The Envelope Theorem, Lecture notes of Mathematics

− b. The Envelope Theorem tells us that the derivative of the value function is v (b) = ∂f ∂b − λ ∂G ∂b = 0 − (λ)(−1) = λ.

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CAE Writing
How to pass the Certificate in Advanced English Writing
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CAE Writing

How to pass the Certificate in Advanced English Writing

Section

Index

Introduction

Who is this book for?

This book is for students who want good marks in the writing section of the Cambridge C Certificate in Advanced English (CAE). It is also useful for any Advanced student who would like to improve his or her writing. It is also for teachers. Use it exactly as you like. Forward it to students. Print it out. Use it in class. It’s completely up to you. I hope you find it useful. Enjoy your English and every success with exams. P.S. You can find other free materials to help you prepare for the C1 Certificate in Advanced English (CAE) at the following website brays.es To buy a Complete CAE Online Course with 100 – 150 hours of Listening, Reading, and Use of English practise (including over 50 Exam Practice Papers) click here. Simply practise and take the mock exams until you are sure of exam success. Spanish speakers can access this page

What’s in the CAE writing exam?

In the two parts of the CAE Writing exam, you have to show that you can write different types of text in English.

Summary

Time allowed : 1 hour 3 0 minutes Number of parts : 2 Number of questions : Part 1: one compulsory question - Part 2: one question from a choice of three Types of test : Essay, letter/email, report or review

❖ Part 1 (Compulsory question)

What is in Part 1? You have to read a text and then write an essay based on the points included in the text. You will be asked to explain which point is more important for you and propose arguments. What do I have to practice? Develop the points as completely as possible in order to demonstrate the use of structures, vocabulary and language functions, for example, evaluation and expression of opinions, hypothesis formulation, justification, persuasion. How many questions are there? One compulsory question. How much do I have to write? 220 – 260 words.

❖ Part 2 (Writing based on situations)

What's in Part 2? You write a text from a choice of text types – article, email/letter, report or review. To guide your writing, you’ll be given information about context, topic, purpose and target reader. What do I have to practice? Writing different types of text that could be included in the exam. How many questions are there? One task to be selected from a choice of three. How much do I have to write? 220 – 26 0 words

How is the exam assessed?

Answers are assessed using both a general mark scheme, which is used for all the questions, and a separate task-specific mark scheme for each question. The criteria used to assess the candidates’ answers in the general mark scheme include:

  • Range of structure, vocabulary and expression
  • Effectiveness of organization, including paragraphing and linking devices
  • Accuracy of grammar and spelling
  • Awareness of the situation and target reader

Five essentials for good answers

  1. Answer the question
  2. Plan
  3. Use paragraphs
  4. Revise your work
  5. Make sure you answer the question exactly and no more. It is essential to plan your writing. This should take at least 10 minutes to plan for each question.
  • like
  • for example
  • for instance Expressing the opinion of someone else:
  • some people say
  • some people say that
  • many people say
  • many people say that
  • people often say
  • it is said
  • it is said that
  • according to

Sample questions (Writing essays)

  1. Should citites ban flat-renting websites such as airbnb? Take into account the following:
  • Impact on rent prices
  • Influx of tourists into the city
  • Impact on the job market Write your essay in 220-260 words in an appropriate style
  1. Your class has listened to a radio discussion programme about facilities which should receive money from local authorities. You have made the notes below: Which facilities should receive money from local authorities?
  • museums
  • sports centres
  • public gardens Some opinions expressed in the discussion: “Museums aren´t popular with everybody!” “Sports centres mean healthier people”
  • “A town needs green spaces – parks are great for everybody” Write an essay for your tutor discussing two of the facilities in your notes. You should explain which facility it is more important for your local authorities to give money to, giving reasons in support of your answer.
  1. You have read an online article about changes in the types of subject taught at secondary schools. The article says that some traditional subjects may no longer be taught at school. Four of the subjects discussed are mentioned below, along with some of the readers’ comments. Which subjects may no longer be taught at secondary school?

Music ‘Most students who are interested in music take lessons out of school.’ Geography ‘Why do we need to know the names of rivers and mountains around the world?’ History ‘It’s all about the past. At schools, we need to be focussing on the future.’ Art ‘Art lessons allow kids to explore their creativity.’ Write an essay discussing TWO of the subjects mentioned above. You should explain why you think these subjects should continue to be taught at secondary schools, giving reasons to support your answer. Write your answer in 220-260 words in an appropriate style

  1. Our class has watched a round-table discussion about what young people can learn from older generations. You have made the notes below: Areas where young people could learn from older generations:
  2. Work
  3. Relationships
  4. money Some opinions expressed in the discussion: ¨People with work experience can tell you what the job you are considering is like.¨ ¨Older people can give wise advice when you have a problem with a friend.¨ ¨It´s hard to manage your money when you start living independently.¨ Write an essay discussing two of the areas in your notes. You should explain in which area young people could gain most from older generations, giving reasons in support of your answer. You may, if you wish, make use of the opinions expressed in the discussion, but you should use your own words as far as possible.
  5. Your class has attended a panel discussion on what methods governments should use to discourage the use of private cars in the centre of the city. You have made the notes below. Methods governments coud use to discourage the use of private cars in the city centre
  • investment
  • education ✔
  • taxes ✔ Some opinions expressed in the discussion 'Make businesses pay parking levies for their employees and they'll move out of the city centre.' 'Improve the public transport system, then people won't need their cars.' 'If people understood how much better pedestrianised ciyt centres are, they wouldn't want to bring their cars in.' Write an essay for your tutor, discussing two of the methods in your notes. You should explain which method you think is more important for governments to consider, giving reasons to support your opinion.
  • My first complaint is
  • The first problem is
  • The first thing I would like to draw your attention to is
  • My first concern is Introducing further complaints:
  • Secondly
  • In the second place
  • Not only …….but also
  • In addition
  • In addition to this
  • Added to this
  • …….was also unacceptable Demanding action:
  • I suggest that you replace the item
  • I therefore suggest that I be given a full refund
  • I would be grateful if my money was refunded
  • I would be grateful if you could give me a full refund Ending the letter:
  • I look forward to hearing from you
  • I look forward to receiving a full refund
  • I look forward to receiving a replacement
  • I look forward to receiving your explanation c) Writing formal letters to make suggestions Reason for writing:
  • I am writing to suggest
  • I am writing to arrange
  • I am writing to offer suggestions
  • I am writing make arrangements Making first suggestion:
  • My first suggestion is
  • First of all I suggest
  • I would like to suggest Making further suggestions:
  • Another possibility is
  • A further possibility is
  • I further suggest
  • I would further suggest
  • Secondly Offering a choice:
  • Would you therefore mind choosing between ….?
  • Either……or
  • You might choose either ……. Or d) Writing formal letters to request information Reason for writing:
  • I am writing to receive further information about
  • I am writing to enquire about
  • I am writing to receive more detailed information about
  • I am writing to receive further details about Requesting first piece of information:
  • The first thing I would like to know is
  • First of all I would like to know
  • I wonder if you would mind telling me first of all ….? Requesting further information: Could you also tell me….?
  • Could you also inform me ….?
  • Would you also mind informing me ….?
  • Would you also mind telling me ….?
  • Do you know ….?
  • I would also like to know if
  • I would also like to know whether
  • I hope you might also let me know about … Thanking for information:
  • I would like to thank you in advance for this information
  • Thanking you in advance for this information
  • Thanking you in advance e) Writing formal letters to give information Reason for writing:
  • I am writing to inform you about
  • I am writing to provide you with information about
  • I am writing to let you know that Providing first point:
  • The first thing I would like to tell you is

Sample questions (Writing formal letters and emails)

  1. Volunteers needed We are looking for volunteers to help out at a famous, international sporting event. We’re looking for friendly, respectful people with good language skills, good team skills and a ‘can-do’ attitude. We need people to welcome delegates, provide customer service and solve problems. If you think you have what it takes, apply now. Write an application to become a volunteer. Mention:
  • your language skills
  • your personal qualities
  • examples of times when you have demonstrated team skills
  • any relevant work experience Write your answer in 220-260 words in an appropriate style. 2. A colleage of yours, Alice Watson, has applied for a jobin the public relations department of a large charity. Poverty Action. You have been asked to write a letter providing a character reference for her. Indicate how long and what capacity you have worked with her, and how her personal characteristics would make her suited for her job. Here is part of the letter you received from Poverty Action: “The job of Public Relations Co-ordinator consists mainly of supervising PR work, and entails travelling around the country and working with various people in our large organization. The successful applicant will need good managerial skills and be committed to the philosophy of our charity” _Write your letter in 220-260 words in an appropriate style
  1. On a recent holiday you lost a valuable item. Fortunately you have travel insurance to cover the cost of anything lost. Write a letter to the manager of your insurance company. In your letter:
  • describe the item you lost
  • explain how lost it
  • tell the insurance company what you would like them to do._
  1. Your company would like to offer work-experience placements to students in an international college. Write a letter for publication in the student newspaper at the college. Your letter should explain what your company dies, what kind of work-experience placements are available, and how students would benefit from the experience. Write your letter in 220 - 260 words in an appropriate style.

Part 2.2: Writing informal letters or emails

Introduction (Writing informal letters or emails)

Writing informal letters and emails involves writing letters or emails to friends or relatives. When writing an informal letter or email our language is more relaxed and we are able to use abbreviations which is rare in other forms of English writing, except perhaps when using direct speech. Look also at “ Writing Formal Letters and Emails ” and compare.

Useful phrases (Writing informal letters or emails)

a) Informal Letters - Greetings:

  • Dear Jim
  • Hello Jim
  • Hi Jim b) Informal Letters - Introductory paragraph:
  • Sorry I haven't written for ages
  • Sorry it's taken me so long to write
  • How's it going?
  • How are you?
  • How are things with you?
  • How are things? c) An informal letter referring to good news:
  • Glad to hear about
  • I'm really glad to hear about
  • I'm very happy to hear about
  • I was very happy to read about
  • Great news about your d) An informal letter referring to bad news:
  • I'm extremely sorry to hear about
  • I'm very sorry to hear about
  • Sorry to read about
  • Its very sad to hear about your
  • I can't tell you how sad I am that e) Informal Letters - Introducing points
  • By the way
  • Did you hear about
  • Did you see
  • Have you seen
  • Tell me about
  • Oh, another thing

Part 2.3: Writing a Proposal

Introduction and tips (Writing proposals)

• ANSWER THE QUESTION

  • PLAN your proposal
  • Give your proposal a title.
  • Make sure you have at least 4 paragraphs.
  • Ask rhetorical questions to get your readers' attention. Eg. What would the world be like without oil? What will life be like in 20 years time? Speak directly to your readers. Eg. Let's just imagine some of the possibilities.
  • Give examples where appropriate.
  • Use humour where appropriate
  • Give a conclusion and summary in the last paragraph.
  • Finally, give your opinion where appropriate.
  • REVISE your proposal to correct mistakes.

Useful phrases (Writing proposals)

a) Rhetorical phrases:

  • Have you ever ……..?
  • What do you think about ……..?
  • Are you one of those people who thinks that ……?
  • Are you one of those people who …....?
  • What would life be like if ……?
  • Will the future bring us …..? b) Introducing your first point:
  • Firstly
  • In the first place
  • First of all
  • The first thing to consider is
  • One thing to consider is
  • To begin with c) Introducing more points:
  • Secondly
  • Another consideration
  • Yet another consideration
  • Another thing to consider is
  • Added to that
  • Apart from that
  • In addition to this
  • Introducing your final points: In conclusion
  • To conclude
  • To sum up

d) Introducing your opinion:

  • I think
  • In my opinion
  • Personally I believe that
  • In my view
  • If you ask me
  • To my mind
  • My personal opinion is

Sample questions (Writing proposals)

  1. There are plans to demolish an old and unused building in the town where you are a student. You feel that the building should be saved. You decide to write a proposal for the town council explaining why you think the building should be preserved, suggesting what could be done to modernise it and saying how the building could benefit the local people. Write your proposal in 220-260 words
  2. Your college currently doesn't provide enough support for students planning to spend time studying in another country. You see this notice in the library. The college is planning to introduce a special course for students planning to spend time studying in another country. The college principal invites students to send a proposal outlining any problems students may face whe studying abroad and suggesting ways in which the course could address these problems. A decision can then be made about what to include on the course. Write your proposal in 220 - 260 words in an appropriate style.
  3. You go to a university that has a high amount of international students and you have realised that the website is not up to scratch. Write a proposal for the University Dean about how it could be improved. Write your proposal in 220 - 260 words in an appropriate style.

Part 2.4: Writing reports

Introduction and tips (Writing reports)

• ANSWER THE QUESTION

  • PLAN your report.
  • Make sure you have at least 4 paragraphs.
  • Every paragraph should have a heading which explains what the paragraph is about.
  • You first paragraph heading will be INTRODUCTION and your last, CONCLUSION
  • Always start with To: E.g. To: Ms Jones
  • Put From: on the line below and then add your name.

Sample questions (Writing reports)

  1. An international magazine is investigating tourism in various areas around the world. You have been asked to write a report for the magazine’s editor, addressing the following questions:
  • How has tourism in your region changed over the last decade?
  • What are the reasons for these changes?
  • What problems exist and can anything be donde to solve them? Write your report in 220-260 words

2. An international development agency has been looking into attitudes to aging around the

world. The research director has asked you to conduct a survey and write a report. Your report should discuss how young people where you live feel about older people in the community and the prospect of growing older themselves. You have also been asked to make recommendations about how attitudes could be changed. Write your report in 220 - 260 words in an appropriate style.

3. Your local authority is conducting a survey into language learning habits of the people between 16-45 in the area. They have asked for a report on the types of methods used in state run schools and language centres. They have asked for some suggestions on how to imporve their facilities, teaching methods and resources. Write your report in 220 - 260 words in an appropriate style.

Part 2.5: Writing reviews

Introduction and tips (Writing reviews)

• ANSWER THE QUESTION

  • PLAN your review.
  • Make sure you have at least 4 paragraphs.
  • Choose an appropriate title.
  • The introduction will talk about what's being reviewed.
  • Use a relaxed, friendly, chatty style.
  • You can use contractions such as I'm, I've etc..
  • Use a new paragraph for each point you want to make.
  • Give your opinion.
  • In the concluding paragraph give your opinion.

Useful phrases (Writing reviews)

a) What I liked

  • What I liked most was …..
  • The thing I liked most was ….
  • I was pleasantly surprised by …..
  • ….. would appeal to …..
  • If you get a chance to …. b) What I disliked
  • What I disliked most was …..
  • I was disappointed by ……
  • I was disappointed with …..
  • I was very disappointed by …..
  • I was very disappointed with …. c) Reviews of books:
  • main character
  • is set in
  • comedy
  • science fiction
  • thriller
  • romance
  • comedy:
  • author
  • written by
  • chapter
  • factual
  • fiction
  • unbelievable
  • bestseller
  • chapter
  • ending
  • Reviews of films, tv programmes, plays:
  • lead role
  • star role
  • star
  • star actor
  • star actress
  • starring
  • secondary role
  • He plays a …….
  • She plays a …….
  • written by ….
  • is set in …..
  • based on a true story ….
  • believable
  • true to life