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Cambridge TMUA Past Papers, Worked Solutions and Answers

Free TMUA Questions & Mark Schemes for all TMUA Past Papers

We've compiled TMUA question and answer documents for all TMUA past papers to help you with your TMUA revision.

If you want support beyond these free TMUA questions, why not check out our TMUA Tutoring programme or our TMUA Online Course.

Want more information? Have a look at our guides on 'What is the TMUA?' and 'Top 10 Tips for Preparing for the TMUA' for more exam advice.

Call us on 020 3305 9593 to find out more.

TMUA Past Papers

1 | 2021 | TMUA Past Papers - 1

Question Paper Mark Scheme

2 | 2021 | TMUA Past Papers - 2

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3 | 2020 | TMUA Past Papers - 1

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4 | 2020 | TMUA Past Papers - 2

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5 | 2019 | TMUA Past Papers - 1

Question Paper Mark Scheme

6 | 2019 | TMUA Past Papers - 2

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7 | 2018 | TMUA Past Papers - 1

Question Paper Mark Scheme

8 | 2018 | TMUA Past Papers - 2

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9 | 2017 | TMUA Past Papers - 1

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10 | 2017 | TMUA Past Papers - 2

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TMUA Specimen Past Papers

1 | TMUA Specimen Paper - 1

Question Paper Mark Scheme

2 | TMUA Specimen Paper - 2

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TMUA Practice Past Papers

1 | TMUA Practice Paper - 1

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2 | TMUA Practice Paper - 2

Question Paper Mark Scheme

Frequently Asked Questions (FAQs)


How many questions does the TMUA exam have?
There are two TMUA papers, each consisting 20 multiple-choice questions. Candidates have 75 minutes to complete each paper.
What were the most difficult questions according to last year's students?
Both TMUA papers are designed to assess students' understanding of mathematics concepts already taught. However, the CAAT has published specifications for the Logic and Proof part of TMUA Paper 2. Some students may not have come across these before so it is best to read the guidance, which outlines the criteria.
Can I prepare for the TMUA Exam by using only past paper questions?
Revising for the TMUA through past papers and questions is necessary to familiarise yourself with the structure of the exam and practise answering questions under timed conditions. However, many TMUA past papers do not give explanations as to why an answer is right or wrong. That's where our TMUA tutors come in! Our experts will take you through practice questions and provide you with the understanding behind why an answer is correct or not, giving you confidence on exam day.
→ Why is it important to get Oxbridge application help?
We know how difficult it is to apply to Oxford or Cambridge in competitive subjects, especially when deadlines are tight and options for concentrating on Oxbridge applications are limited. Getting help with your Oxbridge application ensures that you complete it correctly the first time, allowing you to concentrate on more important things (like your exams!).
→ Who are the Oxbridge Mind TMUA tutors?
Our Oxbridge TMUA tutors are all previous or current Oxbridge students who scored in the top 10% of their class on the Oxbridge admissions test and interview. To ensure that our TMUA tutors are competent, responsible, and considerate, they must pass a comprehensive background check. All tutors are DBS vetted, and all lessons are recorded to provide a safe and friendly learning environment. Throughout the process, your TMUA tutor will establish a bond with you, functioning as a teacher, motivator, and friend!
→ What materials do you use for TMUA 2023?
We understand how challenging it is to apply to Oxford or Cambridge in competitive disciplines, particularly when deadlines are tight. Getting help with your Oxbridge application ensures that you complete it correctly the first time, allowing you to focus on more essential matters (like your exams!). To help supplement your learning, you will have access to an array of video tutorials, question banks and study notes. You can use these resources alongside your lessons to help facilitate your learning and track your progress.
→ How many hours should I book for TMUA tutoring?
That depends! Some students book a couple of hours for final preparation, whereas others prefer 40+ hours spanning their entire revision process. Your hours can be used to a variety of disciplines within 15 months, including your A-Levels (all subjects) and, of course, your Oxbridge Application. The majority of our applicants will begin the programme between March and August 2023 for the 2024 application season, although several will begin later or even earlier. We'll work with you to create a custom schedule that meets your specific requirements.
→ How does enrolment and payment work?
Following your application, you will be scheduled for a one-on-one meeting with one of our Oxbridge experts to assess your suitability and discuss your application. If you are accepted and receive an invitation to study with us, you have the option of paying in full or spreading the cost over 12 months. We offer flexible payment arrangements that you can discuss at your initial consultation.
→ Which package do you recommend I choose?
The Platinum course is our most popular package; it will help you significantly enhance your score, interview performance, and overall application outcome. Over a hundred hours of individual mentoring and tutoring are available to support your application and assist you in developing the most effective application possible. Other packages are available that are equally effective, but they include fewer hours of lessons and less time to go into the depths of areas of weakness.
→ What happens if I have any issues, concerns or questions?
You'll be given access to your own WhatsApp group where you can speak with your tutors and the Oxbridge Mind Support team. You are welcome to express any issues or ask any questions, and our team will do their best to respond. You can utilise the WhatsApp group to plan lectures and obtain revision or course content suggestions. Of course, if you prefer to speak with someone over the phone, our team is always available to assist you.

1-1 TMUA Tutoring

Feeling the strain of TMUA preparation? Why not try our 1-1 TMUA tutoring service to give you the boost and confidence to ace the exam!

TMUA 1-1 Tutoring

TMUA Experts

Out TMUA tutors have scored in the top 10% of the exam themselves and have a wealth of knowledge

Personalised Learning

We don't teach to a generic content list! We tailor the sessions to your needs

1-1 Support

You won't be learning with anyone else so the tutor can focus specifically on your learning and questions

Up-to-date Resources

We use the most up-to-date resources, which are shared with you too so you can continue learning in-between sessions

Download TMUA Free Notes

  • Download TMUA Free Notes
  • Detailed Techniques for TMUA
  • Made for 2023 Specification

    1-1 TMUA Tutors

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    Comprehensive Application Support


    1-1 Premium TMUA Coaching
    We firmly believe that adopting an individualised approach is the most efficient route to success in the TMUA exam. Our Oxbridge TMUA tutors have all experienced the university application process, rendering them uniquely equipped to aid applicants. They will guide you through the optimal exam technique for enhancing your speed and precision when addressing TMUA questions.
    TMUA Video Tutorials
    Feeling uncertain about the TMUA exam? Our Oxbridge TMUA tutors have designed a dedicated course tailored to your TMUA exam success. The TMUA tutorials will guide you through the entire process, offering advice on how to excel and attain the highest score possible on your TMUA exam.
    TMUA Worked Solutions
    Desiring to assess your progress? Upon completing TMUA past papers, we will supply you with solutions to the official TMUA exam papers. Collaborating with a TMUA tutor, we believe, will aid you in conquering your TMUA exam and achieving a score that differentiates you from the competition, securing a place at Cambridge.
    TMUA Practice Questions
    Practice hones skills! You will gain online access to a repository of our current TMUA practice questions, available for you to tackle at your convenience. Working through our TMUA practice questions will augment your exam speed, efficiency, and bolster your confidence in the TMUA exam.
    TMUA Homework
    Craving additional practice? Utilise the extra practice time between sessions to complete assigned homework, ensuring comprehensive readiness for the TMUA exam. Additional assignments will aid in pinpointing weak areas and generating questions for subsequent sessions.
    TMUA Support + Feedback
    Our Oxbridge TMUA tutors will furnish you with thorough feedback and TMUA preparation tips. We keep everyone informed and ensure your triumph by delivering regular progress updates, TMUA revision insights, and structured homework plans. We stand by your side at every step, aiding you in achieving your coveted offer!

    Upon achieving a successful application submission, every student is paired with an Oxbridge TMUA tutor who possesses expertise in their chosen field of study.


    In the initial sessions, your Oxbridge TMUA tutor will collaborate with you to craft an individualized approach for succeeding in your TMUA exam.


    Secure your entry into Cambridge by making the most of our TMUA online resources and participating in routine enrichment seminars during your programme. Dive into our full-day Group Workshops, designed to provide you with invaluable insights to effectively complete your application!

    Read what our students say about our TMUA past papers:

    Great resource for practising TMUA exams.
    Lots of TMUA past papers to practise. I found them useful when revising.
    Great resource for free TMUA questions. I went back to the same one to see how I was progressing.
    The TMUA past papers were useful when I wanted to practise to see if I could answer all the questions within the time. The answers were really helpful when I needed to revise more.