Cambridge Interview - Collated Advice

My personal list of interview prep material

stuff that helped me prepare (and also things that I`ve discovered since) covering the areas that I hear that most people (including myself) tend to panic in

CLARIFICATION: This article does not claim to contain any questions nor discussion on questions that have been planned for, have been asked or are currently being asked (depending on when this is being read), in the Q4 2013 or any other future interview session. It does however contain adaptations by the author, of possible past interview questions and may contain speculation on and references to (from external sources) questions of which similar variants could be, by coincidence and unbeknownst to the author , be asked from applicants in future or ongoing interviews.

A note: this was originally intended as a list of things you could try in your summer but since it`s a bit too late for doing that (in this cycle at least) you could probably skim through the literature and pick out things to try as time permits.

IMPORTANT: Although I`ve listed a lot of books in this article, that doesn`t mean that you need to have gone through them to have a chance, or to improve your chances, of getting in. Nor does it mean that they guarantee you getting in or an improvement of your chances. This is just a compilation of quesitons that I feel have helped me and would have helped me at my interview.

1. Estimation

You`re almost certain to get asked a question to make an estimate of some physical quantity or another in at least one of your subject interviews. From my own experience and from others I`ve heard from, these range from "How many Mars bars do you need to eat to run a 40km marathon? - does it matter how fast you run?" to "Estimate the amount of heat lost by ventilating your house in the winter" to "Estimate the volume of air trapped between grains in a bucket of dry sand". Not only do these questions require you to be able to make reasonable estimates of things like the energy content of a Mars bar, the size of grain of sand and the volume of a house, they also do need you to be confident in quickly plugging values like these into equations that need to be made up on the fly.

Guesstimation 2.0 Lawrence Weinstein

This book is perhaps the best practise for this that I`ve come across in the past two years (a close second is its predecessor Guestimation [1.0] by the same author). Work through it and you`ll have no reason to get caught off guard when you`re asked to guess how much the minimum human-perceptible weight might be.

A link to the book on Amazon is here. At the time of writing it was less than £14 from Amazon and less than £10 new from other sellers.

Back-of-the-Envelope Physics Clifford Swartz

As the name suggests, this book is slightly more physics-focused but covers a very broad range of physical phenomena. While I haven`t personally read it through properly, it comes highly recommended in preparing you for kind of rough calculations you`d be asked to perform. The problems range from all-time classics to physics of some unlikely scenarios. In general, they are somewhat less useful on an everyday basis than those in Guestimation but the preparation it gives for the task is still excellent.

An amazon link is here. This is slightly more expensive than Guestimation 2.0 at £17.50 from Amazon and about £10 new from other sellers, including, at the time of writing, Book Depository.

See Also : http://what-if.xkcd.com - [71 articles at the time of writing] A project by the author of "a webcomic of sarcasm, math and language" - Randall Munroe, the articles that are there are definitely worth a read. Even though the maths isn`t quite rigorous and some steps tend to be left out, this is definitely the general kind of process that needs to be going inside your head (and very importantly, being communicated) at your interview. Note that the many cite notes (that look like the little superscri pt[1] on the word superscri pt) often lead to scientific articles that have cover some very rigourous experimentation on the topic at hand. While you probably shouldn`t be going through all of them (atleast not this year) they can be very useful if you want to go in-depth about something that you find interesting. Who knows, you might even impress your interviewer with all you know.

While you`re at it, why not try www.xkcd.com for some unashamed geeky humour.

2. Sketching Graphs

The second type of question that you`re probably going to get asked is to plot, describe or analyse a function that you`ve probably never seen before. You`re usually then asked to make some physical or chemical inference from the behaviour of the function (or in the somewhat slightly easier case, make a deduction about the function from a physical fact or piece of logic).

I remember that in my case it was y = A(1-e^(c - bx))^2 and another in the form A/x^2 + e^Bx or something similar. While these are beyond the type of thing that you`d see at A- level, even in a Further Maths course, they are nevertheless easy to sketch if you Keep Calm and look for Critical Values.

Functions and Graphs - I.M. Gelfand, E.G. Glagoleva, E.E. Shnol

is one the best around for an introduction to sketching graphs. The book above takes you through plotting graphs right from the fundementals (with linear functions which I doubt you`ll really have much use for reading about) to some familliar power functions, through to the more interesting rational functions that look like (3x^2 + 2x - 10) /(5x^2 + x - 9). There are also some terrific excercises that really stretch and challenge. A quick run through (especially of the last two chapters) should give you more than you need if you make sure to work through most of the excercises. Keep in mind though, that this book doesn`t cover trigonometric, logarithmic or exponential functions, but if you read it, the principles in the book should be more that sufficient to get you going on problems that do include these kinds of functions.

A link to this book on amazon is here. But since you`re only probably interested in he last chapter, you can find it on Scribd here. Beware: this is quite an old book (1969) so if you`re expecting modern layout and chatty text you might be disappointed. Also, the version on Scribd is a scanned upload so you might want to get a PDF onto your computer for more convenient viewing.

If you`re looking for a standard you should have, these problems here (solutions here) should probably be treated as the minimum that you should expect. Typical questions will be of functions that are one or more of these expressions added or composited together and will commonly involve a physical aspect linked to it.

NATURAL SCIENCES:

If you have only one subject interview, the focus on physics or chemistry at your interview will depend on what your interviewers perceive your main interest to be. (Of course if you haven`t done a subject at school then you won`t be expected to know any advanced concepts about it but there is a good chance that you might be asked about material slightly above GCSE level so a little bit of reading could help).

Most likely, your personal statement focuses on one of the two but it could also be a combination (like a focus on Materials or somehow `Natural Sciences` in general if you`re say applying to other NatSci courses such as those at Durham. Either way, the focus of the interviewers still depends on the interviewers themselves and is entirely at their discretion (after all it`s only fair if you`ve claimed that you`ll be studying both (or all) of those subjects at university).

3. Physics problems

The kind of physics problems that catch you off guard tend to come in two varieties. The ones that are genuinely difficult and the ones that are adaptations from genuinely advanced problems that aren`t that difficult but look like they are difficult because of the unfamilliar subject matter.

The key in either case is to stay calm and operate under the assumption that what ever problem that you`re faced with was designed to be solvable by someone with your level of expertise. It might well not be in the mock interview here, the interviewer actually admits that the solution to the problem actually took him a few sides of A4 and a good 30 minutes to write down and so was not really desgined to be solved by the interviewee at all (I recommend looking at all these interviews by the way).

A good way to get practice is to work through problems such as those in this book here:

Brainteaser Physics - G ran Grimvall

Although some problems later on in the book may require the use of some slightly advanced calculus (and not usually interviewable), the vast majority should be do-able (atleast partially) with perhaps occasionally a tiny bit more than an A-level knowledge of mathematics.

Again, here`s the book on Amazon going for £16.50 direct and £11.53 new from other sellers.

4. Chemistry

You can find a mock interview here and the actual questions are likely to be slightly more advanced than that. Again, more often than not, interviewers won`t be trying to catch you out but trying to verify if all those abilities that you claim to have (or should be having) in your personal statement.

In my interview, for example, all the chemistry problems that I was asked were soluble solely with mathematics (these included calculus with rate equations) but you should be prepared for anything from a standard A-level syllabus. Keep in mind that A level syllabuses often repeat the same kind of question over and over again so to get proper practice, it`s a good idea to look at questions on the same topics from as many different exam boards as you can.

Why do Chemical Reactions Happen? - James Keeler

While I couldn`t find a single book like Brainteaser Physics with the kind of questions that you could be asked, this is by far the most interesting book I`ve found aimed at readers with an A-level-but-not-yet-university-level background. Suffice to say it assumes knowledge of a few A level concepts but it tries very hard to explain concepts from scratch (atleast the ones from A-level. More advanced equations though, are just dumped on you which is kind of fair looking at the amount of stuff you`d have to work through first to follow a fundemental derivation of them ie at Uni level)

You can find it on Amazon here. This book is a bit more expensive and is probably not worth right now if you don`t have any background in A level chemistry.

OTHER STUFF
These can include probablility and written discussion of physical phenomena.

The level of probability questions can most often be tackled easily with a knowledge of Combinatorics and Permutations (though officially you don`t need to know either of these) and a careful breakdown of the problem.

Examples:

You play a game of coin-toss with a friend. The only rule of the game is that you keep alternating tosses between each other until one of you gets tails at which point the other person wins.

The coin is fair and has an equal chance of yeilding head or tails for any toss.

Are you more likely to win if you start or let your friend start with the first toss?

Hint: Write down an expression for the probability of you winning in each case and try to convert it into a form that you should be familliar with. (Not neccesarily from a `statistics` course).

[1] - Answer at the end of document

Discussion questions can be verbal (which is good because it`s a conversation and you get support from the interviewer in real time if you need it), or in the case of a pre- interview test, involves a small written account that you would then discuss with the interviewers. Questions could include:

Why is the sky blue? Discuss with reference to the interaction of light with the atmosphere. [Answer with probably more detail that you`d need]

Discuss why the moon sometimes appears red during a full lunar ecclipse. [Answer here]

You are almost guaranteed to get a question about something you have never seen before.

This will probably include a short explanation (which for some can be frustratingly incomplete) and an equation about the behaviour of something that happens. You`ll then be expected to be discuss the what happens to the system as various conditions are changed.

Other miscellaneous sources of practice that aren`t entirely tailored to an A-level syllabus but useful nontheless.

Harvard Physics: Problem of the Week is an excellent set of 90 questions in physics, maths and logic. Unfortunately, a large number of them require knowledge some advanced calculus and mechanics to do that you`re not expected to have for an interview.

Do-able questions with an A-level knowledge and (in my opinion) possible useful for interview preparation may include:

[1]

Problem 1, 3

, 6, 19, 43 and 89

This is list is not comprehensive and there probably are many more that you could do.

[1] I recently had a lecture on this very question

The incredibly rare The Chicken from Minsk: And 99 Other Infuriating Brainteasers Yuri Chernyak, Robert Rose is a classic. I`ve only ever seen one problem from this book and the solution to it (while I understood the mathematics behind it) I still find difficult to convince myself of. This book is expensive (possibly because it`s old and there aren`t too many copies around).

The publicly available Trinity College NatSci sample pre-interview preparation test:
You will, as an applicant, probably get a link this some time before your interview

if you`re applying to Trinity.

[1] Answer to coin-toss problem You have a higher chance of winning in the long run if you let your friend toss first.