Mathematics Interview Questions
Quant Job Interview Questions
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QUANT JOB INTERVIEW QUESTIONS
(6) Let (.) be the cumulative distribution function of a N (0, 1) random variable. Define a function g (x) as Z x2 g (x) = (t + x) dt.
(5) Consider a full-rank matrix A of size m by n and a vector b 2 Rm . (a) Assume that m < n. Find x 2 Rn with the smallest 2-norm that solves Ax = b. (b) Assume that m > n. Find x 2 Rn that minimizes ||Ax b||2 .
QUANT JOB INTERVIEW QUESTIONS
Contents 1. 2. 3. 4. 5. Basic Math Probability Markov Chains Applications Brownian Motion and Stochastic Calculus Option Pricing 1 2 4 5 6
QUANT JOB INTERVIEW QUESTIONS
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(a) Compute the probability density function of X . (b) Compute mean, median, and mode of the distribution of X . (5) Suppose X is a Gaussian variable of mean 0, and standard deviation , and define N (u) as the CDF of a centered Gaussian variable of mean 0 and variance 1, i.e, Z u s2 1 N (u) = p e 2 ds. 2⇡ 1 (a) Calculate the expectation of N (X ). (b) Calculate the expectation of N (X + a), where a > 0. (6) By setting up and solving the appropriate convolution, show that the sum of two independent zero-mean unit-variance Gaussian distributions is Gaussian, with variance 2. (7) If you repeatedly flip a coin whose probability of heads is p then what is the expected number of flips you need to do in order to get a head immediately followed by a tail? (8) Suppose X is a random variable with E [X 2 ] < 1. What is the constant c that minimizes E [(X c)2 ]? (9) Let X be a continuous random variable such that P (X 0) = 0. Let f (·) be its probability density function. Suppose that f (x)/P (X > x) is equal to a constant for all x > 0. What is the distribution function of X ? (10) Let fX (·) be the pdf of a continuous r.v. X . What is the pdf of eX ? (11) You have 1000 coins, one of which is faulty: it has a head on both sides. You randomly draw a coin, and, without examining it, toss it 10 times. As it happens, you get 10 heads in a row. What’s the probability that it’s the faulty one? (12) Let X be a random variable with density distribution function f (X ). Define F (x) = P r[X < x]. What is E [F (X )]? (13) Assume the arrival time, T , of a credit default event follows an exponential distribution such that P (T < t) = 1 e
《the story of math》中出现的所有数学问题(二)
《the story of math》中出现的所有数学问题(二)The Story of MathIntroductionIn the documentary “The Story of Math”, various mathematical problems are discussed. These problems shedlight on the development and application of mathematics throughout history. Below, I have listed and explained some of the key mathematical questions covered in the documentary.1. What is Prime Factorization?•Prime factorization refers to the process of breaking down a number into its prime factors.•The documentary explains how prime factorization is crucial for various mathematical concepts, such asfinding the greatest common divisor or simplifyingfractions.•It also explores the notion of unique factorization theorem and its significance in number theory.2. How does Geometry Influence Architecture?•This question delves into the connection between geometry and architecture.•The documentary showcases examples of ancientarchitectural wonders, such as the Pyramids of Egypt,that were built using mathematical principles.•It highlights the importance of geometric shapes, ratios, and symmetry in constructing magnificent structures.3. What is the Golden Ratio?•The concept of the golden ratio, denoted by the symbol φ (phi), is explored in this section.•The documentary explains how the golden ratio appears in art, nature, and even in the proportions of the humanbody.•Its significance in aesthetic design and its historical relevance in various cultures are also discussed.4. Can We Solve Fermat’s Last Theorem?•Fermat’s Last Theorem, proposed by Pierre de Fermat, states that there are no three positive integers a, b,and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.•The documentary delves into the long and arduous journey mathematicians undertook to finally prove the theorem in 1994.•It discusses the complexity of the problem and the ingenious techniques used to solve it.5. How Does Calculus Transform Mathematics?•This section explores the advent of calculus and its transformative impact on mathematics.•The documentary explains how calculus revolutionized fields such as physics and engineering by providing the tools to study change and motion.•It highlights the contributions of mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz to thedevelopment of calculus.6. What is the significance of Zero?•The concept and significance of zero in mathematics are explored in this segment.•The documentary discusses the origins of zero in different ancient civilizations and its role inpositional numeral systems.•It showcases how zero revolutionized mathematics by introducing the concept of nothingness and the power ofplace value notation.7. How is Probability Calculated?•Probability theory and its applications are discussed in this section.•The documentary delves into the concept of probability, its calculation, and its uses in various fields likegambling, insurance, and decision-making.•It explores the work of mathematicians like Blaise Pascal and Pierre-Simon Laplace in developing the theory of probability.ConclusionThe documentary “The Story of Math” covers a wide range of mathematical questions, showcasing their historical significance and impact on various fields. From prime factorization to the calculus revolution, these questions demonstrate the beauty and versatility of mathematics. Byunderstanding the answers to these questions, we can appreciate the extensive and profound contribution of mathematics to our world.。
数学专业英语单词复试
数学专业英语单词复试Mathematics Major English Vocabulary for Interview1. Can you introduce yourself briefly?Sure. My name is [Your Name], and I am currently a mathematics major at [Your University]. I have a strong passion for numbers and problem-solving, which is why I chose to pursue a degree in mathematics.2. Why did you choose to study mathematics?I have always been fascinated by the beauty andprecision of mathematics. I enjoy the challenge of solving complex problems and the logical reasoning that comes with it. Mathematics offers a unique way of thinking and approaching various real-world issues, which is why I decided to study it.3. What are your strengths as a mathematics student?I believe my strengths lie in my analytical skills and my ability to think critically. I am also very organized and detail-oriented, which helps me when working on complex mathematical problems. Additionally, I have a strongfoundation in calculus, algebra, and statistics, which are essential for a mathematics major.4. Can you give an example of a difficult mathematical problem you have solved?Certainly. I once worked on a research project that involved modeling the spread of a disease usingdifferential equations. It was a challenging problem as it required a deep understanding of both mathematics and epidemiology. However, after several weeks of intense work and collaboration with my peers, we were able to come up with a comprehensive model that accurately predicted the spread of the disease.5. How do you stay motivated when faced with difficult mathematical concepts?I stay motivated by breaking down the problem into smaller, more manageable parts. I also like to seek help from professors, classmates, or online resources when I get stuck. Additionally, I remind myself of the importance of perseverance and hard work in mastering difficult mathematical concepts.6. What are your career goals as a mathematics major?My ultimate goal is to pursue a career in academia as a mathematics professor. I am passionate about teaching and sharing my knowledge with others, and I believe that becoming a professor will allow me to continue learning and growing in the field of mathematics.中文翻译：数学专业英语单词复试1. 你能简要介绍一下自己吗？当然。
Mathematics数学-附答案(1)
MathematicsAnswer all questions1.Given that 2x+y= 16 and In (2x–y) = ½ In 5, find the value of x and of y, leaving youranswers in surd form. [8]X=(4+√5)/3 Y=(8-√5)/32.Given that A = {x:-5 < 2x-3 ≤ 15}, B = {x: -4 ≤ x + 1 < 7} andA UB = {x: a ≤ x -1≤ b}, find the value of a and of b. [5]a=-6 b=83.Functions f, g and h are defined byf:x→ 2 + xg:x→ -|x-1|h:x→ -x2 + 2(a)Find the values of gh(-2) and f-1gh(-2).-3and-1 [4](b)Find in similar form, gf, fg and gh. gf=-|x+1| fg=2-|x-1| gh=-|-x2+1|[3](c)Find the values of x such that fg(x) = -1 x=4 or x=-2[3](d)Show that hg(x) = 1 + 2x- x2. ∵hg(x)=h(-|x-1|)=-(-|x-1|)2+2=-(x-1)2+2=-x2+2x+1 [4]4.Three points have coordinates A(5, -3), B(-2,1) and C(a , 5).(a)Find, in terms of a, the coordinates of M, which is the midpoint of BC. [4]The midpoint of BC is ((a-2)/2,3)(b)Find the value of a for which AM is perpendicular to ABa=132/7. [6]5.Find the fifth and sixth terms of binomial expansion of ( 2- ⅓ x2)9. Hence find thecoefficient of x10 in ( 2- ⅓ x2 )9 (3x2+5 ) . 5th:(-19/3)9 6th:( -10) 9[8]6.Find the coordinates of the points of intersection of the line x + y = 3 and the curvex2– 2x +2y2= 3. [6] x=3, y=0 or x=3/5,y=12/57.Find the range of values of k for which the equation x2– 6x + k2– 7 = 0 has real roots. 36-4×1×（k2-7）≥0 the result is -4≤k≤4[6] 8.Find all the angles between 0° and 360° inclusive which satisfysinxsec2x– 2tan x = 0 x=60°[6] 9. A body moves in a straight line so that its displacement, S m, from a point O at time tsec, is given by S = 5 + 15t2– 5t3.Find(a)The time when the body is instantaneously at rest, [4](b)The acceleration when t = 4, Answer:75[3](c)The total distance moved by the body in 9 seconds, [6](d)The average speed of the moving body. [4]10.A semicircle of centre O and radius 10 cm has diameter AB. The chord AQ is10 cm and the ratio of arc AP to arc AQ is 2 : 3.(a)Show that ∠AOP is 2⁄9 π radians.∵AO=QO=AQ=10 cm ∴∠AOQ=60° and∵the ratio of arc AP to arc AQ is2 : 3. ∴∠AOP=40°(40°/360°)×2л=2л/9[6](b)Calculate the area of segment AQP. the area of segment AQP is (50л/3)-25√3 [4]11.If x2– 2x– 3 is a factor of the expression x4+ px3+ qx– 81, find the value of p and ofq. With these of p and q, factorize the expression completely. [10] 数学回答以下所有问题1.已知2x+y和ln（2x-y）= ½ In 5 求x和y的值，保留根号。
雅思听力词汇
雅思听力高频词汇一直以来是众多老师和学生所追求的精华材料。
面对着市面上存在的各种各样辅导词汇的书籍和综合了所有考试内容的机经，很多烤鸭都会觉得无从下手。
其实笔者认为词汇只是表象，更重要的是要从词汇中悟出场景的考点和出题思路。
掌握雅思听力词汇首先要从基础词汇入手，然后再进入专业场景词汇。
建议广大烤鸭们一定要在背诵词汇时多进行联想，把练习过的剑桥雅思真题集系列中的场景进行串联，这样才可以做到场景和词汇同步学习，从而使听力学习更加深入！在本篇中，专家将重点总结和介绍一些雅思听力必备词汇中的基础词汇部分，供大家研究和学习！一、Listening basics: call每次考试都会有电话号码的听写，尤其在section 1中，有很多场景都是以一男一女打电话的方式来进行的，以下这些词汇能帮助大家把握电话对话的脉络，清晰的辨明考点出现的时机。
除了要清楚的了解外国人报电话号码时的节奏和停顿以外，还要对雅思考查比较少的点比如分机号、来电转移、漫游和付费方式等重点记忆，以防雅思考试向深化和细化的方向发展。
Numbers:Home / work phone number, emergency number, contact number, hot line, information line, enquiry line, mobile phone number, cell phone number, toll free number, code number, extension numberCall: phone, call, ring, give somebody a call, a ring, a telephone call, dial the number, press key, push keyTelephone answering machine, operator, hold on, hang onCall services: call diversion, call roaming, local number, distance number, international callCost: telephone rental, pay per minute, pay per hour, pay per monthExamples: 0903775115, 99281444, 033835071二、Listening basics: personal details个人信息的考查每次都占到考题数目的5道甚至以上，是烤鸭们的必对得分题目，万万不可再错。
fbi测试题及答案
fbi测试题及答案为了帮助您更好地准备FBI测试，以下是一些常见的FBI测试题目以及对应的答案。
请注意，这些题目是基于以往的FBI测试样本，以便您更好地了解测试内容和形式。
1. 认知能力（Cognitive Ability）题目：下列选项中，哪个单词与“Science”最相似？A. MathematicsB. HistoryC. GeographyD. Literature答案：A. Mathematics2. 面试准备（Interview Preparation）题目：在面试中，您应准备以下哪些方面？A. 自我介绍B. 研究职位需求C. 了解FBI的历史D. 具体的项目经验答案：A. 自我介绍、B. 研究职位需求、D. 具体的项目经验3. 人际交往能力（Interpersonal Skills）题目：下列哪种行为是示范良好的人际交往能力？A. 听取他人建议并认真考虑B. 批评他人的决策C. 单方面控制对话D. 优先表达自己的意见答案：A. 听取他人建议并认真考虑4. 身体素质（Physical Fitness）题目：在FBI特工训练中，以下哪项是身体素质评估的指标？A. 灵活性B. 社交技能C. 计算能力D. 技术专长答案：A. 灵活性5. 法律知识（Legal Knowledge）题目：为了通过FBI的法律知识测试，您应熟悉以下哪些法律原则？A. 宪法权利B. 隐私保护C. 刑法法规D. 商业合同答案：A. 宪法权利、B. 隐私保护、C. 刑法法规6. 心理评估（Psychological Assessment）题目：FBI心理评估的目的是什么？A. 评估个体情绪状态B. 测试记忆能力C. 识别可能存在的心理偏差D. 测试智力水平答案：C. 识别可能存在的心理偏差请注意，以上是对应题目的正确答案。
在FBI测试中，除了正确回答题目外，还需要注意时间管理、注意力集中和解答方式等方面的技巧。
如果您对FBI测试感兴趣，建议您深入了解FBI官方网站上提供的更多信息。
Mathematics Interview Questions
Mathematics Interview Questions1.Differentiate x x2.Integrate cos2(x) and cos3(x).3.What is the square root of i?4.If I had a cube and six colours and painted each side a different colour, howmany (different) ways could I paint the cube? What about if I had n colours instead of 6?5.Prove that root 2 is irrational.6.Integrate ln x.7.Sketch the curve (y2-2)2+(x2-2)2=2. What does it look like?8. 3 girls and 4 boys were standing in a circle. What is the probability that twogirls are together but one is not with them?9.Prove that 1+1/2+1/3+...+1/1000<1010.Is there such number N that 7 divided N2=3?11.What is the integral of x2 cos3(x)?12.How many squares can be made from a grid of ten by ten dots (ignorediagonal squares)?13.Integrate tan x.14.Pascal's triangle (prove that every number in the triangle is the sum of the twoabove it)15.Integrate 1/(1-lnx)16.sketch x x17.prove 4n - 1 is a multiple of 318.How many ways there are of getting from one vertex of a cube to the oppositevertex without going over the same edge twice?19.What shape there would be if the cube was cut in half from diagonallyopposite vertices?20.Draw x ln(x).21.Integrate and differentiate xln(x).22.Draw sin(1/X).23.Differentiate x(x^x)24.What do you know about triangles?25.Find a series of consecutive integers such that the sum of the series is a powerof 2.26.Prove Ptolemy's Theorem.27.Find roots of the equation mx=sin x considering different values of m.28.Integrate |sin n(x)+cos n(x)| between 0 and 2 & (pi) for cases n=1,229.x2 + y2 = z2. Prove xyz is a multiple of 6030.Two people are playing a game which involves taking it in turns to eat chillies.There are 5 mild chillies and 1 hot chilli. Assuming the game is over when the hot chilli is eaten (and that I don't like hot chillies), is it a disadvantage to go first? What is the probability that I will eat the chilli if I go first? How about if there are 6 mild and 2 hot?31.kx4=x3-x Find the real roots when k=0. Sketch the graph when k is small andthen when k is large, and find approximations of the real roots in both cases.When else does x have 3 real roots?32.Sketch f(x) = (x - R(x))2, where R(x) is x rounded up or down in the usual way.then sketch g(x) = f(1/x)33.(a+b)/2 is an integer, is the relationship transitive? (a+b)/3?34.Differentiate 1/1+(1/1+(1/1+1/(1 + x))))35.Sketch graph of 1/x, 1/x2, 1/(1+x2)36.Integrate 1/(1+x2)37.Integrate e x x2 between limits of 1 and 0. Draw that graph.38.Integrate x -2 between limits of 1 and -1. Draw the graph. Why is it -2 and notinfinity, as it appears to be on the graph?39.Write down 3 digits, and then write the number again next to itself, eg: 145145.Why is it divisible by 13?40.You are given a triangle with a fixed perimeter but you want to maximise thearea. What shape will it be? Prove it.41.Next you are given a quadrilateral with fixed perimeter and you want tomaximise the area. What shape will it be? Prove it.42.Integrate (1)/(x+x3), (1)/(1+x3), (1)/(1+x n)43.How many 0's are in 100!44.Prove that the angle at the centre of a circle is twice that at the circumference.45.How many ways are there in which you can colour three equal portions of adisc?46.Integrate 1/(9 +x2)47.Draw y=e x, then draw y=kx, then draw a graph of the numbers of solutions ofx against x for e x=kx, and then find the value of k where there is only 1solution.48.Rubik's cube and held it by two diagonally opposite vertices and rotated it tillit reached the same position, by how many degrees did it take a turn?49.Solve a b=b a for all real a and b.50.There is a game with 2 players (A&B) who take turns to roll a die and have toroll a six to win. What is the probability of person A winning?51.Sketch y=x3 and y=x5 on the same axis.52.What the 2 sides of a rectangle (a and b) would be to maximise the area ifa+b=2C (where C is a constant).53.Can 1000003 be written as the sum of 2 square numbers?54.Show that when you square an odd number, you always get one more than amultiple of 8.55.Prove that 1 + 1/2 + 1/3 + 1/4 + ... equals infinity56.Prove that for n E Z ,n>2, n(n+1)>(n+1)n57.Prove that sqrt(3) is irrational58.What are the possible unit digits for perfect squares?59.What are the possible remainders when a cube is divided by 9?60.Prove that 801,279,386,104 can't be written as the sum of 3 cubes61.Sketch y=ln(x)/x and find the maximum.62.What's the probability of flipping n consecutive heads on a fair coin? Whatabout an even number of consecutive heads?63.Two trains starting 30km apart and travelling towards each other. They meetafter 20 mins. If the faster train chases the slower train (starting 30km apart) they meet after 50mins. How fast are the trains moving?64.A 10 digit number is made up of only 5s and 0s. It's also divisible by 9. Howmany possibilities are there for the number?65.There is a set of numbers whose sum is equal to the sum of the elementssquared. What's bigger: the sum of the cubes or the sum of the fourth powers?66.Draw e(-x^2)67.Draw cos(x^2)68.What are the last two digits of the number which is formed by multiplying allthe odd numbers from 1 to 1000000?69.Prove that 1!+ 2!+ 3!+... has no square values for n>370.How many zeros in 365!71.Integrate x sin2x72.Draw e x , ln x, y=x what does show you. As x tends infinity, what does lnx/xtend to?73.Define the term 'prime number'74.Find method to find if a number is prime.75.Prove for a2 + b2 = c2 a and b can't both be odd.76.What are the conditions for which a cubic equation has two, one or nosolutions?77.What is the area between two circles, radius one, that go through each other'scentres?78.If every term in a sequence S is defined by the sum of every item before it,give a formula for the nth term79.Is 0.9 recurring = 1? Why? Prove it80.Why are there no Pythagorean triples in which both x and y are odd?81.draw a graph of sinx, sin2x, sin3x82.prove infinity of primes, prove infinity of primes of form 4n+183.differentiate cos3(x)84.Show (x-a)2 - (x-b)2 = 0 has no real roots if a does not equal b in as many waysas you can.85.Hence show: i) (x-a)3 + (x-b)3 = 0 has 1 real root ii) (x-a)4 + (x-b)4 = 0 has noreal roots iii) (x-a)4 + (x-b)4 = (b-a)4 has 2 real roots86.Find the values of all the derivatives of e(-1/x^2) at x=087.Show that n5-n3 is divisible by 1288.If I have a chance p of winning a point in tennis, what's the chance of winninga game89.Explain what integration is.90.If n is a perfect square and its second last digit is 7, what are the possibilitiesfor the last digit of n and can you show this will always be the case?91.How many subsets can you form from a set of n numbers?92.Prove that (a+b)/2 > sq.root of ab where a>0, b>0 and a does not equal b ieprove that arithmetic mean > geometric mean93.What is 00 (i.e is it 0 or1), and solve it by drawing x x94.If f(x+y)=f(x)f(y) show that f(0) = 1,95.Suggest prime factors of 61261250350396.How many faces are there on an icosahedron97.integrate 1/(1+sin x)98.What is the greatest value of n for which 20 factorial is divisible by 2n?99.Prove that the product of four consecutive integers is divisible by 24.。
外语面试经典问题
No.3：Professional qualities
No.4：Career selection and planning No.5：Scene interview No.6：Behavior based interview No.7：Pressure interview No.8：Closing interview
No.1：Personal information
Tell me about yourself , please ? Tell me about your family, please ? What’s your major strength? What’s your biggest weakness? Tell me your three greatest strengths and one weakness ? What are your hobbies and interests ?
No.5: Scene interview
If a customer crash into your office be ablaze with anger, and he want to meet your leader to talk something , as a secretary, how do you do ? If you have had worked hard, but your boss doesn’t appreciate you, how do you do ? If your leader arrange you to have a business trip with the colleague you have some trouble with him, how do you do ? If your leader ask some person to do the work which you should do, how do you do ? If you have some disagreement with your boss, how did you real to this? How do you set priorities when you are very busy ? If your leader ask you to do something unethical , how do you handle it ? If your leader ask you to do something which you don’t like to do, how do you do ? In team works , not everyone carried their fair share of the workload , how did you handle the situation ?
博士面试常见英语问题
博士面试常见英语问题Doctoral Interview Questions and Answers.1. Why are you interested in pursuing a doctoral degree in this field?My interest in this field has grown over the years, influenced by my undergraduate and graduate studies. I am fascinated by the complexity and challenges it presents, and I am eager to contribute to the existing knowledge. A doctoral degree will allow me to delve deeper into the subject, conduct original research, and make meaningful contributions to the field.2. Can you describe a research project you have worked on and its impact?During my master's program, I was part of a research team that studied the impact of climate change on local ecosystems. We conducted fieldwork, collected data, andanalyzed it to understand the changes in biodiversity and ecosystem functions. Our findings were published in a peer-reviewed journal and have been cited by other researchers. This experience taught me the importance of rigorous methodology, data analysis, and the impact of research on real-world problems.3. How do you approach a research problem?When approached with a research problem, I first identify the key questions that need to be answered. I then conduct a literature review to understand the existing knowledge and identify gaps. This helps me formulate hypotheses and design appropriate methodologies to test them. I believe in iterative research, where findings from one study inform the next, and I am willing to adapt my approach as new evidence emerges.4. How do you handle failure in research?Failure is a common part of research, and I approach it with a positive mindset. When experiments don't work out asexpected, I try to understand why they failed and learnfrom it. I believe that every failure is a step towards success, and it helps me refine my hypotheses and methods.I also seek feedback from my mentors and peers to gain new perspectives and ideas.5. What are your thoughts on collaborative research?Collaborative research is crucial in today's academic environment. It allows researchers to pool their resources, expertise, and ideas to address complex problems. I believe in the power of collaboration and have activelyparticipated in several projects where I have learned from my colleagues and contributed to the team's success. Collaborative research also helps build professional networks and enhances the impact of research.6. How do you stay updated with the latest research in your field?Staying updated with the latest research is essentialfor any researcher. I regularly read peer-reviewed journals,attend conferences and seminars, and participate in online discussion forums to stay informed. I also maintain a bibliography of relevant literature and update it periodically. Staying connected with my peers and mentors through email, social media, and professional networks also helps me keep up with the latest trends and developments.7. What are your career aspirations after completing your doctoral degree?Upon completing my doctoral degree, I aspire to join a research-intensive university as a faculty member. I am interested in teaching undergraduate and graduate courses, supervising research students, and conducting my own research. I also see myself contributing to the academic community through peer reviews, conference presentations, and collaborations with other researchers. Long-term, I hope to make significant contributions to the field and become a recognized expert in my area of specialization.8. How do you manage time and stress during your doctoral studies?Time management and stress management are crucialskills for doctoral students. I have learned to prioritize tasks, set realistic goals, and allocate sufficient timefor each task. I also use various tools and techniques, such as to-do lists, calendars, and reminders, to help me stay organized. To manage stress, I practice relaxation techniques, such as deep breathing and meditation, and engage in physical activities like running and yoga. I also seek support from my family, friends, and mentors when needed.9. How do you ensure the ethical conduct of your research?Ethical conduct is paramount in research. I ensure compliance with all applicable ethical guidelines and regulations by carefully reviewing them before starting any research project. I also obtain informed consent from participants, protect their privacy and confidentiality, and strive to minimize any potential harm to them. Whenever I encounter ethical dilemmas, I seek guidance from mymentors and peers to make informed decisions.10. Why do you want to join our university for your doctoral studies?I am attracted to your university's reputation in my field of study. Your institution has a strong research culture, excellent facilities, and a vibrant academic community. I am also impressed with the quality of your faculty members and their commitment to student success. I believe that the resources and support available at your university will enable me to achieve my research goals and make a significant contribution to the field.These are some common questions and answers that may be encountered during a doctoral interview. Remember to tailor your answers to fit the specific program and university you are applying to, and always present yourself as a passionate, motivated, and ethical researcher. Good luck!。
美国高考数学训练题Free ACT Math Test Practice Questions with Answer1
Free ACT Math Test Practice Questions with Answerssample 2Math questions, with answers and detailed solutions, similar to the questions in the ACT math test. The answers are at the bottom of the page.1. What is the greatest common factor of 45, 135 and 270?A) 5 B) 9 C) 15 D) 25 E) 452. What is the value of 2x + 1/2 when 5x - 3 = -3x + 5A) -1/2 B) -1/4 C) 1 D) 2 and 1/2 (mixed number) E) Value cannot be calculated3. The width W of a rectangle is 2 inches less than half its length L. Express the perimeter P ofthe rectangle in terms of the length L.A) 3L - 4 B) 4L - 4 C) 4L D) 3L - 2 E) 2L - 24. The total surface area of all six sides of the rectangular boxbelow is equal to 80 square inches. What is the volume of therectangular box in inches cubed?.A) 40 B) 48 C) 12 D) 30 E) 165. The points (-4 , -4), (-1 , -2) and (x , -8) are the vertices of a right triangle with the right angleat (-1 , -2). Find the value of x.A) 0 B) 2 C) 3 D) -1 E) -46. In the figure below, L1 and L2 are parallel lines. The correctrelationship between angles y and x is.A) y = x B) x + y = 180o C) x + y = 360oD) y = x + 90o E) y - x = 180180o7. If (x + y)2 = 144 and x2 - y2 = 24, then what is x if x and y are both positive?A) 7 B) 5 C) 12 D) 2 E) 88. How many 3 digit numbers can we make using the digits 4, 5, 7 and 9 and where repetition isallowed?A) 34B) 33C) 44D) 12 E) 439. A boat travels 10 miles East and then 24 miles South to an island. How many miles are therefrom the point of departure of the boat to the island?A) 34 B) 14 C) 26 D) 2√119E) 4410. What is the slope of any line perpendicular to the line -5x + 3y = 9?A) -3/5 B) 5/3 C) 3/5 D) -5/3 E) -1/511. Which of the following is a factor of the polynomial -2x2 + 7x - 6?A) -2x - 3 B) 2x + 2 C) x - 6 D) 2x - 2 E) -2x + 312. √(-9)(-4) + √(-4) = ?A) 6 + 2i B) 6 - 2i C) 8 D) 4 E) 2 + 6i13. Find the linear function f such that f(2) = 5 and f(3) = -5.A) f(x) = 2x + 1 B) f(x) = -10x - 5 C) f(x) = 3x - 1D) f(x) = -10x + 25 E) f(x) = -10x - 2514. A circular garden has an area of 100π feet squared. What is the circumference of the gardenin feet?A) 20 B) 10πC) 20πD) 400πE) 2500π15. If 5/x = 10 and 2/y = 6 then x/y = ?A) 5/3 B) 3/2 C) 3/5 D) 2/3 E) 5/216. If 2m-3 / 42m = 8, then 2m - 1 = ?A) 0 B) 1 C) 2 D) -5 E) -917. In the figure below, ABC is a right triangle. Points B, C and D arecollinear; points D, E and F are also collinear and so are points B,A and F. The length of segments DC and DE are equal. What isthe size, in degrees, of angle AFE?.A) 50o B) 40o C) 30o D) 45o E) 55o18. Which of the following is an equation of a line perpendicular to the line with equation 3x - 6y= 9?A) y = 2 B) 3x + 6y = 9 C) x - 2y = 3 D) 2x + 2y = 3 E) 2x + y = 719. If a and b are any real numbers, then which of the following expressions is always positive?A) |a| B) |a + b| C) |a - b| + 1/2 D) a2 + b2E) (a + b)220. The geometric figure below consists of a right triangle and 2semicircles. The diameters of the semicircles are the sides of thetriangle. What is the area of the shaded region in square centimetersif the length of the hypotenuse of the triangle is 8 centimeters?A) 64 B) 8πC) 64πD) 10πE) 1621. The mean of the numbers a, b, c, d and e is 23. The mean of the numbers a, b, c, d, e and fis 22. What is the value of f?A) 23 B) 18 C) 22 D) 22.5 E) 2022. Which of the following equations corresponds to the graphshown below?.A) y = (x - 3)2 - 1 B) y = -(x - 3)2 + 1C) y = (x - 3)2 + 1 D) y = x – 3 E) y = -(x - 3)2 - 123. Functions f and g are defined by f(x) = x2+ x and g(x) = √(x + 6). What is the value ofg(f(2))?A) 3 B) -3 C) 7 D) 6 E) -624. The sum of three consecutive integers is equal to 192. What is the product of thesenumbers?A) 216000 B) 7077888 C) 576 D) 110592 E) 26208025. What are the x-coordinates of the points intersection of the line with equation y = x + 1 andthe circle with equation x2 + y2 = 5A) -2 , 0 B) 1 , 2 C) -2 , 1 D) -2 , -1 E) 1 , 326. (1/2)sin(2x)(1 + cot2(x)) =A) tan(x) B) sin(x) C) cos(x) D) cot(x) E) sec(x)27. Find the area of the rectangle ABCD shown in the figure below.A) 2500 / √2B) 2500 C) 2500 / √3D) 1250 E) 500028. Solve for x: log x(1024) = -5A) 1/4 B) 4 C) 1/2 D) 1/8 E) 229. Simplify: 6 3√32 + 23√108A) 32 B) 18 3√2C) 36 3√2D) 18 3√4E) 36 3√430. Evaluate: 1 / (-5)2A) - 1 / 25 B) 1 / 25 C) 25 -25 E) 1 / 10 Answers to the Above Questions1. E2. D3. A4. B5. C6. B7. A8. E9. C10. A11. E12. A13. D14. C15. B16. D17. A18. E19. C20. B21. B22. E23. A24. E25. C26. D27. C28. A29. D30. B。
2021年麦肯锡招聘面试案例分析样题和答案英文
McKiney On line case studyTo step through this case example，we will give you some information，ask a question，and then，when you are ready，give you a sample answer. We hope that the exercise will give you a sense of the flow of a case interview. (Please note，you can stop this exercise and pick up where you left off later. Your cookies must be on to use this feature).In this exercise，you will answer a series of questions as the case unfolds. We provide our recommended answers after each question，with which you can compare your own answers. We want to emphasize that most questions in a case study do not have a single right answer. In a live case interview，we are more interested in your explanation of how you arrived at your answer，not just the answer itself. An interviewer can always assess different but equally valid ways of approaching an issue，and then bring you back to the particular line of inquiry that he or she wants to pursue.You should also keep in mind that in a live case，there will be far more interaction with the interviewer than this exercise allows. For example，you will have the opportunity to ask clarifying questions.Finally，a live case interview would typically be completed in 30 - 45 minutes，depending on how the case evolves. In this on-line exercise，there is no time limit. There are eight questions in this on-line case study. This case study is designed to roughly simulate one during your interview，so you will not be able to skip ahead to the next question until you have answered the one you are on. You can refresh yourmemory of previous answers by clicking the highlighted Q&A links to the left. To print the answer，click on the print icon that appears in the TOP RIGHT corner. At the end，you can print the entire on-line case study at once.The caseQuestion 1Client Goal：Double the number of recruits while maintaining their quality with minimal increase in resources expendedOur client recruits graduating college seniors for entry-level positions in locations around the world. It currently hires and places 500 graduates per year but would like to triple in size over the next ten years while maintaining quality. Assume that the increase must all come from hiring graduating seniors. (In an actual case，you may not be given this and other assumptions unless you ask.)The client's current recruiting budget is $2 million annually，and while it is in a strong financial position，it would like to spend as few additional resources as possible on recruiting. McKinsey is advising the client on what steps it will need to take in orderto meet its growth targets，while staying within its budget constraints.Q1：What levers does the organization have at its disposal to achieve its growth goal?A：Some possible levers are given below. It's terrific if you identified several of these and perhaps some others.•Attract more applicants at the same cost•Review the list of campuses targeted (e.g.，optimize resource allocation across schools). The review may result in adding certainhigher potential campuses and eliminating other ones that appear tohave more limited potential.•Review recruiting approach at each campus (e.g.，optimizecost-effectiveness of messages and approaches at each school).•Extend offers to a higher percentage of applicants while maintaining quality(e.g.，reduce the number of people who are turned down who would haveperformed equally well in the job)•Improve acceptance rates among offerees (e.g.，better communicate the benefits of the job relative to alternatives or improve the attractiveness of the job relative to alternatives)Question 2For the remainder of the discussion we'd like to focus on the two specific levers involving attracting more applicants at the same cost.•Review the list of campuses targeted (e.g.，optimize resource allocation across schools). The review may result in adding certain higher potentialcampuses and eliminating other ones that appear to have more limitedpotential.•Review recruiting approach at each campus (e.g.，optimizecost-effectiveness of messages and approaches at each school).Please note that if you identified different but equally valid levers，the interviewer would be able to assess them. But for the purpose of this case study，we are going to focus on these two levers.Q2：How would you initially approach determining whether the client can increase hiring by adjusting the list of campuses targeted?What sort of analysis would you want to conduct and why?A：You might take the following approach，where we've outlined two avenues of analysis：•Estimate the hiring potential across schools•Analyze the number of hires by school over the last several years•Develop a comprehensive list of schools that meet our requirements and a minimum set of standards for recruits•Survey seniors at these schools to determine interest in anentry-level position with the client•Consider the size of the graduating class at each school，determine how that class might be segmented (e.g.，each class could besegmented by discipline or segmented based on career interests inresponse to the survey)，then calculate the size of each segment •Estimate the optimal cost-per-hire across schools•Compare the current cost-per hire across schools•Identify opportunities to decrease the cost-per-hire at each school Helpful TipYou may have a slightly different list. Whatever your approach，we love to see candidates come at a problem in more than one way，but still address the issue as directly and practically as possible. In giving the answer，it's useful if you are clear about how the results of the analysis would help to answer the original question posed.Question 3Twenty-five percent of the annual recruiting budget is spent on candidates (i.e.，attracting，assessing，and getting them to accept). Twenty percent of hires are categorized as "most expensive" and have an average cost-per-hire of $2,000.Q3：What is the average cost-per-hire of all other candidates?Remember that the client hires 500 students per year and its annual recruiting budget is $2 million (information that we hope you noted earlier).A：The answer is $750 per hire (or less than half the cost-per-hire of the "most expensive" candidates).Amount spent on the less expensive candidates:25% of $2 million budget = $500,000 spent on candidates20% of 500 student = 100 students categorized as "most expensive"100 x $2,000 cost-per-hire = $200,000 spent on "most expensive" hires$500,000 recruiting budget - $200,000 = $300,000 remaining for all other hires The number of less expensive candidates:500 hires - 100 = 400 "other hires"Cost-per-hire of the less expensive candidates:$300,000/400 =$750 per hireHelpful TipWhile you may find that doing a straightforward math problem in the context of an interview is a bit tougher，you can see that it is just a matter of breaking the problem down. We are looking for both your ability to set the analysis up properly and then to do the math in real time.Question4Q：In order to decide whether to reduce costs at the least efficient schools (i.e.，those with an average cost per hire of $2,000)，what else would you want to know?A：Some of the possible answers are given below.Basic questions：•What are the components of costs at these schools (why is it so expensive to recruit there)?•What opportunities exist to reduce costs?•How much cost savings would result from implementing each of the opportunities?•What consequences would implementing each of these opportunities have on recruiting at the least efficient schools?Questions demonstrating further insight：•Why is the cost lower at more efficient schools，and are there best practices in resource management that can be applied to the least efficient schools?•If we reduce costs at the least efficient schools，what will we do with the cost savings (i.e.，what would be the benefit of spending the money elsewhere vs.where it is currently being spent)?Helpful TipWe would not expect anyone to come up with all of these answers，but we hope some of your answers head in the same direction as ours. Yours may bring some additional insights. In either case，be sure that you can clearly explain how your question will bring you closer to the right decision.Question 5The McKinsey team conducts some analysis that indicates that increasing spending on blanket advertising (e.g.，advertisements/flyers on campus) does not yield any significant increase in hires.Q5：Given that increased blanket advertising spending seems to be relatively ineffective，and the client doesn't want to increase overall costs，what might be some other ideas for increasing the candidate pool on a specific campus?A：We are looking for at least a couple of answers like the ones given below：•Improve/enhance recruiting messages (e.g.，understand target candidate group，refocus message on this group，understand competitive dynamic on campus)•Utilize referrals (e.g.，faculty，alumni)•Come up with creative ways to target specific departments/clubs of the school•Rethink advertising spending - while increasing blanket ad spending doesn't seem to work，advertising might still be the most efficient and effective way to increase the number of candidates if it is deployed in a more systematic，targeted wayHelpful TipThis question is a good one for demonstrating creativity because there's a long list of possible ideas. Additional insights into how a given idea would be approached and how much it would cost are helpful.Question 6For simplicity's sake，let's say we've conducted market research and found that there are two types of people on each campus，A and B. Historically，our client has also used two types of recruiting messages in its advertising. The first，called "See the World," gets one percent of type A students to apply，but three percent of type B students. The second，called "Pathway to Leadership," gets five percent of Type A students to apply，but only two percent of type B students.The chart below lists the breakdown of types A and B students at some of our major campuses，and the message our client is using on campus.Q6：Assuming there's no difference between the costs of each message，what can you tell me from this information?A：According to these numbers，the client should use the "Pathway to Leadership" message across all four universities. The "See the World" message is preferable onlyif more than 80% of the students at a given university are of type B.Helpful TipAn even more insightful response would mention that the ultimate answer depends on the cost of each message，whether the cost increases depending on the number of students at the campus，and how interested we are in students of Type A vs. Type B (e.g.，will one type be more likely than the other to get an offer and to be successful on the job). One could imagine using both messages on some campuses if the additional cost were justified by the resulting increase in hires.Question7University 4 graduates 1,000 seniors each year.Q7：How many new candidates might be generated by changing the recruiting message at University 4 to Pathway to Leadership?A：The answer is 20 candidates (i.e.，an increase of over 100%).Number of each type of student at University 4:1,000 seniors x 60% = 600 Type A students1,000 seniors x 40% = 400 Type B studentsCandidates attracted be See the World message:(1% x 600) + (3% x 400) = 18 candidatesCandidates attracted by Pathway to Leadership message:(5% x 600) + (2% x 400) = 38 candidatesIncrease in candidates resulting from change in message:38 - 18 = 20 more candidates (an increase of over 100%)Question8Q8：What sort of next steps should we tell our client we'd like to take based on what we have discussed today?A：The ability to come to a logical，defensible synthesis based on the information available at any point in an engagement is critical to the work we do. Even though we'd consider ourselves to be very early in the overall project at this point in the case，we do want to be able to share our current perspective. The ideal answer would include the following points：FINDINGS•There appears to be an opportunity to significantly increase total applicants of the same quality that we are getting today at the same or reduced cost：•Increasing blanket advertising is ineffective and costly，but changing the advertising message on some campuses could increaseapplicants significantly without increasing costs. At one of thecampuses we've looked at，University 4，the number of applicantswould go up more than 100 percent•The cost-per-hire varies dramatically from school to school. This suggests that there may be opportunities to reduce costs in certainplaces or reallocate resources more efficientlyNEXT STEPS•We plan to explore further ideas for increasing quality applications by changing the mix of schools，beginning with a more detailed review of the opportunities to reduce costs at certain schools•After looking at levers to increase total applicants，we will be analyzing opportunities to improve the offer rate (i.e.，ensure we're not turning down quality applicants) and to increase the acceptance rate•We will examine additional methods for attracting more applications from our current campuses (e.g.，referrals，clubs) in addition to assessing the impact of improved messaging on campus。
英语面试数学专业知识
英语面试数学专业知识1. IntroductionThis document aims to provide an overview of the essential mathematical knowledge that may be relevant for an English interview in the field of mathematics. The topics covered in this document include algebra, calculus, probability, and statistics. It is important to note that the information provided here is for reference purposes only and should not be considered an exhaustive list of topics.2. AlgebraAlgebra plays a fundamental role in mathematics and is a crucial subject in the study of numbers, equations, and structures. Some key topics in algebra that may be relevant for an English interview include:•Linear equations and inequalities: Understanding how to solve linear equations and inequalities is essential. This includes the concept of slope, graphing linear equations, and solving systems of linear equations.•Quadratic equations: Knowledge of quadratic equations, including factoring, completing the square, and the quadratic formula, is important. It is also valuable to understand the graphical representation of quadratic functions.•Exponents and logarithms: Familiarity with exponents and logarithms is crucial. This includes knowledge of the laws of exponents,simplifying expressions with exponents, and solving equations involvinglogarithms.3. CalculusCalculus is a branch of mathematics that deals with rates of change and accumulation. Some key topics in calculus that may be relevant for an English interview include:•Differentiation: Understanding the concept of derivatives, including the rules of differentiation, finding derivatives of basic functions, and applying differentiation to solve problems.•Integration: Familiarity with integration is important. This includes knowledge of the fundamental theorem of calculus, techniques of integration, and applications of integration in finding areas and volumes.•Limits: Understanding the concept of limits is crucial for calculus.This includes evaluating limits, understanding the properties of limits, andapplying limits to define derivatives and integrals.4. Probability and StatisticsProbability and statistics are essential branches of mathematics that deal with uncertainty and data analysis. Some key topics in probability and statistics that may be relevant for an English interview include:•Probability theory: Understanding the basic principles of probability, including sample spaces, events, and probability functions. It is also valuable to know how to calculate probabilities using counting techniques, such aspermutations and combinations.•Descriptive statistics: Familiarity with descriptive statistics is important. This includes knowledge of measures of central tendency (mean,median, mode) and measures of variability (variance, standard deviation).•Hypothesis testing: Knowledge of hypothesis testing is valuable. This includes understanding the concepts of null and alternative hypotheses, Type I and Type II errors, and performing hypothesis tests for means and proportions.5. ConclusionIn conclusion, this document has provided an overview of the essential mathematical knowledge that may be relevant for an English interview in the fieldof mathematics. The topics covered include algebra, calculus, probability, and statistics. It is important to note that this is not an exhaustive list, and candidates should be prepared to demonstrate a strong understanding of mathematical concepts beyond what is presented here. Good luck with your interview!。
英文面试问答
Sample Teacher Interview QuestionsTeacher Relationships With Students1.What kind of students do you like to work with? What type of students could you teach most effectively?2.You give an assignment. A student ridicules the assignment, saying it doesn’t make sense. What would you do?3.How do you help students experience success?4.How would you individualize instruction for students?5.What procedures do you use to evaluate student progress besides using tests?6.How would you challenge the slow learner and the advanced learner within the same class?7.What would your students say about you?Teacher Relationships With Colleagues1.What kind of teachers would you prefer to work with? Why?2.What activities would you like to work with in our school?3.What quality or qualities do you have that would enhance our teaching staff?4.What are some personality characteristics you find undesirable in people?5.Who should be responsible for discipline in a school? Why?6.What needs and/or expectations do you have of the school administration?7.How do you collaborate with your colleagues?Teacher Relationships With Parents1. What do you feel is the most effective way to communicate with parents? Describe how you have used this/these technique(s).2. Describe the reasons why you would contact parents.3. What would you include in your Open House presentations to parents?4. What community activities would you like to be associated with? Why?Instructional Techniques1.Describe any school experience you have had, particularly in student teaching (or in another teaching position) that has prepared you for a full-time position at our school.2.How would you integrate technology into the curriculum you would teach?3.Describe any innovative projects you have been involved in developing.4.Give an example of how you have used cooperative learning in your classroom.5.What four words would students use to describe your teaching strategies?6.What rules do you have for your classroom?7.Describe your teaching style and how you accommodate the different learning styles of the students in your classes.8.What do you consider to be your strengths and how will you use them in your teaching?9.In what ways do you keep students on task and well behaved during collaborative group activities?A Potpourri of Topics and Background Information1.Why did you choose to become a teacher?2.What are your hobbies and interests?3.What are your plans for continuing your professional growth?4.Tell me about an interesting article you have read recently ina professional journal.5.What contributions can you make to our school?6.What current trends in public education please you? Displease you?7.Tell me about the three people who have most influenced your own education and educational career.8.Tell us about a golden teaching moment?9.Tell us about yourself, and specifically what brought you to want to be an English, math, science teacher?10.What is your philosophy about teaching English, math, science?Questions for Management Expertise1.Describe the management strategies and techniques you use to maintain an effective classroom environment2.In what ways do you keep students on task and well behaved during collaborative group activities?3.Describe your expectations for student behavior? In other words, if I were to enter your class on an average day, what should I expect to see with regard to student behavior?4.Keith is your busy seventh-grader. He is constantly moving in your class and always ready to throw spitballs. Although his behavior is not seriously disruptive, it is annoying. He is especially active when he believes that you cannot see him. How would you deal with this situation?5.Describe the management strategies and techniques you use to maintain an effective classroom environment6.Describe your expectations for student behavior? In other words, if I were to enter your class on an average day, what should I expect to see with regard to student behavior?7.Keith is your busy seventh-grader. He is constantly moving in your class and always ready to throw spitballs. Although his behavior is not seriously disruptive, it is annoying. He is especially active when he believes that you cannot see him. How would you deal with this situation?Personal Characteristics Questions1.How would a colleague describe you?2.What are your strengths and weaknesses as a teacher?3.As a teacher, how do you relate to students, colleagues, and parents?4.What do you consider to be a major issue in public education today?Questions for Content Area Expertise:1.Describe your knowledge and experience with the California content standards applicable to your content area.2.Describe any specific areas of strength within your content area (e,g., Physical Science, Writing Workshop, Algebra, etc.).3.If you could teach just one grade level and subject within your content area, what would you choose? Why?4.What sorts of assessment, both formal and informal, do you view as being important indicators of successful performance for students learning your content area?5.If you could teach any novel, what would it be and what would your students be doing?6.How do you adjust for reading level differences within your classroom?Questions for English Learner Expertise:1.We have a large number of English learners in our district. What knowledge and experience do you have that is representative of your ability to teach English learners?2.What knowledge and experience do you have regarding the California English Language Development Standards?3.Imagine that you are teaching a “regular” mainstream class in your content area. A new student arrives in your class one day, and you soon find out that this student possesses only limited English fluency (that is, some oral fluency but verylimited reading and writing fluency). You realize that this is probably not the correct placement for the student, so you approach the counselor in charge of scheduling students. You are told that there is no room in the other classrooms for the foreseeable future and that you will just have to do the best you can. What would you do to accommodate this student until a better placement comes up?4.In what ways, both formal and informal, might you assess a student with limited English fluency to be sure the student is truly learning the content of your course curriculum?Short Interview Questions▪How would a colleague describe you?▪What are your strengths and weaknesses as a teacher?▪As a teacher, how do you relate to students, colleagues, and parents?▪What do you consider to be a major issue in public education today?▪Describe your knowledge and experience with the California content standards applicable to your content area.▪Describe any specific areas of strength within your content area (e,g., Physical Science, Writing Workshop, Algebra, etc.). ▪If you could teach just one grade level and subject within your content area, what would you choose? Why?▪What sorts of assessment, both formal and informal, do you view as being important indicators of successful performance for students learning your content area?▪We have a large number of English learners in ourdistrict. What knowledge and experience do you have that is representative of your ability to teach English learners?▪Imagine that you are teaching a “regular” mainstream class in your content area. A new student arrives in your class one day, and you soon find out that this student possesses only limited English fluency (that is, some oral fluency but very limited reading and writing fluency). You realize that this is probably not the correct placement for the student, so you approach the counselor in charge of scheduling students. You are told that there is no room in the other classrooms for the foreseeablefuture and that you will just have to do the best you can. What would you do to accommodate this student until a better placement comes up?▪In what ways, both formal and informal, might you assess a student with limited English fluency to be sure the student is truly learning the content of your course curriculum?▪Discuss a curriculum project you developed which generated high motivation and engagement among your students. Tell us what the project looked like and what resources you used to develop it.▪How do you feel about participating in an advisory period or other master-scheduled differences?▪What kinds of strategies do you use to challenge students to have an in-depth understanding of mathematics, science, English literature?▪What strategies do you use to make curriculum meaningful and relevant to students?▪Since we will be held accountable for standardized test results, what will you do in the area of curriculum development toe3nsure that students do well on the test without teaching the test?▪Describe the evaluation instruments you use to assess student learning.▪Describe your ideas for ensuring that you have positive communication with parents and the larger community.▪What do you envision will be your biggest challenge this year?▪How do you excel in working with students from diverse populations?▪Why are you interested in working at this school?▪Share with us your philosophy of teaching and learning?▪What is the role/responsibility of a teacher in a classroom?▪Tell us about a time when a student really got what you were hoping they would. An “Ah HA” moment.▪Why do you think students from diverse cultural and educational backgrounds do not excel in school in comparison to more traditional students?▪What kinds of things can be done to compensate for inadequacies in English or prior knowledge?▪Tell us about your approach to classroom discipline – how do you ensure your students are on-task, and what steps do you take when they are not?▪What do you think was your most successful lesson you have taught and why?▪What was the most challenging lesson you have had to teach, and how did you overcome the obstacles?▪What would be the ideal teaching position be?。
数学专业复试英语自我介绍
数学专业复试英语自我介绍Good morning, esteemed professors and fellow candidates.I am thrilled to be here today for the mathematics program interview.My passion for mathematics began in high school, where I found joy in solving complex problems and exploring the beauty of mathematical concepts. This love has only grown stronger with time, leading me to pursue a degree in mathematics.Throughout my undergraduate studies, I have not only excelled academically but also engaged in various mathematical competitions, which have honed my analytical and problem-solving skills. I believe these experiences have prepared me for the rigorous challenges of graduate-level mathematics.I am particularly interested in the field of applied mathematics, as I find the real-world applications of abstract concepts fascinating. I am eager to delve deeperinto areas such as optimization and mathematical modeling, which have the potential to make significant contributions to various industries.In addition to my academic pursuits, I am also an active member of the mathematics community. I have volunteered at local schools to tutor students and have participated inorganizing math workshops to promote the subject to a wider audience.I am committed to furthering my education and research in mathematics, and I am confident that the graduate program here will provide me with the resources and mentorship needed to achieve my goals.Thank you for considering my application. I am looking forward to the opportunity to contribute to and learn from this distinguished community.。
数学研究生复试英语问题
数学研究生复试英语问题Sure, I understand your requirements. Let's get started with the math graduate school interview questions.Question 1: Can you tell us about your research experience in mathematics?Answer: I have been actively involved in mathematical research during my undergraduate and graduate studies. My research topics have included algebraic geometry, number theory, and mathematical physics. I have worked on several research projects and have also co-authored papers with my professors. I have presented my research at various conferences and symposiums, and I believe that my research experience has prepared me well for the challenges of graduate study in mathematics.中文回答：我在本科和研究生阶段都积极参与了数学研究。
我的研究课题包括代数几何、数论和数学物理。
我参与了多个研究项目，并与我的教授们合著了论文。
我曾在各种会议和研讨会上展示过我的研究成果，我相信我的研究经验已经为我在数学研究生阶段的挑战做好了准备。
Question 2: What are your career goals in mathematics and how does our graduate program fit into those goals?Answer: My career goal in mathematics is to become a professional mathematician and contribute to the advancement of mathematical knowledge. I believe that your graduate program is well-known for its rigorous training and cutting-edge research opportunities, which will provide me with the necessary skills and knowledge to achieve my career goals. I am particularly interested in the faculty members' research areas and I am excited about the prospect of working with them on research projects.中文回答：我在数学领域的职业目标是成为一名专业数学家，并为数学知识的进步做出贡献。
Punchline Algebra Book B Answer Key Marcy Mathwork
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剑桥数学 笔试
剑桥数学笔试（中英文实用版）Task Title: Cambridge Mathematics InterviewTask Title: 剑桥数学面试Section 1: Problem SolvingSection 1: 问题解决During the Cambridge mathematics interview, candidates are often presented with a problem-solving task.This task is designed to assess the candidate"s ability to think logically and creatively.In order to succeed in this section, it is important for candidates to practice a wide range of mathematical problems and to develop their problem-solving strategies.在剑桥数学面试中，考生通常会面对一个解决问题的任务。
这个任务旨在评估考生逻辑思考和创造性的能力。
为了在这一部分取得成功，考生需要练习各种数学问题，并发展他们的解决问题的策略。
Section 2: Aptitude T estSection 2: 能力测试The Cambridge mathematics interview also includes an aptitude test.This test is designed to assess the candidate"s ability to learn and understand new mathematical concepts quickly.The test may include questions on calculus, algebra, and geometry, among other topics.It is important for candidates to review these topics thoroughly in order to perform well on the test.剑桥数学面试还包括一个能力测试。
剑桥大学三一学院数学系面试题目
TRINITY COLLEGEADMISSIONS QUIZ(MATHEMATICS2)DECEMBER1997.There are ten questions below which are on various areas of mathematics.They are of varying levels of difficulty:some should be easy and others rather hard.You are not expected to answer all of them,or necessarily to complete questions.You should just attempt those that appeal to you,and they will be used as a basis for discussion in the interview that follows.You should bring the question paper with you to the interview afterwards.1.In a tennis tournament there are2n participants.In thefirst round of the tournament,each player plays exactly once,so there are n games.Show that the pairings for thefirst round can be arranged in exactly (2n−1)!/2n−1(n−1)!ways.2.Let L1and L2be two lines in the plane,with equations y=m1x+c1and y=m2x+c2respectively. Suppose that they intersect at an acute angleθ.Show thattan(θ)=m1−m21+m1m2.3.Calculate π(x sin x)2dx.4.Of the numbers1,2,3,...,6000,how many are not multiples of2,3or5?5.There is a pile of129coins on a table,all unbiased except for one which has heads on both sides.Bob chooses a coin at random and tosses it eight times.The coin comes up heads every time.What is the probability that it will come up heads the ninth time as well?6.A packing case is held on the side of a hill and given a kick down the hill.The hill makes an angle ofθto the horizontal,and the coefficient of friction between the packing case and the ground isµ.What relationship betweenµandθguarantees that the packing case eventually comes to rest?Let gravitational acceleration be g.If the relationship above is satisfied,what must the initial speed of the packing case be to ensure that the distance it goes before stopping is d?17.Let nr stand for the number of subsets of size r taken from a set of size n .(This is the number of ways of choosing r objects from n if the order of choice does not matter.You may be more familiar with the notation n C r ,in which case feel free to use it.)Every subset of the set {1,2,...,n }either contains the element 1or it doesn’t.By considering these two possibilities,show thatn −1r −1 + n −1r = n r.By using a similar method,or otherwise,prove thatn −2r −2 +2 n −2r −1 + n −2r = n r.8.One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance.The other end of the rod is held still so that it touches the ceiling as well.Then the second end is released.If the length of the rod is l metres and gravitational acceleration is g metres per second squared,how fast is the unattached end of the rod moving when the rod is first vertical?9.Let M be a large real number.Explain briefly why there must be exactly one root w of the equation Mx =e x with w >1.Why is log M a reasonable approximation to w ?Write w =log M +y .Can you give an approximation to y ,and hence improve on log M as an approximation to w ?10.Twenty balls are placed in an urn.Five are red,five green,five yellow and five blue.Three balls are drawn from the urn at random without replacement.Write down expressions for the probabilities of the following events.(You need not calculate their numerical values.)(i)Exactly one of the balls drawn is red.(ii)The three balls drawn have different colours.(iii)The number of blue balls drawn is strictly greater than the number of yellow balls drawn.2。
面试数学老师英语作文
面试数学老师英语作文Title: Interview Experience for a Math Teacher PositionLast week, I had the opportunity to participate in an interview for a math teacher position at a renowned school. The experience was both exciting and challenging, as I was eager to demonstrate my skills and passion for teaching mathematics.上周，我有机会参加一所著名学校数学教师职位的面试。
这次经历既令人兴奋又充满挑战，因为我渴望展示我的教学技能和对数学教学的热情。
The interview began with an introduction from the principal, who emphasized the school's commitment to excellence in mathematics education. I was then asked to present a brief lesson plan, which I had prepared beforehand, focusing on a challenging mathematical concept.面试开始时，校长向我介绍了学校对数学教育的卓越追求。
随后，我被要求展示一个我事先准备好的简短教学计划，该计划侧重于一个具有挑战性的数学概念。
Following the lesson plan presentation, the interview panel posed a series of questions about my teaching philosophy, classroom management strategies, and experience with different learning styles. I answered confidently, highlighting my belief in student-centered learning and the importance of encouraging critical thinking skills.教学计划展示结束后，面试小组提出了一系列关于我的教学理念、课堂管理策略以及应对不同学习风格的经验的问题。
数学老师求职信的英语作文
数学老师求职信的英语作文Dear Hiring Committee,I am writing to express my interest in the Mathematics Teacher position at your school. With a strong background in mathematics education and a passion for teaching, I believe I would be a valuable addition to your team.I have obtained a Bachelor's degree in Mathematics and a Master's degree in Education, specializing in Mathematics Instruction. My academic background has equipped me with the necessary knowledge and skills to effectively teach mathematics to students of all levels. I have also completed multiple teacher training programs and workshops to stay current with the latest trends and teaching methods in mathematics education.In addition to my formal education, I have extensive experience teaching mathematics at both the high school and college levels. I have worked with students of diverse backgrounds and learning styles, and have developed effective strategies to help them succeed in mathematics. My students consistently achieve high scores on standardized tests and demonstrate a deep understanding of mathematical concepts.I firmly believe that every student has the potential to excel in mathematics with the right guidance and support. As a teacher, my goal is to foster a positive and engaging learning environment where students feel comfortable asking questions and exploring mathematical ideas. I utilize a variety of teaching methods, including hands-on activities, group projects, and technologyintegration, to cater to different learning styles and keep students motivated and engaged.I am also dedicated to fostering a growth mindset in my students, encouraging them to view challenges as opportunities for growth and development. I believe that by instilling a love for learning and a strong work ethic in my students, I can help them achieve their full potential in mathematics and beyond.I am particularly impressed by the innovative approach to education at your school and the dedication to academic excellence.I am confident that my skills and experience align well with your school's mission and values, and I am excited about the possibility of contributing to your team.Thank you for considering my application. I look forward to the opportunity to discuss how my qualifications and teaching philosophy align with the needs of your school. Please feel free to contact me at your convenience to schedule an interview.Sincerely,[Your Name]。
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Mathematics Interview Questions1.Differentiate x x2.Integrate cos2(x) and cos3(x).3.What is the square root of i?4.If I had a cube and six colours and painted each side a different colour, howmany (different) ways could I paint the cube? What about if I had n colours instead of 6?5.Prove that root 2 is irrational.6.Integrate ln x.7.Sketch the curve (y2-2)2+(x2-2)2=2. What does it look like?8. 3 girls and 4 boys were standing in a circle. What is the probability that twogirls are together but one is not with them?9.Prove that 1+1/2+1/3+...+1/1000<1010.Is there such number N that 7 divided N2=3?11.What is the integral of x2 cos3(x)?12.How many squares can be made from a grid of ten by ten dots (ignorediagonal squares)?13.Integrate tan x.14.Pascal's triangle (prove that every number in the triangle is the sum of the twoabove it)15.Integrate 1/(1-lnx)16.sketch x x17.prove 4n - 1 is a multiple of 318.How many ways there are of getting from one vertex of a cube to the oppositevertex without going over the same edge twice?19.What shape there would be if the cube was cut in half from diagonallyopposite vertices?20.Draw x ln(x).21.Integrate and differentiate xln(x).22.Draw sin(1/X).23.Differentiate x(x^x)24.What do you know about triangles?25.Find a series of consecutive integers such that the sum of the series is a powerof 2.26.Prove Ptolemy's Theorem.27.Find roots of the equation mx=sin x considering different values of m.28.Integrate |sin n(x)+cos n(x)| between 0 and 2 & (pi) for cases n=1,229.x2 + y2 = z2. Prove xyz is a multiple of 6030.Two people are playing a game which involves taking it in turns to eat chillies.There are 5 mild chillies and 1 hot chilli. Assuming the game is over when the hot chilli is eaten (and that I don't like hot chillies), is it a disadvantage to go first? What is the probability that I will eat the chilli if I go first? How about if there are 6 mild and 2 hot?31.kx4=x3-x Find the real roots when k=0. Sketch the graph when k is small andthen when k is large, and find approximations of the real roots in both cases.When else does x have 3 real roots?32.Sketch f(x) = (x - R(x))2, where R(x) is x rounded up or down in the usual way.then sketch g(x) = f(1/x)33.(a+b)/2 is an integer, is the relationship transitive? (a+b)/3?34.Differentiate 1/1+(1/1+(1/1+1/(1 + x))))35.Sketch graph of 1/x, 1/x2, 1/(1+x2)36.Integrate 1/(1+x2)37.Integrate e x x2 between limits of 1 and 0. Draw that graph.38.Integrate x -2 between limits of 1 and -1. Draw the graph. Why is it -2 and notinfinity, as it appears to be on the graph?39.Write down 3 digits, and then write the number again next to itself, eg: 145145.Why is it divisible by 13?40.You are given a triangle with a fixed perimeter but you want to maximise thearea. What shape will it be? Prove it.41.Next you are given a quadrilateral with fixed perimeter and you want tomaximise the area. What shape will it be? Prove it.42.Integrate (1)/(x+x3), (1)/(1+x3), (1)/(1+x n)43.How many 0's are in 100!44.Prove that the angle at the centre of a circle is twice that at the circumference.45.How many ways are there in which you can colour three equal portions of adisc?46.Integrate 1/(9 +x2)47.Draw y=e x, then draw y=kx, then draw a graph of the numbers of solutions ofx against x for e x=kx, and then find the value of k where there is only 1solution.48.Rubik's cube and held it by two diagonally opposite vertices and rotated it tillit reached the same position, by how many degrees did it take a turn?49.Solve a b=b a for all real a and b.50.There is a game with 2 players (A&B) who take turns to roll a die and have toroll a six to win. What is the probability of person A winning?51.Sketch y=x3 and y=x5 on the same axis.52.What the 2 sides of a rectangle (a and b) would be to maximise the area ifa+b=2C (where C is a constant).53.Can 1000003 be written as the sum of 2 square numbers?54.Show that when you square an odd number, you always get one more than amultiple of 8.55.Prove that 1 + 1/2 + 1/3 + 1/4 + ... equals infinity56.Prove that for n E Z ,n>2, n(n+1)>(n+1)n57.Prove that sqrt(3) is irrational58.What are the possible unit digits for perfect squares?59.What are the possible remainders when a cube is divided by 9?60.Prove that 801,279,386,104 can't be written as the sum of 3 cubes61.Sketch y=ln(x)/x and find the maximum.62.What's the probability of flipping n consecutive heads on a fair coin? Whatabout an even number of consecutive heads?63.Two trains starting 30km apart and travelling towards each other. They meetafter 20 mins. If the faster train chases the slower train (starting 30km apart) they meet after 50mins. How fast are the trains moving?64.A 10 digit number is made up of only 5s and 0s. It's also divisible by 9. Howmany possibilities are there for the number?65.There is a set of numbers whose sum is equal to the sum of the elementssquared. What's bigger: the sum of the cubes or the sum of the fourth powers?66.Draw e(-x^2)67.Draw cos(x^2)68.What are the last two digits of the number which is formed by multiplying allthe odd numbers from 1 to 1000000?69.Prove that 1!+ 2!+ 3!+... has no square values for n>370.How many zeros in 365!71.Integrate x sin2x72.Draw e x , ln x, y=x what does show you. As x tends infinity, what does lnx/xtend to?73.Define the term 'prime number'74.Find method to find if a number is prime.75.Prove for a2 + b2 = c2 a and b can't both be odd.76.What are the conditions for which a cubic equation has two, one or nosolutions?77.What is the area between two circles, radius one, that go through each other'scentres?78.If every term in a sequence S is defined by the sum of every item before it,give a formula for the nth term79.Is 0.9 recurring = 1? Why? Prove it80.Why are there no Pythagorean triples in which both x and y are odd?81.draw a graph of sinx, sin2x, sin3x82.prove infinity of primes, prove infinity of primes of form 4n+183.differentiate cos3(x)84.Show (x-a)2 - (x-b)2 = 0 has no real roots if a does not equal b in as many waysas you can.85.Hence show: i) (x-a)3 + (x-b)3 = 0 has 1 real root ii) (x-a)4 + (x-b)4 = 0 has noreal roots iii) (x-a)4 + (x-b)4 = (b-a)4 has 2 real roots86.Find the values of all the derivatives of e(-1/x^2) at x=087.Show that n5-n3 is divisible by 1288.If I have a chance p of winning a point in tennis, what's the chance of winninga game89.Explain what integration is.90.If n is a perfect square and its second last digit is 7, what are the possibilitiesfor the last digit of n and can you show this will always be the case?91.How many subsets can you form from a set of n numbers?92.Prove that (a+b)/2 > sq.root of ab where a>0, b>0 and a does not equal b ieprove that arithmetic mean > geometric mean93.What is 00 (i.e is it 0 or1), and solve it by drawing x x94.If f(x+y)=f(x)f(y) show that f(0) = 1,95.Suggest prime factors of 61261250350396.How many faces are there on an icosahedron97.integrate 1/(1+sin x)98.What is the greatest value of n for which 20 factorial is divisible by 2n?99.Prove that the product of four consecutive integers is divisible by 24.。