Preparing for the PAT course: this course is run by the Department of Physics and features a mix of in-person (where possible) and online tuition, including mentoring by current students. This course is for year 12 students from state-funded schools, academies and colleges with little or no history of successful applications to the University of Oxford. More information and the application form can be found here.

Isaac Physics website contains lots of maths and physics problem-solving questions. The following resources are particularly useful:
Mastering essential pre-university physics
Select your own questions within the A-level resources section: select ‘Problem solving’ and click on physics or maths and the level of question you want. Questions at the same level as the PAT tend to be around level 4-5. Remember to register/log in so the website records your progress.
University preparation also contains lots of questions which are suitable as university entrance preparation.

British Physics Olympiad website contains lots of past papers and solutions of problem-solving type questions. Click on the Question bank and find topics on AS and A2 challenge questions you find interesting or want some practise with. Solutions can also be found on the website (click on ‘past papers’ and find the relevant paper the question you are interested in is from).

Physics Lab's 'next time' website contains questions designed to make you think about physical concepts. They are often multiple choice or yes/no questions, and there is usually not much maths involved. The original idea was that the teacher would ask the question at the end of a lesson and answer it 'next time'. Questions are grouped into topics, and each question has a title that is a link to a pdf that includes the question on one page and the solution on a second. Some of the questions are probably more relevant for interview questions than the PAT as they might not contain the level of maths required in the PAT but it can be useful for checking your understanding of general concepts.

I want to study engineering website is just as useful for all applicants not just those applying to engineering. On the first page there is a choice of level of question; you should be looking at the 'mathematics and physics questions at the level of university engineering admissions interviews' for preparation for the PAT or university interview practice. This section then has an index of problems, divided into smaller groups of about 10-20 questions by topic. Each question has a multiple-choice answer, plus hints for a solution strategy and summaries of relevant bits of theory. There is also a (usually concise and mathematical) solution, plus short videos to help with understanding. You might need a paper and pen to work out some of the problems and some of the material is beyond the PAT syllabus – you should double check if you are in doubt.

Brilliant.org website has some resources to test your mathematical and physics knowledge. Questions are usually answered via multiple choice and one of the nice aspects of this website is that you can see how many other people have got the question right or wrong. The ‘daily challenges’ on the home page are always free but quite a large part of the website requires a subscription to get full access. Try the ‘practice’ section of the website for some free questions on maths, electricity and magnetism and classical mechanics.