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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.

GOOD LUCK!

(edited 8 years ago)

Scroll to see replies

So we post solutions for them to be put in? If so I have one for Q2. Also I am not a Trinity applicant, but do you think these questions are worthwhile doing to prepare for my St John's interview (if I get one)?

Edit: Whoops Zacken beat me to it anyway :-)

Edit: Whoops Zacken beat me to it anyway :-)

Original post by 16Characters....

So we post solutions for them to be put in? If so I have one for Q2. Also I am not a Trinity applicant, but do you think these questions are worthwhile doing to prepare for my St John's interview (if I get one)?

Edit: Whoops Zacken beat me to it anyway :-)

Edit: Whoops Zacken beat me to it anyway :-)

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

Original post by 16Characters....

So we post solutions for them to be put in? If so I have one for Q2. Also I am not a Trinity applicant, but do you think these questions are worthwhile doing to prepare for my St John's interview (if I get one)?

Edit: Whoops Zacken beat me to it anyway :-)

Edit: Whoops Zacken beat me to it anyway :-)

Definitely - these will be helpful for any college interview. I myself have applied to Pembroke, and Zacken^ for Kings I believe

Also, If you're solution is any different in the approach it'll still be useful to post it!

Original post by Jordan\

Definitely - these will be helpful for any college interview. I myself have applied to Pembroke, and Zacken^ for Kings I believe

Also, If you're solution is any different in the approach it'll still be useful to post it!

Also, If you're solution is any different in the approach it'll still be useful to post it!

Nope it's pretty much identical. And best of luck to you all :-)

Speciment Test 1, Question 6

Hints

Spoiler

Solution

Spoiler

(edited 8 years ago)

Specimen Test 1 Question 4

Hint:Solution:

Hint:

Spoiler

Spoiler

Original post by Number Nine

Specimen Test 1 Question 4

Hint:Solution:

Hint:

Spoiler

Spoiler

Spoiler

Speciment Test 1, Question 8

HintSolution

Hint

Spoiler

Spoiler

(edited 8 years ago)

SPECIMEN TEST 1, QUESTION 5

HintsSolution

Hints

Spoiler

Spoiler

(edited 8 years ago)

Original post by Jordan\

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.

They may also just ignore any complete solutions that you have done and ask you about the questions you hadn't attempted. This is what happened to my son (several years back).

Original post by atsruser

Question 3

Spoiler

Spoiler

Could anyone help me with question 10 of this paper:

https://share.trin.cam.ac.uk/sites/public/Tutorial/Admissions-UG/sampletest3.pdf

Do I assume that volume of the dust is equal to the volume of the spaceship? Do I also assume that the spaceship has unit length, so the volume equals the cross sectional area? And also my answer has the constant velocity,'u', in it- is it not meant to?

Thank you.

https://share.trin.cam.ac.uk/sites/public/Tutorial/Admissions-UG/sampletest3.pdf

Do I assume that volume of the dust is equal to the volume of the spaceship? Do I also assume that the spaceship has unit length, so the volume equals the cross sectional area? And also my answer has the constant velocity,'u', in it- is it not meant to?

Thank you.

Original post by tiny hobbit

They may also just ignore any complete solutions that you have done and ask you about the questions you hadn't attempted. This is what happened to my son (several years back).

Ah, ok thank you I'll put that in the OP now!

Original post by DFranklin

Spoiler

You're right. Damn. sin^2 breaks this. Haven't got time to think about it in detail now. I'll delete that post forthwith.

Original post by -Gifted-

Could anyone help me with question 10 of this paper:

https://share.trin.cam.ac.uk/sites/public/Tutorial/Admissions-UG/sampletest3.pdf

Do I assume that volume of the dust is equal to the volume of the spaceship? Do I also assume that the spaceship has unit length, so the volume equals the cross sectional area? And also my answer has the constant velocity,'u', in it- is it not meant to?

Thank you.

https://share.trin.cam.ac.uk/sites/public/Tutorial/Admissions-UG/sampletest3.pdf

Do I assume that volume of the dust is equal to the volume of the spaceship? Do I also assume that the spaceship has unit length, so the volume equals the cross sectional area? And also my answer has the constant velocity,'u', in it- is it not meant to?

Thank you.

I don't think you need the length of the spaceship, or to assume anything about the volume of the dust, but, I do think you have to assume that dust only sticks to the front of the ship. I'm not sure if my solution is correct or not, but here it is:

Spoiler

(edited 8 years ago)

Original post by Jordan\

Zacken^ for Kings I believe

ah, some competition for me, then :P

What made you choose Pembroke? I hear the food's fantastic.

Original post by Zacken

x

We may see each other at the interviews. ^^ Why King's, if you don't mind me asking?

(edited 8 years ago)

Original post by StrangeBanana

I don't think you need the length of the spaceship, or to assume anything about the volume of the dust, but, I do think you have to assume that dust only sticks to the front of the ship. I'm not sure if my solution is correct or not, but here it is:

Spoiler

Thanks a ton, it makes sense to me. However, I used conservation of mechanical energy, but that yielded a different result where the velocity doesn't cancel out. Let me scan it.

Specimen Test 1, Question 7

HintSolution

Hint

Spoiler

Spoiler

(edited 8 years ago)

- math at cambridge trinity or churchill
- Official University of Wales Trinity Saint David 2025 Applicant Thread
- The Official Leeds Trinity University Applicants for 2025 Entry Thread
- International Student Cambridge vs Oxford Mathematics
- Worth applying to Trinity as a state comprehensive student
- Weakest Cambridge Medicine offer holder
- Tringineering prep
- Official Trinity Hall Applicants 2022 Entry
- Getting into Econ at Cambridge +UCL, Imperial, LSE and Warwick. Do I have a chance?
- Should i try apply for oxbridge this late?
- Official University of Manchester 2025 Applicant Thread
- Cambridge Trinity Maths Interview 2023
- Discrimination Univ of Sunderland Online Masters Enrolment team/HigherEd Partners
- Is it worth applying to Trinity?
- Which Cambridge colleges give the best chance of acceptance to engineering?
- Imperial admission test then interview
- I feel like a failure
- Most difficult Cambridge colleges to get into for maths
- ENGAA 2023 Worked Solutions - ESAT Preperation
- How competitive is trinity college Cambridge for law?

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