutions

@Jordan\ Youshould also add the solutions for the downing college one for more practice

http://www.dow.cam.ac.uk/documents/ta/Applications/Maths_test.pdf

Reply 81

username1763791

OP

4

Original post by FutureOxford3

@Jordan\ Youshould also add the solutions for the downing college one for more practice

http://www.dow.cam.ac.uk/documents/ta/Applications/Maths_test.pdf

Yeah, of course! I'll add it to the OP.

Reply 82

FutureOxford3

2

Original post by Zacken

Very much so, the questions test general maths and will be useful practice for any college including Oxford. :smile:

Oxford is not a college tho :P

Reply 83

username1162972

18

Original post by Krollo

Two pleasingly different solutions. What maths is all about, perhaps

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The final answer is correct but after spotting that pattern it has been assumed it holds for all n, I would prove it by induction then let n=1000.

I can't found who did the A one, but I can't find so maybe Krollo can make me find the solution-er.
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(edited 8 years ago)

Reply 84

username1763791

OP

4

Original post by physicsmaths

The final answer is correct but after spotting that pattern it has been assumed it holds for all n, I would prove it by induction then let n=1000.

I can't found who did the A one, but I can't find so maybe Krollo can make me find the solution-er.
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Hence why I deleted it

Reply 85

username1162972

18

Original post by Jordan\

Hence why I deleted it

I thought i just could not find it. Assume it holds for. K, show it holds for k+1 (by multiplying by A) and that's it.

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Reply 86

username1162972

18

Did that Z(root2) question on paper, I will write it up soon whilst I learn latex..

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Reply 87

Renzhi10122

11

Original post by physicsmaths

Did that Z(root2) question on paper, I will write it up soon whilst I learn latex..

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Pell equation!

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Reply 88

username1162972

18

Original post by Renzhi10122

Pell equation!

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Yep! Amazing stuff that is

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Reply 89

Zacken

22

Original post by FutureOxford3

@Jordan\ Youshould also add the solutions for the downing college one for more practice

http://www.dow.cam.ac.uk/documents/ta/Applications/Maths_test.pdf

We figured those were far too elementary to provide solutions for. You can check your answers with a quick WA computation.

(edited 8 years ago)

Reply 90

FutureOxford3

2

Original post by Zacken

We figured those were far too elementary to provide solutions for. You can check yoir answers with a quick WA computation.

What is the answer to 5 and 6 then?

Reply 91

Zacken

22

Original post by FutureOxford3

What is the answer to 5 and 6 then?

Don't have the paper with me, but the question is a straightforward sketch and calculus problem. You can check your answers using WA.

Six is admittedly hard, but it's not worth providing 8 solutions if we only really need it for 1 question.

Reply 92

FutureOxford3

2

Original post by Zacken

Don't have the paper with me, but the question is a straightforward sketch and calculus problem. You can check your answers using WA.

Six is admittedly hard, but it's not worth providing 8 solutions if we only really need it for 1 question.

Yea, the only one I can't do is number 6. I will just ask Jordan or physicsmath to help me then.

Reply 93

ForeignStudent34

1

Original post by Krollo

Specimen 2, Q7

Hint

Spoiler

Solution

Spoiler

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Um, didn't the question ask for 2^n+1 not a^n+1? Also, when a = 8 n =2 you get 65.

Reply 94

username1162972

18

Original post by ForeignStudent34

Um, didn't the question ask for 2^n+1 not a^n+1? Also, when a = 8 n =2 you get 65.

Well, they tell you to look at a^n -1 first and see what you can notice, they then want you to notice a form of a^n+1
And then factor and see what you can see when a=2. I have not read through Krollos solution but i trust it is correct as his structure/idea looks fine imo.

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Reply 95

username1162972

18

I think in general they want to see 2^n+1=2^n-(-1)=(3)(some integer) if n is odd 2^n+1 is prime only when n=1 then do a similar thing for n is even, which krollo has done but to a greater depth.

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