2013年CIE剑桥国际考试IGCSE数学真题答案(43)

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九天国际教育GCSE真题June 2013 (v3) QP - Paper 3 CIE Chemistry IGCSE

READ THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use a pencil for any diagrams, graphs or rough working.Do not use staples, paper clips, highlighters, glue or correction ﬂ uid.DO NOT WRITE IN ANY BARCODES.Answer all questions.Electronic calculators may be used.A copy of the Periodic Table is printed on page 12.You may lose marks if you do not show your working or if you do not use appropriate units.At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.CHEMISTRY0620/33Paper 3 (Extended)May/June 20131 hour 15 minutesCandidates answer on the Question Paper.No Additional Materials are required.UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certiﬁ cate of Secondary EducationThis document consists of 11 printed pages and 1blank page.[Turn overIB13 06_0620_33/2RP © UCLES 2013*6258911381*For1S ubstances can be classiﬁ ed as:Examiner’sUseelements mixtures compoundsE lements can be divided into:metals non-metals(a)D eﬁ ne each of the following terms.(i)e lement.................................................................................................................................... (2)(ii)c ompound.................................................................................................................................... (2)(iii)m ixture.................................................................................................................................... (1)(b)C lassify each of the following as either an element, compound or mixture.(i)b rass (1)(ii)c arbon dioxide (1)(iii)c opper (1)(c)W hich physical property is used to distinguish between metals and non-metals?I t is possessed by all metals but by only one non-metal. (1)[Total: 9]© UCLES 20130620/33/M/J/13For2O ne of the factors which determine the reaction rate of solids is particle size.Examiner’sUse(a)A mixture of ﬁ nely powdered aluminium and air may explode when ignited.A n explosion is a very fast exothermic reaction. This causes a large and sudden increasein temperature.E xplain each of the following in terms of collisions between reacting particles.(i)W hy is the reaction between ﬁ nely powdered aluminium and air very fast?.................................................................................................................................... (2)(ii)E xplain why for most reactions the rate of reaction decreases with time..................................................................................................................................... (2)(iii)S uggest an explanation why the rate of reaction in an explosion could increase rather than decrease with time......................................................................................................................................................................................................................................................................... (3)(b)(i)G ive another example of a substance other than a metal which, when ﬁ nelypowdered, might explode when ignited in air. (1)(ii)D escribe a simple test-tube reaction which shows the effect of particle size on the rate at which a solid reacts with a solution......................................................................................................................................................................................................................................................................... (3)[Total: 11]© UCLES 2013[Turn over0620/33/M/J/130620/33/M/J/13© UCLES 2013ForExaminer’sUse3I ron from the blast furnace is impure. It contains 5% of impurities, mainly carbon, sulfur, silicon and phosphorus. Almost all of this impure iron is converted into the alloy, mild steel.(a) (i) S tate a use of mild steel. (1)(ii) N ame and give a use of another iron-containing alloy.name ..........................................................................................................................use (2)(b) T he oxides of carbon and sulfur are gases. The oxides of silicon and phosphorus are not.Explain how these impurities are removed from the impure iron when it is converted into mild steel............................................................................................................................................ ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... (5)[Total: 8]4G ermanium is an element in Group IV. The electron distribution of a germanium atom is 2 + 8 + 18 + 4. It has oxidation states of +2 and +4.(a) G ermanium forms a series of saturated hydrides similar to the alkanes.(i) D raw the structural formula of the hydride which contains three germanium atomsper molecule.[1](ii) P redict the general formula of the germanium hydrides. (1)0620/33/M/J/13© UCLES 2013[Turn overFor Examiner’sUse(b) D raw a diagram showing the arrangement of the valency electrons in one molecule ofthe covalent compound germanium(IV ) chloride, GeC l 4.Use o to represent an electron from a chlorine atom.Use x to represent an electron from a germanium atom.[2](c) D escribe the structure of the giant covalent compound germanium(IV ) oxide, GeO 2.I t has a similar structure to that of silicon(IV ) oxide............................................................................................................................................ ........................................................................................................................................... (3)(d) I s the change GeC l 2 to GeC l 4 reduction, oxidation or neither? Give a reason for your choice............................................................................................................................................ (2)[Total: 9]5A ll metal nitrates decompose when heated. A few form a nitrite and oxygen. Most form the metal oxide, oxygen and a brown gas called nitrogen dioxide.(a) (i) N ame a metal whose nitrate decomposes to form the metal nitrite and oxygen. (1)(ii) C omplete the equation for the action of heat on lead(II ) nitrate.......Pb(NO 3)2 → ......... + ......NO 2 + O 2 [2](iii) S uggest why the nitrate of the metal, named in (a)(i), decomposes less readily thanlead(II ) nitrate..................................................................................................................................... (2)0620/33/M/J/13© UCLES 2013For Examiner’sUse(b) A lmost all samples of nitrogen dioxide are an equilibrium mixture of nitrogen dioxide,NO 2, and dinitrogen tetroxide, N 2O 4.forward reactionreverse reactionN 2O 4(g)colourless2NO 2(g)dark brownI n the forward reaction, a bond forms between the two nitrogen dioxide molecules.NO 2 + NO 2 → O 2N – NO 2(i) E xplain the term equilibrium mixture ..................................................................................................................................... .............................................................................................................................. [1] (ii) T he syringe contains a sample of the equilibrium mixture. The plunger was pulledback reducing the pressure.H ow would the colour of the gas inside the syringe change? Give an explanation foryour answer..................................................................................................................................... .................................................................................................................................... .............................................................................................................................. [3] (iii) A sealed tube containing an equilibrium mixture of nitrogen dioxide and dinitrogentetroxide was placed in a beaker of ice cold water. T he colour of the mixture changed from brown to pale yellow.I s the forward reaction exothermic or endothermic? Give an explanation for your choice..................................................................................................................................... (2)(iv) W hat other piece of information given in the equation supports your answer to (iii)?NO 2 + NO 2 → O 2N–NO 2 (1)[Total: 12]0620/33/M/J/13© UCLES 2013[Turn overForExaminer’sUse6S ulfuric acid and malonic acid are both dibasic acids. One mole of a dibasic acid can form two moles of hydrogen ions.H 2SO 4 → 2H + + SO 42–D ibasic acids can form salts of the type Na 2X and CaX.(a) M alonic acid is a white crystalline solid which is soluble in water. It melts at 135 °C.T he structural formula of malonic acid is given below. It forms salts called malonates.CH 2(COOH)2 or HOOC – CH 2 – COOH(i) H ow could you determine if a sample of malonic acid is pure?technique used .......................................................................................................... result if pure (2)(ii) W hat is the molecular formula of malonic acid? (1)(iii) W hen malonic acid is heated there are two products, carbon dioxide and a simplercarboxylic acid. Deduce the name and molecular formula of this acid..................................................................................................................................... .............................................................................................................................. [2] (iv) M alonic acid reacts with ethanol to form a colourless liquid which has a ‘fruity’ smell.I ts structural formula is given below.CC OOO OCH2CH 2CH 3CH 2CH 3W hat type of compound contains the group which is circled? (1)0620/33/M/J/13© UCLES 2013For Examiner’sUse(b) (i) S uggest why a solution of malonic acid, concentration 0.2 mol / dm 3, has a higher pHthan one of sulfuric acid of the same concentration. (1)(ii) D escribe a test, other than measuring pH, which can be carried out on both acidsolutions to con ﬁ rm the explanation given in (b)(i) for the different pH values of the two acids..................................................................................................................................... (2)(c) C omplete the following equations for reactions of these two acids.(i) sodium hydroxide + malonic acid → .................... + ....................[1].................... (ii) CuO + H 2SO 4 → .................... + .................... [2] (iii) Mg + CH 2(COOH)2 → .................... + ....................[2](iv) K 2CO 3 + H 2SO 4 → .................... + .................... + ....................[2][Total: 16]7 A lkanes and alkenes are both series of hydrocarbons.(a) (i) E xplain the term hydrocarbon ..................................................................................................................................... (1)(ii) W hat is the difference between these two series of hydrocarbons?.................................................................................................................................... (2)(b) A lkenes and simpler alkanes are made from long-chain alkanes by cracking.C omplete the following equation for the cracking of the alkane C 20H 42.C 20H 42 → 2C 4H 8 + 2C 2H 4 + ...............[1]0620/33/M/J/13© UCLES 2013[Turn overForExaminer’sUse(c) Alkenes such as butene and ethene are more reactive than alkanes.A lkenes are used in the petrochemical industry to make a range of products, which includes polymers and alcohols.(i) D ibromoethane is used as a pesticide. Complete the equation for its preparationfrom ethene.C C + Br 2 →HHH H[1](ii) T he structural formula of a poly(alkene) is given below.nC CH 3C CH 3HHD educe the structural formula of its monomer.[2](iii) H ow is butanol made from butene, CH 3 – CH 2 – CH = CH 2? Include an equation in your answer..................................................................................................................................... (2)(iv)C racking changes alkanes into alkenes. How could an alkene be converted into analkane? Include an equation in your answer..................................................................................................................................... (2)0620/33/M/J/13© UCLES 2013ForExaminer’sUse(d) 20 cm 3 of a hydrocarbon was burnt in 175 cm 3 of oxygen. After cooling, the volume ofthe remaining gases was 125 cm 3. The addition of aqueous sodium hydroxide removed carbon dioxide leaving 25 cm 3 of unreacted oxygen.(i) v olume of oxygen used = .......... cm 3 [1] (ii) v olume of carbon dioxide formed = .......... cm 3 [1](iii) D educe the formula of the hydrocarbon and the balanced equation for the reaction..................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (2)[Total: 15]11BLANK PAGEPMT12Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included the publisher will be pleased to make amends at the earliest possible opportunity.University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.G ro u p140C eC e r i u m 58141P rP r a s e o d y m i u m 59144N d N e o d y m i u m 60P mP r o m e t h i u m61150S mS a m a r i u m62152E uE u r o p i u m63157G dG a d o l i n i u m64159T bT e r b i u m65162D yD y s p r o s i u m66165H oH o l m i u m67167E rE r b i u m68169T mT h u l i u m69173Y bY t t e r b i u m70175L uL u t e t i u m71232T hT h o r i u m 90P aP r o t a c t i n i u m 91238UU r a n i u m92N pN e p t u n i u m93P uP l u t o n i u m94A mA m e r i c i u m95C mC u r i u m96B kB e r k e l i u m97C fC a l i f o r n i u m98E sE i n s t e i n i u m99F mF e r m i u m100M dM e n d e l e v i u m101N oN o b e l i u m102L rL a w r e n c i u m1031HH y d r o g e n17L iL i t h i u m 323N aS o d i u m 1124M gM a g n e s i u m1240C aC a l c i u m 2045S c S c a n d i u m 2148T i T i t a n i u m2251V V a n a d i u m 2352C r C h r o m i u m 2455M n M a n g a n e s e 2556F e I r o n 2659C o C o b a l t 2759N i N i c k e l 2864C u C o p p e r 2965Z nZ i n c3070G aG a l l i u m3127A lA l u m i n i u m1311B B o r o n 512C C a r b o n614NN i t r o g e n716OO x y g e n819FF l u o r i n e928S iS i l i c o n1431PP h o s p h o r u s1532SS u l f u r1635.5C lC h l o r i n e1740A rA r g o n1820N eN e o n104H eH e l i u m273G eG e r m a n i u m3275A sA r s e n i c3379S eS e l e n i u m3480B rB r o m i n e3584K rK r y p t o n3639KP o t a s s i u m 1988S rS t r o n t i u m 3889Y Y t t r i u m 3991Z r Z i r c o n i u m4093N b N i o b i u m 4196M o M o l y b d e n u m 42T c T e c h n e t i u m 43101R u R u t h e n i u m 44103R h R h o d i u m 45106P d P a l l a d i u m 46108A gS i l v e r47112C dC a d m i u m48115I nI n d i u m49119S nT i n50122S bA n t i m o n y51128T eT e l l u r i u m52127II o d i n e53131X eX e n o n54137B aB a r i u m 56139L a L a n t h a n u m 57*178H fH a f n i u m72181T a T a n t a l u m 73184W T u n g s t e n 74186R e R h e n i u m 75190O s O s m i u m 76192I rI r i d i u m 77195P t P l a t i n u m78197A uG o l d79201H gM e r c u r y80204T lT h a l l i u m81207P bL e a d82209B iB i s m u t h83P oP o l o n i u m84A tA s t a t i n e85R nR a d o n86F rF r a n c i u m 87227A cA c t i n i u m899B eB e r y l l i u m4II I I I II V V V I V I I 085R bR u b i d i u m 37133C sC a e s i u m 55226R a R a d i u m 88T h e v o l u m e o f o n e m o l e o f a n y g a s i s 24d m 3a t r o o m t e m p e r a t u r e a n d p r e s s u r e (r .t .p .).a Xb a = r e l a t i v e a t o m ic m a s sX = a t o m i c s y m b o lb = p r o t o n (a t o m ic ) n u m b e rK e y *58-71 L a n t h a n o i d s e r i e s 90-103 A c t i n o i d s e r i e s D A T A S H E E T T h e P e r i o d i c T a b l e o f t h e E l e m e n t sPMT。

2013年全国大学生英语竞赛C类真题及答案

2013 National English Contest for College Students(Level C - Preliminary)(总分：150分答题时间：120分钟)Part I Listening Comprehension (30 marks)Section A (5 marks)In this section, you will hear five short conversations. Each conversation will be read only once. At the end of each conversation, there will be a twenty-second pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the center.1.Why didn’t the man go to see Macbeth last week?A.He didn’t manage to get a ticket.B.He had to attend a conference.C.He had a better production to watch.2.What does “Fill Me In” refer to in this conversation?A. A type of upgraded mobile phone.B. A well-selling magazine.C. A writer’s new book series.3.Why doesn’t the woman like the bag?A.She doesn’t like the pattern.B.It’s not easy to carry.C.It’s too big for her.4.What makes a bad CV according to the man?A.Fake information.B. Terrible writing.C. Undesirable length.5.How will Cathy continue her Spanish learning?A.She’s going to make a friend in Spain.B.She’ll communicate with a Spanish friend in Spain.C.She’ll practice speaking Spanish with an English friend.Section B (10 marks)In this section, you will hear two long conversation. Each conversation will be read only once. At the end of each conversation, there will be a one-minute pause. During the pause, read the question and the three choices marked A, B and C, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the center.Conversation One6.What traffic accident are the speakers talking about?A. A kid was knocked down by a car.B.Two cars crashed into a shop.C. A car ran into a wrong place.7.Why did the accident happen according the woman?A.There were many shops around.B.The crossing is in a wrong place.C.There was no crossing here.8.Which of the following is the suggestion they made?A.More traffic lights should be installed.B. A speed camera should be mounted.C.More policemen should patrol that area.9.Where, as the woman mentioned, has got improved traffic?A.Her own neighborhood.B.Her big brother’s neighborhood.C.Her parents’ neighborhood.10.How was the man punished for his traffic offence?A.He was fined 100 pounds with extra penalty points.B.He had to pay 150 pounds and got 6 penalty points.C.He finally paid 600 pounds without any penalty points.Conversation Two11.Why is the expert opposed to the view that memory aids make your memory worse?A.There is no evidence showing that memory aids are invalid.B.Human beings’ brain functions mainly through memory aids in an effective way.C.Memory aids encourage an organized approach which helps the brain functioneffectively.12.What is interview’s attitude towards the idea that visual image help the memoryA.It is hard to believe.B.It is nothing strange.C.It is obviously nonsense.13.Who developed the system of memory aids centuries ago?A.Inhabitants on an isolated island.B.The Ancient Greeks.C. A great psychologists.14.How does mapping out notes affect the brain?A.It is helpful in reflecting the way people link information in the brain.B.It prevents people from arranging things logically.C.It makes people’s brain function t he opposite way.15.What tends to affect people’s ability to think clearly?A.Upbringing and innate differences.B.Worry and anxiety.C.Their aptitudes.Section C (5 marks)In this section, you will hear five short news items. After each item, which will be read only once, there will be a pause. During the pause, read the question and the three choices marked A, B andC, and decide which is the best answer. Then mark the corresponding letter on the answer sheet with a single line through the center.16.How can social media influence the presidential election in the USA according to thelatest research?A.It can help voters to choose their president.B.It can help to ensure the fairness of the elections.C.It can help to increase the number of voters.17.What honorary title has Yaya Toure been granted?A.The African Player of the Year.B.212 Star of the Confederation of African Football.C.The Ivory Coast star.18.Why did Reshma Saujani set up the organization “Girls Who Code”?A.To raise women’s status in the field of science.B.To improve girls’ aptitude and performance in STEM.C.To arouse girls’ interest in science and technology.19.Which tablet computer’s hardware inside is more powerful?A.The CNET Kum.B. The Google Nexus 7.C. The Apple iPad mini.20.What does the company announce that it can do for the United States?A.It can reduce the amount of plastic waste.B.It can help to recycle the plastic waste.C.It can increase the amount of exports.Section D (10 marks)In this section, you will hear a short passage. There are 10 missing words or phrases. Fill in the blanks with the exact words or phrases you hear. The passage will be read twice. Remember to write the answers on the answer sheet.If you (21) ____ smooth skin that glows with youth, the chances are that at some point you will have heard the exhortation to drink lots of water in order to (22) ____ those evil toxins and keep your skin healthy.The exact amount people suggest varies. US – based advice (23) ____ eight glasses a day, while in hotter climates people are advised to drink to more to (24) ____ higher rates of sweating. But regardless of the exact volume of water suggested, the principle behind the advice remains the same --- taking extra water on board will keep your skin hydrated. In other words, water acts like a moisturizer, but from the inside out.This is such a common idea you might be surprised at the (25) ____ to back up. You might expect there to be countless studies where people are (26) ____ two groups, one assigned to sip water all day, the other to drink a normal amount. Then the smoothness of the skin could be (27) ____ a month or so later to establish whether sipping more lead to smoother skin.In fact such studies are rare, partly because water can’t be patented, so it is hard to find anyone to fund such research when there will be no new (28) ____ or cosmetic to sell that could repay the costs. A review by the dermatologist Ronni Wolf at the Kaplan Medical Center in Israel found just one study looking at the effect of long-term water intake on the skin. But the resultswere (29) ____. After four weeks, the group who drank mineral water showed a decrease in skin density, which some believe suggests the skin is retaining more moisture, while those who drank tap water showed an increase in skin density. But regardless of the type of water they drank, it made no difference to their (30) ____ or to the smoothness of their skin.Part II Vocabulary and Structure (15 marks)There are 15 incomplete sentences in this section. For each blank there are four choices marked A, B, C and D. Choose the one that best completes the sentence. Then mark the corresponding letter on the answer sheet with a single line through the center.31. The new star said to the journalists that she _C___ the opportunity to show that she could playa serious film role.A. greetedB. rejoicedC. welcomedD. cheered32. We haven’t really __D__ a solution to the problem yet, which makes the boss really frustrated.A. built upB. fallen back onC. brought overD. come up with33. Personally, I am __C__ banning cigarette smoking completely, especially in public areas.A. in touch withB. apart fromC. in favor ofD. regardless of34. Until a firm agreement has been reached, I am not __C__ to accepting the offer.A. accustomedB. dedicatedC. committedD. entitled35. The government is making every effort to __B__ an economic crisis, but it seems nothing could help.A. eliminateB. avertC. impedeD. swerve36. __B__ a serious crime, what exactly should you do?A. Unless you witnessB. If you were to witnessC. If only you witnessD. since you witness37. During examinations candidates are always supposed to stay in seats, keep their eyes on the work, _A___ to anyone.A. and not speakB. but could not speakC. rather than speakD. instead of speaking38. Realizing that he hadn’t got enough money and _D___ to borrow any from his parents, he decided to sell his house.A. wanted notB. not to wantC. wanting notD. not wanting39. There’s no point waiting here any longer. We _C___ go and have something to eat.A. can hardlyB. are bound toC. might as wellD. will have to40. While many people may refer to up-to-minute news, it is unlikely that television and the Internet _A___ the newspapers completely.A. will replaceB. replaceC. are replacingD. have replaced41. She married a very nice young architect from Belfast, _A___ she met on a bus during her journey to Northern Ireland.A. whoB. whenC. whichD. where42. It is a kind of illness that can result in total blindness if __D__A. to leave untreatedB. is left untreatedC. leaving untreatedD. left untreated43. ----I’m so disappointed with my son! He just wouldn’t practice the piano!----Take it easy. You can lead ___B_ to water, but you can’t make it drink.A. a duckB. a horseC. a cowD. a dog44. ----Good morning, Madam! I’d like some information about the course.----Certainly. _B___A.I’m afraid I don’t know more than you either.B.Is there anything I can do for you?C.What exactly would you like to know?D.How much information did you know?45. ---- How do you feel about countries that don’t try to reduce global warming?---- __A__, those countries care more about money than saving the planet.A.As far as I’m concernedB. It’s none of ou r businessC. We’re not to blameD. Things are under controlPart III Cloze (10 marks)Read the following passage and fill in each blank with one word. Choose the correct word in one of the following three ways: according to the context, by using the correct form of the given word, or by using the given letters of the word. Remember to write the answers on the answer sheet.According to recent surveys, 72% of all Americans believe that the United States government is (46) hiding____ information about UFOs. Almost 68% of people think that the government has secret knowledge of extraterrestrial life. It is not (47) _surprising__ (surprise) that the government has come under more and more (48) pressure____ to declassify its UFO records and make them public. A variety of different groups have been involved in these efforts.One group to become involved is called CFI, the Coalition for Freedom of Information, John Podesta, who was White House Chief of Staff during Bill Clinton’s (49)presidency____(president), is one of the many high-powered people active in this group. CFI’s aim is not to prove the (50) _existence___(exist) of extraterrestrial life, but to make it easier for scientists in general to study unexplained aerial phenomena. Podesta and his group has asked the Pentagon to declassify its UFO records and therefore provide scientists (51) with____ data that will help in the study of UFOs.CFI has requested the release of information on several UFO cases, starting with the Kecksburg, Pennsylvania, incident. This incident took (52) __place__ in 1965 when a large acorn-shaped object, the size of a small car, crashed in Pennsylvania. Some analysts say it could have been the spacecraft Kosmos 96 that had been launched towards Venus by the Soviet Union, but failed to escape Earth’s (53) gravity____. Others say the object did not look anything like spacecraft built on Earth in 1965.(54) Additionally___, the people of Kecksburg want to know what happened. On that (55) afternoon____, hundreds of eyewitnesses watched a fiery streak of light descend from the sky towards Earth. Officials explained that nothing was found or recovered and that maybe the fireball in the sky was a meteor. But many witnesses say they saw a number of military personnel from the Army and the Air Force search the woods, and later that evening, saw a large militarytractor-trailer coming from the area carrying a large object under a tarp.Part IV Reading Comprehension (40 marks)Read the following passage. Each passage is followed by several questions. Respond to the questions using information from the passage. Remember to write the answers on the answer sheet.Section A (10 marks)Questions 56-60 are based on the following passage.The average automatic teller machine (ATM) is not very smart. It will give money to anyone who has the right card and punches four or five keys in the right order. Some analysts estimate that as many as 30% of ATM transaction worldwide are cases of theft. To increase security at cash machines, some banks have tried to make their ATMs a little smarter. A small camera on the machine looks directly into the eye of every customer. It scans one iris and compares the tiny patterns of ridges, dots, and other features to a code in its computer. If there is a match, the ATM will start counting out cash. If not, a message is automatically sent to the nearest police station.Iris-scanning is one fast-growing form of biometric identification --- determining who someone is by examining features the body. One of the earliest biometric techniques was fingerprinting. The line on fingerprints are unique to each person, so not even identical twins have the same fingerprints. Fingerprinting has become famous as a way of finding out who committed a crime, but it very often fails. A careful criminal can swear gloves, avoid touching thing, or even alter his fingerprints by burning, cutting, or scraping them. In the search for a more reliable system, security experts have focused on the eye.Like a fingerprint, every iris is, for all practical purposes, unique. Each person’s right iris is even different from his or her left one. A low-cost digital camera, like the kind installed at ATM machines, can easily detect hundreds of different features in the iris. The chance of two irises having the same features is close to zero. Tests have shown that iris-scanners are very hard to fool. They can tell the difference between a real iris and a false one. They can see right through colored contact lenses, eyeglasses, and even mirrored sunglasses. Although many criminal are willing to burn or cut their fingers in pursuit of the perfect crime, few would be willing or able to alter their irises.T o make iris-scanning work, a computerized database has to match certain iris features with certain people. This means that each A TM customer has to allow a bank to photograph his or her iris and keep that highly personal information in a computer. Some people have worried, however, that an increased use of iris-scanning will lead to a dangerous loss of privacy. By mountingiris-scan cameras in public places, governments could track a private citizen all day long without the person’s knowledge. This would be a great advantage to the police, but it could also give corrupt officials a new way to control their opponents. The military’s development of tiny robots suggests that government iris-scanners could even invade private homes!Questions 56-60Complete the summary with words from the passage, changing the form where necessary, with only one word for each blank.Section B (10 marks)Questions 61-65 are based on the following passage.Seed catalogues feature hundreds of flowering species. For the persons just beginning garden this can be bewildering, and below are the details of some popular choices, nearly all of which should be sown in the spring. With the exception of busy lizzies, which need a little care, they are all very easy to grow from seed.DahliasThese are sturdy plants bearing showy flowers in a wide range of rather gaudy colors. Sow in a frame in April and plant the seedlings out when frosts are over. Dahlias flower throughout the summer and into the autumn. When autumn frosts begin to make them look unhappy, you should dig up the tuberous roots and save them. A frost -free loft, shed or garage is the ideal place. The following spring you plant the tubers instead of sowing seed again.LupinsLupins are hardy perennials. This means that the plants will stay in your garden and carry on flowering year after year. Seed sown in April will usually give you some spikes of colors in the first summer, and year by year the plants get bigger and the flowering stems get taller and grander. Selective breeding has led to the introduction of some fine, bicolored varieties in some dazzling shades. The short -lived flowers make a real misunderstanding spectacle.Busy lizziesLike dahlias, busy lizzies need to be started offunder glass, as they cannot stand frost, and pantingout is best done in May. Outdoor flowering ends inSeptember, so beat the frosts and bring your favoritespecimens indoors to give your home some sintercolor! Indoors they will carry on floweringindefinitely, though you may like to plant them outagain when spring returns. Like pansies (below) they do very well in sun or shade, but the soil must be moist. Most varieties grow to be a height of only 20 cm or so.PotentillasPotentillas are hardy shrubs. In other words, the woody branches spring from groundlevel—there is no central trunk. Seed is probably best sown in autumn, in which case you should keep the plants in a sheltered spot until April offers favorable conditions for planting out. Once flowering begins in early summer the best varieties (such as Melton Fire) will stay in bloomATM transactions are often cases of theft, where an unauthorized user takes (56) __money_. To decrease insecurity, some banks have installed iris -scanning machines at ATMs. These small cameras scan the user’s iris, recording its features and (57) _comping___ them to a digital file. Every person has a (58) _ unique ___ iris, making iris identification highly reliable. Earlier efforts at biometric identification often relied on fingerprints. However, fingerprints can easily be (59) altered____ through cutting, burning or scrapping. Iris scanners are so effective that they can even see through contact lenses and mirrored sunglasses. Use of iris scanners would provide great advantages to the police. However, others worry about a loss of (60) ____.almost ceaselessly for years on end while at the same time spreading out to provide ground cover or a low hedge.PansiesPansies have a good long flowering season year after year, and some varieties can be sown in spring to give truly splendid results the first autumn. Unlike dahlias and lupins, which can easily grow a meter tall, pansies grow no higher than 10 or 20 cm. Their soil, position and moisture requirements are just like those of busy lizzies but pansies differ in being hardy. Give them a try!Questions 61-63Decide whether the following statements are true (T) or false (F) according to the passage.61. Both dahlias and lupins, which are sown in April, need protecting from frost.62. Brought indoors in autumn, dahlias, busy lizzies and potentillas will carry on flowering almost non-stop.63. Among all the flowers busy lizzies are not very easy to grow from seed.Section C (10 marks)Questions 66-70 are based on the following passage.When looking for love, people may go to some extreme lengths. They might go on blind dates set up by family and friends. They might write personal ads to place in newspapers. Or they might use a computer to help them in their search for a soul mate by joining an online dating services. Some people have even tried to find their perfect match through game shows on television. Many of these TV dating shows, including The Bachelor and Who Wants to Marry a Millionaire? have proved to be ratings blockbusters, with millions of viewers watching each week to find out which of the contestants will find true love.Of all these game shows, perhaps the one with the most unexpected ending was Mr. Right, which was shown in England in 2002. On the show, a bachelor, thirty-five-year-old Lance Gerrard-Wright, dated fifteen women to find the one who was his ideal partner. The host of the show was Ulrika Johnson, an English celerity originally from Sweden. For seven weeks on the show, Gerrard-Wright took turns going on dates with each of the women, taking them to expensive restaurants and exotic locations. He even met the women’s families and introduced them to his own. Then at the end of each episode, he would choose between one and three of the contestants with whom he had felt the least compatible, and say goodbye to them.At one point during the series, one contestant volunteered to leave because she said she didn’t find him attractive. After two dates she said she had had enough, and she couldn’t see it working. “He wasn’t my cup of tea.” In another episode the woman he was on a date with burst into tears when he called her by another contestant’s name. “You called me by another girl’s name. I can’t believe you did that. I really liked you,” she sobbed.But in the final episode, the woman he eventually chose decided she didn’t want to marry him after all. “I think you’ve chosen me because you have to choose someone,” she said. Maybe this was because she already knew he had fallen in love---with the show’s host!After leaving the show, Gerrard-Wright and Johnson were seen dining together and attending parties around London more and more often. Finally, on May 1, 2003, Gerrard-Wright proposed to Johnson on the steps of St. Paul’s Cathedral. And she accepted his proposal right away, although it was a conditional acceptance. Johnson has two children from previous relationships—aneight-year-old son, Cameron, and a two-year-old daughter, Bo. She had to make sure that they agreed to the marriage. Luckily, they did. Gerrard-Wright said, “In the end the show did work for me. I grabbed an opportunity to get a girlfriend and I did. Ulrika’s gorgeous.”Questions 66-68Complete the following sentences with information given in the passage in a maximum of 2 words for each blank.66. Lance Gerrard-Wright went to ____ to go on the show Mr. Right in order to find his perfect match.67. On the show, Lance had the opportunity to date many gorgeous women among whom there might be one that he was almost ____.68. Ulrika accepted Lance’s proposal ____ that her children agreed to their marriage as well. Questions 69-70Choose the best answer according to the passage.69. Which of the following did NOT happen on the show?A. Lance went on dates with several women.B. The candidates went to some very good restaurants.C. Ulrika consulted her parents before she made her decision.D. The women met Lance’s family.70. What happened after seven weeks of doing the show?A. All of the women found their beloved.B. Lance started to date with the show’s host.C. One of the women on the show couldn’t help crying.D. Ulrika asked Lance to marry her.Section D (10 marks)Questions 71-75 are based on the following passage.Alaska is disappearing slowly but surely. Since the 1950s, it is estimated that as much as 15 percent of Alaska’s area has disappeared. But how can a whole state be disappearing?One reason for Alaska’s gradual disappearance is the melting its glaciers. According to one geologist at the US Geological Survey, about 98 percent of Alaska’s glaciers are either unmoving or diminishing. This diminishing seems mainly due to the increase in global temperatures. Since the 1960s, the average year-round temperature has increased by 5℉. Furthermore, the average winter temperature has increased by 8℉. Presently, an estimated 24 cubic miles of ice is disappearing from Alaskan glaciers every year. It may be even more in the near future, as some scientists predict that the average world temperature could go up 2.5 to 10℉by the year 2010.Another problem contributing to Alaska’s gradual disappearance is its permafrost. (74) Much of the land in Alaska was permanently frozen, or frozen for most of the year, thus maintaining its integrity. Now, the thawing permafrost is causing a number of problems on land. Roads and utility poles are collapsing. Also, the hard permafrost which originally prevented beaches from eroding during violent storms is now melting. Affected villages are forced to relocate. For villages on small low islands, one terrible storm could wipe out the entire community.The melting permafrost and increasing temperature are also having a negative impact on the forests of Alaska. As the permafrost under the forests melts, insects that normally don’t turn upuntil the warmer seasons are appearing sooner. The spruce-bark beetle, for example, is increasing in numbers as a result of global warming. It usually takes about two years for these beetles to grow and reproduce in a very cold weather. However, due to the increase in temperatures, spruce-bark beetles are damaging as many trees in one year as they previously damaged in two. At this rate, Alaska’s forest won’t survive the turn of the century.Some scientists believe that human activity is linked to a global increase in weather temperature. Whether the rising temperature are caused by human activity or natural changes, the fact remains that Alaska is warming. Some others argue that global warming may be a normal trend on the Earth’s temperature chart. (75) One theory argues that we are near the end of aso-called “Little Ice Age”, and the return of the glaciers is natural result of this cycle. Whether natural or produced by humans, there is little hope for the immediate future of glaciers as we know them. Horribly, this could be a preview of what will happen to the rest of the world in the next century.Questions 71-73Answer the following questions briefly according to the passage.71. What are disappearing in Alaska actually?72. How much ice is melting each year according to the survey?73. Why do insects damage more trees than before?Questions 74-75Translate the underlined sentences in the passage into Chinese.74. Much of the land in Alaska was permanently frozen, or frozen for most of the year, thus maintaining its integrity75. One theory argues that we are near the end of a so-called “Little Ice Age”, and the return of the glaciers is natural result of this cycle. Whether natural or produced by humans, there is little hope for the immediate future of glaciers as we know them.Part V Translation (10 marks)Translate the following sentences into English, using the hints given in brackets. Remember to write the answers on the answer sheet.76. 宴会时间就要到了，但她仍纠结于是否应该去。

2013年GCT数学真题解析

| PF2 |2 + | PF1 |2 −52 1 = , 2 | PF2 || PF1 | 2
| PF2 |2 + | PF1 |2 −2 | PF2 || PF1 | | PF2 |2 + | PF1 |2 −52 = | PF2 || PF1 | 又 4 = (|PF2 | − | PF1 |)2 =
2= a, AD 2= a, AE 2 2= a, AF 4a S =
) cm 2 B．20 C．18 D．16
1 2 (a + 2a 2 + 4a 2 + 8a 2 ) = 30 解 2
得 a = 2 ，所以 = FB 10, = AD 4 ， S阴 =0.5 × 4 × 10=20 7．某个锐角的正弦和余弦是二次方程 ax 2 + bx + c = 0 的不同的两个根，则 a, b, c 之间的关系是( )
D． f (2) < f ( 3) < f (3)
− f ( x + 1) = f ( x) ，所以 f ( x) 的周期为【解析】由于 f ( x +1) = − f ( x) ，令 x= x + 1 ，则 f ( x +2) =
2 ，有 f (3) = f (−1), f (2) = f (0), f ( 3) = f ( 3 − 2) ， f ( x) 在区间 [−1, 0] 上严格单调增则 f (−1) < f ( 3 − 2) < f (0) ，即 f (3) < f ( 3) < f (2) PS：本题还可以证明 f ( x) 在区间 [0, 1] 上严格单调递减的。 10． i 为虚数单位， z = A．0 【答案】A 【解析】由于 i 2 = −1 ， z=

2013 全国大学生英语竞赛B类真题答案

2013 National English Contestfor College Students(Level B - Preliminary)参考答案及评分标准Part I. Listening Comprehension（30 points）1—5CBCBA 6—10 AABBC 11—15 BACAB 16—20 BABAC21. a dictation 22. keep pace. 23. An active listener 24. the topic 25. heading26. paraphrasing 27. summarising 28. rewrite 29. thoughts and comments 30. useful study aid Part II援Multiple Choice (15 points)Section A (10 points)31—35 ACBBC 36—40 DACBASection B (5 points)41—45 ABCBDPart III援Cloze (10 points)46. popular 47. adopted 48. available 49. longer 50. nervous51. space 52. sufficiently 53. but 54. affectionate 55. retiredPart IV. Reading Comprehension (40 points)Section A (10 points)56. D 57. C58. ordering a hamburger 59. ignorant and inexperienced 60. primary source materialsSection B (10 points)61. For sport or because it蒺s part of a traditional culture.62. Stuff and mount the dead animals.63. Overpopulation of certain species.64. Outbreaks of fowl cholera.65. They kill a limited number of bowheads a year.Section C (10 points)66. a smaller firm 67. promotion prospects 68. morale69. his/her life miserable 70. got on withSection D (10 points)71. N 72. Y 73. Y74. 在我们的竞争对手感到拮据的时候出现这种情况，让人感到非常振奋。

2013中国女子数学奥林匹克试题及其解答

2013中国女子数学奥林匹克试题及其解答1.证明（张云华）1.证明（mavropnevma ）Let , . The region is the triangle ,and , thus the triangles of largest possible area are and . But(equality for is for ,disallowed).(equality foris for ).EDIT. Referring to the next post - it is interesting to figure out the envelope of the linesis the parabola , but in some way it is irrelevant, since the problemfunctions for a fixed , with fixed on the parabola for some , and thetriangular area being delimited by the tangent to that parabola at .1.证明（kunny）, thus theparabola is envelope of the linesWhich touches at .The domain of the family of the lines swept by is shown by the shaded region, excluded twopoints .Edit:I was misreading the context problem, thank you for pointing put it, mavropnevma.I have just attached another figure.Needless to say, mavropnevma's solution is perfect.P.S.I remember that the similar problem original problem has been posed in 1970's in Tokyo University entrance exam/Science.According to my memory, let be the maximum area of any triangle which is involved in theregion in original problem, then draw the graph of to find the extrema of .Here is the similar problem posed in Tokyo University entrance exam/Science, second round, 1978In the -plane, let be the part which is correspond to of the parabola ,that is to say, .Let the tangent Line of at intersects with the line at and intersects withthe line at .Let . We are to consider the questions as below in the range of.(1) Let denote the area of triangles by , respectively. Find the rangeof such that .(2) Let be the domain enclosed by line segments and .Note : contains line segments and .Let be the maximum area of the triangle with a vertex which is contained in .Find the function and draw the graph, then find the exterme value.Note : A function has local minimum (or local maximum) at a point, which means for all points which is closed to ,holds. We call local maximum, local minimum as extreme value.2.证明(Luis González)Let and Let be the incircleof touching at Clearly and are homothethic with incirclesbut since are symmetric about the midpoint of (isthe M-excircle of MAB), it follows that and are homotheticwith corresponding cevians2.证明(Andrew64)As shown in the figure below.is the intersection of and .Therefore , , meet at the same point .Attachments:link17.jpg [ 37.23 KiB | Viewed 52 times ]3.证明(mavropnevma)Since it is irrelevant which persons of the same gender know each other, we may assume there ore none such, and consider the bipartite graph having the left shore made ofthe boys and the right shore made of the girls, with an edge connecting a boy and a girl ifthey know each other. The condition means does not contain any induced cycle of length ,and the requirement is to show the number of edges satisfies .Thus it is an extremal graph theory question, for bipartite graphs with forbidden 's; bysymmetry we should also have .Denote by the set of girls that each knows exactly one boy, and by the set of girls that eachknows more than one boy; take and . We obviously have and.Let us count the number of objects , where is a girl, are distinctboys, and knows both . For each of the doubletons there is at mostone girl knowing them both (by the condition), so . Moreover, by pigeonholewe have .On the other hand, we have, by Jensen's inequality.We thus need , so.Finally, we get .For equality to be reached we obviously need , namely for each pair of boys having exactly one girl knowing both of them; and then we need .3.证明(crazyfehmy)Another solution: Consider the bipartite graph where there are girls andboys and denote the girls by 's and boys by 's as vertices.Let denote the number of edges from the vertex to set . If is connected to some andthen for any the girl must not connected to both and . Now let us count suchpairs. For every girl there are many pair of edges. Since all such edge pairs must bedistinct for all girls, and since there are at most such pairs, we haveor equivalentlyNow assume that are greater than or equal to and areor . Then we haveand we need to show that .Since for we have and hence .Now by Cauchy-Schwarz inequality we haveand if , we haveand we need to show that . Assume . Then we havewhich means that which is a contradiction. So, we are done.4.解（crazyfehmy）Let be called a nice pair if satisfies the conditionsstated in the problem.Firstly, we shall prove a lemma:If is a nice pair then for all integers and .Proof: Let or and divides for some integers and. Then we can find another pair such that and. (The proof is easy) Then consider the systemand . By the Chinese Remainder Theorem this system has a solution and such that both and isan element of which means that is not a nice pair becauseis divisible by .Now, we shall show that if or then has asolution for all integers . For the proof assume there exists an integer such thathas no solution in integers. Then it is easy to see thathas also no solution for all integers which are not divisibleby . Now take and consider the numbers . For all of these numbers,we have no solution and there are such numbers. Since all square residues have solutions(take ) and there are square residues modulo including zero, this means that forall nonsquare residues , the equation must have no solution. However, for the numberis not a square residue but so for we have asolution which is a contradiction. For the number is not a square residue buthas a solution since is a square residue. Hence we again obtain a contradiction so the second lemma is also proved.Now, since can take every value modulo and we must have andand also we must have and if is a nice pair. So, can take only three values. We will consider each case separately:If then we must have which meansIf then we must have whichmeansIf then we must have whichmeansIf we count these possibilities, if i am not wrong, we get.4.解（dinoboy）First, remark that it suffices for to be injective modulo and .For modulo simply note that we require .For modulo or we require for some thatNow, what values can take modulo ? It is a simple exercise to show allvalues modulo can be obtained (just express it as and then aswe can transform the problem to what values modulo can beexpressed as , which is known to be all of them). Therefore the only way this problemsworks out is if and .Therefore we simply require that and . For each value of there are valuesof modulo , 10 modulo and modulo so the answer should simply be.Note: To show takes all values modulo without relying onis not hard, but I'm lazy and felt like reducing it to an already solved problem.4.解（yunxiu），so ，hence satisfies the problem.So the answer should be .6.解（crazyfehmy）If let then satisfiessince is equivalent to whichhas always a solution in the set for all and since is odd.Now we will show that if then the condition does not satisfy. Let be theelements of the set . Consider the sums and let. Since 's are different modulo , the numbers 'sare also different modulo . On the other hand, none of 's can be equivalent to modulobecause otherwise we would have two equivalent terms. Hence is apermutation of and by adding up these equations we getwhich means. Now do the same procedure for all's to get. Let and. Then we have . So, we havemany numbers equivalent to each other modulo . However, we know that there are manynumbers modulo which are all equivalent to each other modulo . Hence in order for 's tobe different modulo, we must have which means that and hence. Soand we are done.Hence all possible values are .7.证明（Luis González ） Let cut again at Since is the exsimilicenter ofthen is midpoint of the arc ofbisects externally is midpoint of the arc ofis external bisector of andNote that is a Thebault circle of the cevian of externally tangent to itscircumcircle By Sawayama's lemma passes through its C-excenter isC-excenter ofis M-isosceles, i.e. Hence iscircumcenter of7.证明（Andrew64）As shown in the figure. Let be the intersection of and .It's fairly obviousSo we have, andare concyclic.So , andThus, Consequently .Namely is the bisector of.Attachments:link18.jpg [ 31.39 KiB | Viewed 93 times ]8.证明（duanby）hint:(a-b)(c-b)(a-d)(c-d)in detail: product (a-b)(c-b)(a-d)(c-d) for everya,c be the number on , b,d be the number onfor point x,y if they are not ajjectent then in the product, it will occur twice, if it's ajjectent it's appears only once, and also chick the point that are on and then we get it.iampengcheng1130 2013中国女子数学奥林匹克第7题的解答。

2013滑铁卢竞赛试题答案

The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca
2013 Euclid Contest
Wednesday, April 17, 2013
(in North America and South America)
since AC > 0. Finally, the perimeter of
3. (a) The parity of an integer is whether it is even or odd. Since the Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13, 21, . . ., then the parities of the ﬁrst eight terms are Odd, Odd, Even, Odd, Odd, Even, Odd, Odd. In the sequence, if x and y are consecutive terms, then the next term is x + y . In general, suppose that x and y are integers. If x is even and y is even, then x + y is even. If x is even and y is odd, then x + y is odd. If x is odd and y is even, then x + y is odd. If x is odd and y is odd, then x + y is even. Therefore, the parities of two consecutive terms x and y in the Fibonacci sequence determine the parity of the following term x + y . Also, once there are two consecutive terms whose parities match the parities of two earlier consecutive terms in the sequence, then the parities will repeat in a cycle. In particular, the parities of the fourth and ﬁfth terms (Odd, Odd) are the same as the parities of the ﬁrst and second terms (Odd, Odd). Therefore, the parities in the sequence repeat the cycle Odd, Odd, Even. This cycle has length 3. Therefore, the 99th term in the Fibonacci sequence ends one of these cycles, since 99 is a multiple of 3. In particular, the 99th term ends the 33rd cycle. Each cycle contains two odd terms. Therefore, the ﬁrst 99 terms in the sequence include 2 × 33 = 66 odd terms. Finally, the 100th term in the sequence begins a new cycle, so is odd. Therefore, the ﬁrst 100 terms include 66 + 1 = 67 odd terms. (b) Suppose that the ﬁrst term in the given sequence is a and the common diﬀerence is d. Then the ﬁrst four terms are a, a + d, a + 2d, a + 3d. From the given information, a + (a + 2d) = 6 and (a + d) + (a + 3d) = 20. The ﬁrst equation simpliﬁes to 2a + 2d = 6 or a + d = 3. The second equation simpliﬁes to 2a + 4d = 20 or a + 2d = 10. Therefore, (a + 2d) − (a + d) = 10 − 3 or d = 7. Since a + d = 3 and d = 7, then a = −4. Therefore, the tenth term in the sequence is a + 9d = −4 + 9(7) = 59. 4. (a) There are ﬁve odd digits: 1, 3, 5, 7, 9. We consider the positive integers less than 1000 in three sets: those with one digit, those with two digits, and those with three digits. There are 5 positive one-digit integers with one odd digit (namely 1, 3, 5, 7, 9). Consider the two-digit positive integers with only odd digits. Such an integer has the form XY where X and Y are digits. There are ﬁve possibilities for each of X and Y (since each must be odd). Therefore, there are 5 × 5 = 25 two-digit positive integers with only odd digits. Consider the three-digit positive integers with only odd digits. Such an integer has the form XY Z where X , Y and Z are digits.

2013年全国剑桥杯英语能力竞赛题初中B组

第 1 页共 8 页2013年全国“剑桥杯”英语能力竞赛(重庆赛区)初赛题初中B 组笔试题主办：外语教学与研究出版社剑桥大学出版社重庆片主办：重庆晨报四川外语学院英语学院重庆片承办：重庆晨文文化传播有限公司校园在线考试时间：60分钟总分：100分说明：全卷共五大题50小题，所有答案均填涂在机读卡上，否则将作零分处理，只交机读卡，试卷自己保管。

第一部分基础知识 (44分)I. 单项选择。

(每小题2分，共20分)根据语境，从四个选项中选择一个最佳的答案完成语境，并把机读卡上相应答案的番号涂黑。

1. Here's Mary's plan for one week during her summer vacation. What kind of plan is this? A. A trip plan. B. A party plan. C. An eating plan. D. An exercise plan.2. I put the fish in the ice box to keep it ______.A. freshB. fullC. newD. young3. The pants I bought last year are too small now. I think I need a new ______. A. belt B. pair C. shirt D. space4. How can you study in the living room when other people are watching TV? I think you need a _______ place.A. cleanerB. quieterC. saferD. smaller5. Marsha thought her friends would do something ______ to celebrate her birthday, but they just gave her a little card.A. correctB. honestC. quickD. special6. I cannot understand why Steven bought so many watches but never wears ______ of them. A. any B. both C. every D. others7. Elsa hates going shopping, _______ she went last night when her grandpa asked her to buy some medicine for him.A. becauseB. butC. ifD. so 8. Alex: Why are you still here? It's already eight o'clock.Tom: Because I ______ my work. Don't worry. It's almost done.A. wasn’t finishingB. wouldn’t finishC. haven’t finishedD. won’t finish9. Lucy: Does Aunt Tara enjoy __________?Mark: Yes. She has three dogs, two rabbits, four birds, and some fish in her house.A. collecting dollsB. keeping petsC. visiting the zooD. working on the farm10. 下列成语“熟能生巧”用英语正确的选项是__________。

VCE考试数学2013试题1

Question 7 (6 marks) The probability distribution of a discrete random variable, X, is given by the table below. x Pr(X = x) a. 0 0.2 1 0.6p2 2 0.1 3 1-p 4 0.1 3 marks
b.
On the axes above, sketch the graph of g(x) = | f (x)| + 1, for x [-2, 2]. Label the end points with their coordinates.
2 marks
Question 9 – continued
6
Question 6 (3 marks) Let g: R → R, g(x) = (a – x)2, where a is a real constant. 31 The average value of g on the interval [–1, 1] is . 12 Find all possible values of a.
-x
y = f (x) P (x, f (x))
O
Q
x
a.
Find the area, A, of the triangle OQP in terms of x.
1 mark
Question 10 – continued
13
2013 MATHMETH (CAS) EXAM 1
b.
Find the maximum area of triangle OQP and the value of x for which the maximum occurs.

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Ciscussions about these mark schemes.
Cambridge is publishing the mark schemes for the May/June 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.
(e)
23.1 or 23.07 to 23.08
3
325 − 250 × 100 oe 325 325 − 250 soi by 0.2307… 3sf or Or M1 for 325 better 250 or × 100 soi by 76.9… 325
M2 for
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(ii) (b) (i) (ii) 3 (a) (i) (ii) (iii) (b) (c) (i)
217 to 221 6360 or 6361 to 6363 165 or 164.9 to 165 x≥5 y ≥ 11 x + y ≥ 20 4x + 8y ≤ 160 and divide by 4 x = 5 ruled y = 11 ruled x + y = 20 ruled x + 2y = 40 ruled Correct shading of unwanted region
1 1
Accept 0.3 Accept 0.667 or better and 0.333 or better
1
Accept 0.778 or better and 0.222 or better
(b)
3
M2 for better
7 3 3 7 × + × soi by 0.467 or 10 9 10 9 7 3 3 7 × or × soi by 0.233 or 10 9 10 9
1 1 1 1 1 1 3
(d)
After 0 scored, M1 for y = 2x – 2 drawn B1 for correct tangent
(e)
B2 for answer in range dep on close attempt at tangent
rise used with values soi from run tangent, dep on correct or close attempt at tangent
or M1 for better 7 (a) (i) Triangle at (1, 3) (1, 9) (3, 3) 2
SC1 for correct vertices not joined or triangle(1, 1) (3, 1) (1, 7)
(ii)
1 0 0 3
7 oe their(b)
(c)
8.7 or 8.7 to 8.72 www
3
or M1 for sin =
(d)
217
3
4 ×π×1.53 soi by 14.1 to 14.14 3 and M1 dep for their (a) ÷ their 14.14 soi by 218. Dependent on M1 earned
2
1 SC1 for 0 3 or 0
0580 MATHEMATICS
0580/43 Paper 4 (Extended), maximum raw mark 130
This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers.
M1dep for [–]
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Page 5
Mark Scheme IGCSE – May/June 2013
Syllabus 0580
Paper 43
6
(a)
3 correctly placed 10 6 3 and correctly placed 9 9 7 2 and correctly placed 9 9 42 21 14 7 or or or 90 45 30 15
(e) (i) (ii) 5 (a) (b)
25.13875 final answer 25.14 –5.04, 1.75, 0 Fully correct curve
2 1FT 3 5
(c)
–1.6 to – 1.5 –0.4 to –0.3 1.8 to 1.9 –2.6 to –2.5 www –0.4 to –0.3 1 3.25 to 4.25 with correct tangent
M1 for B1 for 4.55 and 11.05 seen or 25.13875 seen and then spoiled Strict FT their (e)(i) correct to 4s.f. if rounding is possible B1 for each correct value B3FT for 10 correct plots from their (a) B2FT for 8 or 9 correct plots or B1FT for 6 or 7 correct plots and SC1 for two branches not joined
M1 for π × 452 M1 for
210 × 2π × 45 360
–1 once for strict inequalities in (i) to (iii)
If there is a final inequality it must be the given one Must be on correct grid line Must be on correct grid line B1 for one axis intercept correct when extended if necessary but not parallel to an axis B1 for one axis intercept correct when extended if necessary but not parallel to an axis Dependent on 6 marks earned for the boundaries M1 for x + y evaluated where (x, y) is a point in their quadrilateral and x and y are integers
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Page 3
Mark Scheme IGCSE – May/June 2013 Perpendicular bisector of QR ruled with 2 correct sets of arcs centred Q and R Bisector of angle SPQ ruled with correct arcs. (Marks on PS and PQ and correct pair of arcs) Compass drawn arc centre R with radius 6 cm (±2 mm) Correct region shaded cao 2
Syllabus 0580
Paper 43
2
(a) (i)
B1 for correct bisector ruled
2
B1 for correct angle bisector ruled
B2 1dep 1 2 2 1 1 1 1 1 1 2 2 1dep 2
B1 for any compass drawn arc centre R not used in any construction with no feathering Dependent on all B4 marks for the correct loci
Paper 43
4
(a) (b)
M1 for ½ × 7 × 22 × 40 M3 for 7 2 + 22 2 + 40 2 or M2 for 72 + 222 + 402 soi by 2133 or M1 for correct Pythagoras on one face
7 M2 for sin– 1 their(b) oe
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