面試是牛津大學和劍橋大學每年本科生錄取的
重頭戲
。然而儘管經過重重準備，仍有不計其數的大牛們在面試環節紛紛落馬。讓我們一起來看看牛劍智領客戶們所經歷的噩夢面試問題：
數學 Mathematics
資料來源：牛津數學系
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劍橋準備問題
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牛津問題
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。 （The Student Room）
Differentiate x^x and （x^0。5）^（x^0。5）。
Sketch y=cos（1/x）。
What is the square root of i？
If each face of a cube is coloured with one of 6 different colours， how many ways can it be done？
If you have n non-parallel lines in a plane， how many points of intersection are there？
Observation about （6 - （37^0。5））^20 being very small。
By considering （6 + （37^0。5））^20 + previous expression， show this second expression is very close to an integer。
Sketch y^2 = x^3 - x。
Integrate from 0 to infinity the following： Int［xe^（-x^2）］dx and Int［（x^3）e^（-x^2）］dx。
If you could have half an hour with any mathematician past or present， who would it be？
Integrate arctan x！
Do you know where the multiplication sign came from
If we have 25 people， what is the likelihood that at least one of them is born each month of the year？
What makes a tennis ball spin as it’s travelling through the air？
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？
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？
You are given that y = t^t and x = cost。 What is the value of dy/dx？
Differentiate y = x with respect to x^2？
Prove by contradiction that 2（a）^2 - b^2 is true only if a and b are both odd？
劍橋問題
if your friends were here now instead of you， what would they say about you？
Whatever got you into pole dancing？
Why do you play table tennis？
Do you know where the multiplication sign came from？
What is the significance of prime numbers？
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？
推薦書目
如果想要更全面的準備和指導，請參考以下推薦書目：
The Stanford Mathematics Problem Book： With Hints and Solutions （Dover Books on Mathematics）
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Advanced Problems in Mathematics： Preparing for University
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<提示>
牛津劍橋的面試形式並不是單純地提出問題，而是圍繞一個話題，由淺入深地討論。面試官會根據面試學生的回答追加問題，增加難度。想要在面試中脫穎而出，不僅要回答表面的問題，還要吃透話題背後的原理、技術相關的所有問題。
牛劍智領的面試題類文章僅作話題類的收集分享，想要完整的面試指導歡迎聯絡我們的諮詢師。也歡迎參與過面試的同學在評論區分享自己的面試經歷。
<相關文章目錄>
牛劍智領 - 知乎
牛劍智領：最全牛津劍橋面試問題（生物、化學篇）
牛劍智領：最全牛津劍橋面試問題（工程、物理篇）
牛劍智領：最全牛津劍橋面試問題（數學篇）
牛劍智領：最全牛津劍橋面試問題（經濟、PPE篇）
牛劍智領：最全牛津劍橋面試問題（計算機篇）
牛劍智領：最全牛津劍橋面試問題（哲學、心理學、社會科學）
參考
^
牛津數學系
https：//www。maths。ox。ac。uk/study-here/undergraduate-study/interviews
^
劍橋準備問題
https：//nrich。maths。org/6783
^https：//www。amazon。co。uk/dp/0486469247
^https：//www。amazon。co。uk/dp/1783741422
