Oxford Physics Aptitude Test: answers, discussion and advice

This site is designed to help you succeed in the Oxford PAT.  We’ve got free scans of completed solutions, visible one page at a time, with comments and links to background material.  The blog format means you can post your own comments, get clarification of things you don’t understand, suggest improvements or corrections to our answers, and explain your thinking to others.

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Sample papers   |   Changes to the syllabus

Electricity | Mechanics | Problem Solving | Waves | Natural World

Geometry | Algebra | Calculus | Logarithms | Series | Graphs | Probability

Hard questions | Easy questions | Weird questions

138 thoughts on “Oxford Physics Aptitude Test: answers, discussion and advice

  1. Hey,
    In your opinion, if I am pursuing an engineering degree and plan to go to graduate school, is it better to go to another undergraduate school and then apply for an oxford grad school, or does going to oxford undergrad give me a bigger advantage at getting accepted for oxford grad school? Money is also an issue that I have to consider so I was wondering if it is worth going to a cheaper undergrad with less debt or is the oxford undergrad degree worth it enough so that I should take a job for the next couple of years to pay of its debt and then try to get into oxford grad? This is all hypothetical of course but I honestly just need some deeper understanding of what I should do

    1. I’m afraid I really have no idea. Ultimately in your engineering career it doesn’t matter that much where you studied, but this site is just for people who have decided to do the PAT and want to do well — I’m not an expert in different university options.

  2. this is probably the wrong place to post such a thing, but I just want to thank you for taking personal time to make this great and free website. You tirelessly answer questions, they are also always presented logically and clearly! for whatever reason your doing this, i just want to say thanks and keep it up!

    1. Thanks for the kind words Tony. I was lucky enough to have a top-class education for which I paid nothing and this is an opportunity for me to put a little bit back. I know how much effort and commitment the candidates put into the PAT and it’s just a pleasure to be able to help them out.

  3. Hi

    I just have a general question about what exactly “engineering science” is..

    So let’s say I am blessed with the extraordinary opportunity to study engineering science at oxford, if i come to the US do I need additional qualifications if I want to get a job for engineering? Like as in do I need to re study some of the material? I feel like the UK definition of what engineering science is and what the US definition is is different but honestly, I have no idea. I’m just a bit perplexed..

    1. I’m not an expert on the details of the qualifications, but I’ve worked with UK and US engineers and the basic content of engineering courses doesn’t vary that much; I think that a good degree in engineering science from Oxford would be highly valued in the US. Of course in most engineering disciplines you will do some more specialized training after your degree anyway, whether it is via academic or industrial courses, so all hiring managers are looking for in your bachelor’s degree is (most important) that you did well and (second most) that the university has a good reputation.

      1. One more thing–do you know if oxford super scores SAT because in the international qualification section of the cite it doesn’t specify. Would you happen to know if the 1400 on Math and Reading + 700 on Writing is for a single exam or is it a super score criteria? Thank You so much

  4. This website is a Godsend haha 🙂

    Just a specific question–is knowledge about thin films recommended for the PAT? I understand air wedges and single/double slit interference but just have a hard time for some weird reason getting my head around thin films and bubbles!! xd

    Thank you

    1. I don’t have any special or official information. But there has never been a question on thin films, and the topic is not mentioned on the syllabus, so I think you would be best off ignoring it and concentrating your efforts elsewhere.

      Of course, thin film effects do just result from reflection, diffraction and interference, so it’s not impossible for a thin films question to come up, but if it did I would expect that it would be posed in a way that enabled people with no specific knowledge to work it out.

  5. Hi there! Great resource but you already knew that 😉

    I’m in the early days of revision. Looks like simple harmonic motion is one of the past-paper questions but that’s not on the spec? I checked the changes to the spec but couldn’t find any mention.

    If I have any more questions can I keep asking? Thanks anyway 🙂

    1. Hi, glad you think it’s useful. Ask as many questions as you like.

      Simple harmonic motion has come up quite often over the years. I guess the examiners would consider that a full understanding of “distance, velocity, speed, acceleration, and the relationships between them. … Response to forces; Newton’s laws of motion; … Springs and Hooke’s law” would cover cases like SHM even though it is not explicitly mentioned. For example, I think the phrase above covers knowing that velocity = d(distance)/dt, acceleration = d²(distance)/dt², and force = mass x acceleration; given this knowledge, plus Hooke’s law, you can derive the differential equation md²x/dt² = -kx for a mass-spring system. It’s not that hard to solve this equation and “knowledge of elementary mathematics will be assumed”. So while there is no mention of the phrase, I think questions which touch on SHM are consistent with the syllabus.

      In general, if a topic has come up before and it is consistent with the new syllabus, then it’s worth knowing about it. It’s certainly true that some topics have explicitly been dropped from the syllabus since 2014 (e.g. nuclear physics) so there’s no point revising them, but, as you say above, SHM isn’t one of them.

  6. Hey

    How in depth do we need to know in analyzing circuits? I was briefly exploring the topic and found a a wide variety of topics that I wasn’t aware of, such as Wye Delta Transformations, rotational symmetry and node and mesh methods for simplifying circuits. Would it be safe to say that these in depth aren’t required in the pat?

    1. Yes it would be safe to assume that you don’t need sophisticated circuit analysis techniques. Certainly you won’t need to know about Y-Δ transformations or node/mesh methods (the former they would have mentioned in the syllabus, the latter are more suited to writing a program to solve the circuit). Rotational symmetry you won’t be allowed to know about, but it is useful to understand how you can use symmetry to find places where the current in a link is zero. See https://oxfordpat.wordpress.com/oxford-pat-2016-question-20/ for a good example.

    1. Hi Raafiul, thanks for your question.

      No, you don’t need to know anything about thermodynamics or fluid mechanics for the test. It’s important to look at the syllabus and make sure that you cover it (and don’t spend too much time covering things not on the syllabus). Also, be aware that the syllabus has changed so some past papers questions will not come up again. Have a look at this page https://oxfordpat.wordpress.com/changes-to-the-syllabus/, which has the syllabus and describes what has changed, and what you therefore don’t need to worry about.

  7. Hey ! I would like to say thank you! You have played a huge part in getting me an offer for engineering at Oxford ! Will definitely recommend this to aspiring applicants. Thank you again. May God bless you.

    1. I’d also like to give my thanks – your website was extremely helpful for me and I found out on Wednesday that I’ve been offered a place to read Physics! I can’t thank you enough for your help, it really has changed my life for the better!

      1. Thank you very much! It will go up in a couple of months, after the whole admissions process is over, so that I can get all my pieces together. The test went well enough thanks to your helpful answers!

    1. Honestly I thought it was alright compared to some of the other papers? There weren’t any hard graph sketching questions (although I did miss some questions because I didn’t study those parts, haha)

      1. Trust me, you wish that there were more graph sketching questions. The way that graph sketching is taught in school is not great, it just gets you to mechanically learn them instead of figuring them out.

        If you can factorise and differentiate, then you can graph almost anything with the right method! If you are interested, I can send you a pack that teaches you how to use a sign table. They’re quite simple and you might end up using them in your a level maths exams.

        You should learn how to sketch graphs for an eventual interview anyway as I’ve been told it’s a ‘go-to’ maths question. And if you can sketch confidently it kind of makes you look like a badass 🙂

              1. This is material that my teacher gave me so I can’t source its origin. Though, I think it is covered by fair dealing within fair use. (Criteria for fair dealing: The copy is made for the purposes of research or private study. The copy is made for non-commercial purposes. The source of the material is acknowledged.)

                If you feel this is unsatisfactory, by all means, do remove it. I’m just trying to help.

                1. I know you’re just trying to help and I don’t want to remove it. I just want to make sure that if somebody objects (e.g. the copyright owner) they have a mechanism for contacting me so it can be taken down. This ensures that they can’t come after me…

    2. THIS YEAR WAS SO DIFFICULT hahahaha, the Math was actually a bit tricky and what was the last question in Physics😂😂😂, the last question for physics and the Octagon question for math went over my head😂😂

  8. Hi! I was wondering if it’d be possible for us to download the whole solution sets to papers all at once? I think that’d be very helpful! I’ve collated the ones I’ve downloaded (2010, 2014, 2015, 2015 sample), if you’re agreeable I could post them here/invite you to the google drive so that you could upload as well? (And maybe include a link to it in the front page)

    1. Hi Beth — thanks for your suggestion and your offer to share what you’ve done.

      I’m not convinced that it’s a good idea to have collated answers in files, because:
      (1) files get copied — currently if I need to change something (e.g. a mistake) I know that there won’t be incorrect copies circulating, because everyone gets the answers from a single server;
      (2) I want to encourage people to comment and ask questions on the individual answers and this will be less likely if they are available in one big file (for every person who asks a question I guess there are 50 who had the same doubt but just didn’t ask, so the answers can be disproportionately useful; and the easier it is to make a comment, the more likely somebody is to correct any error I might have made);
      (3) it’s useful to me to get statistics on which answers and other pages people actually look at because it is closely correlated with what people find difficult (e.g. in 2016 the second most popular question viewed was #22, 2012, which is no surprise because it’s very hard, but the most popular was #21, 2015, which I thought was really easy but actually has caused many people problems);
      (4) the first thing many people do when they get hold of a file is print it out. At a rough estimate, given the number of visitors to the site each year, this could result in about 300,000 sheets of paper being printed every year, which would be about 30 – 40 trees a year.

      Having said that, I’m always interested in other points of view, and I’m happy to be convinced or to find alternative solutions if you explain in more detail the value of having collated solutions.

      1. (1) I’d agree that it’d be easier with only one main copy. Although, I was planning on handing over access to the file server to you after I’ve uploaded what I have, so that you’d be able to update the files.

        (2) I meant the downloadable version as a supplement to the website. For example, if there was something I wasn’t sure about, I’d come back here to check the comments.

        (3) True, this can’t be replicated!

        (4) I haven’t considered this. I rarely print out my files; downloading is more to avoid the hassle of going online again to look for it. In this case, it was for last minute studying right before the PAT on the train where there was no internet. But I suppose more people would want to print it out.

        Honestly the main boon would be convenience. I’m probably not the only one who has done this and it’d be a big time saver for us users. But now I’m also worried about the trees, haha. Perhaps it won’t be such a good idea after all.

        Thanks for the detailed reply, and also for uploading the answers in the first place! They really have been very helpful.

        1. You make a good point about being able to study where there is no internet, so I’ve made a local copy of the site that it’s possible to download to your machine and use offline. It’s in this (116MB) zip file. I’d be really grateful if you’d give it a try and let me know if that would work for your use cases: if so I can just occasionally update the copy.

          Incidentally if you find yourself having to work without network access a lot, then you should get hold of wget ((this is the windows version, but it’s available on everything). It’s a tool for downloading entire sites — I used it to make the folder on the google drive. Takes a little bit of learning (e.g. see https://www.gnu.org/software/wget/manual/html_node/Advanced-Usage.html) but very useful …

          1. Oh wow, I never knew such software existed! Will be handy the next time I need to study without internet. Thanks for the link!

            I just downloaded the pack and checked it out, yes this works very well.
            Some minor things:
            1. The order for some of the questions is a bit scrambled in the oxfordpat folder (e.g. 2009; and for that year the folder for question 10 actually also contains 11 and 12, despite the name)
            2. When looking at the files in “oxfordpat.files” themselves they are sorted by date of upload (probably a wordpress thing) instead of by year of paper, but just searching for the paper I want and then sorting by name fixes it.

            Again, these are really minor things, so it might not be worth the time to fix them especially if you’d have to refix them each time you upload. This is just a heads up for anyone who wants to use the offline version! (Perhaps the link to the folder could be put into the main page so that people wouldn’t need to look through a comment thread?)

            Overall, it’s exactly what I would have wanted, thank you so much!

    1. Nah, I think this was really one of the hardest ones. So don’t give up too quickly… 😀 I hope to have 50 at least 😀

  9. Thank you so much for the help and support that this website has to offer, honestly motivated me a lot and has provided an excellent resource to prepare myself the best I can during a short period of time! Honestly really appreciate it! And good luck to everyone tomorrow!

    1. I’m really pleased to hear it. Confidence especially is really important in this test. A very few of the questions are really hard, but quite a few are easy. The more confident you are the better you get at spotting the easy ones. Good luck!

  10. Whether tomorrow goes well or not, I’m glad I’ve learned so much new physics from all these solutions. Wish our Advanced Highers would cover all the pulleys and mechanics stuff! Cheers for the help.

  11. You are making me emotional! 🙂
    Thank you for all the help. I do have one question – how do you find the time to do this? I imagine you have a degree/doctoral thesis/job/family also. It is absolutely amazing that somebody has gone out of their way to do so much for others.

    Do you have a PayPal? I think I owe you a beer.

  12. Hi I would just like to say thank you very much for your tremendous help and efforts!!
    I was wondering if you had any advice for final preparation?

  13. Hi! Please could you take a look at question 14 from the 2006 paper? I have managed to work out the velocity (I think it’s correct) which is sqrt(2PT/M). It’s now asking about acceleration and I used V = u +at and substituted into the kinetic energy equation, where U = 0. My answer turns out to be sqrt(2P/MT), but looking at various solutions, the correct answer should be sqrt(P/2MT). Thanks! I really appreciate the work you’ve put into this site, I would not have been able to do many of the questions without it!

    1. You are absolutely right that the velocity is √(2Pt/M). But the equation v = u + at only works for constant acceleration, so you can’t use it here.

      Instead you need to consider the more general definition relating acceleration a with velocity v, which is that a = dv/dt.

      If you differentiate √t you get (1/2√t), therefore if you differentiate √(2Pt/M), you get √(P/2Mt)

      In the next part of the question, working out the distance travelled (call it s), you need to use the definition v = ds/dt, therefore s = ∫v dt.

    1. The front of the paper states “Answers in Part A should be given exactly unless indicated otherwise. Numeric answers in Part B should be calculated to 2 significant figures. Use g= 10ms-2”

      Therefore, if it is maths and it’s a surd, it’s a good idea to keep it exact. If, for example, it is asking for the displacement as part of a suvat equation (unless it states otherwise) 2 sig figs will do.

      I know, it is quite annoying to get to the end of a meaty algebraic question to then be bothered by a long division.

      1. Exactly right. Note that sometimes I haven’t bothered to calculate the numeric answer in answers to Physics questions, and strictly you should do this, so that e.g. 2pi becomes 2*3.14.. = 6.28.. = 6.3 to 2sf. On the minus side, this looks a bit stupid and takes some time; on the plus side, it’s only 2sf.

  14. Hello, am i meant to study angular momentum it’s not in my a2 syllabus neither in the syllabus

    Do you have any advice for the last couple of days and what we should be doing?

    Whatever i score i am very grateful to you for this site, you are a blessing to those of us who could not get good help

    1. I am not an expert- I’m taking it this week too, actually!- but in the last 4 months during which I’ve gone through every paper and had a look at the syllabus I have not seen angular momentum at all.

      1. Yes I think you’re right. I wouldn’t worry too much about angular momentum. I think probably the only thing that might come up related to angular momentum is a variation on the classic ‘ice skater’ theme: when ice skaters spin with arms and legs stretched out they rotate at a certain angular velocity and when they pull their arms and legs in tightly they spin much faster. This is because their angular momentum must be conserved.

        The equivalent in the sort of systems that might be covered in the PAT is a single point mass spinning round on the end of a string. If the string is shortened then the mass will rotate faster. This is an example of conservation of angular momentum but you can explain the behaviour by just using your existing knowledge of conservation of momentum. When a mass is spinning on the end of a string of length r with angular velocity ω, it moves with speed ωr perpendicular to the string. Imagine reducing the length of the string somehow while still spinning the mass; no force is acting parallel to the velocity of the mass, so the momentum of the mass can’t change, and so its speed has to stay the same. This means that ω has to increase when r decreases.

        I think that’s it as far as angular momentum is concerned. I’m pretty sure you won’t need to know anything else.

  15. Hi,
    I really am happy I found this website, it is super helpful! I just had a quick question in terms of a topic that might come up. In the new specimen paper I’ve seen an example answer for a physics question using the application of how time period of an oscillating mass on a spring isn’t affected by a different value of surface gravity. This comes up in Simple Harmonic Motion in my A2 textbook, so I was wondering if we’d have to be well documented on the rest of Simple Harmonic Motion as a topic for the PAT? I’m not sure if I’ve missed seeing it in the spec! Thanks in advance!

  16. Hi do you think we need to know about moment of inertia and angular momentum? I think it once came up in a 2006 paper. Thanks!

    1. I think you should know that angular momentum is conserved, but I don’t think you will need to know much about moments of inertia for the PAT. If there is any reference to moment of inertia I think it will probably be explained.

  17. Hi!

    Could you tell me whether we need to know about Mechanical Advantage? I’ve noticed the PAT likes to use really complicated pulley systems, and I’m still struggling to understand the question from the 2014 paper on motors and Pulleys. To what extent do we need to know about pulleys?
    Thanks!

    1. Also, do you have any specific tips on what to do once you have 2 separate inequalities, and they must satisfy something like -2<f(x)<5
      so that it works for both?

      1. If you are solving two (or more) inequalities then for each inequality you will get a range of values of x that satisfies the inequality. If x satisfies multiple inequalities it must satisfy the conjunction of all of the individual inequalities; each inequality defines a single range, so to find the values of x that satisfy the conjunction of the inequalities you need to find the intersection of all the ranges.

  18. Hello, I’ve covered most of the syllabus except a few things under optics especially on elementary properties of lenses and prisms. What ‘elementary’ properties should I cover on? There was a question regarding Snell’s law in 2014, is that required?

    I’m more comfortable with reflection of plane mirrors but I might have missed a few key details, do you have any tips/resources leading to any possible reading on this?

    1. Good question — I think you probably should know about how real and virtual images are formed by lenses, and also Snell’s law (this came up and I don’t think any changes to the syllabus have removed it).

      As far as plane mirrors are concerned, it’s a shame that there has hardly ever been a PAT question on this subject so there isn’t much to revise. I suggest that you look at this page (http://www.physicsclassroom.com/class/refln/Lesson-2/Other-Multiple-Mirror-Systems) and make sure you can derive the relevant answers and understand the technique.

  19. Hi,
    Awesome website, specifically what calculus techniques are needed? The syllabus says integration of polynomials but I have already seen that further differentiation and integration methods have been used? Which ones are needed, product, quotient, chain? Will I need integration by substitution etc?

  20. Hey I know this is a stupid question but do you have any predictions for the PAT this year?
    Also Where would you reccomend people to focus on and how can I get extra maths practice I started soem STEP papers but they are significantly harder then the pat I believe

    Same question for how to study for physics ( I struggle a lot here, I think they reallt overwrite some of the questions and I lose track, quite funny actually

    Thank you for the site!

    1. Predictions for the PAT this year? Well we can all see into the future a little way, some further than others. But I’m afraid my foresight doesn’t even come close to covering the decisions made by people who set exams. My one prediction is that the questions will definitely only be about topics covered by the current syllabus, so make sure that you look at the ‘Changes to the syllabus’ link above to ensure that when you go through old papers you are not revising for questions that no longer have a chance of being asked.

      On the maths questions, I would cover all the basic topics above (Geometry, Algebra, Calculus, Logarithms, Series, Graphs, Probability) and make sure that you have really understood the answers to the past questions for each one. If you have a gap in your knowledge, use a search engine or a textbook, or ask a question on this site and I can point you to some resource.

      On the physics questions, you are right: many of the questions are quite wordy and describe some complex situations. I think this is on purpose: one of the key skills for a physicist or engineer is to be able to cut through a vague mess of words, spot the real physical situation being described, and produce a simple summary by drawing a diagram or writing down some equations. So if you are having trouble reading the questions, practice this process: try to create a diagram or write down the relevant equations, and then check back against the text of the question to see whether your simplification has actually captured what the examiner was saying. If you do this enough, you will get much better at it.

      1. That is some solid advice! Thank you I will do what you’ve said
        What did you mean by questions that can’t be asked which ones do you think won’t be asked? I’m sorry if I’m being a little dense again

        May I ask what your field of study is and where? Your site and solutions are great very nice and detailed and easy to understand so thank you

        1. Here is a good example of a question that could not be asked in this year’s PAT: https://oxfordpat.wordpress.com/oxford-pat-2011-question-24/. It is all about alpha, beta and gamma radiation, which has been taken off the syllabus. So make sure you look at the othr changes to the syllabus and ensure that you are studying things that are still covered.

          I’m glad you like the site. I actually studied Engineering at Cambridge, quite a while ago. In those days Cambridge had an entrance exam similar to the PAT but with three papers. I was very well-coached by some excellent teachers, and was lucky enough to get straight As, and an entrance scholarship. A few years ago I realised that not everyone is lucky enough to get the level of coaching I got, and that’s why I set up this site.

  21. Hi, thank you for your help, I found it really helpful for the maths section and now I’m doing the physics one and I have some questions about the program I should cover for the test. In the official syllabus it is said that is required a knowledge about “Elementary circuits including batteries, wires, resistors, filament lamps, diodes, capacitors, light dependent resistors and thermistors” but since I’m studying all this stuff by myself I would like to know which aspect I should see about diodes, light dependent resistors and thermistors. Do I have to know everything about them or it is enough a superficial understanding?

    1. That’s a good question. I think that for LDRs and thermistors, you should just know their basic characteristics (resistance dependent on incident light and temperature respectively) and have a look at a response curve for a typical example of each (i.e. how the resistance varies with the input light intensity or temperature). Diodes are much more important components and the examiners, being practical people, will therefore care more about them and set more complex questions on them, so for diodes it is worth having a more detailed grasp of what they do. A good example of a (pretty hard and subtle) question about diodes is https://oxfordpat.wordpress.com/oxford-pat-2014-question-16/.

      For the other components that the syllabus mentions, you should know Ohm’s law and how to use it, understand how to make calculations where batteries have internal resistance (treat as a battery with a resistor in series), and you should know that Q=VC, and I=dQ/dt, and be confident with the differential equations for capacitor charging and discharging that result from those two equations. If you know all that, then I think you will know everything you need for the PAT exam.

      Notice that you don’t need to know anything about inductors for the PAT, but if you want to also learn about inductors and LC circuits you will be at an advantage because this will help your understanding in general (more differential equations, the parallel between mass/spring/drag and inductor/capacitor/resistor, resonance, and lots of other stuff that makes the PAT look easy).

      1. Thank you, I hope I’ll manage to do it all by myself. Do you have any file or link about this elementary circuits? I have only my high school textbook and it covers only Ohm’s law and Kirchhoff’s law, resistors and capacitors with no mentions about LDRs, thermistors and diodes.
        Thank you so much

  22. i am begging for some good help.
    1) i do edexcel currently have given c1 c2 m1, and i am looking to the do the pat, what other edexcel math modules do i need?
    c3 c4? and if so do i need the whole book or specific chapters please inform me :((
    2) for the physics part do i need the entire of edexcel a2 physics?
    3) i do three subjects chem math and physics if i do further maths it can only be AS maths as my school does not even offer as further maths, would i need to show a predicted grade for this as i do not have the grade for AS further maths because i didnt do any of the modules or do i need it at all?

    1. HI — thanks for your question. In general, you should look at the link to the PAT syllabus above and check that you are covering the topics. Having had a brief look I think the summary is:
      1) I think that you will need a fair bit of the c3 and c4 modules, but there are parts that are not in the PAT syllabus.
      2) No you don’t need to cover all the a2 syllabus. The PAT physics syllabus is quite focused, so should be fairly easy to cover. The more mechanics you have done. the better.
      3) You don’t need to offer further maths A2. In any case, predicted grades aren’t that important, because admission is basically decided by PAT score and then interview performance. If you get an offer it will probably be AAA* or AAA, so you need to expect to get that level of grade.

      1. Thank you for your reply!
        In specifics could you tell what of A2 physics and c3,c4 to cover as time is valuable and I don’t want to waste it on things that aren’t needed
        Thank you for putting me at ease about further maths, but would it hinder my application in anyway even thoug Oxford require only 3 alevels,
        Lastly, I just saw the 2015 paper here and the solutions for the inequality question I didn’t understand what you did and I figured out it was from fp2 module edexcel so I thought myself that today, I’m thinking of going on the edexcel specification entering keywords from the syllabus and seeing where they appear are there any other modules in particular besides in c3 and c4 I should be aware of
        Sorry for nagging you but thank you for all the great work you do, I’m from dubai

        1. I think the best answer to your question is to look carefully at the syllabus, taking account of the way it has changed, using this link (https://oxfordpat.wordpress.com/changes-to-the-syllabus/) and just make sure you understand what each topic mentioned in the syllabus is getting at — searching the A level specifications is a good idea.

          If you read the Oxford physics entrance material on their web site, they say pretty clearly that it would make no difference to your application whether or not you study Further Maths, and they are trying to be as open and accurate as possible: they really mean everything that they say. So don’t worry about having to study Further Maths.

          The inequalities question requires you to know that if a > b then if you multiply both sides by the negative number x you get ax < bx. I don’t know much about the A level modules, but by googling around I think for at least some boards this is covered in C1 (see https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Error_bounds_and_Inequalities#Solving_Inequalities_involving_Fractions).

          I hope this helps — to summarize, I am afraid I am no expert on the contents of the various A level modules, but I would recommend that you just look directly at the PAT syllabus and then follow up on those bits that look unfamiliar to you.

          1. Thank you again
            Did the question in the 2015 paper on Inequalities reslly only require that because I think they’re called rational inequalities and I wasn’t able to solve it or really understand your solution so I looked at tutorial on how to do them and I’m going to attempt the question again tomorrow

  23. I sat PAT last year. Based on my performance and other factors, I was interviewed at Oxford to study Engineering Science.
    Not long after the interview, I was offered a place at New College.
    Not long after that, I was offered a full Reach Oxford Scholarship that enables me to study at Oxford University from October 2016. My PAT performance was partly considered in this process.
    Of course, I have been working hard to earn those achievements. But I’m sure I would have faced many more struggles If you didn’t help me to develop my confidence in solving PAT problems.
    Thank you very much for your help. I couldn’t afford to have a tutor and your work substitutes private tuition in a much better way!!
    I hope you will continue with this work and I wish to support you by making a donation.
    Please can you advise ?

    1. Thank you so much for your comment: all the effort that I have put in to this site is made worthwhile by the knowledge that it has been useful.

      You ask about making donations. As it turns out, I am lucky enough to not need any financial support. Space on wordpress.com costs nothing, so the only thing I have ever spent on this site is my time, and we all have plenty of that. I don’t want to suggest any charity that you could donate to, because I don’t think my judgement would be any better than yours, and I know that life in Oxford is expensive, so you would be well-advised to hang on to your cash. Anyway, what goes around comes around: I was taught at one of the best schools in the UK for free; I always felt grateful to my teachers, and so years later I set up this web site so I could give people a little bit of the coaching that I had. You might well find yourself in a similar position one day, and for you to help somebody else in turn would be the best donation you could give.

    1. Hi Raya — do you mean UK year 10 or India class 10? If you mean UK, the answer is easy: just do A level Maths, Physics and ideally Further Maths. If you mean India, I’m afraid I’m not sure what you will already have studied, but you should look in detail at the syllabus on the Oxford PAT website. In a week or two I will be posting some information about how the syllabus has changed over the years and how this impacts the past papers.

  24. Hi Adam, thanks for your comment.

    Yes I would have been inclined to answer C to this because the question seems to be saying that there was some radiation emitted that was stopped by the aluminum plate, even though the emitted radiation was barely above background. The good news is that, now the syllabus has changed, this sort of question won’t come up.

    On the 9i answer, yes that is right. I think a better way of writing down this answer would be that die 1 could be a member of {1,2,3,4,5}, where each of these outcomes has probability 1/6, and for each of those outcomes there is a 1/6 probability of throwing a number on the second die such that the two numbers add up to 6. Therefore the total probability of throwing numbers that add up to six is 5/36.

    Many thanks for pointing this out. It is nice to be admitting to somebody else’s error for a change :-).

    1. Hi, I’m really glad the site has been useful. Yes, I think that showing your working is really important; it doesn’t matter how you show your working as long as the examiners can see that you have understood the maths and physics involved in the problem and can use your knowledge to solve it.

  25. Hi, I was hoping you could help me out with question 14 of the new specimen paper. For the second part, why is the velocity 3u rather than just u? I’d really appreciate any help. Thanks.

  26. Hi, do you know if there is a list of equations that we need to know? It’s just I don’t know all of the ones from the formula sheet by heart and I know which ones I should definitely learn but am unsure about several others such as decay of charge because we haven’t covered some of these topics at school and I have learnt the topic but don’t know as to how often they would come up in a paper?
    Thanks

    1. Hi,

      Can’t seem to add a comment on the solution page but I think the answer to Q10 on the 2015 Specimen paper is pi/3?? (Arccos(1/2)=pi/3)

      Thanks very much for the amazing website, it’s a great help

      Hi Ali — copied over to Question 10 (comments had got disabled somehow). Many thanks for correcting my careless slip.

  27. Hi Ben, thanks for your question.

    You mean the question: “Positron Emission Tomography (PET) scanners frequently operate using the radioactive isotope 18F, which has a half life of about two hours. The isotope is incorporated into a drug, half of which is excreted by the body every two hours. How long will it take before the quantity of radioactive drug in the body halves?”.

    Suppose the initial amount of radioactive drug is D. If the half life is T then the function for amount of radioactive drug left after time t is D 2^(-t/T) (i.e. ” D times two to the minus t over T”). If half the remaining drug is excreted every T seconds then our function becomes D 2^(-t/T) 2^(-t/T), which equals D 2^(-2t/T). So the resulting formula looks like the formula for radioactive decay when the half life is T/2. So, when T is 2 hours the effective half life is 1 hour, so the answer is B.

    1. Dear Sir/Madam,
      Thank you for your prompt response. I have understood the problem now. It is very nice of you to help us. And by the way, when you mention: ‘half the remaining drug is excreted every T seconds’, do you mean every hours since the unit of half-life were hour in the question?

  28. Hello, would you be able to have a look at question 7 (multiple choice) physics paper 2007 ? I haven’t been able to derive an equation to describe the rate of change when 2 simultaneous change happening at the same time. I would be very greatful for any advice on how to tackle this question. Thank you very much.

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