# TMUA Prep Thread 2018

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Welcome to the TMUA preparation thread. This a place to discuss the TMUA exam for 2019 entry and to ask any questions if needs be! 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.

The TMUA is a pre-application maths exam sat in November. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and no universities can 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/

- University of Southampton

Note: LSE take the TMUA as supporting evidence in applications.

Good performance in the TMUA can result in lowered offers from universities. For example, Durham may lower the offer from A*A*A to A*AA and Warwick see a good score equivalent to a 1 in STEP.

Further details can be found on their respective websites.

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 during A-Level.

A couple of fun problems to go along with it:

Rationalise the denominator of

Answer

Let and be two integers such that . How manys pairs of and exist?

Answer

Let . Find the prime factorisation of

Answer

**What is the TMUA?**The TMUA is a pre-application maths exam sat in November. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and no universities can 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?****-**Durham University**-**Lancaster University**-**University of Warwick**-**University of Sheffield- University of Southampton

Note: LSE take the TMUA as supporting evidence in applications.

Good performance in the TMUA can result in lowered offers from universities. For example, Durham may lower the offer from A*A*A to A*AA and Warwick see a good score equivalent to a 1 in STEP.

Further details can be found on their respective websites.

**Important information****-**Entries for the TMUA can be made from the 1st September**-**The date at which standard entries cannot be made after is 1st October.**-**Late entries must be made by the 15th October.**-**The exam takes place on the 31st October.**-**Results are released on the 28th November.**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 during A-Level.

A couple of fun problems to go along with it:

**Problem 1**Rationalise the denominator of

Answer

**Problem 2**Let and be two integers such that . How manys pairs of and exist?

Answer

Spoiler:

4

Show

4

**Problem 3**Let . Find the prime factorisation of

Answer

3

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#2

(Original post by

Welcome to the TMUA preparation thread. This a place to discuss the TMUA exam for 2019 entry and to ask any questions if needs be! 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.

The TMUA is a pre-application maths exam sat in November. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and no universities can 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/

- University of Southampton

Note: LSE take the TMUA as supporting evidence in applications.

Good performance in the TMUA can result in lowered offers from universities. For example, Durham may lower the offer from A*A*A to A*AA and Warwick see a good score equivalent to a 1 in STEP.

Further details can be found on their respective websites.

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 during A-Level.

A couple of fun problems to go along with it:

Rationalise the denominator of

Answer

Let and be two integers such that . How manys pairs of and exist?

Answer

Let . Find the prime factorisation of

Answer

**Cryptokyo**)Welcome to the TMUA preparation thread. This a place to discuss the TMUA exam for 2019 entry and to ask any questions if needs be! 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.

**What is the TMUA?**The TMUA is a pre-application maths exam sat in November. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and no universities can 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?****-**Durham University**-**Lancaster University**-**University of Warwick**-**University of Sheffield- University of Southampton

Note: LSE take the TMUA as supporting evidence in applications.

Good performance in the TMUA can result in lowered offers from universities. For example, Durham may lower the offer from A*A*A to A*AA and Warwick see a good score equivalent to a 1 in STEP.

Further details can be found on their respective websites.

**Important information****-**Entries for the TMUA can be made from the 1st September**-**The date at which standard entries cannot be made after is 1st October.**-**Late entries must be made by the 15th October.**-**The exam takes place on the 31st October.**-**Results are released on the 28th November.**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 during A-Level.

A couple of fun problems to go along with it:

**Problem 1**Rationalise the denominator of

Answer

**Problem 2**Let and be two integers such that . How manys pairs of and exist?

Answer

Spoiler:

4

Show

4

**Problem 3**Let . Find the prime factorisation of

Answer

Funny to see such a cold response towards this thread. Maybe posting a couple of question papers might help.

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#3

**Cryptokyo**)

Welcome to the TMUA preparation thread. This a place to discuss the TMUA exam for 2019 entry and to ask any questions if needs be! 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.

**What is the TMUA?**

The TMUA is a pre-application maths exam sat in November. The exam is run by the Admissions Testing Service (ATS). Your score in the TMUA is personal to you and no universities can 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?**

**-**Durham University

**-**Lancaster University

**-**University of Warwick

**-**University of Sheffield

- University of Southampton

Note: LSE take the TMUA as supporting evidence in applications.

Good performance in the TMUA can result in lowered offers from universities. For example, Durham may lower the offer from A*A*A to A*AA and Warwick see a good score equivalent to a 1 in STEP.

Further details can be found on their respective websites.

**Important information**

**-**Entries for the TMUA can be made from the 1st September

**-**The date at which standard entries cannot be made after is 1st October.

**-**Late entries must be made by the 15th October.

**-**The exam takes place on the 31st October.

**-**Results are released on the 28th November.

**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 during A-Level.

A couple of fun problems to go along with it:

**Problem 1**

Rationalise the denominator of

Answer

**Problem 2**

Let and be two integers such that . How manys pairs of and exist?

Answer

Spoiler:

4

Show

4

**Problem 3**

Let . Find the prime factorisation of

Answer

Could anyone explain number 18 on the specimen paper?

Don't whether I'm overcomplicating it

The one about the median

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#4

(Original post by

Could anyone explain number 18 on the specimen paper?

Don't whether I'm overcomplicating it

The one about the median

**yr13ishard**)Could anyone explain number 18 on the specimen paper?

Don't whether I'm overcomplicating it

The one about the median

Spoiler:

Show

If the five numbers in order are a,b,c,d,e, then the median value is c, so we want c as large as possible.

The mean tells us that a+b+c+d+e = 0.

Note c+d+e >= 3c (with equality when c = d = e).

Also a+b >=2b (with equality when a = b).

So a+b+c+d+e >= 3c+2b. So 3c+2b <=0.

The range tells us that e-a = 20. So c-b <=20 (with equality when a=b and c=d=e)

Since we want to maximize c, and we know we can choose a,b,c,d,e such that we get equalities, we might as well choose c=d=e and a=b.

At which point we have c-b = 20, 3c+2b = 0, so 5c = 40, so c = 8.

Note that to actually answer the question, my thought process would be much more:

OK, so how are we going to maximize the middle value? We're obviously going to want the last 3 the same. And then the first 2 will have to be -3/2 of the last 3 if we want the mean to be 0. And the range is 20. So m + (3/2)m = 20. So m = 8.

And in fact, when I actually did this, I actually skipped some steps; at some point "-12,-12,8,8,8" came to mind as a candidate solution. Since it obviously satisfies the constraints, the only way it could be wrong is if there was some way of getting 20, which it's pretty obvious there isn't.

The mean tells us that a+b+c+d+e = 0.

Note c+d+e >= 3c (with equality when c = d = e).

Also a+b >=2b (with equality when a = b).

So a+b+c+d+e >= 3c+2b. So 3c+2b <=0.

The range tells us that e-a = 20. So c-b <=20 (with equality when a=b and c=d=e)

Since we want to maximize c, and we know we can choose a,b,c,d,e such that we get equalities, we might as well choose c=d=e and a=b.

At which point we have c-b = 20, 3c+2b = 0, so 5c = 40, so c = 8.

Note that to actually answer the question, my thought process would be much more:

OK, so how are we going to maximize the middle value? We're obviously going to want the last 3 the same. And then the first 2 will have to be -3/2 of the last 3 if we want the mean to be 0. And the range is 20. So m + (3/2)m = 20. So m = 8.

And in fact, when I actually did this, I actually skipped some steps; at some point "-12,-12,8,8,8" came to mind as a candidate solution. Since it obviously satisfies the constraints, the only way it could be wrong is if there was some way of getting 20, which it's pretty obvious there isn't.

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#5

(Original post by

**DFranklin**)
Spoiler:

If the five numbers in order are a,b,c,d,e, then the median value is c, so we want c as large as possible.

The mean tells us that a+b+c+d+e = 0.

Note c+d+e >= 3c (with equality when c = d = e).

Also a+b >=2b (with equality when a = b).

So a+b+c+d+e >= 3c+2b. So 3c+2b <=0.

The range tells us that e-a = 20. So c-b <=20 (with equality when a=b and c=d=e)

Since we want to maximize c, and we know we can choose a,b,c,d,e such that we get equalities, we might as well choose c=d=e and a=b.

At which point we have c-b = 20, 3c+2b = 0, so 5c = 40, so c = 8.

Note that to actually answer the question, my thought process would be much more:

OK, so how are we going to maximize the middle value? We're obviously going to want the last 3 the same. And then the first 2 will have to be -3/2 of the last 3 if we want the mean to be 0. And the range is 20. So m + (3/2)m = 20. So m = 8.

And in fact, when I actually did this, I actually skipped some steps; at some point "-12,-12,8,8,8" came to mind as a candidate solution. Since it obviously satisfies the constraints, the only way it could be wrong is if there was some way of getting 20, which it's pretty obvious there isn't.

Show

If the five numbers in order are a,b,c,d,e, then the median value is c, so we want c as large as possible.

The mean tells us that a+b+c+d+e = 0.

Note c+d+e >= 3c (with equality when c = d = e).

Also a+b >=2b (with equality when a = b).

So a+b+c+d+e >= 3c+2b. So 3c+2b <=0.

The range tells us that e-a = 20. So c-b <=20 (with equality when a=b and c=d=e)

Since we want to maximize c, and we know we can choose a,b,c,d,e such that we get equalities, we might as well choose c=d=e and a=b.

At which point we have c-b = 20, 3c+2b = 0, so 5c = 40, so c = 8.

Note that to actually answer the question, my thought process would be much more:

OK, so how are we going to maximize the middle value? We're obviously going to want the last 3 the same. And then the first 2 will have to be -3/2 of the last 3 if we want the mean to be 0. And the range is 20. So m + (3/2)m = 20. So m = 8.

And in fact, when I actually did this, I actually skipped some steps; at some point "-12,-12,8,8,8" came to mind as a candidate solution. Since it obviously satisfies the constraints, the only way it could be wrong is if there was some way of getting 20, which it's pretty obvious there isn't.

Thank you ever so much, I was going in the right direction but didn't think of the equalities leading me to 12 but thank you for your help!

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#6

Argh! I got 13/20 on the practice paper 1. I find the questions easy but I always fall for the tricks because I have to rush so much. Aside from doing MAT papers how else can I get better? I'm pretty good at SMC questions, but I don't think they simulate the TMUA very well.

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#7

All registered for this this week. Anyone else doing the MAT and TMUA double?

Ngl this has kind of been neglected in favour of the MAT, but did a little on Tuesday and there seems to be a few bits I have no clue about but otherwise generally much easier than the MAT question 1

Posted from TSR Mobile

Ngl this has kind of been neglected in favour of the MAT, but did a little on Tuesday and there seems to be a few bits I have no clue about but otherwise generally much easier than the MAT question 1

Posted from TSR Mobile

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#8

(Original post by

All registered for this this week. Anyone else doing the MAT and TMUA double?

Ngl this has kind of been neglected in favour of the MAT, but did a little on Tuesday and there seems to be a few bits I have no clue about but otherwise generally much easier than the MAT question 1

Posted from TSR Mobile

**Lemur14**)All registered for this this week. Anyone else doing the MAT and TMUA double?

Ngl this has kind of been neglected in favour of the MAT, but did a little on Tuesday and there seems to be a few bits I have no clue about but otherwise generally much easier than the MAT question 1

Posted from TSR Mobile

My school just said that I have to chose between the 2.

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#9

(Original post by

How is your school going to handle both exams?

My school just said that I have to chose between the 2.

**Rohan77642**)How is your school going to handle both exams?

My school just said that I have to chose between the 2.

Think I'm the only one doing the double (well given there only seems to be 2 of us doing the TMUA so far and the other person isn't doing MAT I think that's pretty likely)

It's a massive school though so we take external candidates etc. So we'll see

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#10

(Original post by

I have no clue... But they let me register for them so they better let me take them! I assume I'll have a supervised break and then be in an office or something for the second one rather than the main hall

Think I'm the only one doing the double (well given there only seems to be 2 of us doing the TMUA so far and the other person isn't doing MAT I think that's pretty likely)

It's a massive school though so we take external candidates etc. So we'll see

Posted from TSR Mobile

**Lemur14**)I have no clue... But they let me register for them so they better let me take them! I assume I'll have a supervised break and then be in an office or something for the second one rather than the main hall

Think I'm the only one doing the double (well given there only seems to be 2 of us doing the TMUA so far and the other person isn't doing MAT I think that's pretty likely)

It's a massive school though so we take external candidates etc. So we'll see

Posted from TSR Mobile

I was thinking of sitting the test because it might make a good impression on Warwick.

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#11

(Original post by

Yeah, my school is pretty small and they are not letting me take both. But I am not sure if taking the TMUA will be of any use to my application since I am applying post results to Warwick, so reduced offer doesn't matter for me and on top of that I am not applying to Durham.

I was thinking of sitting the test because it might make a good impression on Warwick.

**Rohan77642**)Yeah, my school is pretty small and they are not letting me take both. But I am not sure if taking the TMUA will be of any use to my application since I am applying post results to Warwick, so reduced offer doesn't matter for me and on top of that I am not applying to Durham.

I was thinking of sitting the test because it might make a good impression on Warwick.

I don't really know what Warwick think about it tbh, haven't looked there yet

Posted from TSR Mobile

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#13

(Original post by

Question 7, Paper 1 (2017) anyone? getting p= -1 - clearly wrong though

**SM45367**)Question 7, Paper 1 (2017) anyone? getting p= -1 - clearly wrong though

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#14

(Original post by

I think it's easier to start by using the second statement then putting that into the first. This got me the correct answer.

**psc---maths**)I think it's easier to start by using the second statement then putting that into the first. This got me the correct answer.

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#15

(Original post by

Still getting no where.

**SM45367**)Still getting no where.

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#16

(Original post by

From the second statement we know that q=p^3 since we multiply by a constant amount each time we get a new term in a geometric progression. Putting this into the first part we find that the AP is p, p^3, p^2. As every AP has a constant term to term difference this means we can form a solvable equation using this fact.

**psc---maths**)From the second statement we know that q=p^3 since we multiply by a constant amount each time we get a new term in a geometric progression. Putting this into the first part we find that the AP is p, p^3, p^2. As every AP has a constant term to term difference this means we can form a solvable equation using this fact.

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#17

(Original post by

Ah okay, I was solving my cubic wrong all this time, got it now. Thanks!

**SM45367**)Ah okay, I was solving my cubic wrong all this time, got it now. Thanks!

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#18

Hi, does anyone have access to or can provide a link for worked solutions for the papers? Idm if I have to pay.

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#19

(Original post by

Hi, does anyone have access to or can provide a link for worked solutions for the papers? Idm if I have to pay.

**psycholeo**)Hi, does anyone have access to or can provide a link for worked solutions for the papers? Idm if I have to pay.

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#20

I find most of the questions challenging tbh. I got 26/40 on the specimen papers and thought that was quite good, but I found the past papers so much harder. I only got 21/40 on last year's and I've only done paper 1 of the 2016 paper and I got 6/20

I think I usually get caught out, as I think the TMUA does a lot of things to try and catch you out in a way.

And I know there are worked solutions available. But £80 from stepmaths seems ridiculously expensive

I don't NEED TMUA, but I have been stressing because of my poor scores.

I think I usually get caught out, as I think the TMUA does a lot of things to try and catch you out in a way.

And I know there are worked solutions available. But £80 from stepmaths seems ridiculously expensive

I don't NEED TMUA, but I have been stressing because of my poor scores.

(Original post by

I don't know if there is worked solutions available- but if there is any questions in particular you find challenging I'm sure myself or someone else can (try to!) help

**psc---maths**)I don't know if there is worked solutions available- but if there is any questions in particular you find challenging I'm sure myself or someone else can (try to!) help

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