提速保分1

签约保分协议模板甲方：（学生姓名）乙方：（家长姓名）丙方：（补习机构名称）一、协议目的本协议旨在明确甲方与乙方之间，以及丙方作为补习机构的中介角色之间的权利与义务，保证甲方在学习期间能够取得满意的成绩，提高甲方对高等教育的入学保障。

二、协议内容1. 乙方同意雇佣丙方为甲方的补习机构，提供学习辅导、教育咨询等相关服务，并承诺按时支付所约定的费用。

2. 甲方同意参加由丙方组织的各类考试和评测，以评估学习进度，并配合丙方的指导和要求进行学习。

3. 甲乙双方均同意，若甲方在期末考试中未能达到约定的分数线，乙方将根据双方协商一致的方式对丙方进行处罚，乙方也将从自身角度出发对甲方进行相应的补偿。

三、费用及支付方式1. 乙方同意按照丙方规定的费用标准支付学习辅导费用，并在签署本协议后的三天内支付首次学费；之后的学费将按照双方约定的支付方式进行分期支付。

2. 若甲方在期末考试中达到约定的分数线，乙方同意按照协议约定，支付相应的额外费用作为奖励，以鼓励甲方取得更好的成绩。

四、奖惩措施1. 若甲方欠缴学费超过一个月，乙方将在第一周内进行书面警告，并向丙方汇报。

2. 若甲方在期末考试中未能达到约定的分数线，乙方同意根据双方协商一致的方式对丙方进行处罚，并向甲方提供相应的补偿措施（如继续提供学习服务）。

3. 若乙方未能按时支付学费或其他约定的费用，乙方同意向丙方支付违约金，并应补偿甲方对于学习的影响。

五、协议终止1. 若甲方完成学业或提前解除协议，乙方同意不得要求丙方退还已支付的学费。

2. 乙方与丙方均有权单方解除本协议，但应提前书面通知另一方，并支付相应的违约金。

六、争议解决本协议在履行过程中如发生争议，甲乙双方应友好协商解决，协商不成的，可向所在地法院提起诉讼。

七、其他本协议正本一式两份，甲方、乙方、丙方各持一份，具有同等法律效力。

乙方：甲方：签署日期：签署日期：丙方（补习机构）代表：签署日期：。

第2讲被动语态被动语态的构成英语中的及物动词一般都有主动语态和被动语态两种语态形式。

被动语态由“be＋及物动词的过去分词”构成。

be随着主语的人称、数和时态的不同而变化。

被动语态的各种时态形式见下表：高频考点梳理1.只有及物动词或短语才有被动语态；不及物动词或短语无被动语态。

Manystars appear intheskyatnight.晚上天空会出现很多星星。

Greatchanges havetaken placeinmyhometownsincereformandopening-up.改革开放以来，我的家乡已经发生了巨大的变化。

2.被动语态的构成为“be＋过去分词”，只要变换be的形式就可以得到不同时态的被动语态；除be之外被动语态的构成形式还有：get/become＋过去分词。

Hercar gotstolen attheweekend.她的车在周末被人偷了。

Tigers become endangered.老虎濒临灭绝。

3.在使役动词have，make，get以及感官动词see，watch，notice，hear，feel，observe 等与后面的不定式作宾语补足语时，在主动结构中不定式中的to要省略，但变为被动结构时，不能省to。

Thebossmakesthemworktwelvehourseveryday.→They aremadeto worktwelvehourseveryday.老板让他们每天工作十二个小时。

4.主动形式表示被动含义：(1)某些连系动词feel，look，seem，appear，taste，sound，smell，prove，remain等可用主动形式表示被动意义，主语通常是事物。

Thewater feels warm.水摸上去很温。

Thedish smells good.这道菜闻起来很香。

(2)表示主语的某种属性、特性、性能或品质的词：read，write，act，cut，draw，drive，sell，wash，clean，wear，open，lock，look，shut等。

语法填空技能保分练(一)谓语动词小题夯基练单句语法填空1．[2020·全国卷Ⅰ] The unmanned Chang'e-4 probe (探测器) —the name was inspired by an ancient Chinese moon goddess—________ (touch) down last week in the South Pole-Aitken basin.2．[2020·新高考山东卷] The 80,000 objects collected by Sir Hans Sloane, for example, ________(form) the core collection of the British Museum which/that opened in 1759.3．[2020·全国卷Ⅲ] When he asked the villagers on the banks of the river where he could find the legendary (传奇的) artist, they smiled and ________(point) down the river.4．[2020·浙江卷7月]By about 6000 BC, people ________ (discover) the best crops to grow and animals to raise.5．[2020·新高考山东卷] Often, only a small part of a museum's collection ________ (be) on display. Most of it is stored away or used for research.6．[2020·天津卷]The number of medical schools reached 18 in the early 1990s and ________ (remain) around that level ever since.7．[2020·全国卷Ⅰ] “This really excites scientists，”Carle Pieters, a scientist at Brown University, says, “because it means we have the chance to obtain information about how the moon ________(construct)．”8．[2020·新高考山东卷] The parts of a museum open to the public ________(call) galleries or rooms.9．[2020·浙江卷7月]Farming produced more food per person than hunting and gathering, so people were able to raise more children. And, as more children were born, more food ________(need)．10．[2020·1月浙江卷]People tend to focus on the first factor. However, greater attention should _________ (place) on longevity (长寿)．11．[2019·天津卷]Amy, as well as her brothers, ________ (give) a warm welcome when returning to the village last week.12．[2020·湖南长郡中学模拟]The traditional Chinese marriage usually ________(involve) some necessary procedures, such as match-making, engagement, meeting the bride, and three bows.13．[2020·江西省重点中学盟校第二次联考]At present, Tech giants Apple and Google ________ (team) up to create a system that would let smartphone users know when they've come into contact with someone who has COVID-19.14．[2020·赣州市高三年级适应性考试]They ________ (become) a part of daily life and a part of our throwaway culture for decades. China set a goal of reducing overconsumption in order to get rid of our reliance on single-use plastics.15．[2020·“安徽省示范高中皖北协作区”高三联考]Quanzhou is also known for its thriving private economy. The past four decades ________ (see) the birth of tens of thousands of private businesses and hundreds of famous brands.16．[2020·濮阳市高三毕业班第二次模拟]Greta Thunberg, a 16-year-old Swedish climate change activist, ________ (elect) as 2019's “Person of The Year” last week.大题提能练Test 1[2020·合肥市高三第二次诊断检测]Chopsticks play an important role in Chinese food culture. Chinese chopsticks are round on the eating end which symbolizes heaven，while the other end is square which symbolizes earth.This is because keeping enough food is 1.________(great) concern than anything else.It is important to note that chopsticks are used in many different cultures and there is no single standard for the use of chopsticks.Here are some customs 2.________(associate) with chopsticks in China. Playing with chopsticks 3.________(consider) bad manners. And chopsticks should not be placed 4.________(vertical) in a bowl of rice or other food. Any stick-like object pointing upward 5.________(resemble) the incense(香) sticks that people use 6.________ offerings to their dead family members. It is also bad manners to tap chopsticks on 7.________ edge of one's bowl, because in ancient China beggars often made this noise 8.________(attract) attention.In Chinese, “chopsticks”reads “kuai zi”，which means “to have sons soon”，so a newly-married couple will be very happy to accept chopsticks as 9.________ (they) wedding gift.10．________ has already been found out is that using chopsticks improves one's memory, increases finger dexterity(灵巧) and can be useful in learning and improving skills such as Chinese character printing and brush painting.Test 2[2020·深圳市高三第二次检测] When the winter approaches，tanghulu，a traditional Chinese snack can be found on the street corner in northern China. Since ancient times, it 1.________(be) very popular with natives, especially children.Tanghulu is 2.________(common) made of haws (山楂果), which are rich in vitamin C and are known 3.________(have) traditional Chinese medicinal properties. According to a legend, in Song Dynasty, one of the emperor's 4.________(wife) was sick and had 5.________ poor appetite. The doctor suggested that she eat five to ten haws 6.________(boil) with sugar before each meal. She recovered within half a month. Later, the prescription was passed on 7.________ordinary people. People put haws on a stick, dipped them in hot sugar syrup(糖浆) and dried. The syrup finally turned into a solid coating, like the crystal on the surface of haws. That is 8.________they are also called bingtanghulu. 9.________origin story says that the very first tanghulu only had two haws—a small one on the top and a big one below, making it resemble a hulu, a bringer of good luck.With sour haws and sweet sugar, the taste of tanghulu is a combination of flavors, which often 10.________ (remind) people of their happy childhoods.。

阅读七选五技能保分练(一)段首、段尾主题句类Test1[2020·兰州高三诊断考试]Learning to Give a Pep Talk(打气)Everyone wants to be the type of person who gives the critical talk that turns around a friend's outlook.However,giving a good pep talk isn't easy.__1__.You need to not only listen and understand,but also stress the other person's strengths.You also need to know when to stop talking.“A lot of people think they are giving a pep talk,but they are just saying what they would want to hear，”says Stacy Kaiser,a psychotherapist(心理治疗师)in Los Angeles.Instead of instantly telling someone what to do,ask him what action he has thought about taking and why he thinks it will be beneficial.“Don't jump right in and insist‘You'll be fine，’”says Kaiser.__2__.Repeat the concerns for the person out loud,so he feels heard.Then,show your friend that you believe in him and that he has what it takes to get through this hard time.Stress his strengths.__3__.You can't guarantee success,but you can remind the person that he has been through a tough time before and has gotten through it.At last,Kaiser says you must know when to stop.“__4__.Don't argue if the person disagrees with what you are saying.Instead,tell him‘I am sorry you are having such a hard time.’And then back down.”Kaiser says he has learned to give good pep talks by giving bad ones.He lost a number of loved ones during a short period.“Timing is everything.”There is a time to give a pep talk,and there is a time to just listen.__5__.A．Let your friend have his momentB．Give your pep talk and then shut upC．Arguing with your friend makes no senseD．Show your friend that you understand why he is sadE．He isn't interested in what his best friends really needF．It requires an understanding of what your audienceneedsG．It is also important to remember that pep talks are about hopeTest2[2020·南昌市高三一模]Why Walking in Nature Makes You a Better Worker?We're busy at work,distracted(注意力分散的)by technology and often live in urban environments far from wild spaces.__1__.The average American,for example,spends about90% of their life indoors.But what happens if we make time for an hour outside each day?__2__.You'll have to go out for a walk,which is beneficial if most of your day involves sitting in front of a screen.Research shows short breaks can improve work enthusiasm,and a quick break in natural light will deliver a shot of vitamin D.There are also a lot of mental benefits when you are in nature—you are happy and your brain can make sense of life.“When people are all out in nature,even in urban nature,people tend to have more positive emotion and energy than when they are indoors.__3__，”said Lisa Nisbet, associate professor at Canada's Trent University.The idea that nature is good for us has been gaining grounds since the1980s.__4__.Afterwards, shinrin­yoku,the Japanese concept,which is the practice of taking a short,leisurely visit to a forest for health benefits,followed that.Researchers of shinrin­yoku have since found plenty of physicaland mental benefits,while global studies suggest spending time in nature can,for example,restore our ability to focus,increase our creativity,and even help us live longer.Of course,many of us live in cities with no ready access to forests or the wilderness.__5__. Various studies have shown that green environments in cities have beneficial effects.A．We also don't get out muchB．But it doesn't have to be a forestC．People can get to a forest for a hikeD．In other words,people are happier in natureE．There are some obvious benefits when being outsideF．Green and blue spaces are better than busy city streetsG．First came the theory that humans have a basic desire to be connected with natureTest3[2020·长沙市高三统一模拟]Find a few trusted lists.The publishing industry puts out more than50,000books a year.__1__Nobody does.However,we should get our reading lists from booksellers.There's nothing as nice as getting one person's favorite books.Finding a few trusted lists can be as simple as the email lists.__2__Some of the lists that I personally like are:Bill Gates's reading list and Derek Sivers's reading list.__3__It's one thing to quit reading a book and feel bad about it.It's another to quit reading a book and feel proud of it.All you have to do is to change your mind.Just say,“Now I've finally thrown this brick to make room for that gem(宝石)I'm about to read next.”Usually,I quit reading three or four books to find a book I can read to the end.__4__You may be wondering why I don't read e­books,saving myself all the time and effort required to bring books in and out of the house.In an age when our books,films,and photographs are all going digital,there is something popular about having a growing collection of books in the home.Perhaps there is a nice change in your mind while you're reading physical books.__5__ A．Read physical books.B．Try to read as much as you can.C．Change your mind about quitting.D．Do you have time to read1,000new books a week?E．You'd better find out the most popular reading lists first.F．And it can be a welcome change to hold a physical book in your hands.G．With a bit of digging you can easily find the one that totally satisfies you.Test4[2020·昆明市高三“三诊一模”摸底诊断测试]Impolite cellphone users are anywhere where there's a cellphone signal.__1__.Could that be you?Follow our expert phone rules to avoid being rude and annoying.●Know where not to use your phone.__2__，so avoid talking on your cellphone or having it ring while in such places as hospitals,libraries and movie theaters.Turn your phone off if necessary.●Don't talk too loudly.When in public,try not to raise your voice while on the phone. Generally you don't have to shout on the phone to be heard on the other end.In fact,doing so often makes it harder for you to be understood.__3__.●Don't use your phone when having a meal with someone.If possible,turn it off.If you're waiting for an important call,let the person you're with know beforehand(事先)that you're expecting a call that you'll need to take.__4__.If you have to,step away but don't stay away any longer than a bathroom break.●__5__.When you're in an enclosed space,or you can't put yourself10feet out of everyone's way,it's inappropriate to talk but it's potentially acceptable to receive and send text messages.But you'd better not text while doing anything that requires you to be focused.A．Learn to textB．Focus on your messagesC．Some places are inappropriate for cellphone usageD．Limit phone use during gatherings with your friendsE．Try not to hold a phone conversation at tableF．In addition,shouting on the phone disturbs people around youG．Most people who are impolite don't even realize what they're doing阅读七选五技能保分练(一)Test1语篇类型：说明文主题语境：人与社会——人际沟通——如何给别人打气[文章大意]本文主要论述了给别人打气的方法，包括关心令朋友伤心的事情、注意倾听、将时间交给朋友、选择合适时机停止说话等。

专题二阅读七选五阅读七选五技能保分练(一)小标题类Test 1[2021·合肥市第三次质量检测]Anxiety and depression are complex conditions. Everyone can benefit from learning how to care about our mind. __1__●Self­compassion (自我同情)__2__ This can include feeling like you must be perfect to be accepted. The answer to perfectionism isn't letting it all go — it's self­compassion, which means you are kind and understanding when faced with personal failures — after all, who ever said you were supposed to be perfect? How we treat ourselves through the ups and downs of life can have a huge impact on physical health and mental health.●Social ConnectionFrom the time we were born, we have been needing social connection in order to grow and succeed. __3__ It can be talking to one trusted person about how you're really doing or having a visit with any family member or friend. If this feels out of reach, try making a short list of people who at any point have given you a sense of belonging. __4__●ExerciseExercise can be important for preventing depression since having a sedentary (久坐不动的) lifestyle is a risk factor. __5__ Another study found that 12 weeks of exercise at 30 minutes, three to five times per week reduced symptoms by 47%.So the best approach is: Get whatever support is in reach and care about your mind based on what works for you.A．It is important to be kind to yourself.B．But it doesn't have to be a big party or an office full of people.C．Being constantly self­critical is risky for anxiety and depression.D．It may be vital to understand happiness when we struggle with mood.E．One study found that 15 minutes a day of exercise can significantly prevent depression.F．The following behaviors are some key ones linked to prevention of anxiety and depression.G．Studies have shown that just thinking of positive relationships can help you tolerate stress.Test 2[2021·东北三校一模]It seems that society has placed so much value on the word “humility (谦逊)”. Sometimes we're told to lower ourselves in order to be recognized as a more modest student or employee.__1__，rather than how society looks at you, according to a US­based business magazine. Here are three ways to start developing a more modest personality.1．Stop questioning your worthBeing mild­mannered does not contradict recognizing your worth, because you'll become at peace with your inner self when you accept your own strengths. Humility will then come as a natural consequence. __2__. Worth shouldn't be measured by what you compete for in society. Rather, it's your gifts, talents and hard work that prove who you are.2．__3__Be willing to get coffee for a colleague, sweep the floors of your dormitory, or move to a smaller office at work. __4__. In addition, it may potentially inspire ideas for growth beyond your original vision.Accepting more flexibility in your everyday life will also help you move back and forth in the path, without having to worry about “losing yourself” in any difficulty you may come across. You'll gradually realize that either a step forward or backward won't affect your value.3．Accept uncertainty__5__. Try to appreciate the unknown and regard it as a fresh learning opportunity rather than a nightmare. Just as the band Maroon 5 says, “Life isn't always rainbows and butterflies. It's compromise that moves us along.” This may never be easy. But you can meet uncertainty with a sense of curiosity to learn what can be created from it. Furthermore, apreciating the unknown instead of fearing it is also a way to reduce stress.A．Be eager and flexibleB．Be determined and hard­workingC．Develop a healthier relationship with uncertaintyD．Uncertainty is a double­edged sword in many casesE．Remember that you are valuable regardless of outside variablesF．This can allow you to interact with the people around you in new waysG．The true humility, however, is more about the way you relate to yourself and your surroundingsTest 3[2021·东北三省四市教研体一模]Principles of Developing the Youth's Leadership Skills— Look for leadership potential in everyone__1__. Not everyone feels comfortable leading a meeting or speaking at an event, but they may be able to talk to teachers about a project or draft a letter to the school or community newspaper. It's worthwhile to think about all of the ways the youth can get involved.— Take time to give them meaningful feedback and build their self­confidenceIt can be difficult to find time to meet with the youth individually, but it is important. Plan to meet regularly with core leaders and be on the lookout for impromptu (即兴的) individual meetings. __2__. Further plans can be discussed during the meetings and the youth can have more courage.— Opportunities are when the youth lead projects or activitiesSometimes it's hard to take a step back and play the supportive role, but it is the only way to develop leaders authentically (真正地). But sometimes you ask a youth to take ownership of a task and then decide to do it yourself. __3__. When leaders do not come through with an assignment, it's important to hold them accountable. The youth will feel accomplished after working hard and grow up.— __4__Training can be facilitated with in­house staff or an outside resource person, so the youth feel confident in their knowledge and skills. As tasks get more advanced, the level of training should progress as well. At the same time, you must examine the skills and assistance you provide to the group to ensure that expectations are clear and that follow­ups take place to inquire about any extra support needed. __5__.A．That can leave a negative impactB．Build up their confidence and cheer them upC．Offer lots of training and clear guidanceD．Think of every young person as someone who possesses leadership abilityE．Make sure young people have the guidance needed to complete agreed­upon activitiesF．These could happen while walking with a youth to get a snack before or after a meetingG．Leadership skills can be absorbed in classroom learning through the belief in learned optimismTest 4[2021·河北省高三联考]If your friendships are going to last a long time, you simply have to accept that things will always change. But never fear. __1__. Here is a little of their advice.Start with the friendship triangle (三角形).Shasta Nelson is a friendship expert who gives a concept called the “friendship triangle”. __2__. Anyway, the base is positivity, and two sides of the triangle are consistency (一致性) and vulnerability (脆弱性). If your friendship has something wrong, it's much easier to see what is off balance and adjust it in time.Figure out what you value.Another helpful tool comes from Rachel Wilkerson Miller. Wilkerson Miller recommends looking at friendships through your TME — time, money and energy. “Those are your most valuable resources，” she says. “Think about where your TME is going, how you're spending it and who you're giving it to.” __3__.Don't be afraid to ask for things.__4__. Being direct can feel awkward, but if you get into the habit of stating your needs, you can avoid a pile of hate much later on. “Ask for exactly what you need，” Havrilesky, a famous writer, says. “Sometimes it can work like medicine. So ask！”__5__.During a long life, you go through a lot of different versions of yourself. That can mean that sometimes, a friend is only present for a certain chapter — and that is OK.A．Not every friend is going to be there foreverB．We offer some advice from experts to help you deal with the shifts in your friendshipC．Friendship is like a ship to carry you go furtherD．The friendship triangle is made of three equally long sidesE．If you waste these resources, it might be time to shift the relationshipF．You should get comfortable asking for what you needG．The expert recommends being clear when your friendship is no longer the same阅读七选五技能保分练（一）Test 1语篇类型：说明文主题语境：人与自我——心理健康——防止焦虑和抑郁的几种方法【文章大意】本文主要介绍了防止焦虑和抑郁的几种方法——自我同情、社交联络和锻炼。

2020年高考数学120分(12＋4＋3＋2)保分练(一)(满分：126分 限时：90分钟)一、选择题(本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的)1．已知全集U ＝R ，集合A ＝{x |x ＞3}，B ＝{x |x ≥2}，则(∁U A )∩B ＝( ) A ．{x |x ≤2} B ．{x |x ≥3} C ．{x |2＜x ≤3}D ．{x |2≤x ≤3}解析：选D 由条件，得∁U A ＝{x |x ≤3}， ∴(∁U A )∩B ＝{x |2≤x ≤3}．2．设i 为虚数单位，则满足条件z i ＝3＋4i 的复数z 在复平面内所对应的点位于( ) A ．第四象限 B ．第三象限 C ．第二象限 D ．第一象限解析：选A z ＝3＋4i i ＝(3＋4i )·(－i )i (－i )＝4－3i ，所以z 在复平面内对应的点位于第四象限．3．已知sin ⎝⎛⎭⎫x ＋π3＝13，则cos x ＋cos ⎝⎛⎭⎫π3－x 的值为( ) A ．－33B.33C ．－13D.13解析：选B 因为sin ⎝⎛⎭⎫x ＋π3＝12sin x ＋32cos x ＝13，所以cos x ＋cos ⎝⎛⎭⎫π3－x ＝cos x ＋12cos x ＋32sin x ＝32cos x ＋32sin x ＝3⎝⎛⎭⎫32cos x ＋12sin x ＝33.4．已知S n 为等差数列{a n }的前n 项和，a 1＝－1，S 6＝39，则a 3＋a 4＝( ) A ．13 B ．26 C ．39D ．52解析：选A 法一：由题意，得6×(－1)＋6×52×d ＝39(d 为公差)，解得d ＝3，所以a 3＋a 4＝－1＋2×3－1＋3×3＝13.法二：因为S 6＝6(a 1＋a 6)2＝3(a 1＋a 6)＝39，所以a 3＋a 4＝a 1＋a 6＝13. 5．已知O 为坐标原点，M 是双曲线C ：x 2－y 2＝4上的任意一点，过点M 作双曲线C 的某一条渐近线的垂线，垂足为N ，则|ON |·|MN |的值为( )A ．1B ．2C ．4D ．5解析：选B 因为M 是双曲线C ：x 2－y 2＝4上的任意一点，所以可设M (x ，y )，其中一条渐近线方程为x －y ＝0，则|MN |＝|x －y |2，|OM |＝x 2＋y 2，|ON |＝|OM |2－|MN |2＝|x ＋y |2，所以|ON |·|MN |＝|x 2－y 2|2＝2.6．在区间[0,2]之间随机抽取一个数x ，使x 满足不等式2x －1≥m (m ≤3)的概率为34，则实数m ＝( )A ．0B ．1C ．2D ．3解析：选A 由2x －1≥m ，得x ≥m ＋12，由m ≤3，得m ＋12≤2，由x 满足不等式2x－1≥m (m ≤3)的概率为34，得2－m ＋122－0＝34，解得m ＝0.7．已知x ，y 满足⎩⎪⎨⎪⎧x ＋y －1≥0，x －2y －4≤0，2x －y －2≥0，如果目标函数z ＝y ＋1x －m的取值范围为[0,2)，则实数m 的取值范围为( )A.⎣⎡⎦⎤0，12 B.⎝⎛⎦⎤－∞，12 C.⎝⎛⎭⎫－∞，12 D ．(－∞，0]解析：选C 由约束条件作出可行域如图中阴影部分所示，而目标函数z ＝y ＋1x －m 的几何意义为可行域内的点(x ，y )与A (m ，－1)连线的斜率．由⎩⎪⎨⎪⎧ x ＋y －1＝0，x －2y －4＝0得⎩⎪⎨⎪⎧x ＝2，y ＝－1，即B (2，－1)． 由题意知m ＝2不符合题意，故点A 与点B 不重合， 因而当连接AB 时，斜率取到最小值0， 故点A 在直线y ＝－1上．由y ＝－1与2x －y －2＝0得交点C ⎝⎛⎭⎫12，－1，在点A 由点C 向左移动的过程中，可行域内的点与点A 连线的斜率小于2， 因而目标函数的取值范围满足z ∈[0,2)，则m ＜12.8．函数y ＝e |x |－x 3的大致图象是( )解析：选A 易知函数y ＝e |x |－x 3为非奇非偶函数，排除B ；当x ＜0时，y ＞0，排除C ；当x ＝2时，y ＝e 2－8＜0，排除D ，故选A.9.中国古代数学名著《九章算术》中记载：“今有羡除”．刘徽注：“羡除，隧道也．其所穿地，上平下邪．”现有一个羡除如图所示，四边形ABCD ，ABFE ，CDEF 均为等腰梯形，AB ∥CD ∥EF ，AB ＝6，CD ＝8，EF ＝10，EF 到平面ABCD 的距离为3，CD 与AB 间的距离为10，则这个羡除的体积是( )A ．110B ．116C ．118D ．120解析：选D 如图，过点A 作AP ⊥CD ，AM ⊥EF ，过点B 作BQ ⊥CD ，BN ⊥EF ，垂足分别为P ，M ，Q ，N ，连接PM ，QN ，将一侧的几何体补到另一侧，组成一个直三棱柱，底面积为12×10×3＝15.棱柱的高为8，体积V ＝15×8＝120.10．若正整数N 除以正整数m 后的余数为n ，则记为N ＝n (mod m )，例如10＝4(mod 6)．下面程序框图的算法源于我国古代闻名中外的《中国剩余定理》．执行该程序框图，则输出n 的值为( )A ．17B ．16C ．15D ．13解析：选A 当n ＞10时，被3除余2，被5除也余2的最小整数n ＝17.11．已知三棱锥A -BCD 外接于球O ，底面△BCD 的边CD 经过球心O ，若三棱锥A -BCD 的体积的最大值为643，则球O 的表面积为( )A ．16πB ．64π C.64π3D.128π3解析：选B 设球的半径为r ，因为底面△BCD 的边CD 经过球心O ，所以△BCD 为直角三角形，CD ＝2r .若使三角形的面积最大，则点B 到边CD 的距离最大即可．因为B ，C ，D 三点共面，所以最大距离为半径r ，△BCD 面积的最大值为12×2r ×r ＝r 2.点A 到平面BCD 的最大距离为r ，则三棱锥A -BCD 的体积的最大值为13r 2·r ＝13r 3＝643，解得r ＝4，所以该球的表面积为4π×42＝64π.12．已知数列{a n －2}是公比为12的等比数列，且a 1＝32，设T n ＝12a 1a 2＋122a 2a 3＋…＋12na n a n ＋1(n ∈N *)，则T n 的取值范围为( )A.⎝⎛⎦⎤－∞，421∪⎝⎛⎭⎫13，＋∞ B.⎝⎛⎭⎫－∞，421∪⎝⎛⎭⎫13，＋∞ C.⎝⎛⎭⎫421，13 D.⎣⎡⎭⎫421，13解析：选D 因为a 1－2＝－12，则a n －2＝－⎝⎛⎭⎫12n ，即a n＝2－12n ，于是12n a n a n ＋1＝12n ·2n ＋1－12n ·2n ＋2－12n ＋1＝2n ＋1(2n ＋1－1)(2n ＋2－1)＝12n ＋1－1－12n ＋2－1， 所以T n ＝⎝⎛⎭⎫122－1－123－1＋⎝⎛⎭⎫123－1－124－1＋…＋⎝⎛⎭⎫12n ＋1－1－12n ＋2－1＝13－12n ＋2－1＜13，当n ＝1时，T n 取得最小值421，故421≤T n ＜13. 二、填空题(本大题共4小题，每小题5分，共20分．请把正确答案填在题中的横线上) 13．已知双曲线C ：x 2a 2－y 2b 2＝1(a ＞0，b ＞0)的离心率为2，则双曲线C 的渐近线方程为________．解析：因为双曲线的离心率为2， 所以e ＝ca ＝1＋⎝⎛⎭⎫b a 2＝2，所以b a ＝3，所以双曲线C 的渐近线方程为y ＝±3x . 答案：y ＝±3x14．已知向量AB ―→与AC ―→的夹角为120°，|CB ―→－CA ―→|＝2，|BC ―→－BA ―→|＝3，若向量AP ―→＝λAB ―→＋AC ―→，且AP ―→⊥BC ―→，则实数λ的值为________．解析：由条件可知|AB ―→|＝2，|AC ―→|＝3， 于是AB ―→·AC ―→＝2×3×⎝⎛⎭⎫－12＝－3. 由AP ―→⊥BC ―→，得AP ―→·BC ―→＝0， 即(λAB ―→＋AC ―→)·(AC ―→－AB ―→)＝0， 所以|AC ―→|2＋(λ－1)AB ―→·AC ―→－λ|AB ―→|2＝0， 即9＋(λ－1)×(－3)－4λ＝0，解得λ＝127. 答案：12715．已知函数f (x )＝x ln x ＋mx 2－m 在定义域内不存在极值点，则实数m 的取值范围为________．解析：依题意，f ′(x )＝ln x ＋1＋2mx (x ＞0)， 故函数f ′(x )不存在变号零点． 令f ′(x )＝0，故ln x ＋1＋2mx ＝0， 即－2m ＝ln x ＋1x ；令g (x )＝ln x ＋1x ，故g ′(x )＝－ln xx 2， 当0＜x ＜1时，g ′(x )＞0， 所以g (x )在(0,1)上单调递增； 当x ＞1时，g ′(x )＜0，所以g (x )在(1，＋∞)上单调递减，故当x ＝1时，函数g (x )有极大值也是最大值1，无最小值． 所以要使函数f (x )在定义域内不存在极值点， 则需－2m ≥1，m ≤－12.答案：⎝⎛⎦⎤－∞，－1216．已知点M ，N 是抛物线y ＝4x 2上不同的两点，F 为抛物线的焦点，且满足∠MFN ＝135°，弦MN 的中点P 到直线l ：y ＝－116的距离记为d ，若|MN |2＝λ·d 2，则λ的最小值为________．解析：设|MF |＝m ，|NF |＝n ，∵y ＝－116是抛物线y ＝4x 2的准线，∴d ＝12(m ＋n )．又|MN |2＝m 2＋n 2－2mn cos 135°＝m 2＋n 2＋2mn ＝(m ＋n )2＋(2－2)mn ≥(m ＋n )2＋(2－2)×(m ＋n )24＝(2＋2)4×(m ＋n )2， ∴λ＝|MN |2d 2≥2＋24×(m ＋n )2(m ＋n )24＝2＋2.当且仅当m ＝n 时等号成立，故λ的最小值为2＋2. 答案：2＋2三、解答题(本大题共3小题，共36分，解答时应写出必要的文字说明、证明过程或演算步骤)17．(本小题满分12分)如图，在△ABC 中，已知点D 在BC 边上，且AD ―→·AC ―→＝0，sin ∠BAC ＝223，AB ＝32，BD ＝ 3.(1)求AD 的长； (2)求cos C 的值．解：(1)因为AD ―→·AC ―→＝0，所以AD ⊥AC ， 所以sin ∠BAC ＝sin ⎝⎛⎭⎫π2＋∠BAD ＝cos ∠BAD ， 因为sin ∠BAC ＝223，所以cos ∠BAD ＝223.在△ABD 中，由余弦定理可得， BD 2＝AB 2＋AD 2－2AB ·AD ·cos ∠BAD ，把AB ＝32，BD ＝3代入上式，化简可得AD 2－8AD ＋15＝0， 解得AD ＝5或AD ＝3. 因为AB ＞AD ，所以AD ＝3. (2)在△ABD 中，由正弦定理可得， BD sin ∠BAD ＝ABsin ∠ADB ，又由cos ∠BAD ＝223可得sin ∠BAD ＝13，所以sin ∠ADB ＝AB sin ∠BAD BD ＝63. 因为∠ADB ＝∠DAC ＋C ＝π2＋C ，所以cos C ＝cos ⎝⎛⎭⎫∠ADB －π2＝sin ∠ADB ＝63. 18．(本小题满分12分)在如图所示的四棱锥E -ABCD 中，已知四边形ABCD 是边长为2的正方形，平面ABCD ⊥平面ABE ，∠AEB ＝90°，AE ＝BE .(1)若M 是DE 的中点，试在AC 上找一点N ，使得MN ∥平面ABE ，并给出证明；(2)求四棱锥E -ABCD 的体积．解：(1)连接BD 交AC 于点N ，则点N 即为所求． 证明如下：∵四边形ABCD 是正方形， ∴N 是BD 的中点，又M 是DE 的中点，∴MN ∥BE ，∵BE ⊂平面ABE ，MN ⊄平面ABE ， ∴MN ∥平面ABE .(2)取AB 的中点F ，连接EF ， ∵△ABE 是等腰直角三角形， 且AB ＝2，∴EF ⊥AB ，EF ＝12AB ＝1，∵平面ABCD ⊥平面ABE ， 平面ABCD ∩平面ABE ＝AB ， EF ⊂平面ABE ，∴EF ⊥平面ABCD ，即EF 为四棱锥E -ABCD 的高， ∴V 四棱锥E -ABCD ＝13S 正方形ABCD·EF ＝13×22×1＝43. 19．(本小题满分12分)某地随着经济的发展，居民收入逐年增长，下表是该地一建设银行连续五年的储蓄存款(年底余额)，如下表1：为了研究计算的方便，工作人员将上表的数据进行了处理，t ＝x －2 011，z ＝y －5，得到下表2：(1)求z 关于t 的线性回归方程；(2)通过(1)中的方程，求出y 关于x 的回归方程；(3)用所求回归方程预测到2020年年底，该地储蓄存款额可达多少？附：对于线性回归方程y ^＝b ^x ＋a ^，其中b ^＝∑i ＝1nx i y i －n x ·y ∑i ＝1nx 2i －n x2，a ^＝y －b ^x .解：(1)t ＝3，z ＝2.2，∑i ＝15t i z i ＝45，∑i ＝15t 2i ＝55，b ^＝45－5×3×2.255－5×9＝1.2，a ^＝z －b ^t ＝2.2－3×1.2＝－1.4，∴z ＝1.2t －1.4.(2)将t ＝x －2 011，z ＝y －5，代入z ＝1.2t －1.4， 得y －5＝1.2(x －2 011)－1.4，即y ＝1.2x －2 409.6. (3)∵y ＝1.2×2 020－2 409.6＝14.4，∴预测到2020年年底，该地储蓄存款额可达14.4千亿元．四、选做题(请在第22～23题中任选一题作答，如果多做，则按所做的第一题计分) 22．(本小题满分10分)选修4－4：坐标系与参数方程在直角坐标系xOy 中，直线l 的参数方程为⎩⎪⎨⎪⎧x ＝3－t ，y ＝1＋t (t 为参数)．在以坐标原点为极点，x 轴正半轴为极轴的极坐标系中，曲线C ：ρ＝22cos ⎝⎛⎭⎫θ－π4. (1)求直线l 的普通方程和曲线C 的直角坐标方程； (2)求曲线C 上的点到直线l 的距离的最大值．解：(1)由⎩⎪⎨⎪⎧x ＝3－t ，y ＝1＋t ，消去t 得x ＋y －4＝0，所以直线l 的普通方程为x ＋y －4＝0.由ρ＝22cos θ－π4＝22cos θcos π4＋sin θsin π4＝2cos θ＋2sin θ，得ρ2＝2ρcos θ＋2ρsin θ.将ρ2＝x 2＋y 2，ρcos θ＝x ，ρsin θ＝y 代入上式， 得x 2＋y 2＝2x ＋2y ，即(x －1)2＋(y －1)2＝2. 所以曲线 C 的直角坐标方程为(x －1)2＋(y －1)2＝2.(2)法一：设曲线C 上的点P (1＋2cos α，1＋2sin α)，则点P 到直线l 的距离d ＝|1＋2cos α＋1＋2sin α－4|2＝|2(sin α＋cos α)－2|2＝⎪⎪⎪⎪2sin ⎝⎛⎭⎫α＋π4－22.当sin ⎝⎛⎭⎫α＋π4＝－1时，d max ＝2 2. 所以曲线C 上的点到直线l 的距离的最大值为2 2. 法二：设与直线l 平行的直线l ′：x ＋y ＋b ＝0(b ≠－4)， 当直线l ′与圆C 相切时，|1＋1＋b |2＝2，解得b ＝0或b ＝－4(舍去)， 所以直线l ′的方程为x ＋y ＝0.所以直线l 与直线l ′的距离d ＝|0＋4|2＝2 2.所以曲线C 上的点到直线l 的距离的最大值为2 2. 23．(本小题满分10分)选修4－5：不等式选讲 已知函数f (x )＝|x ＋a －1|＋|x －2a |. (1)若f (1)＜3，求实数a 的取值范围； (2)若a ≥1，x ∈R ，求证：f (x )≥2. 解：(1)因为f (1)＜3，所以|a |＋|1－2a |＜3. 当a ≤0时，得－a ＋(1－2a )＜3， 解得a ＞－32，所以－23＜a ≤0；当0＜a ＜12时，得a ＋(1－2a )＜3，解得a ＞－2，所以0＜a ＜12；当a ≥12时，得a －(1－2a )＜3，解得a ＜43，所以12≤a ＜43.综上所述，实数a 的取值范围是⎝⎛⎭⎫－23，43. (2)证明：f (x )＝|x ＋a －1|＋|x －2a |≥|(x ＋a －1)－(x －2a )|＝|3a －1|， 因为a ≥1，所以f (x )≥3a －1≥2.。

保分题冲关系列(一)(时间：45分钟 分数：60分)1．(14分)(2021·甘肃河西五市联考)在△ABC 中，角A ，B ，C 的对边分别为a ，b ，c ，且b cos C ＝3a cos B －c cos B.(1)求cos B 的值；(2)若BA →·BC→＝2，且b ＝22，求a 和c 的值． 解：(1)由正弦定理得a ＝2R sin A ，b ＝2R sin B ，c ＝2R sin C ， 则2R sin B cos C ＝6R sin A cos B －2R sin C cos B ，故sin B cos C ＝3sin A cos B －sin C cos B ，可得sin B cos C ＋sin C cos B ＝3sin A cos B ，即sin(B ＋C )＝3sin A cos B ，可得sin A ＝3sin A cosB ．又sin A ≠0， 因此cos B ＝13.(2)由BA →·BC →＝2，可得ac cos B ＝2， 又cos B ＝13，故ac ＝6，由b 2＝a 2＋c 2－2ac cos B ，可得a 2＋c 2＝12， 所以(a －c )2＝0，即a ＝c ，所以a ＝c ＝ 6.2．(14分)(2021·贵州七校联考)已知{a n }是等差数列，{b n }是等比数列，S n 为数列{a n }的前n 项和，a 1＝b 1＝1，且b 3S 3＝36，b 2S 2＝8(n ∈N *)．(1)求a n 和b n ；(2)若a n ＜a n ＋1，求数列⎩⎨⎧⎭⎬⎫1a n a n ＋1的前n 项和T n .解：(1)设等差数列{a n }的公差为d ，等比数列{b n }的公比为q ，由题意⎩⎪⎨⎪⎧ b 3S 3＝36，b 2S 2＝8，a 1＝b 1＝1，得⎩⎪⎨⎪⎧q 2(3＋3d )＝36，q (2＋d )＝8，解得⎩⎪⎨⎪⎧d ＝2，q ＝2或⎩⎨⎧d ＝－23，q ＝6.所以，a n ＝2n －1，b n ＝2n －1或a n ＝－23n ＋53，b n ＝6n －1. (2)由于a n ＜a n ＋1，所以d ＞0，故a n ＝2n －1. 所以，1a n a n ＋1＝1()2n －1()2n ＋1＝12⎝⎛⎭⎪⎫12n －1－12n ＋1， 故T n ＝12⎣⎢⎡⎝ ⎛⎭⎪⎫1－13＋⎝ ⎛⎭⎪⎫13－15＋…⎦⎥⎤＋⎝ ⎛⎭⎪⎫12n －1－12n ＋1 ＝n 2n ＋1.3.(14分)(2021·辽宁沈阳一模)如图，四棱锥S －ABCD 的底面是正方形，SD ⊥平面ABCD ，SD ＝AD ＝a ，点E 是SD 上的点，且DE ＝λa (0＜λ≤1)．(1)求证：对任意的λ＝(0,1]，都有AC ⊥BE ；(2)若二面角C －BE －A 的大小为120°，求实数λ的值．解：(1)证明：以D 为原点，DA ，DC ，DS 为x ，y ，z 轴，如图建立空间直角坐标系D －xyz ，则A (a,0,0)，B (a ，a,0)，C (0，a,0)，D (0,0,0)，E (0,0，λa )，AC→＝(－a ，a,0)，BE →＝(－a ，－a ，λa )， ∴AC →·BE →＝0对任意λ∈(0,1]都成立， 即AC ⊥BE 恒成立．(2)设平面ABE 的一个法向量为n 1＝(x 1，y 1，z 1)， ∵AB→＝(0，a,0)，AE →＝(－a,0，λa )， ∴⎩⎨⎧n 1·AB →＝0，n 1·AE→＝0⇒⎩⎪⎨⎪⎧ y 1＝0，－ax 1＋λaz 1＝0⇒⎩⎪⎨⎪⎧y 1＝0，x 1－λz 1＝0，取z 1＝1，则x 1＝λ，n 1＝(x 1，y 1，z 1)＝(λ，0,1)． 设平面BCE 的一个法向量为n 2＝(x 2，y 2，z 2)， ∵BC→＝(－a,0,0)，CE →＝(0，－a ，λa )， ∴⎩⎨⎧n 2·BC→＝0，n 2·CE→＝0⇒⎩⎪⎨⎪⎧ －ax 2x 2＝0，－ay 2＋λax 2＝0⇒⎩⎪⎨⎪⎧x 2＝0，y 2－λz 2＝0，取z 2＝1，则y 2＝λ，n 2＝(0，λ，1)， ∵二面角C －AE －D 的大小为120°， ∴cos 〈n 1，n 2〉＝n 1·n 2|n 1||n 2|＝11＋λ2＝12，又λ∈(0,1]⇒λ＝1， ∴λ＝1为所求．4．(18分)(2021·广东揭阳二模)某校为了调查“学业水平考试”同学的数学成果，随机地抽取该校甲、乙两班各10名同学，获得的数据如下：(单位：分)甲：132,108,112,121,113,121,118,127,118,129； 乙：133,107,120,113,122,114,125,118,129,127.(1)以百位和十位为茎，个位为叶，在图中作出甲、乙两班同学数学成果的茎叶图，并推断哪个班的平均水平较高；(2)若数学成果不低于128分，称为“优秀”，求从甲班这10名同学中随机选取3名，至多有1名“优秀”的概率；(3)以这20人的样本数据来估量整个学校的总体成果，若从该校(人数很多)任选3人，记X 表示抽到“优秀”同学的人数，求X 的数学期望．解：(1)甲、乙两班同学数学成果的茎叶图如图所示：乙班的平均水平较高．(2)由上图数据知，甲班这10人中“优秀”的同学有2名， 则从这10名同学中随机选取3人，至多有1人“优秀”的概率P ＝C 38＋C 28C 12C 310＝1415.(3)因样本20名同学中，“优秀”的有4名，故从这20名同学中任选1名，恰好抽到“优秀”的概率为420＝0.2，据此可估量从该校中任选1名同学，其为“优秀”的概率为0.2，因X ～B(3,0.2)，所以E(X)＝3×0.2＝0.6.。

语法填空保分练(一)Test 1[2024·新课标Ⅰ卷]Xiaolongbao(soup dumplings), those amazing constructions of delicate dumpling wrappers encasing hot, 1.________ (taste) soup and sweet, fresh meat, are far and away my favorite Chinese street food. The dumplings arrive steaming and dangerously hot. To eat one, you have to decide whether 2.________ (bite) a small hole in it first, releasing the stream and risking a spill (溢出), 3.________ to put the whole dumpling in your mouth, letting the hot soup explode on your tongue (舌头).Shanghai may be the 4.________ (recognize) home of the soup dumpling, but food historians will actually point you to the neighboring ancient canal town of Nanxiang as xiaolongbao's birthplace. There, you'll find them prepared differently—more dumpling and less soup—and the wrappers are pressed 5.________ hand rather than rolled.Nanxiang aside, the best xiaolongbao have a fine skin, allowing them 6.________ (lift) out of the steamer basket without tearing or spilling any of 7.________ (they) contents. The meat should be fresh with 8.________ touch of sweetness, and the surrounding soup hot, clear and delicious.No matter where I buy them, though, one steamer basket is 9.________ (rare) enough, yet two seems greedy, and so I am always left 10.________ (want) more next time.[答题区]1．________ 2.________ 3.________ 4.________ 5.________6．________ 7.________ 8.________ 9.________ 10.________Test 2[2024·保定市高三一模]The field of nutrition can be divided into three main settings in which dieticians (养分师) and nutritionists can work. 1.________ (register) dieticians and nutritionists can work in clinics, in the community, and in management.In clinics, they work 2.________ (individual) with patients and their families. They evaluate, plan, and make dietary strategies and nutritional treatments 3.________ are concentrated on improving varieties of medical problems such as high blood pressure and obesity. In addition, dieticians and nutritionists in this setting come up 4.________ plans to help patients to improve their diets and appetite, like cancer patients 5.________ (receive) chemical treatments.In the community, dieticians and nutritionists work in health and recreation 6.________ (center). They work with and target specific populations such as the elderly and children. The goal of this targeting 7.________ (be) to inform the public and make new plans 8.________ (achieve) healthier lifestyles.Lastly, dieticians and nutritionists can work in management. They may work in 9.________ (vary) large­scale food service operations that feed the community. They are needed in these settings to help maintain 10.________ better the performanceof these operations through food sourcing, long­term budgeting, and menu planning.[答题区]1．________ 2.________ 3.________ 4.________ 5.________6．________ 7.________ 8.________ 9.________ 10.________Test 3[2024·成都市高三检测]A herd (兽群) of wild elephants that hiked northward for months last year was recently spotted 1.________ (enter) Wild Elephant Valley in Yunnan Province.“The adults and babies in the herd are all in good health，” said Chen Fei, 2.________ (direct) of the National Forestry and Grassland Administration's Asian Elephant Research Center.The herd still has 14 members, but Chen said that could include some new members as it 3.________ (possible) came into contact with other groups along the route.“We have not introduced electronic identity chips for elephant monitoring，” Chen said. “Observers usually recognize differ ent groups 4.________ (base) on their years of experience and some special features on the elephants' bodies.”Yunnan is the only place in China where wild Asian elephants 5.________ (find). They live in the south of the province—in Xishuangbanna and the cities of Pu'er and Lincang.The Asian elephant, 6.________ is included on the International Union for Conservation of Nature's Red List of Threatened Species as “endangered”， enjoys Class­A protection in China, the same level afforded to the 7.________ (ad ore) giant panda.Yunnan has established 11 nature reserves with a total area of 414，600 hectares (公顷), nearly double 8.________ amount in the 1980s. The province has also piloted the use of elephant canteens 9.________ (solve) the problem of human­elephan t conflict.Thanks to the determined protection efforts in recent decades, the Asian elephant population in China has risen 10.________ 170 in the 1970s to 300.[答题区]1．________ 2.________ 3.________ 4.________ 5.________6．________ 7.________ 8.________ 9.________ 10.________Test 4[2024·云南省高三统考]The China­Laos Railway, 1.________ connects Kunming in southwest China's Yunnan Province with the Laotian capital, Vientiane, 2.________ (start) operation on Dec. 3, 2024. The 1035­kilometer­lo ng railway is a landmark project and an important part of the pan­Asian railway network. It will not only benefit the two peoples, but also 3.________ (significant) improve regional connectivity.4．________ (locate) on the southwest of China, Laos is the only landlocked country in Southeast Asia and mainly depends on road, water and air transport for the movement of people and goods. It has long been a dream for the Lao people to see their country change from a landlocked country 5.________ a land­linked on e, and the opening of the new railway is a big step toward turning 6.________ (they)dream into reality.The new railway will improve Laos' transportation and promote its tourism as well as agricultural processing industries. It will also enable Lao businesses to 7.________ (well) fit into regional and global supply chains.China and Laos have stood together through thick and thin and engaged in mutually beneficial cooperation on the basis of equality. Besides, China and Laos are the first 8.________ (sign) an agreement based on the Belt and Road Initiative. The opening of the China­Laos Railway will thus help speed the 9.________ (develop) of the China­Laos Economic Corridor, and will further advance the building of a China­Laos community with 10.________ s hared future.[答题区]1．________ 2.________ 3.________ 4.________ 5.________6．________ 7.________ 8.________ 9.________ 10.________语法填空保分练（一）Test 1语篇类型：说明文主题语境：人与社会——中国美食——小笼包【文章大意】文章介绍了中国美食——小笼包，讲解并描述了小笼包的美味，发源地以及制作方法等等。

小题分层练三中档小题保分练1 建议用时：40分钟一、选择题1．角α的终边与单位圆交于点，则cos2α＝B．－D．－2．王老师给班里同学出了两道数学题，她预估做对第一道题的概率为，做对两道题的概率为，则预估做对第二道题的概率是A．．C．．3．2022·永州市三模下列函数中，与函数y＝2－2－的定义域、单调性与奇偶性均一致的函数是A．y＝sinB．y＝3C．y＝D．y＝log24．2022·全国卷Ⅰ直线l经过椭圆的一个顶点和一个焦点，若椭圆中心到l的距离为其短轴长的，则该椭圆的离心率为5．2022·济南模拟要得到函数y＝sin的图象，只需将函数y＝sin2的图象A．向左平移个单位B．向右平移个单位C．向左平移个单位D．向右平移个单位6．某几何体的三视图如图18所示，若图中小正方形的边长均为1，则该几何体的体积是图18A．16＋πB．16＋π＋π＋π7．2022·淮南市一模在△ABC中，角A，B，C的对边分别是a，b，c，已知b＝c，a2＝2b21－sin A，则A＝8．已知等差数列{a n}一共有9项，前4项和为3，最后3项和为4，则中间一项的值为C．9．直线a＋by－a－b＝0a≠0与圆2＋y2－2＝0的位置关系为A．相离B．相切C．相交或相切D．相交10．若点in＝min＝－e2＋1，选A]13答案：－2解析：[y′＝＝，将＝3代入，得曲线y＝在点3,2处的切线斜率＝－，故与切线垂直的直线的斜率为2，即－a＝2，得a ＝－2]14．答案：解析：[由题意，F10，c，F20，－c，不妨取A点坐标为，∴直线AF1的方程为y－c＝－，即2ac＋b2y－b2c＝0∵直线AF1与圆2＋y2＝相切，∴＝∴b2＝ac，∴e2－e－＝0，∵e>1，∴e＝]15．答案：解析：[由题意得∠BOC＝180°－＝120°，在△OBC中，BC2＝OB2＋OC2－2OB·OC·cos120°，即1＝OB2＋OC2＋OB·OC≥3OB·OC，即OB·OC≤，所以S△OBC＝OB·OC sin120°≤，当OB＝OC时取最大值．]16．答案：，2解析：[由f＋4＝f，即函数f的周期为4，因为当∈[－2,0]时，f＝－6，所以若∈[0,2]，则－∈[－2,0]，则f－＝－6＝3－6因为f是偶函数，所以f－＝3－6＝f，即f＝3－6，∈[0,2]，由f－log a＋2＝0得f＝log a＋2，作出函数f的图象如图所示．当a＞1时，要使方程f－log a＋2＝0恰有3个不同的实数根，则等价于函数f与g＝log a＋2有3个不同的交点，则满足即解得＜a＜2，故a的取值范围是，2．]。