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英国本科桥梁课程A-level、Foundation及Access的介绍对于想去英国留学的中国学生来说，一般来说有两类途径可供学生作为参考：英国高中A-level课程和英国大学预科课程。
英国高中A-level课程简介：英国高中课程(General Certificate of Education Advanced Level)简称A-Level课程。
A-Level课程相当于英国教育的高中阶段。
入学年龄为年满16周岁的学生，相当于中国的高一以上学生，学制两年，但是学费昂贵。
A-level科目的选择与未来的大学的专业密切相关；A-Level毕业后将参加英国的高考，考试成绩的好坏，决定了是去重点大学还是一般的大学；A-level毕业后，择校的范围为英国的所有的大学，同时美国及其他英联邦国家也接受英国的A-Level，A-Level的入学标准为中国高中高一以上，年满16周岁的学生；无英语成绩者，可加修1至6个月的英语。
A-level优势劣势优势：A-level 的优势在于毕业后可选择英国大学排名较好的学校，成绩优异者还可进入像牛津剑桥、伦敦大学这样的世界名校。
一、中国学生在国内的高一或高二的在校学生可以赴英国学习A-Level课程。
这样，他们再经过两年的学习就可以进入英国大学就读，而不是像在中国那样，高中毕业然后还要学习一年的大学预科课程，才能入读英国大学。
二、这种课程是为中国学生进入英国大学做准备的理想课程。
无论是在学业方面还是在语言方面都会高于大学基础课程可达到的程度。
中国学生要用英语学习各门课程，亲自体验新的教学方法，其英语也会达到相当熟练的程度。
三、牛津、剑桥、帝国理工和伦敦大学学院这样的名牌英国大学几乎是从不录取大学预科的学生，而只录取A-Level毕业证书或同等学历的学生。
同样，如果没有A-Level毕业证书或同等学历，要想就读像医科或医疗卫生领域的某些课程也是难上加难。
但是，如果中国学生在A-Level课程考试中取得了好成绩，他们就会有很多机会进入英国非常好的大学攻读任何学科的课程。
60 Second Adventures in EconomicsNumber one: The Invisible HandAn economy is a tricky thing to control, and governments are always trying to figure out how to do it.Back in 1776 economist Adam Smith shocked everyone by saying that what governments should actually do is just to leave people alone to buy and sell freely among themselves. He suggested that if they just leave self-interested traders to compete with one another, markets are guided to positive outcomes “as if by an invisible hand”. If someo ne charges less than you, customers will buy from them instead, as you have to lower the price, or offer something better. Wherever enough people demand something, they will be supplied by the market like spoilt children--only in this case, everyone is happy.Later free-marketeers like Austrian economist Friedrich Hayek, argued that this “hands off” approach actually works better than any kind of central plan. But the problem is, economies can take a long time to reach their “equilibrium”, and may even stall along the way. And in the meantime people can get a little frustrated, which is why governments usually end up taking things into their own more visible hands instead.Number 2: The Paradox of ThriftMuch like a child getting his pocket money, one of the biggest economic questions is still whether it’s better to save or spend. Free-marketeers like Hayek and Milton Friedman say that, even in difficult times, it’s best to be thrifty and save. Banks then channel the savings into investment, in new plants, skills and techniques that let us produce more. And even if this new technology destroys jobs, wages will drop, and businesses hire more people so unemployment falls again. Simple-- At least in the long run. But then a “live-fast-die-young” kind of chap called John Maynar d Keynes cheerfully pointed out that “in the long run we’re all dead”. So, to avoid the misery of unemployment, the government should instead spend money to create jobs. Whereas if the government tightens its belt when people and businesses are doing the same, less is spent, so unemployment gets even worse. That is the paradox of thrift. So instead they should spend now and tax later when everyone’s happy to pay. Though making people happy to pay tax was something even Keynes didn’t solve.Number Three: The Phillips Curve.Bill Phillips was crocodile hunter and economist from New Zealand, who spotted that, when employment levels are high, wages rise faster people have more money to spend, so prices go up, and so does inflation. And likewise, when unemployment is high, the lack of money to spend means that inflation goes down. This became known as the Phillips Curve. Governments even set policy by the curve, tolerating the inflation when they spent extra money creating jobs. But they forgot that the workers could also see the effects of the curve. So, whenunemployment went down, they expected inflation and demanded higher wages, causing unemployment to go back up, while inflation remained high--Which is what happened in the 1970s, when both inflation and unemployment rose. Then in the 90s, umployment dropped while inflation stayed low, which all rather took the bend out of Phillips’curve. But at least part of Phillips’ troublesome trade–off lives on: when faster growth and full employment return, you can bet inflation will be along to spoil the party.Number Four: The Principle of Comparative Advantage.Whether you think the economies work best if they’re left alone, or that governments need to do something to get them working, the one thing that can’t be controlled is the rest of the world. Fear of foreign competition once led countries to try and produce everything they needed, and impose heavy taxes to keep out foreign goods. However, economist David Ricardo showed that international trade would actually make everyone better off, bringing in one of the first great economic models. He pointed out that, even if a country can produce pretty much everything at the lowest possible cost, with what economists call an “absolute advantage”, it’s sti ll better to focus on the products it can make most efficiently. That sacrifice the least amount of other goods, and let the rest of the world do the same. By specializing, they can then export these surpluses to each other and both end up better off. This is the principle of comparative advantages, and it has persuaded many countries to sign up to free-trade agreements, but unfortunately, it takes long time for countries to trade their way to prosperity. And because it’s much easier to move to where the mo ney is, it increasingly not only goods that cross borders, but people which has somewhat uprooted Ricardo’ theory.Number Five: The Impossible Trinity. 三元论Most counties trade with one an other, which is usually pretty good for all involved, but it does mean it’s a big harder for each to keep control of its own finances. There are three things that governments are particularly keen on. They like to keep the exchange rate stable, so that import and export prices don’t suddenly jump around. They also like to control interest rates, so they can keep borrowers happy, without upsetting savers. And they like money flow in and out of their country, without causing too much disruption. But there’s a problem, when you try all of these at once. Say for example, the Eurozone tries to lower its interest rate, to boost investment and reduce unemployment. Money flows out to earn higher interest rates everywhere. Exchange rates low, which causes inflation, so the Euro interest rate is forced back up again. You can either fix your exchange rate, and let money flows freely across national borders, but have no control over your interest rates. Or control your interest and exchange rates, but then you can’t stop the capital flowing in and out. But, like an overzealous triathlete, you can’t do all three at once.Number Six: Rational Choice Theory.Of all the things to factor in when to running an economy, the most troublesome is people.Now by and large humans are a rational lot. When the price of something rises, people would supply more of it and buy less of it. If they expect inflation to go up, people would usually ask for higher wages (Though they might not get them.) And if they can see interest and exchange rates falling in one country, people with lots of money there w ill try to move it out, faster than you can say “double dip”.And government often decides economic policies, assuming such rational actions--w hich would be great, if it weren’t for the fact that those pesky humans don’t always do what’s best for them.Sometimes they mistakenly think they know all the facts, or may be the facts are just too complicated. And sometimes people just decided to follow the crowd, relying on others to know what they are doing.When too many cheap mortgages were being sold in 2007, a lot of people did not know what was going on, and a lot of others just followed the crowd. Some lenders may have rationally believed that, when the crunch came, the scale of the problem would force the government to rescue them, which was true for the banks--if not for all their customers.。
会计用英语如何学好Understand the Basic Principles of AccountingThe first step in learning accounting is to understand the basic principles of accounting. These principles are the foundation of accounting and are used to record, interpret, and communicate financial information. Some of the basic accounting principles include the accrual principle, the matching principle, the consistency principle, and the materiality principle.It is important to familiarize yourself with these principles and understand how they are applied in practice. This will help you to understand the logic behind accounting transactions and financial statements.Take an Accounting CourseOne of the best ways to learn accounting is to take a structured accounting course. There are many options available, including online courses, in-person classes, and self-study materials. Taking a course will help you to learn the key concepts of accounting, gain practical skills, and improve your knowledge of accounting principles and practices.There are many reputable institutions that offer accounting courses, such as universities, colleges, and professional organizations. Choose a course that fits your schedule and learning style, and be sure to review the curriculum to ensure that it covers the topics you want to learn.Practice, Practice, PracticeAs with any skill, practice is essential for learning accounting. To become proficient in accounting, you need to practice solving accounting problems, working with financial statements, and analyzing transactions. There are many resources available to help you practice, including textbooks, online exercises, and practice exams.Set aside time each day to practice accounting and be consistent with your efforts. The more you practice, the better you will become at accounting, and the more confident you will feel in your skills.Stay Updated with Accounting StandardsAccounting standards are constantly evolving, and it is important to stay updated with the latest changes in the accounting industry. This will help you to stay current with changes in financial reporting requirements, understand new accounting principles, and comply with regulatory requirements.There are many resources available to help you stay updated with accounting standards, including accounting publications, accounting websites, and professional organizations.Make it a habit to read the latest accounting news and stay informed about changes in accounting standards.Network with Other AccountantsNetworking with other accountants is a valuable way to learn more about the accounting industry, connect with professionals, and gain insights into new trends and developments in accounting. Attend accounting conferences, join accounting associations, and participate in accounting events to meet other accountants and build your network.Networking can also help you to find job opportunities, gain mentorship from experienced accountants, and expand your knowledge of the accounting profession. Stay active in the accounting community and be open to learning from others.Seek Feedback and AdviceTo improve your accounting skills, it is important to seek feedback and advice from others. This can help you to identify areas for improvement, learn new techniques, and gain perspectives from others in the field. Ask your instructors, mentors, colleagues, or peers for feedback on your accounting work, and be open to constructive criticism.Feedback can help you to refine your accounting skills, overcome challenges, and make progress in your accounting learning journey. Use feedback as a tool for improvement and strive to continually enhance your accounting abilities.Stay Committed and MotivatedLearning accounting requires commitment, dedication, and motivation. It is not always easy, and there may be challenges along the way. Stay focused on your goals, remind yourself of the reasons why you want to learn accounting, and stay motivated to continue learning.Set realistic goals for yourself, celebrate your progress, and keep a positive attitude towards learning accounting. Remember that learning accounting is a lifelong journey, and with perseverance and determination, you can achieve success in the field of accounting.In conclusion, learning accounting is a valuable skill that can open up many career opportunities and help you make informed financial decisions. By following these tips, you can learn accounting effectively, improve your skills, and achieve success in the accounting industry. Stay committed to your learning journey, practice consistently, and stay updated with accounting standards to become a proficient accountant.。
a-level课程科目摘要：一、前言二、A-level 课程简介1.A-level 课程的起源2.A-level 课程的学制和年龄限制三、A-level 课程科目1.科学类1.物理2.化学3.生物2.社会科学类1.经济2.历史3.地理3.艺术类1.艺术与设计2.音乐4.语言类1.英语2.汉语5.数学类1.数学2.进阶数学四、A-level 课程的优势和挑战五、结论正文：一、前言A-level 课程是英国高中课程，面向年龄在16-19 岁的学生。
它在国际上具有很高的认可度，吸引了众多国内外的学生学习。
本文将对A-level 课程的科目进行详细的介绍。
二、A-level 课程简介A-level 课程起源于英国，是英国普通教育证书高级水平课程。
该课程为期两年，通常在12 年级和13 年级进行。
年龄限制在16-19 岁之间。
A-level 课程结束后，学生将参加统一的考试，成绩将作为大学录取的依据。
三、A-level 课程科目A-level 课程涵盖了多个领域，共有70 多门课程供学生选择。
以下是部分科目的介绍：1.科学类物理、化学和生物是科学类课程的重要组成部分。
这些课程旨在培养学生的实验能力和理论基础，为大学的理工科专业奠定基础。
2.社会科学类社会科学课程包括经济、历史和地理等。
这些课程帮助学生了解社会现象、经济体系和人类历史，为学习政治、法律、社会学等社会科学专业做好准备。
3.艺术类艺术类课程包括艺术与设计、音乐等。
这些课程培养学生的审美能力和创造力，为进入艺术类院校和从事创意产业奠定基础。
4.语言类语言类课程包括英语和汉语等。
这些课程旨在提高学生的语言运用和沟通能力，为学习语言学、翻译和文学专业做好准备。
5.数学类数学课程包括基础数学和进阶数学。
这些课程培养学生的逻辑思维和问题解决能力，为大学的理工科专业奠定基础。
四、A-level 课程的优势和挑战A-level 课程的优势在于其多样化的科目选择，让学生可以根据兴趣和特长进行深入学习。
Alevel的全称叫做General Certificate Of EducationAdvanced Level中文翻译为普通教育高级证书，它是英国学生进入大学所需要学习的主要测试课程，相当于我们的高考。
而Alevel的课程试卷都是由剑桥进行统一命题的、阅卷，全球的考生可以在当地或者所在国家进行统一考试，其考试结果具有广泛的公认性。
Level的证书由剑桥大学颁发，学生可以凭借Alevel申报世界上大部分的名牌大学。
课程科目介绍总的来说大部分的英国学生在两年之内完成这种课程，但是有一些能力突出的学生也可以在较短的时间内修完。
国内是学生可以自学3-4门Alevel课程然后去北上广参加英国文化委员会参加考试。
ALevel有70余种课程供学生自由选择，中国学生只要选择其中自己擅长并感兴趣的3-4门科目学习并参加A-Level大考就可以了（其中也包含必修课），非常适合偏科的同学学习。
Alevel课程的学分制分为两年，第一年也就是高一称为AS水准。
学生必须选址3-4门学科学习，通过考试后获得AS证书，高二学习的是A2课程，学生可以做自由选择AS水准中的3门学习，获得证书。
A2学年开始时（9-10月份），学生凭AS阶段成绩及老师对其A2阶段的预测成绩，进行大学申请。
12月参加给予自己面试机会的学校的面试，12月至次年3月，学校会给初步合格的学生有条件的录取（海外学生有雅思要求）。
8月份拿到正式高中毕业成绩且雅思达标，则自动录取，随后学校就会发Offer及CAS文件。
学通国际课程培训中心自2008年起一直致力于ALEVEL、IGCSE、IB、AP、SAT2等主流国际课程中30多门科目的提分与培优，经11年深耕教学，目前已拥有教师团队80余人，其中20%为博士，80%为名校海归硕士，平均国际课程教龄8年以上，每年为学生提供50000小时以上的高品质课程。
除常规国际课程培训外，我们还提供“G5全程护航计划”——全天候全脱产式学习，“全球TOP10大学冲击计划”——高考留学两不误双轨制ALEVEL课程，国际学校备考与衔接课程，英国G5名校STEP、MAT、PAT、TSA、牛剑面试等附加考试辅导，海外学校iTEP、Ukiset、AEAS、AEIS、维立克面试等入学考试辅导课程；同时还提供个性化的学术背景提升项目。
alevels1公式A-levels (Advanced Level Examination) is an internationally recognized qualification for high school students. It is commonly used as a prerequisite for admission into prestigious universities around the world. A-levels are rigorous and demanding, requiring students to demonstrate their knowledge and understanding of various subjects. In this article, we will discuss the structure of A-levels and provide some tips for success.1. Structure of A-levels:A-levels are typically a two-year program, with students taking exams at the end of the second year. The number of subjects taken can vary, but most students choose to study three or four subjects. Each subject is divided into different modules or units, and students are assessed through written exams at the end of each module. The final A-level grade is determined by the combined marks obtained in all the modules.2. Subject choices:Students have a wide range of subjects to choose from for their A-level studies. Some popular subjects include Mathematics, English Literature, Sciences (Physics, Chemistry, Biology), History, Geography, and Foreign Languages. It is important to choose subjects that align with your interests and abilities, as this will make studying and revising for exams more enjoyable.3. Study techniques:Effective study techniques are essential for success in A-levels. Here are some tips:- Create a study schedule: Plan your study sessions in advance, allocating dedicated time for each subject. This will help you stay organized and ensure you cover all the necessary material.- Take comprehensive notes: During classes, make sure to take detailed notes. This will help you review the material later and reinforce your understanding of the subject.- Use active learning techniques: Instead of simply reading textbooks, actively engage with the material by summarizing key concepts, asking questions, and relating the content to real-life examples.- Seek help when needed: If you are struggling with a particular subject or topic, don't hesitate to ask for help. Consult your teachers, classmates, or seek additional resources such as textbooks or online tutorials.4. Revision strategies:A-level exams are challenging, and effective revision is crucial. Here are some strategies to consider:- Begin early: Start revising well in advance of the exams to allow sufficient time to cover all the material. Cramming at the last minute is ineffective and can lead to stress and poor performance.- Practice past papers: Familiarize yourself with the exam format by practicing past papers. This will help you become familiar with the types of questions asked and improve your time management skills.- Create revision notes: Summarize key information in concise revision notes. This will make it easier to review the material quickly and refresh your memory before the exams.- Form study groups: Collaborate with classmates to form study groups. Discussing and explaining concepts to each other can enhance understanding and improve retention.5. Exam techniques:Lastly, mastering exam techniques is crucial for performing well in A-levels. Here are some tips:- Read the questions carefully: Take the time to read and understand each question before answering. Identify keywords and ensure you address all aspects of the question.- Plan your answers: Before diving into writing your answer, take a few minutes to plan your response. Outline the key points you want to include to ensure a well-structured and coherent answer. - Manage your time: A-level exams are time-pressured, so it's important to manage your time effectively. Allocate specific time slots for each question and stick to them.- Review your answers: If time allows, review your answers before submitting the exam. Check for any errors or omissions and make any necessary corrections.In conclusion, A-levels are a rigorous qualification that requires dedication and effective study techniques. By choosing the right subjects, planning your study sessions, and employing effective revision and exam techniques, you can increase your chances of success in A-level exams. Remember to pace yourself and seek help when needed. Good luck!。
a-level 课程体系
A-Level课程体系是一种普遍采用于英国和其他国家的高中水平学术课程体系。
A-Level是Advanced Level的简称，意为“高级水平”。
A-Level课程体系旨在为学生提供深入学习和研究各个学科领域的机会，以为他们的大学教育做好准备。
A-Level课程体系通常分为两个层次，即AS-Level（Advanced Subsidiary Level）和A2-Level（Advanced 2 Level）。
学生通常在16至18岁之间修读这些课程。
AS-Level是A-Level课程的第一部分，学生需要选修3-4门不同的学科。
AS-Level的学习时间为一年，学生通常会在AS-Level结束后进行考试。
A2-Level是A-Level课程的第二部分，学生需要继续选修他们在AS-Level中学习的学科，并有时可以加入新的学科。
A2-Level的学习时间为一年，学生通常会在A2-Level结束后进行考试。
A-Level的考试成绩通常是进入大学的关键因素之一。
学生的A-Level成绩将会被大学录取委员会考虑在内，以决定他们是否有资格进入特定的大学及专业。
A-Level课程体系提供了广泛的学科选择，包括科学、数学、人文科学、社会科学和艺术等。
学生可以根据个人兴趣和职业目标选择适合自己的学科组合。
总的来说，A-Level课程体系通过深入学习和专业化学科，为学生提供了进一步学习和职业发展的机会，帮助他们在大学和职业道路上取得成功。
江西省南昌市2015-2016学年度第一学期期末试卷（江西师大附中使用）高三理科数学分析一、整体解读试卷紧扣教材和考试说明，从考生熟悉的基础知识入手，多角度、多层次地考查了学生的数学理性思维能力及对数学本质的理解能力，立足基础，先易后难，难易适中，强调应用，不偏不怪，达到了“考基础、考能力、考素质”的目标。
试卷所涉及的知识内容都在考试大纲的范围内，几乎覆盖了高中所学知识的全部重要内容，体现了“重点知识重点考查”的原则。
1．回归教材，注重基础试卷遵循了考查基础知识为主体的原则，尤其是考试说明中的大部分知识点均有涉及，其中应用题与抗战胜利70周年为背景，把爱国主义教育渗透到试题当中，使学生感受到了数学的育才价值，所有这些题目的设计都回归教材和中学教学实际，操作性强。
2．适当设置题目难度与区分度选择题第12题和填空题第16题以及解答题的第21题，都是综合性问题，难度较大，学生不仅要有较强的分析问题和解决问题的能力，以及扎实深厚的数学基本功，而且还要掌握必须的数学思想与方法，否则在有限的时间内，很难完成。
3．布局合理，考查全面，着重数学方法和数学思想的考察在选择题，填空题，解答题和三选一问题中，试卷均对高中数学中的重点内容进行了反复考查。
包括函数，三角函数，数列、立体几何、概率统计、解析几何、导数等几大版块问题。
这些问题都是以知识为载体，立意于能力，让数学思想方法和数学思维方式贯穿于整个试题的解答过程之中。
二、亮点试题分析1．【试卷原题】11.已知,,A B C 是单位圆上互不相同的三点，且满足AB AC →→=，则AB AC →→⋅的最小值为（ ）A ．14-B ．12-C ．34-D ．1-【考查方向】本题主要考查了平面向量的线性运算及向量的数量积等知识，是向量与三角的典型综合题。
解法较多，属于较难题，得分率较低。
【易错点】1．不能正确用OA ，OB ，OC 表示其它向量。
2．找不出OB 与OA 的夹角和OB 与OC 的夹角的倍数关系。
【解题思路】1．把向量用OA ，OB ，OC 表示出来。
2．把求最值问题转化为三角函数的最值求解。
【解析】设单位圆的圆心为O ，由AB AC →→=得，22()()OB OA OC OA -=-，因为1OA OB OC ===，所以有，OB OA OC OA ⋅=⋅则()()AB AC OB OA OC OA ⋅=-⋅-2OB OC OB OA OA OC OA =⋅-⋅-⋅+ 21OB OC OB OA =⋅-⋅+设OB 与OA 的夹角为α，则OB 与OC 的夹角为2α所以，cos 22cos 1AB AC αα⋅=-+2112(cos )22α=--即，AB AC ⋅的最小值为12-，故选B 。
【举一反三】【相似较难试题】【2015高考天津，理14】在等腰梯形ABCD 中,已知//,2,1,60AB DC AB BC ABC ==∠= ,动点E 和F 分别在线段BC 和DC 上,且,1,,9BE BC DF DC λλ==则AE AF ⋅的最小值为 .【试题分析】本题主要考查向量的几何运算、向量的数量积与基本不等式.运用向量的几何运算求,AE AF ，体现了数形结合的基本思想，再运用向量数量积的定义计算AE AF ⋅，体现了数学定义的运用，再利用基本不等式求最小值，体现了数学知识的综合应用能力.是思维能力与计算能力的综合体现. 【答案】2918【解析】因为1,9DF DC λ=12DC AB =，119199918CF DF DC DC DC DC AB λλλλλ--=-=-==， AE AB BE AB BC λ=+=+，19191818AF AB BC CF AB BC AB AB BC λλλλ-+=++=++=+，()221919191181818AE AF AB BC AB BC AB BC AB BCλλλλλλλλλ+++⎛⎫⎛⎫⋅=+⋅+=+++⋅⋅ ⎪ ⎪⎝⎭⎝⎭19199421cos1201818λλλλ++=⨯++⨯⨯⨯︒2117172992181818λλ=++≥+= 当且仅当2192λλ=即23λ=时AE AF ⋅的最小值为2918. 2．【试卷原题】20. （本小题满分12分）已知抛物线C 的焦点()1,0F ，其准线与x 轴的交点为K ，过点K 的直线l 与C 交于,A B 两点，点A 关于x 轴的对称点为D ． （Ⅰ）证明：点F 在直线BD 上； （Ⅱ）设89FA FB →→⋅=，求BDK ∆内切圆M 的方程. 【考查方向】本题主要考查抛物线的标准方程和性质，直线与抛物线的位置关系，圆的标准方程，韦达定理，点到直线距离公式等知识，考查了解析几何设而不求和化归与转化的数学思想方法，是直线与圆锥曲线的综合问题，属于较难题。
【易错点】1．设直线l 的方程为(1)y m x =+，致使解法不严密。
2．不能正确运用韦达定理，设而不求，使得运算繁琐，最后得不到正确答案。
【解题思路】1．设出点的坐标，列出方程。
2．利用韦达定理，设而不求，简化运算过程。
3．根据圆的性质，巧用点到直线的距离公式求解。
【解析】（Ⅰ）由题可知()1,0K -，抛物线的方程为24y x =则可设直线l 的方程为1x my =-，()()()112211,,,,,A x y B x y D x y -，故214x my y x =-⎧⎨=⎩整理得2440y my -+=，故121244y y m y y +=⎧⎨=⎩则直线BD 的方程为()212221y y y y x x x x +-=--即2222144y y y x y y ⎛⎫-=- ⎪-⎝⎭令0y =，得1214y yx ==，所以()1,0F 在直线BD 上.（Ⅱ）由（Ⅰ）可知121244y y m y y +=⎧⎨=⎩，所以()()212121142x x my my m +=-+-=-，()()1211111x x my my =--= 又()111,FA x y →=-，()221,FB x y →=-故()()()21212121211584FA FB x x y y x x x x m →→⋅=--+=-++=-，则28484,93m m -=∴=±，故直线l 的方程为3430x y ++=或3430x y -+=213y y -===±，故直线BD 的方程330x -=或330x -=，又KF 为BKD ∠的平分线，故可设圆心()(),011M t t -<<，(),0M t 到直线l 及BD 的距离分别为3131,54t t +--------------10分 由313154t t +-=得19t =或9t =（舍去）.故圆M 的半径为31253t r +== 所以圆M 的方程为221499x y ⎛⎫-+= ⎪⎝⎭【举一反三】【相似较难试题】【2014高考全国，22】 已知抛物线C ：y 2＝2px(p>0)的焦点为F ，直线y ＝4与y 轴的交点为P ，与C 的交点为Q ，且|QF|＝54|PQ|.（1）求C 的方程；（2）过F 的直线l 与C 相交于A ，B 两点，若AB 的垂直平分线l′与C 相交于M ，N 两点，且A ，M ，B ，N 四点在同一圆上，求l 的方程．【试题分析】本题主要考查求抛物线的标准方程,直线和圆锥曲线的位置关系的应用,韦达定理,弦长公式的应用,解法及所涉及的知识和上题基本相同. 【答案】（1）y 2＝4x. （2）x －y －1＝0或x ＋y －1＝0. 【解析】（1）设Q(x 0，4)，代入y 2＝2px ，得x 0＝8p，所以|PQ|＝8p ，|QF|＝p 2＋x 0＝p 2＋8p.由题设得p 2＋8p ＝54×8p ，解得p ＝－2(舍去)或p ＝2，所以C 的方程为y 2＝4x.（2）依题意知l 与坐标轴不垂直，故可设l 的方程为x ＝my ＋1(m≠0)． 代入y 2＝4x ，得y 2－4my －4＝0. 设A(x 1，y 1)，B(x 2，y 2)， 则y 1＋y 2＝4m ，y 1y 2＝－4.故线段的AB 的中点为D(2m 2＋1，2m)， |AB|＝m 2＋1|y 1－y 2|＝4(m 2＋1)．又直线l ′的斜率为－m ，所以l ′的方程为x ＝－1m y ＋2m 2＋3.将上式代入y 2＝4x ，并整理得y 2＋4m y －4(2m 2＋3)＝0.设M(x 3，y 3)，N(x 4，y 4)，则y 3＋y 4＝－4m，y 3y 4＝－4(2m 2＋3)．故线段MN 的中点为E ⎝ ⎛⎭⎪⎫2m2＋2m 2＋3，－2m ，|MN|＝1＋1m 2|y 3－y 4|＝4（m 2＋1）2m 2＋1m 2.由于线段MN 垂直平分线段AB ，故A ，M ，B ，N 四点在同一圆上等价于|AE|＝|BE|＝12|MN|，从而14|AB|2＋|DE|2＝14|MN|2，即 4(m 2＋1)2＋⎝ ⎛⎭⎪⎫2m ＋2m 2＋⎝ ⎛⎭⎪⎫2m 2＋22＝4（m 2＋1）2（2m 2＋1）m 4，化简得m 2－1＝0，解得m ＝1或m ＝－1， 故所求直线l 的方程为x －y －1＝0或x ＋y －1＝0.三、考卷比较本试卷新课标全国卷Ⅰ相比较，基本相似，具体表现在以下方面： 1. 对学生的考查要求上完全一致。
即在考查基础知识的同时，注重考查能力的原则，确立以能力立意命题的指导思想，将知识、能力和素质融为一体，全面检测考生的数学素养，既考查了考生对中学数学的基础知识、基本技能的掌握程度，又考查了对数学思想方法和数学本质的理解水平，符合考试大纲所提倡的“高考应有较高的信度、效度、必要的区分度和适当的难度”的原则． 2. 试题结构形式大体相同，即选择题12个，每题5分，填空题4 个，每题5分，解答题8个（必做题5个），其中第22，23，24题是三选一题。
题型分值完全一样。
选择题、填空题考查了复数、三角函数、简易逻辑、概率、解析几何、向量、框图、二项式定理、线性规划等知识点，大部分属于常规题型，是学生在平时训练中常见的类型．解答题中仍涵盖了数列，三角函数，立体何，解析几何，导数等重点内容。
3. 在考查范围上略有不同，如本试卷第3题，是一个积分题，尽管简单，但全国卷已经不考查了。
四、本考试卷考点分析表（考点/知识点，难易程度、分值、解题方式、易错点、是否区分度题）。
