Trinity Admissions Test Solutions

Hi, please could you explain how you realised it was 2n!/n!2^n in solution 1?

What happened to the 4th paper / maths with physics paper, sorry?

I'll hunt around a bit - might be able to track down a copy somewhere in my downloads.

Posted from TSR Mobile

Since you're only tossing the same coin 9 times, the ninth time should be independent of the first 8.

Therefore the correct solution is
Method 1:


Method 2:

Welcome to the Trinity Admissions Test Solutions Thread. This is the place to discuss, post problems, or ask any questions you may have regarding the exam before your interview!

Here we are going to post solutions to all of the sample Trinity College Cambridge Admissions Tests available online, in the hope to help those preparing for interviews in the coming years. These tests will be useful preparation for all Cambridge Colleges, and Oxford for any mathematical interview.

We do ask that any solutions are spoilers, and, if you are stuck with any questions to first ask for any hints or look at the hints given before the TSR solutions.

When preparing for your interview at Trinity College specifically, please remember that you are not expected to answer all of the questions, or necessarily to give complete answers to questions. You should just attempt those that appeal to you, and they will be used as a basis for discussion in the interview that follows. It has also been mentioned that they will most likely ignore any full solutions you have done in the test, and have you attempt the questions you have not done.

Once finished, each solution will be linked below to the relevant post!



SPECIMEN TEST I
1. Solution by Edothero
2. Solution by Zacken
3. Solution by Zacken
4. (1) Solution by Number Nine (2) DFranklin
5. Solution by Jordan\
6. Solution by 16Characters...
7. Solution by 16Characters...
8. Solution by 16Characters...
9. Solution by Joostan
10. Solution by Edothero; Part C by DFranklin

SPECIMEN TEST II
1. (1) Solution by Zacken (2) DFrankin
2. Solution by Zacken
3. Solution by Krollo
4. Solution by Zacken
5. Solution by MadChickenMan
6. Solution by Jordan\
7. Solution by Krollo
8. Solution by Renzhi10122
9. Solution by Joosten
10. Solution by Krollo /with some further comments (1) astruser (2) DFranklin


SPECIMEN TEST III
1. Solution by Joostan
2. Solution by Joostan
3. Solution by Hauss
4. Solution by ManChickenMan
5. Solution by Krollo
6. Solution by Joostan
7. Solution by Krollo
8. Solution by Euclidean
9. Solution by MadChickenMan
10. Solution by Krollo

SPECIMEN TEST IV
1. Solution by Krollo
2. Solution by 16Characters
3. Solution by Zacken
4.
5. Solution by Krollo
6. Solution by joostan
7. Solution by Krollo
8. Solution by Mop3476
9. Solution by Krollo
10. Solution by Krollo

Maths and Physics Paper I

We have also came across the Downing Admissions Paper,
where you can also find the solutions to below:
1.
2.
3.
4. Solution by Number Nine
5.
6.
7.
8.

Anyone saved copies of the sample test IV or Downing Admission Paper ? It seems that these two papers have been removed
Help....

The problem with your logic is that you assume that a new coin is picked in the 9th toss. In this regard your calculation is flawless. However, the thing is that the same coin from previous 8 tosses is used, and we don't know whether it is real or fake. So we have to draw inferences upon this from the given fact -- 8 heads were obtained. The original solution is in fact correct, using the conditional probability model (u might encounter this in S1 if u are doing CIE). It turns out that the chance (clearly this is not reality, but as we don't know the nature of the coin we just establish a model) of the coin being fake and real are 2/3 and 1/3 respectively.

BTW: Chinese?

The Downing Admissions Paper was largely useless and easy, so I wouldn't worry too much about that missing. I'll see if I have a copy of IV on my computer, but I doubt it.

Yeah Chinese you too?
I did S1 and S2 lol (2 years ago) but i don't understand how its 1/3 and 2/3 pls explain :'

From Zhejiang~
It's very nice to meet you here ! (Are you applying to Cambridge this year?)

Total possibility of getting 8 heads (taking into account both situations of picking a biased or an unbiased coin at first):

The original proof is a formulated one, so you may want to find your S1 text and revise on conditional probability (2 years is a long time....

PS: I was doing the sample paper II and found that Question 5 resembles this one (probably it's a bit harder) You might have a go at it!

ooh i'm from singapore but i'm technically local in the UK.
Yeah I'm applying this year for Engineering so statistics isn't too important hehe. I'll have a go anyway! I know how to use conditional probability, but I just didn't (and still kinda don't haha) see how the 9th throw depends on the last 8 because to me it doesn't look like it does... but I'll have another think about it
Did you apply for maths?

How is ENGAA going?
I applied to maths at Queens' and got the invitation last week. From the TSR stalking sheet, however, my choice is super popular and many of the applicants are competitive international students.
So I don't know... Just try my best. At least I have IC, NUS, Waterloo and UC (as if I can travel around the globe lol

Test 2, Question 2:

Solution:

Part 1:

Hi, Please could you elaborate a little on the part where you say, "This gives (by multiplying the integrand by... ) " -- you seem to be multiplying the integrand by a fraction essentially equal to one which then allows you to split it into two separate integrands. Is this correct?

Thanks!

yes

Test 3, Question 7:
Thanks to Krollo for this solution.


Hints:

Solution: