exam1f09sol
F1-2011.06-examiner's report
Examiner’s reportF1 Accounting in BusinessJune 2011General CommentsThe candidates were generally well prepared and most questions had pass rates in excess of 50%. Only seven questions had pass rate lower than this.The areas on which candidates performed exceptionally well included Macgregor’s Theory X and Y, roles within the accounting department, computerised v. manual systems and remuneration systems.Questions with lower pass rates included those on the differences between a team and a group, SWOT analysis, PEST (environmental) factors, Kolb’s theory of learning, non-executive directors, team briefing, and the role of external auditors in reducing the risks of fraud. It was surprising that candidates performed relatively poorly on SWOT and PEST analyses, as such questions had caused less difficulty in the past. Likewise, only just over half the candidates selected the correct answers for questions on IFAC and the ACCA Code of Ethics.Candidates continued to do well on questions relating to the accounting function, which has been a common observation since inception of the paper. There was a good awareness of the role of internal auditors, the role of external auditors, the purposes of an aged receivables listing and the roles of the managers of specific areas of accounting within a company’s finance department. This did not apply across the whole paper, however, as over 40% of candidates chose incorrect answers for questions on the role of an audit committee, management of working capital and recording transactions.It was encouraging to note that there seems no longer to be major problems with questions on human resources management or management theories in general. In particular, the pass rates on questions relating to Tuckman’s theory of team development, the separation of management and ownership, certain aspects of corporate governance and organisational culture were very satisfactory.Both economics and marketing featured less prominently on this paper than in previous examination sessions, but the pass rates on these questions were reasonable.Marginal candidates may have compromised their results by failing to answer the required number of questions. Even if the candidate has little grasp of a topic, it is worth making some attempt at the question when there is a 25%, 33% or 50% probability of getting the question right.Candidates performed quite well on scenario questions, suggesting that even if these take longer to answer, they are no more difficult than briefer questions, if considered carefully.Of the 10 single mark questions on the paper, only two of these saw very high pass rates, which seems to indicate that candidates do not find them easier than two mark questions.Sample Questions for DiscussionQuestion 2 required an understanding of how the characteristics of a team differ from those of a group.Which of the following is a characteristic of a team but not of a group?A The sense of identity brought about by common objectivesB The bonding and loyalty of the members to one anotherC The emergence of one particular individual as a leaderD The organisation of work through strictly formal processesThis topic is covered quite well in approved teaching materials, but only 34% of candidates selected the correct answer.The correct answer is D.A sense of identity can be brought about by common objectives in both a team and a group. Likewise, bonding and loyalty can apply to both. Distractor C is more tricky, in that a working team usually has an appointed leader, but it is not impossible for leaders to emerge, especially when working groups are loosely configurated. Example 2:Question 28 required knowledge of Kolb’s theory of learning. This is one of two theories that candidates need to learn, the other being that of Honey and Mumford.Kolb’s learning cycle comprises active experimentation, experience, observation and reflection, and which other element?A AssimilationB ApplicationC Abstract conceptualisationD Positive reinforcementThe correct answer is C. Only 34% of candidates selected the correct answer.The question is a good example of the necessity to remember stages of the various models encountered in the course of study for paper F1. To some extent, tackling this type of question is dependent on a good memory, as it is quite clearly impossible to remember every stage of every model studied for the paper. The best way to deal with such theoretical models is to look at their practical significance by using real examples to demonstrate how to apply them.Example 3:Question 38 required an knowledge of the PEST (or PESTEL) factors that must be considered by those responsible for strategic planning in an organisation.Eatkleen is a pressure group that seeks to encourage food producers to eliminate harmful preservatives from food and make the public aware of the potential dangers of these additives. Frustrated with the government’s explicit policy not to act on this in the near future, Eatkleen is campaigning for consumers to boycott certain products. What combination of environmental factors is Eatkleen bringing to bear on food producers?A Political and socialB Social and economicC Political and technologicalD Economic and technologicalThe correct answer is B, which was selected by 38% of candidates.Making the public more aware of the potential dangers of additives is an attempt to affect social trends. A boycott of certain products, if effective, will lead to lower sales revenues and therefore lower profits, bringing pressure to bear on the companies concerned. This is clearly an economic influence.Distractors C and D should have been ruled out quite quickly, as there was nothing in the question to suggest that technological factors were relevant.Conclusions:The performance in June 2011 continues the trend suggesting that candidates have been taking an appropriately broad approach to their studies. None of the individual sections of the syllabus caused significantly greater difficulty than others, though perhaps understandably there are higher pass rates on questions directly relating to accounting and finance.Theories applicable to ‘softer’ management and human resources topics are often more difficult to grasp, but this reflects in pass rates for only certain questions. Generally, theories that are more easily remembered due to the words used (for example, Tuckman’s theory includes forming, storming, performing and so on) are more straightforward, and candidates can remember the words used, the order in which they appear in the theory, and apply them to scenarios. By contrast, the theories of writers such as Belbin and Kolb often present greater difficulty, the former because there are nine typologies to remember and the latter because the terminology is difficult. This suggests that perhaps a little more time should be spent on these in order to make the concepts clearer.Scenario questions take longer because there are more words to read, and it is sometimes necessary to read the scenario several times in order to understand the issues involved. As mentioned above, however, these questions seem not to prove any more difficult to candidates, demonstrating that most candidates are reading them thoroughly before selecting their answers. By contrast, some single mark questions have lower pass rates that expected, and this may be because candidates afford them too little time. It should be noted that the F1 syllabus has been amended and is a shared syllabus with FAB as part of the Foundations in Accounting suite of papers with effect from December 2011. The structure of the paper has also changed slightly as single marks questions will not appear on at least the next two papers.This examination session produced some surprises, in that this was the first examination in which questions on environmental factors and SWOT analysis created any significant difficulties for some candidates. It is therefore important to assume that these subjects will not always yield ‘easy’ marks.There was no evidence that the examination was time pressured.。
新加坡AEIS考试S1测试卷V3
AEIS PLACEMENT TEST FOR SECONDAY ONESuggested Time: 2 hoursPart One: POSITIONFor the following part, the examinee will write a short passage based on either of the materials given below along with the specific requirements and information. The passage should be no less than 200 words and contain more than one paragraph. Easily recognizable handwriting will be appreciated.Question 1:You were at a crowded departmental store when you heard someone shouting for help. You looked in the direction where the shouts were ing from.Make use of the following points in your position. You may reorder the points. You are encouraged to include other relevant points to make your position interesting.In your story, make use of the points below:•What you did•How you felt•What the people around you did•What happened in the endQuestion 2:Write a story based on the pictures below. Give the story your own ending. You are encouraged to include other relevant points to make your position interesting.Part Two: Multiple Choice QuestionsFor the following part, four alternatives will be given to each of the questions, meanwhile out of which one option will be more suitable in the context, please carefully pare all the options and choose the most suitable one.Section A: GrammarFor each question 1 to 10, four options are given. One of them is more suitable than the rest. Fill in the most suitable answer in the bracketsFor each question 11 to 20, four options are given. One of them is more suitable than the rest. Fill in the most suitable answer in the brackets provided.Read the following two passages carefully and answer the questions 41 to 55. Fill in the most suitable answer in the brackets provided.Passage AMost children love sweet food. However, eating too much candy or drinking too many sugary drinks is 21 for our health. Many countries have started to do 22 to control the amount of sugary drinks kids can have.The sale and advertisement of 23 drinks have been limited in Boston, US. It will be impossible to buy sugary drinks in 24. It's reported that about one half of the US population aged 2 and older 25 sugary drinks every day. One in five American children aged 12 to 19 is overweight.Many other 26 have taken similar actions. The governments of France and Hungary started a new tax on sugary drinks. They27 this will keep populations healthier.China is facing the same problem. Middle school students in bigcities in China 28 drink about 1,200 ml of sugary drinks every day according to a recent study. The number of overweight 29 has increased 5 to 10 times in the last 20 years. Gao Xiang of Harvard Medical School 30 the Chinese government to deal with the situation actively. Gao gave some suggestions, including limiting the sale ofThe Malaysian government announced that Malaysian flight MH370 lost the contact with the Air Traffic Control 31 the morning of March eighth. The flight 32 at 0:41 a.m. that morning and planned to arrive in Beijing at half past six a.m. It carried 239 passengers, 33 154 Chinese. The passengers e from fourteen countries and areas. Nobody knows what happened to the plane. Over twenty countries took part in 34 it. On March twenty-fourth, Prime Minister of Malaysia said that MH370 crashed in southern Indian Ocean and none of the passengerssurvived. When we heard the bad news, we were very sad. So far theRead the passages carefully and answer the questions that follow. Fill in the most suitable answers in the brackets provided.Passage AIt was a public holiday that day. Two burglars decided to try their luck. They met as soon as it was dark enough. The night was unusually quiet and the air was still. It was a moonless night. They were very happy as everything was perfect for them to work.They reached the house which they had set their eyes upon. They were glad to see the house in total darkness. It was a sign that the family was out.The two men climbed through an open window into one of the rooms. They ransacked all the rooms on the ground floor of the house, taking with them all the valuables they found. Finally, they made their way upstairs. They were shining their torches around when suddenly their torches shone on a man!They could not believe their eyes. There was a man sitting on a rocking chair in a corner of the room. The man was looking at them with eyes that never moved!The two men cried out in fright, headed straight for the door and threw it open. They dashed out of the house, leaving behind the loot. Their mission had failed. A blind man had frightened them off andHow would you like to e home after a long day, open the door and walk into an elephant" That is what you would do if you lived in Elephant House in Margate, New Jersey in America. The elephant-shaped house was built in 1881 by James Lafferty. Herbert Green built a chicken-shaped house in 1962.Sarah Winchester tried to build a ghost-proof house in San Jose, California. Workers built fake chimneys, doors that open onto blank walls and stairs that lead nowhere. Many rooms were torn down and then rebuilt in a new way to confuse the ghosts. It took 38 years to plete the house!Some houses are built of strange materials. A house in Pigeon Cove, Massachusetts, is built from more than 100,000 newspapers. In Canada, George Plumb built a house entirely out of bottles.Some homes stand for great wealth and power. The Palace of Alhambra in Spain is one of the most beautiful homes in the world. The man who built it loved water. A stream runs through all 36,500 square meters of the palace. In each room, there is a small pool of sparkling water. Dream house do not have to be expensive. A man named Baldasera built a house with 90 rooms for about $500 by digging under the earth.Baldasera worked alone. He spent 40 years pleting his underground house.。
国际会计考试题及答案英文
国际会计考试题及答案英文International Accounting Exam Questions and AnswersQuestion 1: Define the term "Double Entry Accounting" and explain its significance in the accounting process.Answer 1: Double Entry Accounting is a system of recording financial transactions in which every entry to the debit side of an account must be balanced with an entry of equal value to the credit side of another account. It is significant because it ensures that all financial transactions are accurately recorded and that the accounting equation (Assets = Liabilities + Owner's Equity) remains balanced.Question 2: What is the purpose of the statement of cash flows in a set of financial statements?Answer 2: The statement of cash flows provides information about a company's cash receipts and cash payments during a particular period. It helps investors and creditors to understand the liquidity and solvency of the company, as well as its ability to generate cash and support its operations.Question 3: Explain the difference between "Historical Cost" and "Fair Value" in accounting.Answer 3: Historical Cost is the original purchase price of an asset or the original cost of a liability, while FairValue is the estimated amount for which an asset could be exchanged or a liability settled between knowledgeable,willing parties in an arm's length transaction. Historical Cost is used in the preparation of financial statements under the accrual basis of accounting, whereas Fair Value is often used for valuation purposes, particularly in the context of financial instruments.Question 4: What are the main components of the International Financial Reporting Standards (IFRS)?Answer 4: The main components of IFRS include the IFRS Standards, the International Accounting Standards (IAS), the Interpretations developed by the International Financial Reporting Interpretations Committee (IFRIC), and theStandards Advisory Council (SAC). These components provide a comprehensive set of rules and guidelines for the preparation and presentation of financial statements.Question 5: Describe the process of preparing a balance sheet.Answer 5: Preparing a balance sheet involves listing all of a company's assets, liabilities, and equity at a specific point in time. Assets are listed on the left side of the balance sheet and are categorized as current (short-term) or non-current (long-term). Liabilities are listed on the right side and are also categorized as current or non-current. Theequity section shows the owner's investment and retained earnings. The balance sheet must always balance, reflectingthe equation: Assets = Liabilities + Equity.Question 6: What is the role of an auditor in the financial reporting process?Answer 6: An auditor's role is to provide an independent assessment of a company's financial statements to ensure they are free from material misstatement and are presented fairly, in all material respects, in accordance with the applicable financial reporting framework, such as IFRS or Generally Accepted Accounting Principles (GAAP). The auditor's report provides assurance to stakeholders that the financial statements are reliable.Question 7: Explain the concept of "Conservatism" infinancial accounting.Answer 7: Conservatism is a principle in financial accounting that suggests that accountants should exercise caution when making estimates and judgments. It involves recognizing potential losses immediately but delaying the recognition of gains until they are realized. This principle helps to avoid overstatement of assets and income, thus providing a more prudent and cautious view of a company's financial position.Question 8: What is the difference between "Revenue Recognition" and "Matching Principle"?Answer 8: Revenue Recognition is the process of recognizing revenue in the accounting records when it is earned or realizable and has been measured reliably. The Matching Principle, on the other hand, is the accounting concept that requires expenses to be recognized in the same period as therevenues they helped to generate. This ensures that the financial statements reflect the actual performance of the company for a given period.Question 9: Describe the purpose of the "Going Concern" assumption in financial accounting.Answer 9: The Going Concern assumption is the basis for preparing financial statements under the accrual basis of accounting. It assumes that the business will continue to operate for the foreseeable future and that it is not in the process of liquidation or bankruptcy. This assumption allows accountants to spread the costs of assets over their useful lives and to recognize revenues and expenses when they are earned or incurred, rather than when cash is received or paid.Question 10: What is the "Materiality" concept in the context of financial statements?Answer 10: Materiality is a concept in financial accounting that refers to the significance of an item or event inrelation to the financial statements. Information is considered material if its omission or misstatement could influence the economic decisions of users taken on the basisof the financial statements. The assessment of materiality depends on the size and nature of the item, the nature of the financial statements, and the needs of the users.End of Exam。
2023年USMLE考试真题
2023年USMLE考试真题Part 1: Multiple Choice Questions (单项选择题)1. The mechanism of action of aspirin is:a) ACE inhibitorb) Beta blockerc) Calcium channel blockerd) Cyclooxygenase inhibitor2. Which of the following is not a characteristic of a gram-negative bacterium?a) Outer membraneb) Peptidoglycan layerc) Lipopolysaccharide componentd) Thin cell wall3. The function of the sinoatrial (SA) node is to:a) Conduct electrical impulses to the atrioventricular (AV) nodeb) Initiate and regulate the heartbeatc) Transmit electrical signals from the atria to the ventriclesd) Regulate blood pressure4. Which of the following is an autoimmune disease?a) Rheumatoid arthritisb) Asthmac) Osteoporosisd) Hypertension5. In the citric acid cycle, one molecule of glucose produces how many ATP molecules?a) 2b) 4c) 6d) 8Part 2: Short Answer Questions (简答题)1. Define osmosis and explain its significance in biological systems.2. Compare and contrast innate and adaptive immunity.3. Describe the structure and function of a neuron.4. Explain the process of gene transcription and translation.5. Discuss the role of enzymes in biochemical reactions.Part 3: Clinical Case Study (临床案例研究)You are a medical student working in the emergency department. A 45-year-old male presents with severe chest pain radiating to his left arm. He also complains of shortness of breath and diaphoresis. His vital signs include a blood pressure of 160/100 mmHg, heart rate of 110 beats per minute, and respiratory rate of 24 breaths per minute. Upon examination, you hear a murmur over the apex of the heart. Based on the patient's history and presentation, answer the following questions:1. What is the most likely diagnosis for this patient?2. What diagnostic tests would you order to confirm your diagnosis?3. What is the recommended initial treatment for this condition?4. What are the potential complications if left untreated?5. Discuss the long-term management and prognosis for this patient.Part 4: Essay Questions (论述题)1. Discuss the impact of dietary choices on cardiovascular health. Include the effects of different macronutrients, micronutrients, and lifestyle factors.2. Explain the pathophysiology, clinical presentation, and treatment options for atherosclerosis.3. Compare and contrast the different types of diabetes mellitus, including their etiology, clinical features, and management.4. Discuss the role of the immune system in cancer development and progression. Include the concepts of immunosurveillance, tumor evasion, and immunotherapy.5. Explain the pharmacodynamics and pharmacokinetics of a commonly used antihypertensive medication. Discuss its mechanism of action, therapeutic uses, side effects, and drug interactions.Note: The above questions are examples and do not represent actual USMLE exam questions. Please refer to appropriate study materials for accurate and up-to-date information on the USMLE exam.。
Midsol
x 4 y, x y x. y Analyze the point’s stability. What type of the fixed point is it? (node? saddle? focus? center?) Sketch the phase plane [x,y] in as much detail as you can. Solution: This system of equations is linear, so it has only one (trivial) fixed point x = y = 0, and no linearization is necessary. Solving the characteristic equation of the system, 1 1 4 0, 1
1
C:\User\Teaching\501\F09\Midsol.doc
(see Fig. on the right). With account of Eq. (3.66) of the lecture notes, this formula turns into Eb 2 U ef (r ) n 2 . (*) r r It is evident that rmin may be found from equation dUef/dr = 0. Differentiating Eq. (*), we find that
U (r )
rn
,
with n 2, 0.
FinalExamS
Final Examination DescriptionsExam Date: July 3, 2015Duration: 90 minutesSections:I.Define the following terms. Give examples to illustrate your answers. (15%) (每题3分, 共15分)e.g.1. morphemePlease refer to Appendix A for more information about this section.II.Identify the word-formation process involved in the creation of each of the underlined words below. Write your answer on the line provided. (10%) (每题1分，共10分)e.g.1. bitter, sw eet → bittersweet________(Based on Lectures 5, 6 and 7.)III.Fill in the blanks with words formed from the given stems. (15%) (每题1分，共15分)e.g.1. The local people were actually __________; they often spoke three, four, five languages.(lingual)(Based on Lectures 5, 6 and 8.)IV. Provide the meaning and an example word for each of the following roots below. (30%)(每题1.5分, 共30分)Please refer to Appendix B for more information about this section.V. For each sentence or sentence pair below, classify the meaning relation between the two words marked in bold into one of the following types of relation: homonymy, synonymy, antonymy, hyponymy, meronymy, portion-mass, or member-collection. (10%) (每题1分，共10分）e.g.1. It was a remark made in private, not in public.(Based on Lectures 12, 13 and 14.)VI. Each sentence below contains an incomplete collocation. Complete the collocation by filling in the blank with a suitable word from the words provided in the box. Use the words in their proper forms. Each word can only be used once. (20%) (每题1分，共20分）e.g.1.The Titanic sank on her __________ voyage.(Based on Lectures 14 and 15)Appendix ADefine the following terms. (You may want to use examples from the respective lectures or come up with your own examples to support your answer.)1.morphemeA morpheme is the smallest unit of language that has its own meaning, either a word or a part of a word. Inother words, it is a meaningful form that cannot be divided into smaller meaningful parts. (Lecture 4)2.morphologyMorphology is the study of the internal structure of words. In particular, it is the study of morphemes and their arrangements in forming words. (Lecture 4)3.free morphemeA free morpheme is a morpheme that can occur alone as an independent word. (Lecture 4)4.bound morphemeA bound morpheme is a morpheme that cannot occur as an independent word on its own but must becombined with other morphemes to form words. (Lecture 4)5.rootThe root of a word is the morpheme that conveys the main meaning of the word. (Lecture 4)6.affixAn affix is a bound morpheme added to the beginning (prefix) or end (suffix) of a stem. (Lecture 4)poundingCompounding is a word-formation process where two or more independent words are combined to form a new word. (Lecture 6)8.conversionConversion is a word-formation process by which a word of one part of speech is converted to another part of speech without any change of form, either in pronunciation or spelling. (Lecture 7)9.homonymyHomonymy refers to the relation between two words that are spelled or pronounced the same but differ in meaning. (Lecture 12)10.hyponymyHyponymy refers to the hierarchical relation that holds between a word with a more general meaning and a word with a more specific meaning. (Lecture 13)Appendix B。
testinside提供SCO Caldera 090-554题库分享
SCO Caldera 090-554 examSCO OPENSERVER(TM) RELEASE 5 NETWORK ADMINISTRATION V30A1科目编号：090-554科目名称：SCO OPENSERVER(TM) RELEASE 5 NETWORK ADMINISTRATION V30A1090-554 考试是 SCO CALDERA 公司的SCO OPENSERVER(TM) RELEASE 5 NETWORK ADMINISTRATION V30A1认证考试官方代号，SCO OPENSERVER(TM) RELEASE 5 NETWORK ADMINISTRATION V30A1认证作为全球IT领域专家 SCO CALDERA 认证之一，是许多大中IT企业选择人才标准的必备条件。
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Exam : SCO Caldera 090-554Title : SCO OPENSERVER(TM) RELEASE 5 NETWORK ADMINISTRATIONV30A11. Which item is the administrator NOT asked to enter when adding a new network adapter?A. Hardware addressB. IP addressC. NetmaskD. Broadcast addressAnswer: A2. Which statement regarding the ARP protocal is ture?A. The ARP protocol uses the /ect/hosts file to resolve addresses.B. The ARP protocol provides the IP address of the host that owns a given hardware address.C. The ARP protocol uses a cache to keep track of addresses it has already discovered.D. The ARP protocol uses the/etc/ethers file to resolve addresses.Answer: C3. Which statement regarding Ethernet addresses is ture?A. The address is a unique 48-bit value.B. The address value is configured in the /etc/hosts file.C. A host discovers its own Ethernet address with the RARP protocol.D. A host's Enternet address dose not change when it gets a new network interface card.Answer: A4. How many octets are reserved for the HOST portion of a Class A IP address(with no subnets)?A. 1B. 2C. 3D. 4Answer: C5. Which is an example of a valid Class A address?A. 119.32.259.134B. 126.80.1.96C. 129.222.101.17D. 192.127.212.88Answer: B6. Which command,if run on an SCO OpenServer system with an IP address of 192.168.11.11,would send packets onto the network?A. ping 127.0.0.1B. ping localhostC. ping 192.168.11.11D. None of these commands would send packets onto the network. Answer: Dtestinside 的 920-808 权威考试题库软件是 Nortel 认证厂商的授权产品，是考试原题的完美组合，覆盖率95％以上，答案由多位专业资深讲师原版破解得出，正确率100％。
剑桥fce 试题 系列之一
More informationMore informationPaper 1 Reading1Why were some people in Brackham annoyed after the storm?A The town looked different.B The police had done little to help.C No market could be held.D Fallen trees had not been removed.2In the third paragraph,what do we learn about Chief Inspector Pelham’s general attitude to his work?A He finds it extremely annoying.B He is sure that he fulfils a vital role.C He considers the systems are not clear enough.D He does not trust the decisions made by his superiors.3Who does ‘her’ in line 16 refer to?A Molly PelhamB the doctorC the chemistD Sergeant Lloyd4When Inspector Pelham’s wife first told him about the walnut tree, he appeared to beA worried.B shocked.C saddened.D uninterested.5What aspect of the Pelhams’ furniture does ‘shabbiness’ in line 33 describe?A its colourB its conditionC its positionD its design6As a result of the storm, the Pelhams’ living-roomA was pleasantly lighter.B felt less private.C had a better view.D was in need of repair.7Why did Molly sound pleased by her husband’s comment?A It proved that he was well again.B She agreed about the tree.C She thought he meant the sofa.D It was what she expected him to say.8From what we learn of Inspector Pelham, he could best be described asA open-minded.B well-liked.C warm-hearted.D strong-willed.More informationThe England te am are curre ntly ranke d fourth inworld. But, as Ke ndra points out, the WorldChampionships will be tough. ‘You have to pushMore informationMore informationMore informationMore informationMore informationMore informationMore informationPaper 3 Use of English 1A However B Despite C Although D Conversely2A make out B take up C put out D turn into3A sad B poor C short D weak4A sense B do C feel D be5A state B mention C remark D tell6A submit B give C provide D deal7A save B hold C deliver D return8A extensive B extreme C intensive D intentional9A pass B escape C miss D avoid10A spot B part C side D slice11A worry B upset C ache D depress12A discouragingly B tightly C uncomfortably D heavily。
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Math215—First Midterm
October22,2009
Name:EXAM SOLUTIONS
Section:
1.Do not open this exam until you are told to do so.
2.This exam has9pages including this cover.There are8problems.Note that the problems
are not of equal difficulty,so you may want to skip over and return to a problem on which you are stuck.
3.Do not separate the pages of this exam.If they do become separated,write your name on
every page and point this out to your instructor when you hand in the exam.
4.Please read the instructions for each individual problem carefully.One of the skills being
tested on this exam is your ability to interpret mathematical questions,so instructors will not answer questions about exam problems during the exam.
5.Show an appropriate amount of work(including appropriate explanation)for each problem,
so that graders can see not only your answer but how you obtained it.Include units in your answer where that is appropriate.
6.You may use no aids(e.g.,calculators or notecards)on this exam.
7.If you use graphs or tables tofind an answer,be sure to include an explanation and sketch
of the graph,and to write out the entries of the table that you use.
8.Turn offall cell phones and pagers,and remove all headphones.
9.Because no calculators or notecards are allowed,you are not required to evaluate expressions
you may obtain in the solution of these problems.In some cases it may be to your advantage to simplify expressions,but it will not be required for full credit.
10.Note that problems1–4will be graded giving very little partial credit.
11.There is a list of possibly useful formulas included as the second page of this exam.
Points
12
2
12
4
12
6
12
8
Total
2b h,where b is the length of one side and h the length of the
perpendicular from that side to the opposite angle.
2.Area of a circle:A=πr2,where r is the radius of the circle.
3.Area of a sector of a circle:A=1
3
πr3;S=4πr2.
5.Volume of right circular cylinder:V=πr2h,where r is the radius and h the height of the
cylinder.
6.Volume of a cone:V=1
2
(1+cos(2x))
7.sin2x=1
9−xy−3x,so that the distance from a point(x,y,z)on the surface to the origin is D(x,y)=
x2+y2+9−xy−3x.To minimize D,we want tofind a point where the gradient∇D= 0.For ease of calculation,consider C=D2;minimizing this willfind the same point as minimizing D.Then we have the equations
C x=2x−y−3=0and C y=2y−x=0.
Adding twice the second to thefirst,we get3y=3,so y=1,and thus x=2.Thus the point(s)is(are)(2,1,±1).We can prove that this is a minimum by considering the second derivative test.Here,C xx=2,C yy=2,and C xy=−1,so C xx C yy−(C xy)2=3>0,with C xx>0,and the point is a minimum.Clearly as x and y get large,C→∞,so this must be the global minimum.
Alternately,we can minimize the function f(x,y,z)=x2+y2+z2subject to the constraint g(x,y,z)=xy+3x+z2=9.Letting∇f=λ∇g,we have
2x=λ(y+3),2y=2λx,and2z=λ(2z),with xy+3x+z2=9.
From the third equation,λ=1or z=0.According to the hint,z=0,so we considerλ=1. Ifλ=1,then from the second equation2y=x,and thefirst equation gives us y=1.Thus x=2,and from the constraint z=±1,as we found before.
We can show that the minimum occurs for z=0by considering the case z=0.If z=0, we have2x=λ(y+3),2y=λx,and x(y+3)=9.Solving these is a bit messy;wefind (x,y)≈(−3.662,−5.458)and(2.173,1.141).At the points(2,1,±1),the squared distance to the origin is6;at(2.173,1.141,0)it is6.03,so the minimum occurs at the former.In the absence of this calculation,we can convincingly argue that the distances we found must be the minimum because the origin is not on the surface,and there is no upper bound to the distance function;thus the critical point(s)we found should give the minimum.。