牛津面试样题大公开！这些题目你能hold住吗？

每年牛津大学会收到20000份申请，其中10000份左右会通过初步审核，申请人会被邀请到当地面试，最终，约3200人会通过面试，收到录取通知书。所以说，收到面试邀请本身已经是非常不容易了，而要在面试中杀出一条血路，则更加困难。牛津大学的面试重在考察候选人的学术潜能，而其核心就是独立思考能力，以及举一反三的思维拓展能力。那么这对于参加面试的学生来说意味着什么呢?

一言以蔽之：speak your mind！也就是要把你的思考过程用语言表达出来。如果时间反应不过来？不确定答案？觉得已知条件不够用？千万别憋着，脑袋里怎么想的统统说出来！用个比喻，不要把牛津的面试题当成填空题，纠结于最后那个完美的答案，而要当成解答题，把你的解题过程完全展现，每一个步骤，都会为你挣分。正确答案并不重要，重要的是他们要看到候选人能够用已有的知识考虑新的问题，如何通过合理论证得到结论，以及能否考虑到多种可能性。小学诚为各位牛剑候选人收集了这些【牛津样本面试问题】，这些样题均来自进行面试的导师们。希望他们能引起各位候选人的思考，并帮助大家理解为什么会提出这些问题。

Mathematics

Interviewer: Rebecca Cotton-Barratt, Christ Church

Imagine a ladder leaning against a vertical wall with its feet on the ground. The middle rung of the ladder has been painted a different colour on the side, so that we can see it when we look at the ladder from the side on. What shape does that middle rung trace out as the ladder falls to the floor?

This question tests whether you can do what mathematicians do, which is to abstract away all the unimportant information and use mathematics to represent what’s going on. I’d initially ask the candidate what shape they think will be formed, and then ask them how they can test this hypothesis. They might initially try sketching the ladder at different stages – this is fine, but ultimately what we want is something that we can generalise and that is accurate (you can’t be sure that your drawing is that accurate, particularly when you’re making a sketch on a whiteboard and don’t have a ruler). So eventually they will fall back on maths, and try to model the situation using equations. If they get stuck we would ask them what shape the ladder makes with the wall and floor, and they’ll eventually spot that at each stage the ladder is forming a right-angled triangle. Some might then immediately leap to Pythagoras’ Theorem and use that to find the answer (which is that it forms a quarter circle centred on the point where the floor meets the wall).

This is a fun question because the answer is typically the opposite of what they expect because they think about the shape the ladder makes when it falls (which is a series of tangents to a curve centred away from the wall and the floor). A nice extension is what happens when we look at a point 1/3 or 2/3 up the ladder.

Interviewer: Richard Earl, Worcester College

How many ways are there to cover a 2 x n rectangular grid with 2 x 1 tiles?

The question would typically be posed with the caveat – “I don’t expect you to have the answer straight away; try working out the answer when n = 1,2,3,4 say”. So here is something to investigate. Maths interviews are usually conducted over a piece of paper, sometimes at a white board and so diagrams will get drawn and the student will find the answers are 1, 2, 3, 5 for the first four cases. Some systematic care may be needed to explain why the fourth answer is 5 and why no sixth solution has been missed.

A relatively comfortable few minutes has been spent on this, but it’s also important that the student and I aren’t talking at cross-purposes. At this point I usually tell the student the next two answers at 8 and 13 – any thoughts on the emerging pattern? The answer is the Fibonacci sequence – where a term of the sequence is the sum of the previous two eg 8 = 5 + 3, though it’s not important if the student hasn’t met this before or has forgotten the name. The next stage of the interview is about understanding why that pattern should be appearing here.

When done with this bit of the interview hopefully the student has taken on board a few new ideas. So the question moves on to: 3 x n rectangular grids and 3 x 1 tiles, to 3 x n rectangular grids and 2 x 1 tiles. Hints will continue to be needed, but also there will be plenty of chance to see just how much the student has taken on board from earlier and how well s/he can adapt what’s been learned.

One of the reasons I found this a good question in the past was that its knowledge content is low, no more than GCSE. But its internal complexity is sufficiently difficult to test the brightest students, especially in the final part, whilst also allowing students repeated chances to show what they were learning and share their thinking.

Physics

Interviewer: Jeffrey Tseng, St Edmund Hall

A ball, initially at rest, is pushed upwards by a constant force for a certain amount of time.  Sketch the velocity of the ball as a function of time, from start to when it hits the ground.

Physics interview questions often start with a question like this which looks as though it could have come from the Physics Admissions Test. In this example, I've asked the student to sketch a graph, and then I’d help him or her to get through the problem. Students do make mistakes, and that’s fine as I don’t expect them to know all the material, especially as the interview progresses.  It's not assumed that a less-talented student will need more help on any given problem, and for this reason it can be difficult for students to judge how well they're doing during the interview.

If a student gets things correct straight away, I just move on, either to further aspects of the original question, or to others.  For instance, the above line of questioning could easily result in a discussion of satellites, orbits, weightlessness or dark matter.  It's usually a guided discussion rather than a matter of getting answers right or wrong straight away.  I want to see how students respond to guidance and how they correct themselves, hopefully less by guessing than by thinking through what they know and what I've told them.  Or in other words, while I am looking for a correct answer in the end, I'm even more interested in rigorous thinking.

Engineering

Interviewer: Steve Collins, University College

Place a 30cm ruler on top of one finger from each hand so that you have one finger at each end of the ruler, and the ruler is resting on your fingertips. What happens when you bring your fingers together?

This would never be the opening question in an interview - we usually start with a first question that gives the candidate an opportunity to get comfortable by discussing something familiar. We then ask more technical questions based on material in the GCSE and A-level syllabi. This question would come later in the interview, when we present candidates with an unfamiliar scenario and ask them to use what they know about familiar concepts (such as friction) to explain something.

Almost everyone in this example will expect the ruler to topple off the side where the finger is closest to the centre to the ruler because they expect this finger to reach the centre of the ruler first. They then complete the 'experiment' and find both fingers reach the centre of the ruler at the same time and the ruler remains balanced on two fingers. We like to see how candidates react to what is usually an unexpected result, and then encourage them to repeat the experiment slowly. This helps them observe that the ruler slides over each finger in turn, starting with the finger that is furthest from the centre.  With prompting to consider moments and friction, the candidate will come to the conclusion that moments mean that there is a larger force on the finger that is closest to the centre of the ruler. This means that there is more friction between the ruler and this finger and therefore the rule slides over the finger furthest from the centre first. This argument will apply until the fingers are the same distance from the centre. The candidate should then be able to explain why both fingers reach the centre of the rule at the same time as observed. In some cases, particularly if we have not done a quantitative question already, we might then proceed with a quantitative analysis of forces and moments. We might even discuss the fact that the coefficient of static friction is higher than the coefficient of dynamic friction and therefore the 'moving' finger gets closer to the centre than the static finger before the finger starts to move over the other finger.

Interviewer: Byron Byrne, Department of Engineering Science

How would you design a gravity dam for holding back water?

This is a great question because the candidate first has to determine the forces acting on the dam before considering the stability of the wall under the action of those forces. Candidates will probably recognise that the water could push the dam over. The candidate would then be expected to construct simple mathematical expressions that predict when this would occur. Some may also discuss failure by sliding, issues of structural design, the effects of water seeping under the dam, and so on. The candidate will not have covered all the material at school so guidance is provided to assess how quickly new ideas are absorbed. The question also probes the candidate's ability to apply physics and maths to new situations and can test interest in and enthusiasm for the engineered world.

无论是申请牛津，还是剑桥等其他顶尖学校，面试作为最后一关，在申请过程中一定是占据了极其重要的位置的。在面试前做好充分的准备是非常必要的，否则将功亏一篑。为了帮助大家更好的应对面试，学诚邀请了我们往届亲身经历过牛剑面试并成功入读的学长学姐们组成“学诚牛剑面试护航团”，帮助收获面邀的小伙伴们进行答疑。重点是这个护航团是不收取任何“保护费”的哟~纯属志愿帮忙哦，在此也感谢我们这些可爱的学霸们。