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2019年的申请早已落下帷幕，2020年的申请已在如火如荼地进行，还在抓耳挠腮地苦苦冥思自己文书的内容吗？还在为如何进牛津剑桥而发愁吗？
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Math（大类）
There's a torus/ring doughnut shaped space station with 2 spacemen on a spacewalk standing diametrically oppositie each other. Can then ask a variety of questions such as if spaceman A wants to throw a spanner to spaceman B, what angle and speed should they choose (stating any assumptions made, e.g. that gravity = 0)?
Show that if n is an integer, n^3 - n is divisible by 6.
Differentiate x^x, then sketch it.
Is it possible to cover a chess-board with dominoes, when two corner squares have been removed from the chessboard and they are (a) adjacent corners, or conversely, (b) diagonally opposite.
Integrate 1/(x^2) between -1 and 1. Describe any difficulties in doing this?
If a cannon is pointed straight at a monkey in a tree, and the monkey lets go and falls towards the ground at the same instant the cannon is fired, will the monkey be hit? Describe any assumptions you make.
Integrate xlog(x).
How many solutions to kx=e^x for different values of k?
Prove by contradiction that when z^2 = x^2 + y^2 has whole number solutions that x and y cannot both be odd.
Sketch y=ln(x) explaining its shape.
Compare the integrals between the values e and 1: a) int[ln(x^2)]dx; b) int[(lnx)^2]dx and c) int[lnx]dx. Which is largest?.
Sketch y=(lnx)/x.
Differentiate x^x and (x^0.5)^(x^0.5).
Sketch y=cos(1/x).
What is the square root of i?
Imagine a ladder leaning against a vertical wall with its feet on hte groun. The middle rung of the ladder has been painted a differnt colour on the side, so that we can see it when we look at the ladder from side on. What shape does that middle rung trace out as the ladder falls to the floor?
Natural Science Engineering
What are the main differences between the engines in jet fighters and the engines in jet airliners; which type of engine is the more efficient, and (qualitatively) why?
How would you design a gravity dam for holding back water?
What would happen if you drilled through the Earth all the way to the other side and then jumped into the hole?
Why did they used to make the mill chimneys so tall?
Explain the following to someone with no knowledge of physics: force, momentum, power, work.
What are the fundamental differences between Engineering and Physics?
If you had a cylinder, sealed at both ends, with the pressure rising inside, would it blow at the end or split along the side first?
If I am in a room with 5 people and guess all their birthdays what is the probability of getting (only) one correct?
Sketch a velocity time graph for a skydiver jumping out of a plane.
PPE
Is there essentially any difference between taxation and the state taking away one of your arms?
Do you really consent to any government given that there is barely anywhere in the world to escape some government or other?
Put a monetary value on this teapot?
If you’re not in California, how do you know it exists?
Is it a matter of fact or knowledge that time travels in only one direction?
Differentiate between power and authority.
Why do we need government?
Would it be feasible to have an economy entirely based on the service sector?
Do you believe in free will? How far does it extend to - an oyster, for example?
If there were three beautiful, naked women standing in front of you, which one would you pick? Does this have any relevance to economics?
What have you enjoyed most about your A Level Economics course?
If there were three beautiful, naked women standing in front of you, which one would you pick? does this have any relevance to economics?
Of all nineteenth century politicians which was most like Tony Blair?
Put a monetary value on this teapot!
Medicine
What makes a good doctor?
What keeps you awake at night?
Why are manholes round?
I got shown a drawing of nerves from them ear to the auditory centre and asked to explain why it was like that.
So how good are your teachers at school then?
How would you measure the weight of your own head?
How would you poison someone without the police finding out?
Why does your heart rate increase when you exercise?
Why is it a disadvantage for humans to have two egs?
Should someone sell their kidney?
At what point is a person "dead"?
how can reindeer tell the difference between spring and autumn?
how is a city like a cell? how many genes are there in the genome of a rice plant?
how would you design a better brain
How many moles of h2O is there in that cup of water? (tutor randomly pointed at his cup on the table)
How many people believe in evolution in the united states?
How would I solve the aids crisis in south Africa
How would you design an experiment to disprove the existence of god
What leaves you drier if it's raining: running or walking?
Why can you not see many stars when you stand on top of a mountain?
About 1 in 4 deaths in the UK is due to some form of cancer, yet in the Philipines the figure is only around 1 in 10. What factors might undelie this differnce?
小林友情提示
■ 牛津数学专业的面试中，有时候会有两到三轮，而某一轮的题目会比其余几轮的要难一些。
■ 牛津的王牌政治经济哲学（PPE）专业的面试共分为三轮，分别是政治系、经济系、哲学系的教授来测试。
■ 诸如化学和物理类的面试，通常会考到数学问题，所以准备一些数学问题是非常有用的。
以上内容只是牛剑面试真题的冰山一角
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