31道牛津大学数学专业面试真题汇总 赶紧来练练手吧

对于报考牛津大学数学专业的同学来说，面试是他们入学的最后一道关卡，也是最重要的一环。因为面试不仅会考察学员的学术能力更会考察同学们的思维、推理和判断等能力。如今已经11月了，离牛津大学面试的日子越来越近了，本期橡沐给同学们带来一些牛津大学数学专业面试真题，赶紧先来练练手吧！【2020牛津大学面试时间发布 点击收获亲妈级面试教程】

1、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)?

2、Show that if n is an integer, n^3 - n is divisible by 6.

3、Differentiate x^x, then sketch it.

4、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.

5、Integrate 1/(x^2) between -1 and 1. Describe any difficulties in doing this?

6、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.

7、ntegrate xlog(x).

8、How many solutions to kx=e^x for different values of k?

9、Prove by contradiction that when z^2 = x^2 + y^2 has whole number solutions that x and y cannot both be odd.

10、Sketch y=ln(x) explaining its shape.

11、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?

12、Sketch y=(lnx)/x. (The Student Room)

13、Differentiate x^x and (x^0.5)^(x^0.5).

14、Sketch y=cos(1/x).

15、What is the square root of i?

16、If each face of a cube is coloured with one of 6 different colours, how many ways can it be done?

17、If you have n non-parallel lines in a plane, how many points of intersection are there?

18、Observation about (6 - (37^0.5))^20 being very small.

19、By considering (6 + (37^0.5))^20 + previous expression, show this second expression is very close to an integer.

20、Sketch y^2 = x^3 - x.

21、Integrate from 0 to infinity the following: Int[xe^(-x^2)]dx and Int[(x^3)e^(-x^2)]dx.

22、If you could have half an hour with any mathematician past or present, who would it be?

23、Integrate arctan x!

24、Do you know where the multiplication sign came from

25、If we have 25 people, what is the likelihood that at least one of them is born each month of the year?

26、What makes a tennis ball spin as it's travelling through the air?

27、If (cos(x))^2 = 2sin(a), what are the intervals of values of a in the interval 0 ≤ a ≤ pi so that this equation has a solution?

28、If a round table has n people sitting around it, what is the probability of person A sitting exactly k seats away from person B?

29、You are given that y = t^t and x = cost. What is the value of dy/dx?

30、Differentiate y = x with respect to x^2?

31、Prove by contradiction that 2(a)^2 - b^2 is true only if a and b are both odd?

以上这31道数学题同学们可以仔细的读题，认真的思考，从思维处着手，站在招生官的角度考虑，想一想究竟怎样才能从这些试题中找到特点，让自己在面试中呈现牛津大学想要的特性。【深扒5个重要牛津大学面试问题 看完今年面试就稳了】、【牛津大学面试通知什么时候发 这8个面试问题不懂不行】离面试还有一个月的时间，同学们想要来一场真实的模式面试吗？如果您有这个需求的话，赶紧来橡沐吧，橡沐精英联合牛剑招生官独立出题，给你一场难忘的面试感受。

2019年橡沐团队牛剑录取再创业界记录，113位录取牛津、剑桥的学员占中国总录取名额的49%。至今辅导了来自700多所国际学校的超5000名学员，90%学员成绩提升一个等级以上。