Cryptokyo
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TMUA Preparation Thread 2019

Welcome to the TMUA preparation thread 2019!!! This a place to discuss the TMUA exam for 2020 entry, discuss past paper problems and to ask any questions you may have!

The TMUA is the new kid on the block in terms of mathematics tests for university admissions so it doesn't quite have the notoriety of the MAT or STEP. Although, the TMUA may offer an alternative route to getting an offer so do look at the university websites and it is applicable to lots of universities! Also, it is in October as to not clash with an A-Level papers unlike STEP.

What is the TMUA?

The TMUA is a pre-university application maths exam sat at the end of October. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and universities cannot see your score unless you release it to them via the online results system. Thus, it is a test that only advantages applicants rather than disadvantages them.

The test is comprised of two 75 minute non-calculator papers, each with 20 multiple choice questions. The questions are based on AS maths level content and thus no special preparation is required prior to sitting the exam. The official page for the TMUA, with practice materials, can be found here: http://www.admissionstestingservice....ity-admission/

Who uses the TMUA?

A list of universities that consider the TMUA in some capacity:

  • The University of Bath
  • Cardiff University
  • Durham University
  • Lancaster University
  • London School of Economics and Political Science
  • The University of Nottingham
  • The University of Sheffield
  • The University of Southampton
  • The University of Warwick

Further details can be found on their respective websites as each university handles the test differently with respect to admissions. Some universities give lowered offers for sufficiently good performance on this test.

Important information

The key dates for the TMUA are as follows:

  • 1st September: Registration opens
  • 1st October: Registration deadline with standard fee
  • 15th October: FINAL REGISTRATION DEADLINE (with higher fee)
  • 30th October: TMUA exam
  • 27th November: Results are released

Your schools exams office should be able to sort this for you.

How to prepare

Practice is really the key to this test. There are a variety of ways which you can practice the sort of problems that could come up such as doing problems from the UKMT Intermediate and Senior Maths Challenges and the Kangaroo papers. The MAT may also offer some good practice with its multiple choice section. I would strongly advise looking through the notes on Logic and Proof on the "preparing for the test" section on the TMUA website as these topics can come up and are not really covered fully in the A-Level syllabus.

Key scores

Overall mark out of 40 required to achieve a 6.5 each year:

  • 2016: 21 marks
  • 2017: 24 marks
  • 2018: 24 marks

FYI

I'm a 3rd Year studying maths at Durham who sat the TMUA in its inaugural year (2016) and have created this thread as a place to get help and advice. Unfortunately, last year due to personal circumstances I was unable to properly engage in the thread but this year I should be at least once a day to answer questions people may have.

Problem 1
Rationalise the denominator of \frac{1}{1+\sqrt{2}+\sqrt{3}}

Answer
Spoiler:
Show
\frac{2+\sqrt{2}-\sqrt{6}}{4}

Problem 2
Let a and b be two integers such that 2a+b=ab. How manys pairs of a and b exist?

Answer
Spoiler:
Show
4


Problem 3
Let a_{i}=\frac{i!}{i+1}. Find the prime factorisation of a_{1} \times a_{2} \times \cdots \times a_{11}

Answer
Spoiler:
Show
2^{36} \times 3^{16} \times 5^{7} \times 7^{4}

Problems file attached to this post (will be updated over time, check version number). I have not added solutions to the problems on the sheet so you'll need to contact me or talk with others to check your answer.

This post will be updated as time goes on
Attached files
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Hapax_42
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Was waiting for something like this, forums are really helpful just knowing other people are in the same boat and discussing ideas etc. Hopefully it gets more active as we near the date XD
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Cryptokyo
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(Original post by Hapax_42)
Was waiting for something like this, forums are really helpful just knowing other people are in the same boat and discussing ideas etc. Hopefully it gets more active as we near the date XD
Yeah hopefully more should join! But the admissions testing service have released detailed solutions for the 2017 an d 2018 paper so a lot of support particularly queries regarding questions is already available.

But we'll see how it goes :dontknow:
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JDudd161
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Is the
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JDudd161
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Is the TMUA required for Durham?
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Cryptokyo
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Is the TMUA required for Durham?
You don't need it to get it in. But it does help as Durham receive MAT and TMUA scores before making offers so it can very much boost your application. You can always decide if you want to share your TMUA score with Durham.

The possible offers for A-Level students are:

  • A*AA (or A*A*B) + >6.5 in the TMUA
  • A*AA (or A*A*B) + MAT (at a suitable score)
  • A*AA (or A*A*B) + 1 in any STEP paper
  • A*A*A
  • A*AAa (where 'a' denotes an A in AS Further Maths)


See here for more details (particularly if you don't do A-Levels!): https://www.dur.ac.uk/mathematical.s...ternateoffers/

Basically you always need an A* in maths (and an A* in further maths with no extra papers)
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JDudd161
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(Original post by Cryptokyo)
You don't need it to get it in. But it does help as Durham receive MAT and TMUA scores before making offers so it can very much boost your application. You can always decide if you want to share your TMUA score with Durham.

The possible offers for A-Level students are:

  • A*AA (or A*A*B) + >6.5 in the TMUA
  • A*AA (or A*A*B) + MAT (at a suitable score)
  • A*AA (or A*A*B) + 1 in any STEP paper
  • A*A*A
  • A*AAa (where 'a' denotes an A in AS Further Maths)


See here for more details (particularly if you don't do A-Levels!): https://www.dur.ac.uk/mathematical.s...ternateoffers/

Basically you always need an A* in maths (and an A* in further maths with no extra papers)
Perfect, thanks for the reply
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physchem19
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(Original post by Cryptokyo)

TMUA Preparation Thread 2019

Welcome to the TMUA preparation thread 2019!!! This a place to discuss the TMUA exam for 2020 entry, discuss past paper problems and to ask any questions you may have!

The TMUA is the new kid on the block in terms of mathematics tests for university admissions so it doesn't quite have the notoriety of the MAT or STEP. Although, the TMUA may offer an alternative route to getting an offer so do look at the university websites and it is applicable to lots of universities! Also, it is in October as to not clash with an A-Level papers unlike STEP.

What is the TMUA?

The TMUA is a pre-university application maths exam sat at the end of October. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and universities cannot see your score unless you release it to them via the online results system. Thus, it is a test that only advantages applicants rather than disadvantages them.

The test is comprised of two 75 minute non-calculator papers, each with 20 multiple choice questions. The questions are based on AS maths level content and thus no special preparation is required prior to sitting the exam. The official page for the TMUA, with practice materials, can be found here: http://www.admissionstestingservice....ity-admission/

Who uses the TMUA?

A list of universities that consider the TMUA in some capacity:

  • The University of Bath
  • Cardiff University
  • Durham University
  • Lancaster University
  • London School of Economics and Political Science
  • The University of Nottingham
  • The University of Sheffield
  • The University of Southampton
  • The University of Warwick

Further details can be found on their respective websites as each university handles the test differently with respect to admissions. Some universities give lowered offers for sufficiently good performance on this test.

Important information

The key dates for the TMUA are as follows:

  • 1st September: Registration opens
  • 1st October: Registration deadline with standard fee
  • 15th October: FINAL REGISTRATION DEADLINE (with higher fee)
  • 30th October: TMUA exam
  • 27th November: Results are released

Your schools exams office should be able to sort this for you.

How to prepare

Practice is really the key to this test. There are a variety of ways which you can practice the sort of problems that could come up such as doing problems from the UKMT Intermediate and Senior Maths Challenges and the Kangaroo papers. The MAT may also offer some good practice with its multiple choice section. I would strongly advise looking through the notes on Logic and Proof on the "preparing for the test" section on the TMUA website as these topics can come up and are not really covered fully in the A-Level syllabus.

FYI

I'm a 3rd Year studying maths at Durham who sat the TMUA in its inaugural year (2016) and have created this thread as a place to get help and advice. Unfortunately, last year due to personal circumstances I was unable to properly engage in the thread but this year I should be at least once a day to answer questions people may have.

Problem 1
Rationalise the denominator of \frac{1}{1+\sqrt{2}+\sqrt{3}}

Answer
Spoiler:
Show
\frac{2+\sqrt{2}-\sqrt{6}}{4}

Problem 2
Let a and b be two integers such that 2a+b=ab. How manys pairs of a and b exist?

Answer
Spoiler:
Show
4


Problem 3
Let a_{i}=\frac{i!}{i+1}. Find the prime factorisation of a_{1} \times a_{2} \times \cdots \times a_{11}

Answer
Spoiler:
Show
2^{36} \times 3^{16} \times 5^{7} \times 7^{4}


This post will be updated as time goes on
Hi thanks so much for this thread please could you explain problem 3? I would really appreciate it! Also can you recommend any place I can get questions similar to these.

thank you!
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Cryptokyo
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Hi thanks so much for this thread please could you explain problem 3? I would really appreciate it! Also can you recommend any place I can get questions similar to these.

thank you!
This problem is pretty much about attacking it directly.

So here we have that

a_{1}\times a_{2}\times \cdots \times a_{11} = \frac{1!}{2}\times \frac{2!}{3} \times \cdots \times \frac{11!}{12} = \frac{1!2!3!\cdots 11!}{12!}

Now a bit of cancellation simplifies it from here. But then you need to determine the exponent of each prime that appears in the factorials.

e.g. 4!=4\times 3\times 2\times 1 = 2^{2}\times 3 \times 2 = 2^{3}\times 3.

Hopefully, this gets you a good way there.

If you haven't done the TMUA papers already then they are a good source of similar problems. Slightly more fiendish ones can be found on the Oxford MAT paper. Other than that, I don't particularly know of any source unfortunately.

I may come up with more of my own over time in a little document and publish them here in a week or so

Edit: I'll publish an extended set of problems here on Sunday!!!
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physchem19
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(Original post by Cryptokyo)
This problem is pretty much about attacking it directly.

So here we have that

a_{1}\times a_{2}\times \cdots \times a_{11} = \frac{1!}{2}\times \frac{2!}{3} \times \cdots \times \frac{11!}{12} = \frac{1!2!3!\cdots 11!}{12!}

Now a bit of cancellation simplifies it from here. But then you need to determine the exponent of each prime that appears in the factorials.

e.g. 4!=4\times 3\times 2\times 1 = 2^{2}\times 3 \times 2 = 2^{3}\times 3.

Hopefully, this gets you a good way there.

If you haven't done the TMUA papers already then they are a good source of similar problems. Slightly more fiendish ones can be found on the Oxford MAT paper. Other than that, I don't particularly know of any source unfortunately.

I may come up with more of my own over time in a little document and publish them here in a week or so

Edit: I'll publish an extended set of problems here on Sunday!!!
Thank you ever so much for your answer I understand it much better! I'd really appreciate your extra problems as I'm thinking of leaving the tmua papers for practice although I have attempted the specimen paper which was quite hard! As well as using the logic and proof book they published is there anything else I should use to get better at logic I am doing my best with it. Thank you again for your help
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Cryptokyo
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(Original post by physchem19)
Thank you ever so much for your answer I understand it much better! I'd really appreciate your extra problems as I'm thinking of leaving the tmua papers for practice although I have attempted the specimen paper which was quite hard! As well as using the logic and proof book they published is there anything else I should use to get better at logic I am doing my best with it. Thank you again for your help
The logic guide they have published is the best thing to use as it is directly relevant to the exam and has a more detailed discussion of the ideas than I have seen elsewhere. Other sources may just lead to more confusion.

If you have any problems with logic, just tag me on here and I'll try my best to help!

An important to remember is that this test is meant to be hard. Most likely, you won't be able to answer every question in 75 minutes because it's only 3 minutes 45 seconds per problem and some of the problems make you think very differently to in A-Level. Some of the problems make me stop and think and I'm a maths undergraduate so they are not straightforward! You can still score very well even if you don't necessarily answer all the questions.
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physchem19
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Thank you very much. Yes, I am using the guide as much as I can and day by day I am doing my best to get better at truth tables aghh
I was wondering whether the specimen paper solutions on the TMUA were correct as for paper 2 I got the square root of 11/2 however the answer is saying otherwise and I am really not sure! Thank you very much I will definitely tag you with any questions I'm stuck on. You're really a great help as I am so worried about the test!
And I know it's very hard to manage time on this test and I think your advice is best focus on the questions we can get right.
Thanks again I would rep but it doesn't let me haha
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physchem19
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(Original post by Cryptokyo)
The logic guide they have published is the best thing to use as it is directly relevant to the exam and has a more detailed discussion of the ideas than I have seen elsewhere. Other sources may just lead to more confusion.

If you have any problems with logic, just tag me on here and I'll try my best to help!

An important to remember is that this test is meant to be hard. Most likely, you won't be able to answer every question in 75 minutes because it's only 3 minutes 45 seconds per problem and some of the problems make you think very differently to in A-Level. Some of the problems make me stop and think and I'm a maths undergraduate so they are not straightforward! You can still score very well even if you don't necessarily answer all the questions.
I meant to quote you and it was paper 2 Q1 I was on about!
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Cryptokyo
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(Original post by physchem19)
Thank you very much. Yes, I am using the guide as much as I can and day by day I am doing my best to get better at truth tables aghh
I was wondering whether the specimen paper solutions on the TMUA were correct as for paper 2 I got the square root of 11/2 however the answer is saying otherwise and I am really not sure! Thank you very much I will definitely tag you with any questions I'm stuck on. You're really a great help as I am so worried about the test!
And I know it's very hard to manage time on this test and I think your advice is best focus on the questions we can get right.
Thanks again I would rep but it doesn't let me haha
You are correct, the radius is \sqrt{\frac{11}{2}}. The provided answers match this: https://www.admissionstesting.org/Im...nswer-keys.pdf. You may have just read the wrong answer sheet

Also, if you can't do any of the questions on the day you can have a cheeky guess at them
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physchem19
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(Original post by Cryptokyo)
You are correct, the radius is \sqrt{\frac{11}{2}}. The provided answers match this: https://www.admissionstesting.org/Im...nswer-keys.pdf. You may have just read the wrong answer sheet

Also, if you can't do any of the questions on the day you can have a cheeky guess at them
Thank you! I guess I clicked on the wrong one haha! And that's very true I can always do that! I'm trying to think of the harder log questions like the MAT ones that could come in the exam.
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LiveOnTSR
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Anyone know what a TMUA reduced Warwick offer looks like?
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reggie2001_
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(Original post by Cryptokyo)

TMUA Preparation Thread 2019

Welcome to the TMUA preparation thread 2019!!! This a place to discuss the TMUA exam for 2020 entry, discuss past paper problems and to ask any questions you may have!

The TMUA is the new kid on the block in terms of mathematics tests for university admissions so it doesn't quite have the notoriety of the MAT or STEP. Although, the TMUA may offer an alternative route to getting an offer so do look at the university websites and it is applicable to lots of universities! Also, it is in October as to not clash with an A-Level papers unlike STEP.

What is the TMUA?

The TMUA is a pre-university application maths exam sat at the end of October. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and universities cannot see your score unless you release it to them via the online results system. Thus, it is a test that only advantages applicants rather than disadvantages them.

The test is comprised of two 75 minute non-calculator papers, each with 20 multiple choice questions. The questions are based on AS maths level content and thus no special preparation is required prior to sitting the exam. The official page for the TMUA, with practice materials, can be found here: http://www.admissionstestingservice....ity-admission/

Who uses the TMUA?

A list of universities that consider the TMUA in some capacity:

  • The University of Bath
  • Cardiff University
  • Durham University
  • Lancaster University
  • London School of Economics and Political Science
  • The University of Nottingham
  • The University of Sheffield
  • The University of Southampton
  • The University of Warwick

Further details can be found on their respective websites as each university handles the test differently with respect to admissions. Some universities give lowered offers for sufficiently good performance on this test.

Important information

The key dates for the TMUA are as follows:

  • 1st September: Registration opens
  • 1st October: Registration deadline with standard fee
  • 15th October: FINAL REGISTRATION DEADLINE (with higher fee)
  • 30th October: TMUA exam
  • 27th November: Results are released

Your schools exams office should be able to sort this for you.

How to prepare

Practice is really the key to this test. There are a variety of ways which you can practice the sort of problems that could come up such as doing problems from the UKMT Intermediate and Senior Maths Challenges and the Kangaroo papers. The MAT may also offer some good practice with its multiple choice section. I would strongly advise looking through the notes on Logic and Proof on the "preparing for the test" section on the TMUA website as these topics can come up and are not really covered fully in the A-Level syllabus.

FYI

I'm a 3rd Year studying maths at Durham who sat the TMUA in its inaugural year (2016) and have created this thread as a place to get help and advice. Unfortunately, last year due to personal circumstances I was unable to properly engage in the thread but this year I should be at least once a day to answer questions people may have.

Problem 1
Rationalise the denominator of \frac{1}{1+\sqrt{2}+\sqrt{3}}

Answer
Spoiler:
Show
\frac{2+\sqrt{2}-\sqrt{6}}{4}

Problem 2
Let a and b be two integers such that 2a+b=ab. How manys pairs of a and b exist?

Answer
Spoiler:
Show
4


Problem 3
Let a_{i}=\frac{i!}{i+1}. Find the prime factorisation of a_{1} \times a_{2} \times \cdots \times a_{11}

Answer
Spoiler:
Show
2^{36} \times 3^{16} \times 5^{7} \times 7^{4}


This post will be updated as time goes on
Are both the papers taken consecutively,a in do you get them at the same time or do you do one and then get a small break and then do the next one?
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Cryptokyo
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(Original post by LiveOnTSR)
Anyone know what a TMUA reduced Warwick offer looks like?
For 2019 entry it was if you got >6.5 in the TMUA their offer was A*A*A with the A*'s in maths and further maths.

I assume it is the same this year.

Cited from the 2019 offer, details here: https://warwick.ac.uk/fac/sci/maths/...ions/ug/offer/
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asliceofpi
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Do we have to list TMUA on our UCAS form?
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asliceofpi
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Could someone please help me with this question? Thank you!
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