步步高大一轮复习讲义
2025高考英语步步高大一轮复习讲义人教版必修第二册——选择性必修第四册语法专题答案精析
2025高考英语步步高大一轮复习讲义人教版必修第二册——选择性必修第四册语法专题答案精析语法专题专题一复杂多变的动词第1讲谓语动词考点精讲一对点练习1 1.will tell 2.is 3.hired对点练习2 1.was playing 2.will be playing 3.am filling对点练习3 1.had learned/learnt had said 2.have told3．had expected对点练习4 1.has been writing 2.would be would change解题技法1．were stewing 2.took/should take 3.have been 4.will miss考点精讲二对点练习 1.has been recognized 2.is being repaired 3.is regarded 4.to blame解题技法1．is designed 2.reading 3.consists 4.been carried考点精讲三对点练习 1.gives 2.is 3.is are 4.were 5.has caused6．is解题技法1．were 2.reminds 3.is考点精讲四对点练习 1.might not 2.can’t 3.can’t 4.could5．couldn’t 6.should7.mustn’t 8.shall9.must10．needn’t解题技法1．could 2.have scolded考点精讲五对点练习 1.had been 2.(should) be settled 3.would have arrived 4.had taken 5.had解题技法1．wouldn’t be 2.would stop 3.(should) get 4.focused考点分层演练层级一1．was working 2.have kept 3.had sunk 4.have been made5．was brought 6.is being taken 7.will be distributed8．is designed9.was listed10.have become层级二1．be employed 2.means 3.have promised 4.was fixing 5.threw 6.was built7.connects 8.had been offered9．will deliver/will be delivering10.are being displayed层级三Passage 11．was established 2.built 3.consisted 4.were replaced 5.(were) kept 6.understood7.have tried/have been trying8．to save9.(are) watched10.are playingPassage 21．needn’t 2.danced 3.can 4.did/should do 5.will6．(should) not allow7.must 8.didn’t wear9.shall10．should语法链接写作1．Though I felt a little sorry that you left China last year，I am pleased to know you are leading a happy life in your hometown.2．If you are available next Sunday，I will wait for you at the school gate and I’m sure we will have a good time together.3．It can easily be seen that the percentage of students who choose listening to English songs and watching English movies is respectively 65% and 50%.4．(1)If I hadn’t read the newspaper Youth，I wouldn’t have made such great progress in English.(2)In a word，it is high time that we should raise/raised our awareness of environmental protection.(3)It is required that anyone who wants to participate should arrive at the lecture hall on time to watch the movie and take part in the discussion.(4)But for/Without her help and professional instruction，I couldn’t have made such great progress in English study.5．From the learning experience，I fully understand that only by practicing a lot can we overcome many kinds of difficulties.第2讲非谓语动词考点精讲一对点练习 1.to have 2.carried 3.having completed 4.to have been robbed 5.being settled考点精讲二对点练习 1.to walk cated 3.forming 4.thinking5．getting 6.encouraging考点精讲三对点练习 1.being discussed 2.to support 3.marked4．living考点精讲四对点练习 1.making 2.to teach 3.permitting pleted 5.absorbed考点精讲五对点练习 1.smoking 2.delivered 3.to process解题策略1．Knowing 2.Being offered 3.to have received 4.Having been shown 5.making考点分层演练层级一1．being charged 2.applied 3.desiring 4.to be cheered5．Having suffered 6.absorbed 7.associated8.to master9．driven10.putting层级二1．borrowing intended 2.built 3.Having visited recording4．to continue 5.to journey 6.held 7.planning8.To strengthen inviting9. Covering10.to see层级三1．Going 2.are 3.refreshed 4.amazing 5.gets 6.astonished7.wondering8.to put 9.aching10.to visit语法链接写作1．Persuading him into accepting my views was impossible，so I didn’t want to waste my time discussing.2．(1)Hearing of the unexpected news，she was so surprised that she froze with her mouth wide open.(2)Worn out，David reached the finishing line and all the students cheered for him.3．To learn English more efficiently，you had better choose the Listening and Speaking course. 4．Having sold out all the popcorn，they decided to call it a day and go home.专题二需要变形的名词、数词、形容词和副词第1讲名词考点精讲一对点练习 1.championships 2.activities 3.weaknesses4．passersby 5.heroes 6.barber’s 考点精讲二对点练习 1.Word word 2.experiences experience 3.a/考点精讲三对点练习 1.arrival 2.invitation 3.responsibility 4.marriage 5.accuracy解题策略1．requirement professions 2.pollution 3.conditions4．dishes第2讲数词对点练习 1.thirteenth 2.thirds 3.ninth 4.twenties5．thousands解题技法1．second 2.has been polluted 3.fifth第3讲形容词和副词考点精讲一对点练习 1.personal 2.disappointed 3.amazing 4.hungry 5.highly 6.officially 7.Luckily8.terribly考点精讲二对点练习 1.more 2.wider 3.biggest 4.faster 5.as/so解题策略1．smaller 2.tasty 3.finest 4.gently考点分层演练层级一1．carrots 2.achievement 3.intention 4.fifties 5.twelfth6．third7.industrial8.surprising rgest10.widely层级二1．sixth 2.Different 3.warning 4.remarkable 5.rarely6．visiting7.interviews 8.Basically9.photographer10．meaningful层级三1．dynastic 2.classes 3.originally 4.closer 5.wealthy6．beautifully7.spacious 8.simpler/more simple9.cultural10.events语法链接写作1．When it comes to ocean，it’s of great importance to the world；however，its pollution isbecoming more and more serious.2．Last weekend，I participated in a “Getting to Know the Plants Around Us” activity organised by our Student Council with curiosity.3．(1)As you know，the more people are involved，the better the ocean environment is.(2)Nothing is more important than my teacher’s encouragement.Without it，I couldn’t have won the prize.专题三不可忽视的小词第1讲冠词考点精讲一对点练习 1.a 2.an 3.a 4.a考点精讲二对点练习 1.the 2.the 3.the 4.The 5.The考点精讲三解题策略1．a 2.the第2讲代词考点精讲一对点练习 1.himself 2.our 4.it 5.it 6.It考点精讲二对点练习 1.other 2.another 3.none 4.neither 5.one解题策略1．mine 2.their 3.herself 4.it第3讲介词对点练习 1.on 2.with 3.by 4.in 5.for 6.on解题技法1．by 2.for 3.in考点分层演练层级一1．an 2.the 3.the 4.his 5.them 6.myself7.it8．their9.on10.like层级二1．the 2.as 3.to 4.by 5.a 6.the7.by8.its9.the10．neither层级三1．a 2.their 3.of 4.for 5.with 6.a7.them8.her9.the10.by语法链接写作1．Because I am attracted by the contents，reading Youth becomes a must for me every day.2．It was exciting to learn that I had gained first prize and an award ceremony would be held in three days.3．Although online learning makes it easier for people to gain knowledge，being online is also a challenge for people who lack selfdiscipline.4．Eventually，because of my persistence and painstaking efforts，I could skate freely all by myself.专题四三大从句与特殊句式第1讲定语从句考点精讲一对点练习 1.which/that 2.whose 3.is 4.As 5.that6．which考点精讲二对点练习 1.when 2.where 3.which 4.why考点精讲三对点练习 1.which 2.whom 3.them 4.which解题策略1．which/that 2.where 3.who/that 4.whose 5.As考点分层演练层级一1．which 2.where 3.who 4.where 5.who/that 6.when7．whose8.As9.why 10.whom层级二1．which/that 2.where 3.who/that 4.who 5.that6．that 7.where8.whose9.which/that 10.where层级三1．when 2.why 3.where 4.whose 5.whom 6.that/which7.who8.which9.which 10.As语法链接写作1．运用1Confucius，also known as Kong Qiu，was a Chinese philosopher and politician who lived during the Spring and Autumn Period.运用2World Ocean Day which/that falls on June 8th is aimed at raising people’s awareness of ocean conservation.2．First，you’ll be shown around our school and have lunch at a local restaurant，where you can have a taste of authentic Chinese food.3．For students，what is most beneficial to their study is reading English books，from which they can learn what they can’t in class.4．To begin with，I suggest organizing a walking tour around the city to explore the green spaces in Beijing，which will allow participants to experience the beauty of the city’s parks.第2讲名词性从句对点练习 1.why 2.what 3.how 4.that 5.that6．whether解题技法1．What 2.how 3.whoever 4.where 5.whether/if考点分层演练层级一1．whether 2.why 3.how 4.what/whatever 5.where6．that7.What8.when9.who 10.because层级二1．why 2.whether/if 3.how 4.where 5.what 6.why/that7.what8.whether/if9.what 10.that层级三1．What 2.that 3.whether 4.why 5.How 6.who7．that8.that9.when10.because语法链接写作1．What surprised me was that my dad allowed me to use the money as I wished.2．No one can deny the fact that online learning is becoming more and more popular.3．I’m sorry that I can’t go out with you as planned.The reason is that my younger brother broke his leg the other day and I must look after him.4．The exhibition is fantastic and shows the charm of Chinese culture.This is why I would like to recommend my fellow students to attend this art show as well.5．I recommend that you (should) choose the Listening and Speaking course，because the course is entirely taught in Chinese，which will benefit you a lot.第3讲并列句和状语从句考点精讲一对点练习 1.while 2.when 3.or 4.but/yet 5.so考点精讲二对点练习 1.until 2.before 3.than 4.before 5.since考点精讲三对点练习 1.if 2.Wherever 3.as/though 4.that 5.because/as 6.that7.though/if8.how 解题策略1．and 2.While 3.because 4.before考点分层演练层级一1．that 2.because/as 3.but 4.and 5.when 6.while7．if8.though/although9.until/till 10.whatever层级二1．and 2.but/yet 3.or 4.because 5.whether 6.until/till7．or8.When/As9.if/though 10.unless层级三1．who/that 2.than 3.visiting 4.when 5.While/Though/Although 6.but7.higher8.If 9.for10.but语法链接写作1．Not only does the ocean offer us sufficient food，but it also maintains the balance of nature. 2．Come to the exhibition，and you will enjoy a visual feast.3．So difficult and painful for me was writing that my teacher had allowed me to present my paper on the sinking of the Titanic by acting out a play，where I played all the parts.4．We were looking for a place to put up the tent when Mother told us that she had forgotten to take it.5．Not until yesterday was I informed that our class was going to hold an important meeting this weekend—exactly the time when we shall meet.第4讲特殊句式考点精讲一对点练习 1.and 2.What 3.that考点精讲二对点练习 1.live 2.as/though 3.did 4.are 5.did考点精讲三对点练习 1.expected 2.writing 3.dealt 4.to make解题策略1．are 2.that考点分层演练层级一1．that 2.Sitting 3.warned 4.were 5.that 6.If层级二1．that 2.Were 3.that 4.did 5.came层级三1．a 2.that 3.without 4.continuing 5.permission6．logical7.were said8.further 9.Inspired10.whose语法链接写作1．What a fantastic Chinese painting show it is!2．“Hurry up，or the bear will catch up with us，” said Elli.3．It was at that festival that you shared so many interesting things about your country.4．Only when all the people make their efforts to protect the ocean will the ocean environment become better and better.5．So happy was Bernard that he gave John a big hug.6．In the backyard were two happy dogs tumbling about on the grassland.。
2025高考语文步步高大一轮复习讲义板块七 名篇名句默写 学案65 掌握默写要点——选准句写对字形
2025高考语文步步高大一轮复习讲义板块七名篇名句默写学案65掌握默写要点——选准句子，写对字形复习任务能够准确无误地背诵出高考要求的背诵篇目，并在试题语境中选准句、写对字。
课标要求古诗文背诵推荐篇目共72篇(文言文32篇、诗词曲40首，详见《高考必背》)。
考情微观年份卷别试题组成命题特点第(1)题第(2)题第(3)题2023新高考Ⅰ卷《报任安书》《李凭箜篌引》与诸葛亮有关的诗句①诗文并重，以诗为主。
选句均为“名句”，不回避生疏的句子与难写字。
②题型稳定，前两题是情境式默写，后一题为开放式默写(飞花令式默写)主要考查的诗句。
③命题范围不超出高考规定的篇目，但鼓励考生进行范围外的积累。
如第(3)题。
新高考Ⅱ卷《五代史伶官传序》《临安春雨初霁》壮阔的写景名句2022新高考Ⅰ卷(广东、河北、湖南、湖北、福建)《荀子·劝学》鸟啼引起悲思的诗句新高考Ⅰ卷(山东、江苏)《拟行路难》《短歌行》《梦游天姥吟留别》新高考Ⅱ卷(辽宁、海南)《归园田居》(其一)《蜀相》与京华有关的诗句新高考Ⅱ卷(重庆)《短歌行》花鸟对举出现的诗句2021新高考Ⅰ卷(广东、河北、湖南、湖北、福建)《庄子·逍遥游》与“三秦”有关的诗句新高考Ⅰ卷(山东)《过秦论》与“青草”“王孙”有关的诗句新高考Ⅰ卷(江苏)《屈原列传》《答司马谏议书》与“杜康”有关的诗句新高考Ⅱ卷《归园田居》(其一)《五代史伶官传序》与“落木”有关的诗句(说明：卷中涉及的老课标背诵篇目，不在统计之列；因背诵篇目前几年各省未统一，个别省份试卷不在统计之列。
)活动一研练高考真题1．(2023·新高考Ⅰ)补写出下列句子中的空缺部分。
(6分)(1)司马迁在《报任安书》中说，自己编写《史记》“________________”，便遭遇了李陵之祸，因痛惜这部书不能完成，所以“_____________________________________________”。
2025高考英语步步高大一轮复习讲义人教版必修第一册高考题型组合练必修第一册 Unit 4 Nat
2025高考英语步步高大一轮复习讲义人教版必修第一册高考题型组合练必修第一册Unit 4Natural DisastersⅠ.阅读理解A(★)As a shift in the polar vortex(极地涡旋) swept across much of the US，many people in the country were hit with a sudden snap of cold.Heavy ice and snow coupled with fallen trees caused the outages in major cities，with companies unable to tell their customers when power will be restored.Polar vortices were noticed long ago.But the first known use of the term “polar vortex” was in a magazine in 1853.Polar vortices are present year-round，but we don’t hear about them until they cause problems.They maintain freezing temperatures at the North and South Poles by moving in tight counterclockwise patterns.Polar vortices grow stronger in winter and weaken in summer.They are kept in place at the poles by another atmospheric current called the jet stream.However，when the jet streams weaken，the cold winds of the polar vortex are pushed southwards and it is during this time that people begin to pay attention!In Texas，roads froze over，causing six traffic deaths，and many schools were shut down.People are not the only Earthlings to struggle with the cold.Crops and animals are also freezing.This could have major consequences，especially if herds of cattle die.If snow blocks cattle，the animals can’t reach basic necessities like food and fresh water.On a brighter note，some Texas cities were more prepared than others，for instance，Amarillo，which is located in North Texas，so they are more accustomed to colder temperatures.Amarillo is notable because the city was redesigned to stand up to severe winter storms.Officials have spread out fire stations to increase coverage of first responders，employed modified dump trucks for clearing ice，and upgraded civic centers to provide shelter during storms.Hopefully，other Texas cities will follow the good example set by Amarillo!1．What does the underlined word “outages” refer to in paragraph 1?A．Traffic jams. B．Power struggles. C．Power cuts. D．Traffic accidents.2．What can we learn about polar vortices?A．They grow stronger in summer. B．They are affected by jet streams.C．They were first observed in 1853. D．They move in a clockwise direction.3．What is the last but one paragraph mainly about?A．The definition of the polar vortex.B．The characteristics of the polar vortex.C．The ways to deal with the polar vortex.D．The serious impact made by the polar vortex.4．Why is Amarillo striking?A．Because it is located in the north of Texas.B．Because it has been upgraded and modernized.C．Because it has been regarded as an example to other cities.D．Because it has taken effective measures to resist winter storms.BWhat is the 15-minute city？It’s the urban planning concept that everything city residents need should be a short walk or bike ride away—about 15 minutes from home to work，shopping，entertainment，restaurants，schools，parks and health care.Supporters argue that 15-minute cities are healthier for residents and the environment，creating united mini-communities，boosting local businesses，and encouraging people to get outside walk，and cycle.Many cities across Europe offer similar ideas，but Paris has become its poster child.Mayor Anne Hidalgo has sought to fight climate change by decreasing choking traffic in the streets and fuel emissions.In 2015，Paris was 17th on the list of bike-friendly cities; by 2019，it was 8th.Car ownership，meanwhile，dropped from 60 percent of households in 2001 to 35 percent in 2019.The 15-minute city figured largely in Hidalgo’s successful 2020 re-election campaign.The idea has also gained support in the U．S.It clearly won’t work everywhere：Not every city is as centralized and walkable as Paris.Some car-dominated cities like Los Angeles and Phoenix would be hard-pressed to provide everything people need within walking distance.In addition，some urban planners argue that the 15-minute city could increase the separation of neighborhoods by income.Neighborhoods equipped with all the conveniences required by the 15-minute city also tend to have high housing costs and wealthier residents.Despite some resistance，the basic principles behind the 15-minute city are influencing planning in cities around the world，including Melbourne，Barcelona，Buenos Aires，Singapore，and Shanghai.Urban designer and thinker Jay Pitter says cities where basic needs are within walking distance create more individual freedom than needing to drive everywhere.“In a city where services are always close by，” he says，“mobility is a choice：You go where you want because you want to，not because you have to.My fight is not against the car.My fight is how we could improve the quality of life.”5．Which best describes the 15-minute city?A．Modern. B．Smart. C．Entertaining. D．Convenient.6．What’s the original intention for Paris to advocate the 15-minute city?A．To address climate issues. B．To beautify the city.C．To promote the bike industry. D．To help Hidalgo get re-elected.7．What’s some urban planners’ worry about the 15-minute city?A．It slows the city’s expansion.B．It represents a setback for society.C．It may widen the gap between neighborhoods.D．It can cause the specialization of neighborhoods.8.What’s Jay Pitter’s attitude to the concept of 15-minute city?A．Doubtful. B．Favorable. C．Critical. D．Uninterested.C(★)Earthquake forecasting is one of the most ancient skills known to mankind.From ancient Greece to the present day，countless scientists have tried to develop tools to predict earthquakes.Their attempts usually focused on searching for reliable evidence of coming quakes.However，there are many reasons why predicting quakes is so hard.“We don’t understand some basic physics of earthquakes，” said Egill，a research professor at the California Institute of Technology.Scientists have also attempted to create mathematical models of movement，but precisely predicting would require great mapping and analysis of the Earth’s crust.Other challenges include a lack of data on the early warning signs，given that these warning signs are not yet entirely understood.Actually，real earthquake prediction is very similar to the diagnosis of potential human illnesses based on observing and analyzing each patient’s signs and symptoms.As it turns out，quake prediction is extremely difficult.Many sources show that earthquake forecasting was recognized science in ancient Greece.Ancient Greeks lived very close to nature and were able to detect unusual phenomena and forecast earthquakes.The first known forecast was made by Pherecydes of Syros about 2,500 years ago：he made it as he scooped water from a well and noticed that usually very clean water had suddenly become muddy.Indeed，an earthquake occurred two days later，making Pherecydes famous.Nowadays，seismic(地震的) and remote-sensing methods are considered to have the greatest potential in terms of solving the earthquake prediction problem.Currently，Terra Seismic can identify a forthcoming earthquake with a high level of confidence.Generally，Terra Seismic does not predict a quake if the earthquake’s epicenter is located beyond a depth of 40km.Fortunately，such quakes are almost always harmless，since quake’s energy reduces before reaching the Earth’s surface.“Scientists have tried every possible method to try to predict earthquakes，” Bruneau said.“Nobody has been able to crack it and make a believable prediction.”9．What do we know about earthquake forecasting?A．Scientists have been passionate about accurately predicting earthquakes.B．As long as enough data is collected，earthquakes can be avoided.C．Mathematical models of motion can simulate and predict earthquakes.D．Scientists have fully studied the structure of earthquakes.10．How did Pherecydes successfully predict that earthquake?A．By seismic and remote-sensing methods.B．By observing unusual natural phenomena.C．By living in seismic zones throughout the year.D．By looking into data on the early warning signs.11．What was Bruneau’s opinion about the current methods of earthquake prediction? A．He strongly believed the Terra Seismic can solve the difficult problem.B．He was sure that humans could accurately predict earthquakes in the future.C．He considered it harmless to humans for an earthquake deeper than 40km.D．He thought that scientists had no reliable method to predict earthquakes.12．What is the text mainly about?A．Why do humans predict earthquakes.B．How to protect oneself during an earthquake.C．What methods can be used to forecast earthquakes.D．When to achieve accurate earthquake forecasting.Ⅱ.七选五(★)Hurricane season can be wild and unpredictable. 1 Here are some ways you can beef up your home security in hurricane weather，even if you need to move out.2 That actually does nothing to ensure your safety in the powerful winds.Sticking to hurricane shelters or plywood(胶合板) is the only way to go when it comes to protecting those points of entry in hurricane conditions.Buy sheets of plywood，measure your windows and use brackets(支架) to hold the plywood in place.Sandbags are very useful.While sandbags won’t be able to help in the extreme storm，many people will be able to prevent flooding and extensive damage to their belongings by placing sandbags. 3 Any storm water that is kept out of your home is storm water that won’t be able to damage the belongings inside your home，so sandbags are well worth having at your doorways during a hurricane.It’s important to prepare the inside of your home for strong winds and rain.But you should also keep an eye on the outside of your house，too.Trim(修剪) trees，especially dead branches，to prevent anything else that could fly through a window and cause damage during a hurricane. 4 You should also take pictures of expensive items like electronics and keep notes of their serialnumbers. 5 Also，there are always bad people out right after a storm.If the worst happens and your home is broken into right after a bad storm，having pictures and detailed notes about what was in your home prior to the hurricane will make it easier for police to track down stolen items. A．You should have a camera at home.B．It can be strong enough to resist the forceful winds.C．Making sure nothing is loose in your yard is important.D．You may see people taping windows before a hurricane comes.E．They will be able to effectively keep storm water out in many cases.F．It will aid with your insurance company if anything needs to be replaced.G．These dangerous storms can bring damage to your home and belongings.必修第一册Unit 5Languages Around the WorldⅠ.阅读理解AMost of us take the task of buying a cup of coffee for granted，as it seems simple enough.However，we have no idea just how stressful tasks like this can be for people who suffer from disabilities.That’s why it’s so heart-warming to see a story like this in which a barista (咖啡师) does something small to make life a little easier for someone who is deaf.Ibby Piracha lost his hearing when he was only two years old，and he now goes to his local cafe in Leesburg，Virginia to order a cup of coffee at least three times a week.Though all the baristas who work there have his order memorized，Ibby always writes his order on his phone and shows it to the barista.One day，however，one of the baristas did something that changed everything! After Ibby ordered his coffee，he was amazed when barista Krystal Pane handed him a note in response.“I’ve been learning sign language just so you can have the same experience as everyone else，” the note read.Krystal then asked Ibby in sign language what he would like to order.Ibby was touched that she would learn sign language just to help him feel welcome.“I was just so moved that she actually wanted to learn sign language.It is really a totally different language and it was something that she wanted to do because of me.Because I was a deaf customer.I was very，very impressed，” Ibby said.Krystal had spent hours watching teaching videos so that she could learn enough sign language to give Ibby the best customer service that she could! “My job is to make sure peoplehave the experience they expect and that’s what I gave him，” Krystal says.Ibby posted a photo of Krystal’s note online，and it quickly went viral，getting hundreds of likes and comments that praised Krystal for her kind action.1．What can we learn about Ibby Piracha from paragraph 2?A．He was born deaf. B．He lives a hard life.C．He loves to order take-out food. D．He visits the cafe regularly.2．Why did Krystal learn sign language?A．To serve Ibby better. B．To attract more customers.C．To give Ibby a big surprise. D．To make herself more popular.3．Which of the following can best describe Krystal?A．Kind and considerate. B．Honest and responsible.C．Sociable and humorous. D．Ambitious and sensitive.4．What message does the author want to convey in the text?A．Two heads are better than one. B．A small act makes a difference.C．One good turn deserves another. D．Actions speak louder than words.B(★)(2024·湖北武汉调研)When I mentioned to some friends that we all have accents，most of them proudly replied，“Well，I speak perfect English/Chinese/etc.” But this kind of saying misses the point.More often than not，what we mean when we say someone “has an accent” is that their accent is different from the local one，or that pronunciations are different from our own.But this definition of accents is limiting and could give rise to prejudice.Funnily enough，in terms of the language study，every person speaks with an accent.It is the regular differences in how we produce sounds that define our accents.Even if you don’t hear it yourself，you speak with some sort of accent.In this sense，it’s pointless to point out that someone “has an accent”．We all do!Every person speaks a dialect，too.In the field of language study，a dialect is a version of a language that is characterized by its variations of structure，phrases and words.For instance，“You got eat or not？”(meaning “Have you eaten？”) is an acceptable and understood question in Singapore Oral English.The fact that this expression would cause a standard American English speaker to take pause doesn’t mean that Singapore Oral English is “wrong”or “ungrammatical”．The sentence is well-formed and clearly communicative，according to native Singapore English speakers’ solid system of grammar.Why should it be wrong just because it’s different?We need to move beyond a narrow conception of accents and dialects—for the benefit ofeveryone.Language differences like these provide insights into people’s cultural experiences and backgrounds.In a global age，the way one speaks is a distinct part of one’s identity.Most people would be happy to talk about the cultures behind their speech.We’d learn more about the world we live in and make friends along the way.5．What does the author think of his/her friends’ response in paragraph 1?A．It reflects their self confidence.B．It reflects their language levels.C．It misses the point of communication.D．It misses the real meaning of accents.6．Why does the author use the example of Singapore Oral English?A．To justify the use of dialects. B．To show the diversity of dialects.C．To correct a grammatical mistake. D．To highlight a traditional approach.7．What does the author recommend us to do in the last paragraph?A．Learn to speak with your local dialect.B．Seek for an official definition of accents.C．Appreciate the value of accents and dialects.D．Distinguish our local languages from others’．8．What can be a suitable title for the passage?A．Everyone Has an Accent B．Standard English Is at RiskC．Accents Enhance Our Identities D．Dialects Lead to MisunderstandingⅡ.完形填空One summer night in a seaside cottage，a small boy was in bed，sound asleep.Suddenly，he felt himself 1 from bed and carried in his father’s arms onto the beach.Overhead was the clear starry sky.“Watch！” As his father spoke， 2 ，one of the stars moved.It 3 across the sky like a golden fire.And before the 4 of this could fade，another star leapt from its place，then another...“What is it？” the child asked in 5 .“Shooting stars.They 6 every year on a certain night in August.”That was all：just an 7 encounter of something magic and beautiful.But，back in bed，the child stared into the dark，with mind full of the falling stars.I was the 8 seven-year-old boy whose father believed that a new experience 9 more for a small boy than an unbroken night’s sleep.That night，my father opened a door for his child，leading him into an area of splendid10 .Children are naturally curious，but they need someone to 11 them.This art of adding new dimensions to a child’s world doesn’t 12 require a great deal of time.It simply 13 doing things more often with children instead of for them or to them.Good parents know this：The most precious gift they can give a child is to spark their flame of 14 .That night is still deeply 15 in my memory.Next year，when August comes with its shooting stars，my son will be seven.1．A.hidden B．robbed C．lifted D．kicked2．A.incredibly B．accidentally C．apparently D．actually3．A.exploded B．circled C．spread D．flashed4．A.success B．wonder C．exhibition D．discovery5．A.amazement B．horror C．relief D．delight6．A.blow up B．turn up C．show off D．give out7．A.uncomfortable B．unbearable C．undetected D．unexpected8．A.curious B．fortunate C．determined D．chosen9．A.worked B．mattered C．deserved D．proved10．A.newness B．emptiness C．freedom D．innovation11．A.protect B．challenge C．guide D．believe12．A.absolutely B．basically C．possibly D．necessarily13．A.involves B．risks C．admits D．resists14．A.hope B．faith C．curiosity D．wisdom15.A.trapped B．set C．lost D．rootedⅢ.语法填空(★)The Olympics are a series of international athletic competitions held in different countries.They’re 1. important multi-sport event that takes place every four years.For the Olympics，participants from all over the world train for years and try their best 2. (win)．Pierre Coubertin，a French man,3. (found) the International Olympic Committee (IOC) in 1894.He was once a teacher and historian.In his honor，French had the official status(地位) and 4. (prior) over other languages at the Olympics.According to the Olympic Charter，English and French are the official languages of the Olympics.Therefore，every participant needs to have their documents 5. (translate) in both languages.Besides，real-time interpretations in Arabic，German，Russian，and Spanish must be available for all sessions.The IOC has a complete guide for those 6. want to apply to these contests.French has the status of being the first official language for Olympic events and it was the language of diplomacy (外交) in the beginning.But later，more countries considered 7. (participate) in this contest.The IOC then made French and English the official languages of the Olympics.8．(actual)，more than 100 countries in the world speak English now.Besides，almost every country has made 9. a must that children learn English in schools and colleges.This 10. (influence) status has caused the IOC to make English one of the official languages.必修第一册Welcome UnitⅠ.阅读理解AThroughout all the events in my life，one in particular sticks out more than the others.As I reflect on this significant event，a smile spreads across my face.As I think of Shanda，I feel loved and grateful.It was my twelfth year of dancing，I thought it would end up like any other year：stuck in emptiness，forgotten and without the belief of any teacher or friend that I really had the potential to achieve greatness.However，I met Shanda，a young，talented choreographer(编舞者)．She influenced me to work to the best of my ability，pushed me to keep going when I wanted to give up，encouraged me and showed me the real importance of dancing.Throughout our hard work，not only did my ability to dance grow，but my friendship with Shanda grew as well.With the end of the year came our show time.As I walked to a backstage filled with other dancers，I hoped for a good performance that would prove my improvement.I waited anxiously for my turn.Finally，after what seemed like days，the loudspeaker announced my name.Butterflies filled my stomach as I took trembling steps onto the big lighted stage.But，with the determination to succeed and eagerness to live up to Shanda’s expectations for me，I began to dance.All my troubles and nerves went away as I danced my whole heart out.As I walked up to the judge to receive my first-place shining，gold trophy(奖杯)，I realized that dance is not about becoming the best.It is about loving dance for dance itself，a getaway from all my problems in the world.Shanda showed me that you could let everything go and just dance what you feel at that moment.After all the doubts that people had in me，I believed in myself and did not care what others thought.Thanks to Shanda，dance became more than a love of mine，but a passion.1．What did the author think her dancing would be for the twelfth year?A．A change for the better. B．A disappointment as before.C．A proof of her potential. D．A pride of her teachers and friends.2．How did Shanda help the author?A．By offering her financial help. B．By entering her in a competition.C．By coaching her for longer hours. D．By awakening her passion for dancing.3．How did the author feel when she stepped on the stage?A．Proud. B．Nervous. C．Scared. D．Relieved.4．What can we learn from the author’s story?A．Success lies in patience. B．Fame is a great thirst of the young.C．A good teacher matters. D．A youth is to be treated with respect.B(★)Are you a good judge of character？Can you make an accurate judgement of someone’s personality based only on your first impression of them？Interestingly，the answer lies as much in them as it does in you.One of the first people to try to identify good judges of character was US psychologist Henry F Adams in 1927.His research led him to conclude that people fell into two groups—good judges of themselves and good judges of others.Adams’s research has been widely criticized since then，but he wasn’t entirely wrong about there being two clearly different types.More on that in a moment，but first we need to define what a good judge of character is.Is it someone who can read personality or someone who can read emotion？Those are two different skills.Emotions such as anger or joy or sadness can generate easily identifiable physical signs.Most of us would probably be able to accurately identify these signs，even in a stranger.As such，most of us are probably good judges of emotion.In order to be a good judge of personality，however，there needs to be an interaction with the other person，and that person needs to be a “good target”．“Good targets” are people who reveal relevant and useful signals to their personality.So this means “the good judge” will only manifest when reading “good targets”．This is according to Rogers and Biesanz in their 2019 journal entitled “Reassessing the good judge of personality”．“We found consistent，clear and strong evidence that the good judge does exist，” Rogers and Biesanz concluded.But their key finding is that the good judge does not have magical gifts of perception—they are simply able to “detect and use the information provided by the good target”．So，are first impressions really accurate？Well，if you’re a good judge talking to a “good target”，then it seems the answer is “yes”．And now we know that good judges probably do exist，more research can be done into how they read personality，what kind of people they are—and whether their skills can be taught.5．What can we learn about Adams from paragraph 2?A．He is a good judge of character.B．He divided psychologists into two groups.C．His research result has been widely accepted.D．His research on good judges was partially right.6．What does the author think of emotion reading?A．Annoying. B．Joyful. C．Simple. D．Strange.7.Which of the following would Rogers and Biesanz agree with?A．A good target is necessary for personality judgement.B．A good target needs to get his personality reassessed.C．A good judge can provide useful signals to our personality.D．It’s possible to be a good judge just by looking at the other person.8．What does the author think future research should focus on?A．The skills of good communication. B．The features of good judges.C．The ways to read personality. D．The accuracy of first impressions.C(2023·新课标Ⅱ，C)Reading Art: Art for Book Lo v ers is a celebration of an everyday object—the book，represented here in almost three hundred artworks from museums around the world.The image of the reader appears throughout history，in art made long before books as we now know them came into being.In artists’ representations of books and reading，we see moments of shared humanity that go beyond culture and time.In this “book of books”，artworks are selected and arranged in a way that emphasizes these connections between different eras and cultures.We see scenes of children learning to read at home or at school，with the book as a focus for relations between the generations.Adults are portrayed(描绘) alone in many settings and poses—absorbed in a volume，deep in thought or lost in a moment of leisure.These scenes may have been painted hundreds of years ago，but they record moments we can all relate to.Books themselves may be used symbolically in paintings to demonstrate the intellect(才智)，wealth or faith of the subject.Before the wide use of the printing press，books were treasured objects and could be works of art in their own right.More recently，as books have become inexpensive or even throwaway，artists have used them as the raw material for artworks—transforming covers，pages or even complete volumes into paintings and sculptures.Continued developments in communication technologies were once believed to make the printed page outdated.From a 21st-century point of view，the printed book is certainly ancient，but it remains as interactive as any battery-powered e-reader.To serve its function，a book must be activated by a user: the cover opened，the pages parted，the contents reviewed，perhaps notes written down or words underlined.And in contrast to our increasingly networked lives where theinformation we consume is monitored and tracked，a printed book still offers the chance of a wholly private，“off-line” activity.9．Where is the text most probably taken from?A．An introduction to a book. B．An essay on the art of writing.C．A guidebook to a museum. D．A review of modern paintings.10．What are the selected artworks about?A．Wealth and intellect. B．Home and school.C．Books and reading. D．Work and leisure.11．What do the underlined words “relate to” in paragraph 2 mean?A．Understand. B．Paint. C．Seize. D．Transform.12．What does the author want to say by mentioning the e-reader?A．The printed book is not totally out of date.B．Technology has changed the way we read.C．Our lives in the 21st century are networked.D．People now rarely have the patience to read.Ⅱ.七选五Wonderful views from the mountains，breathtaking places waiting to explore，fresh air，as well as all the special health benefits，are the main rewards of mountain hiking. 1You need to train your lower body muscles，anytime and anywhere.Strong legs and core muscles will improve your balance and help you hike longer.Focus on your lower body strength and on your cardiovascular(心血管的) workout. 2 You really can train anywhere：use your backyard，living room，or bedroom to keep your body ready for the true conditions in the mountains.You will need a stronger back.Who’s going to carry your backpack？ 3 So we are quite sure what the true answer is.Develop back muscles with exercises like V-ups，deadlifts，diver push-ups，and exercise named “mountain climbers”：Start in a traditional plank(平板支撑) position and then bring your knee forward under your chest.You will start to feel your abs(腹肌) for sure，too.4 Even Rome wasn’t built in a day so give yourself the pleasure to enjoy discovering what your body is capable of! All the perfect benefits will improve your blood pressure and blood sugar levels，helping you strengthen your core，and even help you control your weight as an additional benefit.5 Just don’t forget to stretch after each training.Please remember that your training for mountain hiking should be combined with real hiking.And don’t miss the other clues on what to do for mountaineering training!。
2025高考语文步步高大一轮复习讲义教材文言文点线面必修下册(一) 单篇梳理1 子路、曾公西华侍坐
2025高考语文步步高大一轮复习讲义教材文言文点线面复习重点 1.积累并记牢“方”“作”“如”“让”“爱”“若”“徒”“御”“族”等重要实词。
2.背诵《子路、曾皙、冉有、公西华侍坐》，翻译重点句子。
3.掌握通假字及形容词活用的特点。
单篇梳理1子路、曾皙、冉有、公西华侍坐通读全文，解释加点的词语。
(第1段)子路、曾皙、冉有、公西华侍坐。
(第2段)子曰：“以．①()吾一日长乎尔，毋吾以．②()也。
居．③()则曰：‘不吾知．④()也！’如或知尔，则何以哉？”(第3段)子路率尔．．①()而对曰：“千乘之国，摄．②()乎大国之间，加之以师旅．．．．③()，因．④()之以饥馑．．⑤()；由也为之，比及⑥()三年，可使有勇，且知方也。
”(第4段)夫子哂．()之。
(第5段)“求！尔何如？”(第6段)对曰：“方六七十，如五六十，求也为之，比及三年，可使足民．．①()。
如其礼乐，以俟．②()君子。
”(第7段)“赤！尔何如？”(第8段)对曰：“非曰能．()之，愿学焉。
宗庙之事，如会同，端章甫，愿为小相焉。
”(第9段)“点！尔何如？”(第10段)鼓瑟希，铿尔，舍瑟而作，对曰：“异乎三子者之撰．()。
”(第11段)子曰：“何伤．．()乎？亦各言其志也。
”(第12段)曰：“莫春者，春服既．①()成．②()，冠者五六人，童子六七人，浴乎沂，风乎舞雩，咏．③()而归。
”(第13段)夫子喟然．．①()叹曰：“吾与．②()点也！”(第14段)三子者出，曾皙后。
曾皙曰：“夫三子者之言何如？”(第15段)子曰：“亦各言其．()志也已矣。
”(第16段)曰：“夫子何哂由也？”(第17段)曰：“为国以礼，其言不让．()，是故哂之。
”(第18段)“唯求则非邦也与？”(第19段)“安见方六七十如五六十而非邦也者？”(第20段)“唯赤则非邦也与？”(第21段)“宗庙会同，非诸侯而何？赤也为之小，孰能为之大？”[记忆导图]1．通假字例句本字及意义①毋吾以．也②鼓瑟希．③莫．春者④唯求则非邦也与．2.古今异义词词语例句解析(古今义)3.多义词语(1)方(2)作(3)如(4)让4.词类活用5.特殊句式6.常识梳理(1)千乘之国．．．．千乘之国，指有一千辆兵车的诸侯国。
2025高考语文步步高大一轮复习讲义教材文言文点线面必修上册(一) 整合迁移1 古今同形异义双含答案
2025高考语文步步高大一轮复习讲义教材文言文点线面必修上册(一) 整合迁移1 古今同形异义双音节词与动词活用含答案整合迁移1 古今同形异义双音节词与动词活用一、连点成线，基础整合1．下列各组句子中，加点词的意思相同的一组是( )A.⎩⎪⎨⎪⎧ 虽有槁暴，不复．挺者师道之不复．，可知矣 B.⎩⎪⎨⎪⎧ 冰，水为．之圣人之所以为．圣 C.⎩⎪⎨⎪⎧ 则知．明而行无过矣句读之不知．D.⎩⎪⎨⎪⎧不如．须臾之所学也是故弟子不必不如．师 答案 D解析 D 项均为“及，比得上”。
A 项又，再/恢复。
B 项凝结/成为。
C 项同“智”，见识/知道。
2．下列各组句子中，加点词的意思与现代汉语不同的一项是( )①蚓无爪牙．．之利 ②不如须臾．．之所学也 ③师不必．．贤于弟子 ④非蛇鳝之穴无可寄托．．者 ⑤曰师曰弟子云者．． ⑥古之学者．．必有师 ⑦积土成山，风雨．．兴焉 ⑧吾从而．．师之 A ．①②④⑦⑧B ．②③⑤⑥⑧C ．①③④⑥⑧D ．②④⑥⑦⑧答案 C解析 ①古义：爪子和牙齿。
今义：坏人的党羽。
③古义：不一定。
今义：表示事理上或情理上不需要。
④古义：托身，藏身。
今义：托付；把理想、希望、感情等放在(某人身上或某种事物上)。
⑥古义：求学的人。
今义：在学术上有一定成就的人。
⑧古义：从，跟从；而，并且。
今义：连词，上文是原因、方法等，下文是结果、目的等；因此就。
3．下列各组句子中，加点词的意思和用法相同的一组是( )A.⎩⎪⎨⎪⎧ 其下．圣人也亦远矣上食埃土，下．饮黄泉 B.⎩⎪⎨⎪⎧ 不积小．流，无以成江海小．学而大遗，吾未见其明也 C.⎩⎪⎨⎪⎧ 君子博学而日．参省乎己日．削月割，以趋于亡 D.⎩⎪⎨⎪⎧登高．而招，臂非加长也而高．其直，亦无售者 答案 C解析 C 项均为名词作状语，每天。
A 项名词作动词，低于/名词作状语，向下。
B 项形容词，与“大”相对/形容词作名词，小的方面。
D 项形容词作名词，高处/形容词作动词，抬高。
步步高大一轮复习讲义数学答案
步步高大一轮复习讲义数学答案第一章：概率论基础1.1 集合与概率题目：设集合A={1,2,3,4,5}，B={3,4,5,6,7}，求A与B的交集、并集和差集。
答案：•交集：A∩B = {3,4,5}•并集：A∪B = {1,2,3,4,5,6,7}•差集：A-B = {1,2}1.2 条件概率与事件独立题目：某班级有40名男生和30名女生，从中随机抽取一名学生，求抽到男生的概率。
答案： - 总人数：40 + 30 = 70 - 抽到男生的概率：40/70 = 4/72.1 随机变量与离散型随机变量题目：设随机变量X表示投掷一枚骰子出现的点数，求X 的概率分布。
答案：X123456P(X)1/61/61/61/61/61/62.2 连续型随机变量与概率密度函数题目：设随机变量X表示一位学生的身高，其概率密度函数为f(x) = 0.01，0<x<100，求X在区间[50,70]的概率。
答案： - X在区间[50,70]的概率：P(50<=X<=70) =∫(50,70)0.01dx = 0.01*(70-50) = 0.23.1 矩阵与线性方程组题目：解下列线性方程组： - 2x + 3y = 8 - 3x + 2y = 7答案： - 通过消元法可得：x = 1，y = 23.2 行列式与矩阵的逆题目：求下列矩阵的逆矩阵： - A = [1, 2; 3, 4]答案： - A的逆矩阵：A^(-1) = [ -2, 1/2; 3/2, -1/2]第四章：数学分析基础4.1 极限与连续题目：求极限lim(x->0)(sinx/x)的值。
答案： - 极限lim(x->0)(sinx/x) = 14.2 导数与微分题目：求函数y=3x^2的导数。
答案： - y的导数：dy/dx = 6x以上是《步步高大一轮复习讲义》中关于数学部分的答案，希望对你的复习有所帮助。
祝你学习顺利！。
2025步步高大一轮复习讲义人教版高考化学大单元一 第一章 热点强化1 与量有关的离子方程式的含答案
2025步步高大一轮复习讲义人教版高考化学热点强化1与量有关的离子方程式的书写1．反应生成的离子又能与剩余(过量)的反应物继续反应。
(1)CO2通入NaOH溶液中：①CO2少量：CO2＋2OH－===CO2－3＋H2O；②CO2过量：CO2＋OH－===HCO－3。
(2)盐酸滴入Na2CO3溶液中：①盐酸少量：CO2－3＋H＋===HCO－3；②盐酸过量：CO2－3＋2H＋===CO2↑＋H2O。
(3)盐酸滴入NaAlO2溶液中：①盐酸少量：AlO－2＋H＋＋H2O===Al(OH)3↓；②盐酸过量：AlO－2＋4H＋===Al3＋＋2H2O。
(4)CO2通入NaAlO2溶液中：①CO2少量：2AlO－2＋CO2＋3H2O===2Al(OH)3↓＋CO2－3；②CO2过量：AlO－2＋CO2＋2H2O===Al(OH)3↓＋HCO－3。
(5)NaOH滴入AlCl3溶液中：①NaOH少量：Al3＋＋3OH－===Al(OH)3↓；②NaOH过量：Al3＋＋4OH－===AlO－2＋2H2O。
(6)Fe加入稀HNO3中：①Fe少量：Fe＋NO－3＋4H＋===Fe3＋＋NO↑＋2H2O；②Fe过量：3Fe＋2NO－3＋8H＋===3Fe2＋＋2NO↑＋4H2O。
2．当一种反应物中有两种或两种以上组成离子参与反应时，因其组成比例不协调(一般为复盐或酸式盐)，当一种组成离子恰好完全反应时，另一种组成离子不能恰好完全反应(有剩余或不足)，因而跟用量有关。
(1)Ca(HCO3)2溶液与NaOH溶液反应：①NaOH不足：Ca2＋＋HCO－3＋OH－===CaCO3↓＋H2O；②NaOH过量：Ca2＋＋2HCO－3＋2OH－===CaCO3↓＋2H2O＋CO2－3。
(2)NaHCO3溶液与Ca(OH)2溶液反应：①NaHCO3不足：HCO－3＋OH－＋Ca2＋===CaCO3↓＋H2O；②NaHCO3过量：Ca2＋＋2OH－＋2HCO－3===CaCO3↓＋CO2－3＋2H2O。
2025高考英语步步高大一轮复习讲义人教版话题晨背进阶写作三 语言学习的规律、方法等
2025高考英语步步高大一轮复习讲义人教版话题晨背进阶写作一、写作词汇——力求精准[第一组]1．absorb v t.吸收；使全神贯注2．accent n．口音；腔调3．communication n．交流，沟通4．express v．表达5．fluently ad v.流利地6．grammar n．语法7．improve v．提高8．knowledge n．知识，学问9．master v t.精通，掌握10．overcome v．克服；解决11．idiom n．成语12．dialect n．地方话；方言13．concentrate on集中注意力于……14．point of view 观点；看法15．keep/bear...in mind记住……[第二组]16．practice n．& v．练习17．pronounce v．发音18．review v．复习19．speech n．演说；演讲20．usage n．使用；用法21．vocabulary n．词汇22．saying n．谚语23．retell v．重讲，复述24．acquire v．获得25．recite v．背诵26．look up查阅27．make progress取得进步28．set/take/write/note down写下，记下29．attach importance to重视30．benefit from从……获益二、阅读词汇——扫除障碍[第三组]31．consult v．咨询；请教32．memorize v．记忆33．standard n．& adj.标准(的)34．dictation n．听写35．skim v．浏览；略读36．scan v．& n．扫描；浏览37．summary n．摘要；概要38．remark n．& v．评述；谈论；评论39．classify v．分类；归类40．error n．错误，谬误41．resource n．资料，(教学)资源42．informal adj.(书写或言谈)非正式的43．symbolic adj.象征的；符号的；使用符号的44．globalization n．全球化45．means n．方式；方法；途径三、拔高词汇——高人一筹(学四六级词汇)[第四组]46．explicit adj.清楚明白的；易于理解的47．precise adj.准确的；精确的；确切的48．seminar n．研讨会49．alphabet n．字母表；字母50．enlarge v t.使扩大51．capitalized adj.大写的52．stutter n．结巴，口吃53．oral adj.口头的，口述的54．verbal adj.口头的；言语的；动词的；照字面的55．forum n．(因特网上的)论坛，讨论区56．extinction n．灭绝；消失；消灭；废止57．course n．科目；课程58．semester n．学期；半年59．interpreter n．解释者；口译者；注释器60．have a frog in one’s throat (尤因喉咙痛)说话困难1．The way to learn a language is to practice speaking it as often as possible.学习一门语言的方法就是要尽可能经常地练习说它。
2025高考英语步步高大一轮复习讲义人教版必修第二册——选择性必修第四册进阶写作答案精析
2025高考英语步步高大一轮复习讲义人教版必修第二册——选择性必修第四册进阶写作答案精析进阶写作答案第一章应用文写作一、实战演练Dear Glen，I am Li Hua, monitor of Class 1, Senior 3. I am writing to invite you to join us to climb a mountain next Friday，which is the Double Ninth Festival.Mountain climbing serves as a traditional activity on that day.Standing on the top of the mountain，we can enjoy broader horizons.We will gather at the school gate at 4：00 p．m.on that day.The school bus will take us to the Qingyun Mountain.Bottled water and snacks will be offered.And there are stone steps up to the mountaintop，so it won’t be so challenging and tiring.We would appreciate it if you could join us.Yours sincerely，Li Hua 二、实战演练Dear Sir or Madam，I have read your advertisement for a junior reporter at the “Campus V oice” section in the English school newspaper and I show great interest in it.I feel quite qualified for the position so I am writing to apply for it.I have been learning English for more than 10 years with a good command of oral and written English，which enables me to communicate with others fluently.Moreover，not only am I good at researching and presenting information in a compelling and informative way but I am also experienced in interviewing and st but not least，I’m outgoing as well as warmhearted，which makes me get along well with others.If given the chance，I plan to fully utilize my skills and work diligently to contribute to the “Campus V oice” section.I am looking forward to your reply.Yours sincerely，Li Hua 三、实战演练Dear Mr Smith，I’m glad to provide you with some suggestions on your upcoming trip to Beijing during the MidAutumn Festival.Beijing，as the capital of China，offers a rich cultural experience.The Palace Museum showcases Chinese history.The Tian’anmen Square is a symbol of China.The Great Wall offers breathtaking views.You can also explore hutongs(traditional alleyways) to experience traditional Chinese culture.As for fine food，you can try Beijing Roast Duck，Zhajiangmian and Bingtanghulu.By the way，use the subways，buses or taxis to get around.Renting a bike or using shared bicycles is also convenient.I hope these suggestions will be helpful.Enjoy your trip to Beijing during the MidAutumn Festival!Yours sincerely，Li Hua 四、实战演练Dear Anne，I’m writing to convey my sincere appreciation for your kind help and care during my stay in London，without which I wouldn’t have enjoyed it so much.During the week，the comfortable room，delicious meals and especially your friendly family members all made me feel at home，leaving me lasting memories.Moreover，guided by you，I was honored to have a chance to visit those tourist attractions in London and be exposed to such an amazing culture as well as beautiful scenery.It was your generous help that enabled me to have a better understanding of your country and culture.Thanks again for your kind help and I will be more than pleased if I have the opportunity to repay your kindness by showing you around Beijing.Yours，Li Hua 五、实战演练Dear Wilson，How’s everything with you? I’m excessively sorry to tell you that I can’t attend your lecture concerning Internet Plus.I’m writing you this letter of apology to show my deep regret.The reason for my being absent is that my mother is seriously ill，so I will take her to hospital tomorrow since my father is on a business trip for an urgent matter.I will care for my mother.To be frank，I am extremely interested in the topic of Internet Plus.Therefore，it is really a pity that I will miss it.I wonder if there are any relevant materials of the lecture.If so，I can learn it by myself when it’s convenient.I want to extend my apology to you once again.I hope it won’t cause you much trouble.I sincerely hope you can understand my situation/think in my position and accept my apology.Yours，Li Hua 六、实战演练Dear Mr Green，How is everything going? I am writing in sincerity to ask you a favor regarding a play we adapted for the upcoming English Evening.The play is based on the story of Hua Mulan who，after disguising herself as a man，joined the army instead of her father in the Northern Wei Dynasty.To us，however，the adaption of such an epic is quite challenging and we don’t want anything inappropriate to spoil the play.So would you please spare some time to revise the draft script attached to this email? If possible，may I pay you a visit at your office next Tuesday to give you more details?Any of your professional advice would be highly appreciated.Best wishes.Yours truly，Li Hua 七、实战演练Dear Michael，Learning that a study trip will be held，I’d like to recommend a wonderful destination：Nanjing.Here are the reasons.As an ancient capital of six dynasties and a modern city with highquality development，Nanjing has much to provide for a study trip.For example，the grand museums and solemn monuments will undoubtedly educate us students not to forget history and motivate us to cherish the present.Meanwhile，efficient and convenient transportation adds attraction and vitality to this charming city.A study trip to Nanjing promises to be fruitful!Yours，Li Hua 八、实战演练Dear Li Jin，I’m going to study Chinese in Tianjin this summer vacation.I’m writing to see if it is possible for you to provide me with information regarding relevant courses in your school.First of all，I want to know how many students there will be in each class and if the courses focus on listening and speaking practice.Besides，I wonder whether I’ll have the opportunity to communicate with Chinese students，which will surely be a good chance for me to learn more aboutChina.At last，I would be grateful if you could tell me whether accommodations are included.I’m looking forward to your early response.Yours faithfully，Chris 九、实战演练Dear Terry，I’m glad to know you desire to be a volunteer of the Sunshine V olunteer Club.As a member，I do think it is worthwhile to be engaged in voluntary work.I’m writing to share with you the details concerning it.A wide variety of regular activities are scheduled on a weekly basis，such as visiting the nursing home and organizing events to raise people’s awareness of environmental st weekend we collected books for the children in remote areas who have little access to them.We make great efforts to spread warmth and care，and it does pay off.Once you decide，please fill in the attached application form and send it to me.Eagerly looking forward to your participation.Yours，Li Hua 十、实战演练Dear Australian friends，On behalf of our school，I feel greatly privileged to convey warm welcome to you.We are delighted to have you with us.To make your stay here memorable，various activities will be arranged to enhance our mutual understanding and experience different culture.As planned，we will hold a talent show where everyone can show their outstanding performances.Classes on traditional Chinese culture are also scheduled，such as papercutting，Chinese opera，calligraphy，etc.，followed by a giftexchanging activity.Additionally，you’re invited to pay a visit to surrounding tourist attractions.I sincerely hope that you can enjoy yourselves and wish you a pleasant journey.Thank you!Yours，Li Hua 十一、实战演练NOTICETo promote our traditional Chinese culture，“Tang Suit Design Contest” will be held in the school hall next Friday.Every participant is allowed to hand in only one entry，which must be designed on your own.Besides，each piece is required to be displayed with a brief introduction of your designphilosophy.All entries will be submitted to the Students’ Council before next Tuesday.Those that stand out as the top ten will be awarded.Pictures of the winners’works will be posted on our school website.Every student studying in the International Department is welcome to take part in the competition.The Students’ Council十二、实战演练World Environment Day on CampusJune 5th,2023 marked the 50th anniversary of World Environment Day，with the slogan “Beat Plastic Pollution”．In honor of this occasion，our school organized various activities to sensitize students about the urgent need to combat plastic pollution and promote sustainable practices.The event started with an engaging presentation by environmental experts，who highlighted the detrimental impact of plastic and emphasized the importance of reducing，reusing，and recycling plastic.Then a plastic collection drive was held so as to encourage everyone to bring in their plastic waste for proper disposal.Additionally，students participated in a postermaking competition，creating thoughtprovoking artworks that showcased the importance of sustainable alternatives.The response to these activities was overwhelming.It is through such collective efforts that we can hope to “Beat Plastic Pollution”and create a cleaner，healthier environment for future generations.English Club 十三、实战演练Last week，I participated in our school sports meeting，competing in the 400meter race—a thrilling and unforgettable experience.On hearing the sharp whistle，I dashed out，the wind rushing against my face and the crowd’s cheers echoing around me.My attempts to match the pace of fellow runners proved challenging，but I did not give up.I pushed myself to the limit and crossed the finishing line with all my strength.I was glad that I took part in the sports meeting，which not only pushed my limits but also made me realize the importance of persistence.十四、实战演练Dear schoolmates，V olunteering is playing a crucial role in students’ overall development.With the approach of winter vacation, it’s high time that we took up volunteering.A willing heart to volunteer provides us with massive benefits.V olunteering not only makes us feel connected with the community but also is beneficial to our wellbeing.Blessed with a sense ofpurpose in life，we are offered an amazing opportunity to learn valuable skills.There are different ways of serving people，ranging from volunteering at children’s home or libraries to virtual volunteering，such as helping pupils with schoolwork online.Why not throw ourselves into volunteering? It makes us a better person and creates a better world.Yours sincerely，Li Hua 十五、实战演练The Person I Admire MostWhen it comes to the person I admire most，I can’t help thinking of Fan Jinshi who is an archaeologist and a guard of Dunhuang.After graduating from Peking University，Fan Jinshi chose to work in Mogao Caves，Dunhuang.Although the living environment was terrible，she was deeply attracted by the works of art and desired to protect them for the future generations.She and her team overcame difficulties，explored scientific concepts and built a “digital Dunhuang”，which has balanced the relationship between cultural relics protection and tourism.Fan Jinshi is called the daughter of Dunhuang.She deserves the respect of all at home and abroad.第二章读后续写第2节技法指导技法三A few weeks later，when I almost forgot the contest，there came the news.To everyone’s surprise，I，an immigrant，won first place in the writing contest.Hearing the good news，I felt a sense of joy surging through me.I leapt into the air and shouted out loud，“I made it！”During the award presentation ceremony，I was invited to deliver a speech.Patiently and confidently，I told the audience how I once didn’t love writing and now enjoyed writing and how I realized the value of perseverance with the help of my teacher.I went to my teacher’s office after the award presentation.With the trophy in hand，I entered the office.My teacher rose from the seat and came up to me.“Congratulations！” he said，slapping me on the back.He grinned from ear to ear as I showed him the trophy.“I owe my success to you，” I said sincerely.“Without your encouragement and belief，I wouldn’t have succeeded.”He laughed，his eyes shining with excitement.“I knew you had it in you.I’m proud of you for notgiving up.” Whenever looking back on this incident，I feel extremely grateful to him.It was my social studies teacher who encouraged me to realize my potential and thus changed the course of my life.技法四实战演练Ⅰ.1.Relieved，Jenny told the truth to everyone.2．Feeling scared and helpless，Jane sat beside a tree and held her shoulders in her arms to make herself warm.3．They hugged and kissed with tears rolling/pouring/streaming down their cheeks. 4．“I...I don’t know，” he stammered, his voice trembling with fear.5．If she had not quarreled with Tom, they would have enjoyed a great time near the lake. 6．Mother hugged the twins tightly，whose faces were glowing with excitement.7．Since he continued speaking about wanting to share his paintings with the world, I knew what had to be done.8．I thanked him，saying that not only did he mend my shirt with his craftsmanship but he also repaired my dream with sportsmanship.9．It was at that moment that I was overwhelmed with gratitude to my teacher.10．A cold feeling crept over his heart and made him shiver.11．Drowned in happiness，Jimmy dashed out of the school gate like a free bird.12．Seeing such extraordinary beauty, I think every cell in my body woke up.Ⅱ.But Molly insisted that they should wait and keep the book.She didn’t place the illustrated book on the bookshelf，hoping Rick would show up soon.A kid might make all kinds of promises and fail to keep them.But Rick was so sincere and eager that Molly believed he wouldn’t break his promise.A kid’s promise is more valuable than the cost of the book.The book would rest in the drawer still until Rick showed up.Then on one sunny morning，Molly found a little boy running all the way towards her bookstore holding something.The little boy was exactly Rick.Rick pushed the door open and rushed to the counter holding his money box.Molly excitedly pulled the drawer open，took out the illustrated book and walked out from the counter immediately.She knelt with one leg and smiled at Rick，handing the book to Rick.Rick’s eyes were shining looking at the book，and he put the box on the floor and held the book.“I think you guys had better make your deal here at the coffee table，”said Rex.Molly winked at him delightedly.The sunlight came through the glass window and cast on the little customer and the nice lady.第3节语料素材一、实战演练1．Her face lit up with happiness as she received the presents prepared by the children.2．They jumped to their feet at the news, with their eyes filled with joy.Hearing the news, they jumped to their feet with joy in their eyes.3．Overwhelmed with gratitude, I couldn’t say a word.4．I was so deeply moved that tears welled up in my eyes.5．Hearing the news that his father passed away, his eyes welled up with tears.6．She got lost and it began to rain, a deep sense of despair overwhelming her.7．Her face turning pale, she stood there, tonguetied.8．My heart was in my mouth when I walked into her office.9．At the thought of the frightening bear, a sense of fear welled up in him.10．He was half dead with fear when he found he was surrounded by wolves.实战演练1．Having known others’ attitude, he shook/trembled with anger, holding his clothes firmly. 2．Filled with anger, Mike was unable to speak a word.3．I was about to explode and waved my fist at him.4．I was ashamed of my bad performance in the contest.5．I stared at him in shock, with a small sound of disappointment escaping my throat.6．What surprised me was that there was a path here.7．A look of surprise crossed her face but she soon calmed down.8．Uncontrollably, a wave of regret washed over me as I heard the bad news.9．If only I had not left the farm alone!10．If I had followed his advice, we would be having fun together.二、实战演练Ⅰ.1.She jumped up，dashed forward and hugged the boy tightly.2．Standing beside the empty road，they looked up into the sky, feeling the precious peace. 3．As night was beginning to fall, Jane sat on the grass, staring at the vast sky, frightened and hungry.4．With a bunch of flowers in her hands，Mindy stood beside the sea and looked down at the flowers with a smile，wondering what to do tomorrow.5．She crept along the path，bent over swiftly and cupped her hands around the butterfly gently. 6．With her heart beating wildly，the innocent girl，held by her mom and screaming withexcitement，unwrapped her delicate gift box which she had been looking forward to without any hesitation.7．Every one of us on the bus looked on and laughed crazily.Ryan struggled to his feet，dusted the jacket and made his way to an empty seat.8．Looking straight into my eyes，Mike stroked my hair, whispering，“You are the most beautiful girl I’ve ever met.”Ⅱ.1.the twins got up early, tiptoed to the kitchen and scooped some flour out of the bag their father slid into the kitchen，patting the twins’ shoulders and comforting them in a soft voice they carried the breakfast，advanced upstairs and woke up their mother2．I signaled to him with a thumbsup, feeling proud of him He smiled, took a deep breath and got ready for the race，eyes brimming with determination every runner shot like an arrow三、实战演练1．The gentle breeze stroked his head，as if comforting all his tiredness.2．I closed my eyes and daydreamed in the speeding car.Winding rivers, lofty mountains, deep alleys and sunny beaches held me entirely in their fascination.3．The sun looked at her with a glowing smile and the flowers nodded merrily towards her. 4．The wind was howling dreadfully and the rain was pouring from the heaven，whipping against the branches of lined trees.5．On the day back to school，dark clouds hung low in the sky.The rain poured down，with cold drops and angry winds slapping my face.I was drowned in floods of warm tears and freezing rain.四、实战演练1．Festivals let us enjoy life，be proud of our customs and forget our work for a little while. 2．The precious tricycle not only helped me through that tough period，but also carried Father’s love forward into the far，far future.3．Seeing the paper bag，I felt as if it had been reminding me that I should pass on the kindness that the Mexican family offered me every time I meet someone in need.4．No matter how ordinary a job is，it plays a part in society and therefore deserves our respect. 5．Cold as the rain was，great warmth filled his heart like never before.6．It dawned on me that we should always be an honest person whatever situations we are in.7．I am firmly convinced that the slight power of every person can make our country more prosperous.8．All the students came to realize that everyone wants and deserves to be treated with respect，dignity and warmth.9．It is not how much we do but how much love we put into what we do that benefits our work most.10．The gift you give is not something your loved one keeps，but a voluntary contribution towards the people who really need it in their lives.第4节分类集训一、When my Monday came，I again took the bus to KMTV alone and waited.Everything was familiar this time.But hearing the musical sounds and applause from time to time，I felt my heart was pounding with excitement and nervousness.Eventually，it was my turn.Taking a deep breath，I calmed down.Confident，I went to the piano and began to play.Easy，so easy! Fun almost...right up to the coda at the end.I suddenly realized I should not be at the end! My heart jumped to my mouth.I had skipped a part.A huge part.How did that happen?Somehow my brain went to work and I continued playing.I tried to smile at the camera and played the rest smoothly as if no skipping had happened.After what seemed an eternity，I stopped playing.However，it turned out that my performance had probably lasted barely a minute.Surely the result was as expected—I wasn’t the winner.On my way home，I surprised myself by feeling more relieved than disappointed.I could not pretend that my performance was best.In truth，the other three were far superior.When I came back home to talk about “The Big Skip”，Daddy smiled，“It may not have been noticed by someone who doesn’t know Schubert’s ‘Ave Maria’．Your movement was smooth.You didn’t fall apart.All in all，a worthwhile experience.”二、No sooner had I picked up my phone than Lisa called me.“Belle，how is it going? Do you still need my help？” Lisa asked.“Thanks，Lisa.Everything is OK.And I’d like to tell you about it，” I said.I told her exactly what had happened，and specifically described how I had solved the problem.Lisa praised me for my quick wit.Then I asked her to teach me German in case I needed it later.She promised.By the end of the holiday，I could have already communicated with her in some simple German words.So I was ready for the new term with confidence.When the German teacher entered the classroom in the new term，I felt I’d seen her somewhere before.What amazed me was that she came over to me，saying，“Glad to see you again！I’m Florence.” I was surprised to find that she was the daughter of the lady that I had helped during the holiday.What a fantastic fate! As our new foreign teacher，Florence was patient and considerate.We all respected her and took every lesson seriously.I even made friends with her mother，so I had more opportunities to practise speaking German.I was resolved to visit Germany the next summer holiday.三、Giving or keeping? I struggled with myself.Giving it? Hardly could I imagine life without the model car! After all，it was my most precious treasure，which I had been proud of.My heart kept aching at the prospect of giving it away.Nope! I shook my head determinedly.Glancing at mymother’s expectant eyes，I couldn’t help sobbing.Keeping it? Definitely，it would otherwise upset Alex.Torn between the two tough choices，I was totally at a loss.Nevertheless，deep down，I could feel my affection for Alex.Yep! I resolved to do the right thing.In the moment of parting，my model car went with Alex.Though I was crushed to see it go，my heart sang when I saw his beaming face as he tightly clutched it.Seeing the thumbsup from my mother and sister，I did swell with relief，pride and joy，for I knew it was not a gift；to some extent，it was our concern and love for him.Plus，sharing the model car also strengthened our bond，which，I was fully convinced，would always uplift him.An effort made for the happiness of others lifted us above ourselves as well.四、Then came the final testing day.The whole class gathered in the science classroom，watching breathlessly as Jeff carefully loaded their selfmade robotic hand onto Sergio’s right arm.It fitted quite well! So excited was Sergio that his arm trembled slightly.Having put a baseball on the desk，Jeff signed to Sergio to pick it up.Slowly，Sergio extended his right hand and reached for the ball.Successfully he caught hold of it and everyone present broke into cheers! Holding the ball，Sergio couldn’t contain his tears.Never in his life did he expect to catch something with his right hand!The lifechanging gift for Sergio drew huge attention.Jeff and his students became an instant hit and various media competed to cover the news.When interviewed about the intention of the project，Jeff said，“I intended Sergio’s robotic hand to show our support for him.Meanwhile，I hope to foster students’ scientific spirit through this handson operation.” His students stated that Jeff challenged them to transform abstract concepts into reality，from which they benefited greatly.Soon voluntary donations poured in，which would go to the school’s scientific research and help students develop better.五、Ruby walked over to my mother，we girls holding our breath.We waited to see who would shout first and what terrible things would be said.“We are sorry about the flowers.The girls will fix them and help weed the roses，” said Mom.My sisters and I looked at each other in horror，but Ruby smiled through her tears.“I know we’re particular about these roses，but they’re very special because they remind me of my mother.”Soon both women were down on their knees examining the damaged bushes together.A few weeks later，the plants all came back to life.My mother and Ruby worked together on the roses all summer and many summers to follow.So did my sisters and I．A friendship was formed between the families.Ruby became part of our family，spending many happy hours at our house，especially during countless birthdays，graduations and weddings.And the rose fence wasn’t a fence any longer.My mother had turned it into a bridge.六、Suddenly，I remembered the door to the basement.I dashed to the door and opened it withoutany hesitation.There she sat on the top step，quiet as a mouse，head down，ears hanging down.She had been following me，as she always did，and I had casually closed the door on her.So she had to wait quietly for me to find her.I don’t know whether she assumed that she was being punished，but it was clear that she was hurt，for she behaved differently this time.I held her in my arms tightly，telling her how sorry I was.I touched her head and rubbed her belly gently，telling her that she was not making trouble.She let me hold her for exactly one minute and then suddenly ran off，returning with a toy for me to throw.At that very moment，Dottie taught me a valuable lesson：Forgive quickly because forgiveness is to light a lamp not just for others but also for ourselves.Life is short.There is so much love to offer and receive and so many toys to chase.。
2025高考语文步步高大一轮复习讲义板块二 文学类阅读小说 学案8 研练两年高考真题——吃透精握方向
2025高考语文步步高大一轮复习讲义板块二文学类阅读小说前备知识——小说文体知识与教材学考关联梳理一、小说文体知识(一)小说文体特征小说是以刻画人物形象为中心，通过完整的故事情节和环境描写来反映社会生活的文学体裁。
小说的本质特征是虚构，通过叙述虚构世界与人生。
1．小说与散文的文体区别(1)小说虚构，散文写实。
小说中的人物往往是作者虚构出来的；而散文中的人物是在真人真事的基础上进行剪裁加工，写意式描绘的。
(2)小说重在表达作者对人、对人生、对生活、对世界的看法，散文重在表达作者的情感。
(3)小说的主体是讲故事，讲究讲故事的技巧以及结构的安排；而散文不讲究情节安排，所谓“形散神聚”也只是它结构上的特点之一。
(4)写景状物对于小说而言，是小说的环境描写；而对于散文而言，则是突出景物的特点，表达对景物的赞美以及自身情感。
2．小说四要素(一说三要素)关系图在小说中，情节是其骨架，环境是其依托，人物是其核心，主题是其灵魂。
它们具体的相互关系如下：另外，小说常见主题有：(二)小说文体分类二、教材学考关联梳理单元篇名文体可能关联点必修上册第一单元《百合花》散文化(诗化)小说关联主题青春激扬关联文体散文化(诗化)小说阅读《哦，香雪》关联考点①意象作用；②景物描写必修下册第六单元《祝福》现实主义小说关联主题观察与批判《林教头风雪山神庙》章回体小说关联文体章回小说与现代主义小说阅读《装在套子里的人》批判现实主义小说《促织》文言小说关联考点①情节结构(情节突转)与叙事特点；②虚构与写实特征；③人物的典型性格及作用；④环境对人的影响《变形记(节选)》现代主义小说选择性必修上册第三单元《大卫·科波菲尔(节选)》自传体小说关联主题多样的文化《复活(节选)》批判现实主义小说关联文体外国小说(魔幻现实主义小说)阅读《老人与海(节“迷惘的一关联考点①独特的叙述视角；②心理描写选)》 代”小说 及其作用；③“魔幻”手法；④圆形人物与扁平人物《百年孤独(节选)》魔幻现实主义小说 选择性必修中册第二单元《荷花淀》“荷花淀派”(诗化)小说 关联主题 苦难与新生《小二黑结婚(节选)》“山药蛋派”小说 关联文体红色小说及荷花淀派、山药蛋派小说阅读《党费》 红色小说 关联考点 ①革命英雄形象特点；②理解革命文化主题选择性必修下册第二单元《阿Q 正传(节选)》讽刺小说(中篇小说)关联主题 时代镜像 关联文体乡土小说阅读《边城(节选)》散文化(诗化)小说(中篇小说)关联考点 ①人物形象特点；②丰富的主旨意蕴；③作家的创作风格和语言风格学案8 研练两年高考真题——吃透精髓，把握方向复习任务 1.掌握小说整体阅读的方法及步骤。
2025高考语文步步高大一轮复习讲义65练板块五 文言文阅读学案26 《劝学》《师说》
2025高考语文步步高大一轮复习讲义65练板块五文言文阅读学案26《劝学》《师说》复习任务 1.梳理积累两文中的文言基础知识，重点掌握古今异义词和多义实词“中”“已”“常”“攻”。
2.背诵课文，翻译重点句子。
活动一基础梳理1．通假字请指出下列句中的通假字，并解释意思。
①以为轮“________”同“________”，____________________________________________________②虽有槁暴“________”同“________”，____________________________________________________③则知明而行无过矣“________”同“________”，_____________________________________________________④君子生非异也“________”同“________”，_____________________________________________________⑤师者，所以传道受业解惑也“________”同“________”，_____________________________________________________⑥或师焉，或不焉“________”同“________”，____________________________________________________ 2．古今异义请写出下列加点词语的古义。
①劝．学古义：___________________________________________________________________________今义：拿道理说服人，使人听从②金．就砺则利古义：___________________________________________________________________________今义：黄金③君子博学．．而日参省乎己古义：___________________________________________________________________________今义：学问广博精深④蚓无爪牙．．之利古义：___________________________________________________________________________今义：比喻坏人的党羽⑤非蛇鳝之穴无可寄托．．者古义：___________________________________________________________________________今义：托付；把理想、希望、感情等放在(某人身上或某种事物上)⑥古之学者．．必有师古义：___________________________________________________________________________今义：在学术上有一定成就的人⑦a.师者，所以．．传道受业解惑也古义：___________________________________________________________________________b．圣人之所以．．为圣古义：___________________________________________________________________________今义：表示因果关系的连词⑧吾从而．．师之古义：___________________________________________________________________________今义：连词，上文是原因、方法等，下文是结果、目的等；因此就⑨今之众人．．，其下圣人也亦远矣古义：___________________________________________________________________________今义：大家；许多人⑩小学．．而大遗，吾未见其明也古义：___________________________________________________________________________今义：对儿童、少年实施初等教育的学校，给儿童、少年以全面的基础教育⑪师不必．．贤于弟子古义：___________________________________________________________________________今义：表示事理上或情理上不需要3．多义实词请解释下列加点词的意思。
2022版步步高《大一轮复习讲义》人教版第1章 第2讲 物质的分离和提纯
第2讲物质的分离和提纯复习目标 1.掌握常见物质分离和提纯的方法。
2.能综合运用物质的不同性质对常见的物质进行分离和提纯。
考点一分离、提纯的常用物理方法及装置1．物质分离、提纯的区别(1)物质的分离将混合物的各组分分离开来，获得几种纯净物的过程。
(2)物质的提纯将混合物中的杂质除去而得到纯净物的过程，又叫物质的净化或除杂。
2．依据物理性质选择分离、提纯的方法(1)“固＋固”混合物的分离(提纯)(2)“固＋液”混合物的分离(提纯)(3)“液＋液”混合物的分离(提纯)3．物理法分离、提纯物质所选装置(1)常用装置①过滤适用范围分离不溶性固体与液体注意事项一贴滤纸紧贴漏斗内壁二低滤纸边缘低于漏斗边缘液面低于滤纸边缘三靠烧杯杯口紧靠玻璃棒玻璃棒下端抵靠三层滤纸处漏斗下端长的那侧管口紧靠烧杯内壁②蒸发适用范围分离易溶性固体的溶质和溶剂注意事项玻璃棒的作用：搅拌，防止液体局部过热而飞溅停止加热的标准：当有大量晶体析出时停止加热，利用余热蒸干③萃取和分液适用范围萃取：利用溶质在互不相溶的溶剂里的溶解度不同，用一种溶剂把溶质从它与另一种溶剂组成的溶液里提取出来分液：分离两种互不相溶且易分层的液体注意事项①溶质在萃取剂中的溶解度比在原溶剂中大的多②萃取剂与原溶剂不反应、不相溶③萃取剂与溶质不反应④常用的萃取剂是苯或CCl4，一般不用酒精作萃取剂④蒸馏适用范围分离沸点相差较大且互溶的液体混合物注意事项①温度计的水银球在蒸馏烧瓶的支管口处②蒸馏烧瓶中要加沸石或碎瓷片，目的是防止暴沸③冷凝管水流方向为下口进，上口出⑤升华适用范围对于某种组分易升华的混合物，利用物质易升华的性质在加热条件下将其分离注意事项如NaCl固体中的I2可用该方法，但NH4Cl固体中的I2不能用升华的方法分离(2)创新装置①过滤装置的创新——抽滤由于水流的作用，使装置a、b中气体的压强减小，故使过滤速率加快②蒸馏装置的创新由于冷凝管竖立，使液体混合物能冷凝回流，若以此容器作反应容器，可使反应物能循环利用，提高了反应物的转化率(1)过滤时，为加快过滤速度，应用玻璃棒不断搅拌漏斗中液体(×)错因：不能搅拌，以防弄破滤纸。
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§2.9 函数的应用2014高考会这样考 1.综合考查函数的性质；2.考查一次函数、二次函数、分段函数及基本初等函数的建模问题；3.考查函数的最值．复习备考要这样做 1.讨论函数的性质一定要先考虑定义域；2.充分搜集、应用题目信息，正确建立函数模型；3.注重函数与不等式、数列、导数等知识的综合．1． 几类函数模型及其增长差异(1)几类函数模型函数模型 函数解析式一次函数模型 f (x )＝ax ＋b (a 、b 为常数，a ≠0) 反比例函数模型f (x )＝kx＋b (k ，b 为常数且k ≠0)二次函数模型f (x )＝ax 2＋bx ＋c(a ，b ，c 为常数，a ≠0)指数函数模型f (x )＝ba x ＋c(a ，b ，c 为常数，b ≠0，a >0且a ≠1)对数函数模型 f (x )＝b log a x ＋c(a ，b ，c 为常数，b ≠0，a >0且a ≠1)幂函数模型f (x )＝ax n ＋b (a ，b 为常数，a ≠0)函数性质 y ＝a x (a >1) y ＝log a x (a >1) y ＝x n (n >0)在(0，＋∞)上的增减性 单调递增 单调递增 单调递增 增长速度 越来越快 越来越慢 相对平稳 图像的变化 随x 的增大逐渐表现为与y 轴平行随x 的增大逐渐表现为与x 轴平行随n 值变化而各有不同值的比较存在一个x 0，当x >x 0时，有log a x <x n<a x(1)审题：弄清题意，分清条件和结论，理顺数量关系，初步选择数学模型；(2)建模：将自然语言转化为数学语言，将文字语言转化为符号语言，利用数学知识，建立相应的数学模型；(3)解模：求解数学模型，得出数学结论；(4)还原：将数学问题还原为实际问题的意义．以上过程用框图表示如下：[难点正本疑点清源]1．要注意实际问题的自变量的取值范围，合理确定函数的定义域．2．解决函数应用问题重点解决以下问题(1)阅读理解、整理数据：通过分析、画图、列表、归类等方法，快速弄清数据之间的关系，数据的单位等等；(2)建立函数模型：关键是正确选择自变量将问题的目标表示为这个变量的函数，建立函数的模型的过程主要是抓住某些量之间的相等关系列出函数式，注意不要忘记考察函数的定义域；(3)求解函数模型：主要是研究函数的单调性，求函数的值域、最大(小)值，计算函数的特殊值等，注意发挥函数图像的作用；(4)回答实际问题结果：将函数问题的结论还原成实际问题，结果明确表述出来．1．某物体一天中的温度T(单位：℃)是时间t(单位：h)的函数：T(t)＝t3－3t＋60，t＝0表示中午12∶00，其后t取正值，则下午3时的温度为________．答案78℃解析T(3)＝33－3×3＋60＝78(℃)．2．某工厂生产某种产品固定成本为2 000万元，并且每生产一单位产品，成本增加10万元．又知总收入K是单位产品数Q的函数，K(Q)＝40Q－120Q2，则总利润L(Q)的最大值是________万元．答案 2 500解析L(Q)＝40Q－120Q2－10Q－2 000＝－120Q2＋30Q－2 000＝－120(Q－300)2＋2 500当Q＝300时，L(Q)的最大值为2 500万元．3． (2011·湖北)放射性元素由于不断有原子放射出微粒子而变成其他元素，其含量不断减少，这种现象称为衰变．假设在放射性同位素铯137的衰变过程中，其含量M(单位：太贝克)与时间t(单位：年)满足函数关系：M(t)＝M02－t30，其中M0为t＝0时铯137的含量．已知t＝30时，铯137含量的变化率．．．是－10ln 2(太贝克/年)，则M(60)等于( ) A．5太贝克B．75ln 2太贝克C．150ln 2太贝克D．150太贝克答案D解析∵M′(t)＝－130M02－t30·ln 2，∴M′(30)＝－130×12M0ln 2＝－10ln 2，∴M0＝600.∴M(t)＝600×2－t30，∴M(60)＝600×2－2＝150(太贝克)．4．某企业第三年的产量比第一年的产量增长44%，若每年的平均增长率相同(设为x)，则以下结论正确的是( ) A．x>22%B．x<22%C．x＝22%D．x的大小由第一年的产量确定答案B解析设第一年的产量为a，则a(1＋x)2＝a(1＋44%)，∴x＝20%.5．某公司租地建仓库，已知仓库每月占用费y1与仓库到车站的距离成反比，而每月车载货物的运费y2与仓库到车站的距离成正比．据测算，如果在距离车站10千米处建仓库，这两项费用y1，y2分别是2万元和8万元，那么要使这两项费用之和最小，仓库应建在离车站( ) A．5千米处B．4千米处C．3千米处D．2千米处答案 A解析 由题意得，y 1＝k 1x，y 2＝k 2x ，其中x >0，当x ＝10时，代入两项费用y 1，y 2分别是2万元和8万元，可得k 1＝20，k 2＝45，y 1＋y 2＝20x ＋45x ≥220x ·45x ＝8，当且仅当20x＝45x ，即x ＝5时取等号，故选A.题型一 二次函数模型例1 某化工厂引进一条先进生产线生产某种化工产品，其生产的总成本y (万元)与年产量x (吨)之间的函数关系式可以近似地表示为y ＝x 25－48x ＋8 000，已知此生产线年产量最大为210吨．(1)求年产量为多少吨时，生产每吨产品的平均成本最低，并求最低成本；(2)若每吨产品平均出厂价为40万元，那么当年产量为多少吨时，可以获得最大利润？最大利润是多少？思维启迪：(1)根据函数模型，建立函数解析式．(2)求函数最值． 解 (1)每吨平均成本为y x(万元)．则y x ＝x 5＋8 000x －48≥2x 5·8 000x－48＝32， 当且仅当x 5＝8 000x，即x ＝200时取等号．∴年产量为200吨时，每吨平均成本最低，最低为32万元． (2)设可获得总利润为R (x )万元， 则R (x )＝40x －y ＝40x －x 25＋48x －8 000＝－x 25＋88x －8 000＝－15(x －220)2＋1 680 (0≤x ≤210)．∵R (x )在[0,210]上是增函数，∴x ＝210时，R (x )有最大值为－15(210－220)2＋1 680＝1 660.∴年产量为210吨时，可获得最大利润1 660万元．探究提高二次函数是常用的函数模型，建立二次函数模型可以求出函数的值域或最值．解决实际中的优化问题时，一定要分析自变量的取值范围．利用配方法求最值时，一定要注意对称轴与给定区间的关系：若对称轴在给定的区间内，可在对称轴处取最值，在离对称轴较远的端点处取另一最值；若对称轴不在给定的区间内，最值都在区间的端点处取得．某产品的总成本y (万元)与产量x (台)之间的函数关系是y ＝3 000＋20x －0.1x 2(0<x <240，x ∈N *)，若每台产品的售价为25万元，则生产者不亏本时(销售收入不小于总成本)的最低产量是( )A ．100台B ．120台C ．150台D ．180台答案 C解析 设利润为f (x )万元，则f (x )＝25x －(3 000＋20x －0.1x 2)＝0.1x 2＋5x －3 000 (0<x <240，x ∈N *)． 令f (x )≥0，得x ≥150，∴生产者不亏本时的最低产量是150台． 题型二 指数函数模型例2 诺贝尔奖发放方式为每年一发，把奖金总额平均分成6份，奖励给分别在6项(物理、化学、文学、经济学、生理学和医学、和平)为人类作出最有益贡献的人，每年发放奖金的总金额是基金在该年度所获利息的一半，另一半利息作基金总额，以便保证奖金数逐年增加．假设基金平均年利率为r ＝6.24%.资料显示：1999年诺贝尔奖金发放后基金总额约为19 800万美元．设f (x )表示第x (x ∈N *)年诺贝尔奖发放后的基金总额(1999年记为f (1)，2000年记为f (2)，…，依次类推)．(1)用f (1)表示f (2)与f (3)，并根据所求结果归纳出函数f (x )的表达式；(2)试根据f (x )的表达式判断网上一则新闻“2009年度诺贝尔奖各项奖金高达150万美元”是否为真，并说明理由．(参考数据：1.031 29＝1.32)思维启迪：从所给信息中找出关键词，增长率问题可以建立指数函数模型． 解 (1)由题意知，f (2)＝f (1)(1＋6.24%)－12f (1)·6.24%＝f (1)(1＋3.12%)，f (3)＝f (2)(1＋6.24%)－12f (2)·6.24%＝f (2)(1＋3.12%)＝f (1)(1＋3.12%)2， ∴f (x )＝19 800(1＋3.12%)x －1(x ∈N *)．(2)2008年诺贝尔奖发放后基金总额为f (10)＝19 800(1＋3.12%)9＝26 136，故2009年度诺贝尔奖各项奖金为16·12f (10)·6.24%≈136(万美元)，与150万美元相比少了约14万美元，是假新闻．探究提高 此类增长率问题，在实际问题中常可以用指数函数模型y ＝N (1＋p )x(其中N 是基础数，p 为增长率，x 为时间)和幂函数模型y ＝a (1＋x )n(其中a 为基础数，x 为增长率，n 为时间)的形式．解题时，往往用到对数运算，要注意与已知表格中给定的值对应求解．已知某物体的温度θ(单位：摄氏度)随时间t (单位：分钟)的变化规律：θ＝m ·2t＋21－t(t ≥0，并且m >0)．(1)如果m ＝2，求经过多少时间，物体的温度为5摄氏度； (2)若物体的温度总不低于2摄氏度，求m 的取值范围． 解 (1)若m ＝2，则θ＝2·2t＋21－t＝2⎝⎛⎭⎪⎫2t ＋12t ，当θ＝5时，2t ＋12t ＝52，令2t＝x ≥1，则x ＋1x ＝52，即2x 2－5x ＋2＝0，解得x ＝2或x ＝12(舍去)，此时t ＝1.所以经过1分钟，物体的温度为5摄氏度．(2)物体的温度总不低于2摄氏度，即θ≥2恒成立， 亦m ·2t＋22t ≥2恒成立，亦即m ≥2⎝ ⎛⎭⎪⎫12t －122t 恒成立．令12t ＝x ，则0<x ≤1，∴m ≥2(x －x 2)， 由于x －x 2≤14，∴m ≥12.因此，当物体的温度总不低于2摄氏度时，m 的取值范围是⎣⎢⎡⎭⎪⎫12，＋∞.题型三 分段函数模型例3 为了保护环境，发展低碳经济，某单位在国家科研部门的支持下，进行技术攻关，新上了把二氧化碳处理转化为一种可利用的化工产品的项目，经测算，该项目月处理成本y (元)与月处理量x (吨)之间的函数关系可近似地表示为y ＝⎩⎪⎨⎪⎧13x 3－80x 2＋5 040x ，x ∈[120，144，12x 2－200x ＋80 000，x ∈[144，500]，且每处理一吨二氧化碳得到可利用的化工产品价值为200元，若该项目不获利，国家将给予补偿．(1)当x ∈[200,300]时，判断该项目能否获利？如果获利，求出最大利润；如果不获利，则国家每月至少需要补贴多少元才能使该项目不亏损？(2)该项目每月处理量为多少吨时，才能使每吨的平均处理成本最低？思维启迪：题目中月处理成本与月处理量的关系为分段函数关系，项目获利和月处理量的关系也是分段函数关系．解(1)当x∈[200,300]时，设该项目获利为S，则S ＝200x －⎝ ⎛⎭⎪⎫12x 2－200x ＋80 000 ＝－12x 2＋400x －80 000＝－12(x －400)2，所以当x ∈[200,300]时，S <0，因此该单位不会获利． 当x ＝300时，S 取得最大值－5 000，所以国家每月至少补贴5 000元才能使该项目不亏损． (2)由题意，可知二氧化碳的每吨处理成本为 y x ＝⎩⎪⎨⎪⎧13x 2－80x ＋5 040，x ∈[120，144.12x ＋80 000x －200，x ∈[144，500].①当x ∈[120,144)时，y x ＝13x 2－80x ＋5 040＝13(x －120)2＋240， 所以当x ＝120时，y x取得最小值240. ②当x ∈[144,500]时，y x ＝12x ＋80 000x －200≥212x ×80 000x－200＝200， 当且仅当12x ＝80 000x ，即x ＝400时，yx取得最小值200.因为200<240，所以当每月的处理量为400吨时，才能使每吨的平均处理成本最低． 探究提高 本题的难点是函数模型是一个分段函数，由于月处理量在不同范围内，处理的成本对应的函数解析式也不同，故此类最值的求解必须先求出每个区间内的最值，然后将这些区间内的最值进行比较确定最值．(2011·北京)根据统计，一名工人组装第x 件某产品所用的时间(单位：分钟)为f (x )＝⎩⎪⎨⎪⎧c x ，x <A ，cA ，x ≥A(A ，c 为常数)．已知工人组装第4件产品用时30分钟，组装第A 件产品用时15分钟，那么c 和A 的值分别是( )A ．75,25B ．75,16C ．60,25D ．60,16答案D解析由函数解析式可以看出，组装第A件产品所需时间为cA＝15，故组装第4件产品所需时间为c4＝30，解得c＝60，将c＝60代入cA＝15，得A＝16.函数建模问题典例：(12分)在扶贫活动中，为了尽快脱贫(无债务)致富，企业甲将经营状况良好的某种消费品专卖店以5.8万元的优惠价格转让给了尚有5万元无息贷款没有偿还的小型企业乙，并约定从该店经营的利润中，首先保证企业乙的全体职工每月最低生活费的开支3 600元后，逐步偿还转让费(不计息)．在甲提供的资料中：①这种消费品的进价为每件14元；②该店月销量Q (百件)与销售价格P (元)的关系如图所示；③每月需各种开支2 000元．(1)当商品的价格为每件多少元时，月利润扣除职工最低生活费的余额最大？并求最大余额；(2)企业乙只依靠该店，最早可望在几年后脱贫？审题视角 (1)认真阅读题干内容，理清数量关系．(2)分析图形提供的信息，从图形可看出函数是分段的．(3)建立函数模型，确定解决模型的方法． 规范解答解 设该店月利润余额为L ，则由题设得L ＝Q (P －14)×100－3 600－2 000，① 由销量图易得Q ＝⎩⎪⎨⎪⎧－2P ＋50 14≤P ≤20，－32P ＋40 20<P ≤26，[2分]代入①式得L ＝⎩⎪⎨⎪⎧－2P ＋50P －14×100－5 600 14≤P ≤20，⎝ ⎛⎭⎪⎫－32P ＋40P －14×100－5 600 20<P ≤26，[4分](1)当14≤P ≤20时，L max ＝450元，此时P ＝19.5元； 当20<P ≤26时，L max ＝1 2503元，此时P ＝613元．故当P ＝19.5元时，月利润余额最大，为450元．[8分] (2)设可在n 年后脱贫，依题意有12n ×450－50 000－58 000≥0，解得n ≥20. 即最早可望在20年后脱贫．[12分]解函数应用题的一般程序：第一步：审题——弄清题意，分清条件和结论，理顺数量 关系；第二步：建模——将文字语言转化成数学语言，用数学知识建立相应的数学模型；第三步：求模——求解数学模型，得到数学结论；第四步：还原——将用数学方法得到的结论还原为实际问题的意义．第五步：反思回顾——对于数学模型得到的数学结果，必须验证这个数学解对实际问题的合理性．温馨提醒(1)本题经过了三次建模：①根据月销量图建立Q与P的函数关系；②建立利润余额函数；③建立脱贫不等式．(2)本题的函数模型是分段的一次函数和二次函数，在实际问题中，由于在不同的背景下解决的问题发生了变化，因此在不同范围中，建立函数模型也不一样，所以现实生活中分段函数的应用非常广泛．(3)在构造分段函数时，分段不合理、不准确，是易出现的错误.方法与技巧1．认真分析题意，合理选择数学模型是解决应用问题的基础；2．实际问题中往往解决一些最值问题，我们可以利用二次函数的最值、函数的单调性、基本不等式等求得最值．失误与防范1．函数模型应用不当是常见的解题错误．所以，正确理解题意，选择适当的函数模型是正确解决这类问题的前提和基础．2．要特别关注实际问题的自变量的取值范围，合理确定函数的定义域．3．注意问题反馈．在解决函数模型后，必须验证这个数学结果对实际问题的合理性.A组专项基础训练(时间：35分钟，满分：57分)一、选择题(每小题5分，共20分)1. 有一批材料可以围成200 m长的围墙，现用此材料在一边靠墙的地方围成一块矩形场地(如图)，且内部用此材料隔成三个面积相等的矩形，则围成的矩形场地的最大面积为 ( )A ．1 000 m 2B ．2 000 m 2C ．2 500 m 2D ．3 000 m 2答案 C解析 设围成的场地宽为x m ，面积为y m 2， 则y ＝3x (200－4x )×13＝－4x 2＋200x (0<x <50)． 当x ＝25时，y max ＝25×100＝2 500. ∴围成的矩形场地的最大面积为2 500 m 2.2． (2011·湖北改编)里氏震级M 的计算公式：M ＝lg A －lg A 0，其中A 是测震仪记录的地震曲线的最大振幅，A 0是相应的标准地震的振幅．假设在一次地震中，测震仪记录的最大振幅是1 000，此时标准地震的振幅为0.001，则此次地震的震级为________级；9级地震的最大振幅是5级地震最大振幅的________倍．( )A ．6 1 000B ．4 1 000C ．6 10 000D ．4 10 000答案 C解析 由M ＝lg A －lg A 0知，M ＝lg 1 000－lg 0.001＝3－(－3)＝6，∴此次地震的震级为6级．设9级地震的最大振幅为A 1,5级地震的最大振幅为A 2，则lg A 1A 2＝lg A 1－lg A 2＝(lg A 1－lg A 0)－(lg A 2－lg A 0)＝9－5＝4.∴A 1A 2＝104＝10 000，∴9级地震的最大振幅是5级地震最大振幅的10 000倍．3． 将甲桶中的a 升水缓慢注入空桶乙中，t 分钟后甲桶中剩余的水符合指数衰减曲线y ＝a e nt ，假设5分钟后甲桶和乙桶的水量相等，若再过m 分钟后甲桶中的水只有a8升，则m的值为( )A ．8B ．10C ．12D ．15答案 B解析 由已知条件可得a e 5n＝a 2，e 5n ＝12.由a e nt ＝a 8，得e nt＝18，所以t ＝15，m ＝15－5＝10.4. 某汽车运输公司购买了一批豪华大客车投入营运，据市场分析每辆客车营运的总利润y (单位：10万元)与营运年数x (x ∈N *)为二次函数关系(如右图所示)，则每辆客车营运多少年时，其营运的平均利润最大( ) A ．3 B ．4C ．5D ．6答案 C解析 由题图可得营运总利润y ＝－(x －6)2＋11，则营运的年平均利润y x＝－x －25x＋12，∵x ∈N *，∴y x≤－2x ·25x＋12＝2，当且仅当x ＝25x，即x ＝5时取“＝”．∴x ＝5时营运的平均利润最大． 二、填空题(每小题5分，共15分)5． 某种病毒经30分钟繁殖为原来的2倍，且知病毒的繁殖规律为y ＝e kt(其中k 为常数，t表示时间，单位：小时，y 表示病毒个数)，则k ＝________，经过5小时，1个病毒能繁殖为________个． 答案 2ln 2 1 024解析 当t ＝0.5时，y ＝2，∴2＝e 12k ，∴k ＝2ln 2，∴y ＝e2t ln 2，当t ＝5时，∴y ＝e10ln 2＝210＝1 024.6． 某市出租车收费标准如下：起步价为8元，起步里程为3 km(不超过3 km 按起步价付费)；超过3 km 但不超过8 km 时，超过部分按每千米2.15元收费；超过8 km 时，超过部分按每千米2.85元收费，另每次乘坐需付燃油附加费1元．现某人乘坐一次出租车付费22.6元，则此次出租车行驶了________ km. 答案 9解析 设出租车行驶x km 时，付费y 元， 则y ＝⎩⎪⎨⎪⎧9，0<x ≤38＋2.15x －3＋1，3<x ≤88＋2.15×5＋2.85x －8＋1，x >8由y ＝22.6，解得x ＝9.7． 2008年我国人口总数为14亿，如果人口的自然年增长率控制在1.25%，则________年我国人口将超过20亿．(lg 2≈0.301 0，lg 3≈0.477 1，lg 7≈0.845 1) 答案 2037解析 由已知条件：14(1＋1.25%)x －2 008>20，x － 2 008>lg107lg 8180＝1－lg 74lg 3－3lg 2－1＝28.7，则x >2 036.7，即x ＝2 037. 三、解答题(共22分)8． (10分)某种出口产品的关税税率为t ，市场价格x (单位：千元)与市场供应量p (单位：万件)之间近似满足关系式：p ＝2(1－kt )(x －b )2，其中k ，b 均为常数．当关税税率t ＝75%时，若市场价格为5千元，则市场供应量为1万件；若市场价格为7千元，则市场供应量约为2万件． (1)试确定k ，b 的值；(2)市场需求量q (单位：万件)与市场价格x 近似满足关系式：q ＝2－x，当p ＝q 时，市场价格称为市场平衡价格，当市场平衡价格不超过4千元时，试确定关税税率的最大值．解 (1)由已知⎩⎪⎨⎪⎧1＝21－0.75k 5－b 22＝21－0.75k7－b 2，⇒⎩⎪⎨⎪⎧1－0.75k 5－b 2＝01－0.75k7－b2＝1.解得b ＝5，k ＝1.(2)当p ＝q 时，2(1－t )(x －5)2＝2－x， ∴(1－t )(x －5)2＝－x ⇒t ＝1＋x x －52＝1＋1x ＋25x－10而f (x )＝x ＋25x在(0,4]上单调递减，∴当x ＝4时，f (x )有最小值414，故当x ＝4时，关税税率的最大值为500%.9．(12分)如图所示，在矩形ABCD 中，已知AB ＝a ，BC ＝b (a >b )．在AB 、AD 、CD 、CB 上分别截取AE 、AH 、CG 、CF 都等于x ，当x 为何值时，四边形EFGH 的面积最大？求出这个最大面积． 解 设四边形EFGH 的面积为S ， 由题意得S △AEH ＝S △CFG ＝12x 2，S △BEF ＝S △DHG ＝12(a －x )·(b －x )．由此得S ＝ab －2⎣⎢⎡⎦⎥⎤12x 2＋12a －xb －x＝－2x 2＋(a ＋b )x ＝－2⎝⎛⎭⎪⎫x －a ＋b 42＋a ＋b28.函数的定义域为{x |0<x ≤b }， 因为a >b >0，所以0<b <a ＋b2.若a ＋b4≤b ，即a ≤3b ，x ＝a ＋b4时面积S 取得最大值a ＋b28；若a ＋b4>b ，即a >3b 时，函数S ＝－2⎝ ⎛⎭⎪⎫x －a ＋b 42＋a ＋b 28在(0，b ]上是增函数，因此，当x ＝b 时，面积S 取得最大值ab －b 2. 综上可知，若a ≤3b ，当x ＝a ＋b4时，四边形EFGH 的面积取得最大值a ＋b28；若a >3b ，当x ＝b 时，四边形EFGH 的面积取得最大值ab －b 2.B 组 专项能力提升 (时间：25分钟，满分：43分)一、选择题(每小题5分，共20分)1． 某公司在甲、乙两地销售一种品牌车，利润(单位：万元)分别为L 1＝5.06x －0.15x 2和L 2＝2x ，其中x 为销售量(单位：辆)．若该公司在这两地共销售15辆车，则能获得最大利润为( )A ．45.606万元B ．45.6万元C ．45.56万元D ．45.51万元答案 B解析 依题意可设甲销售x 辆，则乙销售(15－x )辆，总利润S ＝L 1＋L 2，则总利润S ＝5.06x －0.15x 2＋2(15－x )＝－0.15x 2＋3.06x ＋30＝－0.15(x －10.2)2＋0.15×10.22＋30 (x ≥0)．∴当x ＝10时，S max ＝45.6(万元)．2. 某厂有许多形状为直角梯形的铁皮边角料，如图，为降低消耗，开源节流，现要从这些边角料上截取矩形铁片(如图中阴影部分)备用，当截取的矩形面积最大时，矩形两边长x 、y 应为( ) A ．x ＝15，y ＝12 B ．x ＝12，y ＝15 C ．x ＝14，y ＝10 D ．x ＝10，y ＝14答案 A解析 由三角形相似得24－y 24－8＝x 20，得x ＝54(24－y )，∴S ＝xy ＝－54(y －12)2＋180，∴当y ＝12时，S 有最大值，此时x ＝15.3． 汽车经过启动、加速行驶、匀速行驶、减速行驶之后停车，若把这一过程中汽车的行驶路程s 看作时间t 的函数，其图像可能是( )答案 A解析 汽车加速行驶时，速度变化越来越快，而汽车匀速行驶时，速度保持不变，体现在s 与t 的函数图像上是一条直线，减速行驶时，速度变化越来越慢，但路程仍是增加的．二、填空题(每小题5分，共15分)4. 如图，书的一页的面积为600 cm 2，设计要求书面上方空出2 cm 的边，下、左、右方都空出1 cm 的边，为使中间文字部分的面积最大，这页书的长、宽应分别为____________． 答案 30 cm 、20 cm解析 设长为a cm ，宽为b cm ，则ab ＝600， 则中间文字部分的面积S ＝(a －2－1)(b －2) ＝606－(2a ＋3b )≤606－26×600＝486， 当且仅当2a ＝3b ，即a ＝30，b ＝20时，S 最大＝486.5． 某商人购货，进价已按原价a 扣去25%.他希望对货物订一新价，以便按新价让利20%销售后仍可获得售价25%的利润，则此商人经营这种货物的件数x 与按新价让利总额y 之间的函数关系式为______________． 答案 y ＝a4x (x ∈N *)解析 设新价为b ，依题意，有b (1－20%)－a (1－25%)＝b (1－20%)·25%，化简得b ＝ 54a .∴y ＝b ·20%·x ＝54a ·20%·x ，即y ＝a4x (x ∈N *)． 6． 某医院为了提高服务质量，对挂号处的排队人数进行了调查，发现：当还未开始挂号时，有N 个人已经在排队等候挂号；开始挂号后排队的人数平均每分钟增加M 人．假定挂号的速度是每个窗口每分钟K 个人，当开放一个窗口时，40分钟后恰好不会出现排队现象；若同时开放两个窗口时，则15分钟后恰好不会出现排队现象．根据以上信息，若要求8分钟后不出现排队现象，则需要同时开放的窗口至少应有________个．答案 4解析 设要同时开放x 个窗口才能满足要求，则⎩⎪⎨⎪⎧ N ＋40M ＝40K ， ①N ＋15M ＝15K ×2， ②N ＋8M ≤8Kx . ③由①②，得⎩⎪⎨⎪⎧ K ＝2.5M ，N ＝60M ，代入③，得60M ＋8M ≤8×2.5Mx ，解得x ≥3.4.故至少同时开放4个窗口才能满足要求．三、解答题7． (13分)(2011·湖北)提高过江大桥的车辆通行能力可改善整个城市的交通状况．在一般情况下，大桥上的车流速度v (单位：千米/时)是车流密度x (单位：辆/千米)的函数．当桥上的车流密度达到200辆/千米时，造成堵塞，此时车流速度为0；当车流密度不超过20辆/千米时，车流速度为60千米/时．研究表明：当20≤x ≤200时，车流速度v 是车流密度x 的一次函数．(1)当0≤x ≤200时，求函数v (x )的表达式；(2)当车流密度x 为多大时，车流量(单位时间内通过桥上某观测点的车辆数，单位：辆/时)f (x )＝x ·v (x )可以达到最大，并求出最大值．(精确到1辆/时)解 (1)由题意，当0≤x ≤20时，v (x )＝60；当20≤x ≤200时，设v (x )＝ax ＋b ，再由已知得⎩⎪⎨⎪⎧ 200a ＋b ＝0，20a ＋b ＝60， 解得⎩⎪⎨⎪⎧ a ＝－13，b ＝2003.故函数v (x )的表达式为v (x )＝⎩⎪⎨⎪⎧ 60， 0≤x ≤20，13200－x ， 20<x ≤200. (2)依题意并由(1)可得f (x )＝⎩⎪⎨⎪⎧60x ， 0≤x ≤20，13x 200－x ， 20<x ≤200.当0≤x ≤20时，f (x )为增函数，故当x ＝20时，其最大值为60×20＝1 200；当20<x ≤200时，f (x )＝13x (200－x ) ≤13⎣⎢⎡⎦⎥⎤x ＋200－x 22＝10 0003， 当且仅当x ＝200－x ，即x ＝100时，等号成立．所以当x ＝100时，f (x )在区间(20,200]上取得最大值10 0003. 综上，当x ＝100时，f (x )在区间[0,200]上取得最大值10 0003≈3 333， 即当车流密度为100辆/千米时，车流量可以达到最大，最大值约为3 333辆/时．（注：本资料素材和资料部分来自网络，仅供参考。