Unit 2 随堂训练一
I.单词拼写
1. Can you imagine what the world in the (遥远的) future will become?
2. We are at a (关键的) time in history.
3. He hasn’ t realized his full (潜力)yet.
4.There are (漏洞) in the water pipe; water is getting out.
5. Now (电的) appliances have entered into ordinary families.
6. I don't think his remarks are relevant (相关) to our discussion.
7. Some of the old fantasies (幻想) about the space age are coming true.
8. There is no end to practice or (创新) .
9. We can' t take your advice. (然而), thank you for putting it.
10. Can you analyze the (结构)) of the sentence for me?
Ⅱ.单句语法填空
1. After a little gentle (persuade), he agreed to come.
2. Every time I switch the TV, there’s football. It's boring
3. The beach is within walking (distant) of my house.
4. They have tightened (secure) along the border.
5. The machine is (automatic) controlled.
6. This requires that a number of people work together quickly and (efficient)
7. Many people expressed a strong (prefer) for the original plan.
8. The firm is working on a new product in (combine) with several overseas partners.
9. The (detect) thought the stick was relative to the murder case.
10. The buildings are well (integrate).with the landscape.
Ⅲ.完成句子
1.他下令修建连接各地城堡的道路。
He commanded that roads to link castles across the land.
2. 我一看到他就认出他正是警方在寻找的那个人。
I saw him I knew he was the man the police were looking for.
3. 他按完门铃后过了一会儿门才打开。
the door opened in response to his ring.
4.无论如何这个问题都不能说解决了。
In no sense the problem to be solved
5我们自然会尽力劝说大家购买我们的产品。
Naturally, we'll do our best to our products.
Unit 2课时训练一
I.单词拼写
1. The disease was detected during a (常规) check-up.
2. Switch the camera into the automatic ((模式)
3. The newspaper articles call for severe punishment for this （罪行）.
4. That's exactly the (短语) I was looking for myself.
5. I wish to turn on the light, where is the (开关)?
6. Soldiers are expected to (遵守) their orders without questions.
7. We must create a (安全的) and reliable international environment of lasting peace and stability.
8. My house is only a mile (远的) from the zoo.
9. The news may be unexpected; （然而），it is true.
10. We'll send you a copy as soon as it becomes (得到的）.
Ⅱ.单句语法填空
1. The dead are believed to be alive some sense.
2 We need greater (secure) in car parks.
3. How can I persuade you my sincerity?
4. All these are precious gifts. I have no preference any one.
5. The soldiers opened fire without ( warn).
6. We were very surprised at his ( normal) behavior
7. The cooker isn't working because of an (electricity) fault.
8. The captain commanded the crew (report) to the main deck.
9. The screen is sensitive and can respond slight touch.
10. It will be eight years we meet
Unit 2 随堂检测二
I.单句语法填空
1.--Will you be available at three o'clock tomorrow afternoon？
-- No. I (attend) a lecture then.
2. I (fly) from Miami to New York to meet the other members of the group at this time tomorrow.
3. Paula says that she (work) late every evening next month.
4. At 7 o'clock this evening we (celebrate) Tom's birthday.
5. When you reach the other end of the bridge, I (wait) right there to show you the way.
6. You (arrive) in time if you hurry.
7. –Look! The light is still on at noon.
-- Sorry. I (turn) it off.
8. Look at the dark clouds! It (rain).
9. The car (go) at the present speed until it reaches the foot of mountain at about nine o'clock tonight?
10. He describes what houses (look) like in thirty years.
Ⅱ.完成句子
1.今天下午6点葆拉正在淋浴。
Paula at 6 this afternoon.
2.明天我不能来参加他的婚礼，因为那时我在开会。
I can’t attend his wedding tomorrow, for .
3.我很兴奋！明天上午的这个时候我正飞往上海
I feel so excited At this time tomorrow morning I .
4. 她不在时，她的丈夫将照料这些孩子们。
Her husband while she is away.
5. 下星期的这个时候我就会躺在沙滩上了。
This time next week
6. 今天下午玛丽可能会告诉你这个消息的。
this afternoon.
7. 当她到家时，她丈夫可能正在睡觉。
When she get home,
III. 语法填空
Chinese high-speed railways are, a very (comfort) way to travel. They are clean, quiet and efficient. China has led other developing countries and even some developed ones in this field since the first high-speed train (come) into use in 2008.
The stations are (main) built outside the town center, but local transport has been lengthened (connect) the high-speed network. The facilities on the train are new and the staff are well trained. Even the second class (chair) provide plenty of space. The passages are so wide you can move without disturbing anyone. You can use your mobile phone, access Internet or work on your laptop. There is also a restaurant car, though the kinds of food (be) limited. The toilets are large, clean and user-friendly too. The train almost doesn't rock. Even when the train brakes, you can hardly feel it shake.
Unit 2 随堂训练三
I.单词拼写
1. Her (矫揉造作的) manner made me sick.
2. It is almost impossible to (预测) the future development of a very young child.
3. He carried on several (职业) at a time.
4. When she got to the place, she could not (抵制住) going in.
5. She gave us an (准确的) description of the house.
6. Many people (提倡) keeping all children at school until the age of sixteen.
7. He was going to (终止) working for them.
8.It' s handmade and (因而) expensive.
II. 选词填空
apologise for; in the absence of; care about; benefit from; keep in touch with; look on; place emphasis on; be opposed to
1. You should what your child really needs.
2. Our English course great conversational kills.
3. I can friends and family by using email.
4. We strongly racial discrimination.
5. We daily exercises.
6. I must beg to coming so late.
7. water and air, nothing could live.
8.For a time he was as a promising writer.
Unit 2课时训练二
I. 单句语法填空
1. He (lie) on one of the sunny beaches in Hawaii all day when he spends his holiday there.
2. Don’t call me between 2:00 and 4:00 this afternoon. I (have) an test then.
3. Nobody knew what (happen) to the Earth in a century’s time.
4. Mr. Lee said he would give the CD to me as soon as he (return) from Canada.
5. When we were young, father (take) us for a special treat on Mother’s day.
6. –Did you invite Sarah to your birthday party?
-- Sorry, I forget. I (call) her now.
7. You have to put in more effort if you were (pass) the test.
8. I (tell) you about my plan, but you stopped me before I could speak.
9. Will you (use) your computer this time tomorrow?
10. I (close) the kitchen door when a little mouse popped its head out. II. 完成句子
1. 明天的这个时间，他们正坐在电影院。
This time tomorrow they at the cinema.
2. 我以为要下雨了。
I thought it rain.
3. 下星期一的这个时间你会在做什么？
What at this time next Monday?
4. 我们不知道她是否会在会上发言。
We don’t know whether she at the meeting.
5. 学生们那时正在为考试做准备。他们将参加一次英语考试。
The students were getting ready for the exam at that moment. They an English exam.
Unit 2课时训练三
I.单句语法填空
1. The results of the experiment confirmed our (predict).
2. You will be asked to fill in a form with details of your birth and (occupy).
3. She remained badly (oppose) to the idea of moving abroad.
4. She did not mention her mother’s (absent).
5. Discuss pollution with your child, (emphasize) how nice a clean street, lawn, or park looks.
6. There has been a lot of (resist) to this new law.
7. (accurate) is more important than speed in his new job.
8. The (library) saved the rare books from the fire.
9. I do not advocate (build) large factories.
10. She can't resist (make) jokes about his baldness.
Ⅱ.完成句子
1.他们以往做这件事不像我们现在这样做.
They didn't do it the way
2.我们认为你人爬山是极度危险的.
We for you to climb the mountain alone.
3简不在的时候，玛丽替代了她。
Jean, Mary took her place.
4.他们在亚洲长大，因此对东方文化产生了兴趣。
They grew up in Asia, and their interest in oriental culture.
5.从长远来看，我们都会从这项活动中受益.
All of us the activity in the long run
Unit 5 随堂训练一
I.单词拼写
1. It is up to the government to (处理) the air pollution problem and work out measures in line with the crimell's suggestions.
2. The new assembly line (增加) production by twenty percent.
3. A (特点) of the camel is its ability to live for a long time without water.
4. To (获得) the purpose, he kept on working day and night.
5. Her feelings are so (热切的) as to move the present into tears.
6. Were it not for the support of the teachers, the student could not (克服) her difficulty.
7. The new technology, if applied to rice growing, will help increase the grain (产量).
8. Water power can be used to (产生) electricity.
9. He's a gentleman of large (闲暇).
10. This plant requires a muddy (土壤), therefore a mixture of clay and sand is ideal. Ⅱ.单句语法填空
1. Quantities of water polluted, we are faced with serious (short) of water.
2. Only five years after Steve Jobs' death, smart-phones defeated (convention) PCs in sales.
3. A lot of people make the (assume) that poverty only exists in the third world.
4. The firm estimated the cost of new house $3000.
5. The fountain was comprised three stone basins.
6. The old teacher all his life to educating his students and he was admired for his to his education cause. (devote)
7. His words finally me, and I was that he was innocent. (convince)
8. They all agreed to the new company, but the will cost them a lot of money. (expand)
Ⅲ.完成句子
1. 据估计国内投资总额今年将继续增加.
total investment in the country will continue to increase this year.
2. 我们说服了他坐火车去而不是坐飞机去。
We by train rather than by plane.
3. 珊瑚礁不但看起来好看，而且非常有用
Coral reefs are very useful.
4. 随着越来越多的森林被砍伐，大量的土壤被冲走.
With , large quantities of soil are being washed away.
5. 真正麻烦的是她穿了一双白鞋.
is that she wore a pair of white shoes.
Unit 5 课时规范一
I. 单词拼写
1. This increase in demand is likely to (提高) prices.
2. He's been under (强烈的) pressure.
3. They have been affected by trends in Italy too much to keep their own (特征).
4. There's too great a (消费) of alcohol in China.
5. A （炮弹）exploded suddenly by the bedside and destroyed his car.
6. We can't (生产) enough power for the entire city.
7. I like French fries because they are (咸的).
8. (名人) has become one of the most important representatives of popular culture.
9. Chinese children grow up with warnings not to waste a single (粮食) of rice, out of respect for farmers' labor.
10. I’ve had my eyes tested and the report says that my (视力) is perfect.
II. 单句语法填空
1. I am firmly convinced the significance of honesty, which will contribute to building
a warm and harmonious society.
2. The theory is based on a series of wrong (assume).
3. From my first job at the restaurant, I learned teamwork and (devote).
4. (give) that they're inexperienced, they have done a good job.
5. His personal wealth is estimated around $50 billion.
6. The mother continued to care the young panda for more than two years.
7. He succeeded in (pull) through the illness.
8. We need to dream a marketing plan for our product.
9. What was regarded as impossible has now become reality.
10. The narrow path in the village expanded a wide road.
Unit 5 随堂练习二
I. 根据句意用适当的词填空
1. They lost their way in the forest and made matters worse was night began to fall.
2. It is said Peter will have a chance to travel abroad next month.
3. the astronomers eat in space is we want to know.
4. I read about it in this book or that one. Does it matter it was?
5. answers the question correctly will be given a prize.
6. he didn't come yesterday is unknown.
7. we wil l go there tomorrow or not hasn’t been decided yet.
8. will be sent to help them is very important.
9. the delayed flight will take off depends much on the weather.
10. He explained why he did it, but he did often remained a mystery. No one knew about the process.
Ⅱ.请将下列每组句子合并成带主语从句的复合句
1. Some schools in Guangzhou took in students from Sichuan. It is true
________________________________________________________________________ 2. What caused this strange phenomenon? It remains unknown.
_________________________________________________________________________ 3. Can he catch the bus? It is not clear.
__________________________________________________________________________ 4. When will the meeting be held? It is still a question.
__________________________________________________________________________ 5. The young man died soon after he was saved. It made the rescuers very sad.
__________________________________________________________________________ Ⅲ.语法填空
Tuan was a farmer. For decades, he (struggle) to rid his family hunger. However, always confused him to expand the output of his crops. This (disturb) problem led to his regretting being a farmer. He would rather have chosen another job.
One day, when (skim) through a newspaper, Tuan read a comment on Yuan Longping. He underlined Yuan's nationality and occupation, and then focused on his discovery and the statistics of his research. He found the knowledge Yuan circulated very (practice). Therefore, he made a summary and began to build up a new farming method. He planted super grain of rich nutrition and equipped (him) to keep his crops roots free from bacteria and pests. He also enriched minerals in the soil while reducing chemical fertilizers. Though it cost him more time and freedom, he was full of hope.
The next year, Tuan was sunburnt but (satisfy) with his production very much. ______(thank) to Yuan Longping, he not only won the battle against hunger, but he could also export his crops abroad.
Unit 5 课时规范二
I.单句语法填空
1. will be in charge of the company is a mystery.
2. we will hold a party tomorrow depends on the weather.
3. cars will be parked in the future is a question.
4. It is very important a student should learn English well.
5. is a pity that you missed the film.
6. made her happy was that she won the game in such an important match.
7. breaks the law should be punished.
8. role he will play in the film hasn't been known.
9. is reported that about 30 volunteers who are at least 18 years old will be chosen from all over the world to go to the Mars.
10. he will attend the meeting has excited everyone of us.
Ⅱ.完成句子
1. (不管谁去接他) must have a driver's licence.
2. (他能否买到票) doesn't matter much?
3. (我们要去哪里) is a question.
4. (你刚才告诉我的) was really a surprise.
5. (他什么时候出国) is being discussed.
6. (他为什么在哭) is not known.
7. It is clear that (他是一个乞丐).
8. (你要邀请谁) is not important.
Unit 5 随堂练习三
I.单词拼写
1. Metals usually occur in nature as (矿石).
2. I can' t (消化) milk products.
3. Her mother began to operate a small (杂货店).
4. The young man dived to a (深度) of 40 feet.
5. Ann caught her foot on a tree (根) and stumbled.
6. He has no (可能的选择) but to try hard to finish it on time.
7. In life, we will succeed and fail often for reasons that are (完全地) out of our control.
8. Technological change is everywhere and affects every (方面) of life, mostly for the better.
9. The peasant bought a bag of chemical （肥料）in the marketplace.
10. A balanced diet provides (营养) for your body.
Ⅱ.选词填空
1. Later, he learned his uncle lived the station.
2. Unlike most sports, which evolved from street games, basketball was designed by one man to suit a particular purpose.
3. This year our meeting the question of children’s rights.
4. The local government the peasants tax.
5. The girls called out their names .
6. you, you ought to be ashamed of yourself
7. , you can elect to share your files with others.
8. The food in Britain is very different from our Chinese food. , they eat a lot of potatoes.
Unit 5 课时规范三
I.单句语法填空
1. His words are (entire) in character with his actions.
2. If you don't like the school lunch, you have the alternative bringing your own.
3. As is known to all, nutrition and exercise are essential fitness and health.
4. instance, one of our cargo ships sank last week in typhoon.
5. He spends too much time on maths, and this turn affects the progress of his other subjects.
6. Please read more books in order to improve your (digest) of the question.
7. The audience focused its attention the speaker.
8. The path of life leads upward for the wise to keep him from (go) down to the grave.
9. In terms of value, it is very . (nutrition)
10. The lake is over 20 meters in . So we were all moved by the man who dived into the deep lake to save the boy. (deep)
Ⅱ.完成句子
1. 为了不让书受灰尘污染，我们把它们放在书柜里
We put our books in bookcases to
2. 护士轮流照顾那个病人
The nurses attended the patient . →The nurses the patient.
3. 问题太难了，小孩子不能理解。
The problem is
4. 她非常生气，把玩具扔在地上，摔成了碎片。
She was so angry that she threw the toy on the ground,
5.骑车时，不要忘记看红绿灯。
, don't forget the traffic lights.
课时跟踪检测（二十六） 电流 电阻 电功 电功率 [A 级——基础小题练熟练快] 1．(2020·山东淄博一中模拟)某家用电热水壶铭牌如图所示，其正常工作时电流的最大值是( ) A ．0.2 A B ．52 2 A C ．5 A D ．5 2 A 解析：选D 电热水壶的有效电流为I ＝P U ＝1 100220 A ＝5 A ，故电流的最大值为：I m ＝2I ＝5 2 A ，D 正确。 2．下列说法中正确的是( ) A ．由R ＝U I 可知，电阻与电压、电流都有关系 B ．由R ＝ρl S 可知，电阻只与导体的长度和横截面积有关系 C ．各种材料的电阻率都与温度有关，金属的电阻率随温度的升高而减小 D ．所谓超导现象，就是当温度降低到接近绝对零度的某个临界温度时，导体的电阻率突然变为零的现象 解析：选D R ＝U I 是电阻的定义式，R 与电压和电流无关，故A 错误；而R ＝ρl S 是电阻的决定式，即电阻与ρ、l 、S 都有关系，故B 错误；电阻率一般与温度有关，金属的电阻率随温度的升高而增大，故C 错误；当温度降低到接近绝对零度的某个临界温度时，导体的电阻率突然变为零的现象叫超导现象，故D 正确。 3．(2019·宿州模拟)白炽灯接在220 V 的电源上能正常发光。现将其接在一可调电压的电源上，使电压从零逐渐增加到220 V 。在电压从零逐渐增加的过程中( ) A ．灯丝的电阻值不变 B ．电流将逐渐减小 C ．每增加1 V 电压而引起的电流变化量是逐渐增大的 D ．每增加1 V 电压而引起的电流变化量是逐渐减小的 解析：选D 金属材料的电阻率会随温度升高而增大，通电后，随着电压的增加，电流
课时跟踪检测(六十七) 离散型随机变量及其分布列 (分A 、B 卷，共2页) A 卷：夯基保分 一、选择题 1．设某项试验的成功率是失败率的2倍，用随机变量X 去描述1次试验的成功次数，则P (X ＝0)等于( ) A ．0 2．(2015·长沙模拟)一只袋内装有m 个白球，n －m 个黑球，连续不放回地从袋中取球，直到取出黑球为止，设此时取出了X 个白球，下列概率等于?n －m ?A 2 m A 3 n 的是( ) A ．P (X ＝3) B ．P (X ≥2) C ．P (X ≤3) D ．P (X ＝2) 3．设X 是一个离散型随机变量，其分布列为： 则q 的值为( ) A ．1 ± 336 －336 ＋ 336 4．随机变量X 的概率分布规律为P (X ＝n )＝a n ?n ＋1? (n ＝1,2,3，4)，其中a 是常数， 则P ? ????1 2 ＜X ＜52的值为( ) 5．(2015·厦门质检)设随机变量X 的分布列为P (X ＝k )＝m ? ?? ??23k (k ＝1,2,3)，则m 的值 为( ) 6．若随机变量X 的分布列为
则当P(X＜a)＝时，实数a的取值范围是( ) A．(－∞，2] B．[1,2] C．(1,2] D．(1,2) 二、填空题 7．若P(X≤x2)＝1－β，P(X≥x1)＝1－α，其中x1 课时跟踪检测（二十八）交通运输方式和布局 一、选择题 甲、乙两城市间的直线距离为590 km，连接甲、乙两城有三条交通线路。图a为甲、乙两城三条交通线沿线海拔随距离变化图，图b为影响交通运价的因素及关联图。据此完成1～3 题。 1．线路M、N、P对应的交通运输方式最可能的是( ) A．公路、高铁、高速公路 B．公路、航空、河运 C．高铁、高速公路、省道 D．航空、高铁、村村通 2．线路M沿线海拔变化最小，距离最短，下列关于线路M所对应的运输方式的说法最恰当的是( ) A．运价最低B．沿线多桥梁和隧道 C．沿线停靠站点最多 D．终点在乙城外32 km 3．结合图b中的四图，下列说法符合Ⅰ、Ⅱ、Ⅲ、Ⅳ特点的是( ) A．看Ⅰ图，运距、重量和运输方式相同，棉花的运价大于铁锭 B．看Ⅱ图，线路P上的运价大于线路M C．看Ⅲ图，重量相同的活鱼和杏仁运价相等 D．看Ⅳ图，其他条件相同，黄金单位重量运费小于铁锭 解析：1.C 2.B 3.A 第1题，读图可知，线路M长度距离最短，为622 km，但大于两地的直线距离，且海拔基本没有变化；线路N长度为651 km，海拔变化很小；即线路M、N具有距离近、线路平直的特点，说明级别较高，而且沿线海拔较低不可能是航空，有可能是高铁、高速公路。线路P长度为899 km，距离较长且沿线海拔变化大，有可能是省道。第2题，首先，依据上题确定，线路M为高铁。高铁的运费高；沿线站点最少；速度较快， 为了保证安全性，高铁线路一般较为平直，桥梁、隧道较多；终点距乙城距离从图中读不出来，高铁线路长度不可能等于两城市站点之间的直线距离。第3题，据Ⅰ图，在其他条件相同的条件下，棉花的密度小于铁锭，故运费贵；据Ⅱ图，运距越长，运价越高，但P为省道，运费低，M为高铁，运费高；据Ⅲ图，活鱼在水中才可以存活，需要运输的重量更大，故运费更贵；据Ⅳ图，其他条件相同，黄金价格高，运费高于铁锭。 被誉为“天路”的青藏铁路已成功运营十多年。现今它如同一棵参天大树，正将更多的“枝叶”伸向广袤的雪域大地。其中，川藏铁路于2014年动工修建，计划在2025年全线建成通车，预估算投资超过2 000亿元。下图是青藏铁路旅客和货物周转量图。据此完成4～6题。 4．上图可以反映出( ) A．旅客和货物周转量均保持逐年增长 B．旅客周转量2014年增长最快 C．货物周转增长幅度超过旅客周转增长幅度 D．旅客周转总量超过货物周转总量 5．修建川藏铁路的意义为( ) ①重构了我国中西部区域发展格局 ②打造了西藏连接长三角、珠三角的便捷通道 ③使西藏成为连接东亚和南亚的“枢纽” ④与青藏铁路相比成本更高 A．①②③ B．②③④ C．①②④ D．①③④ 6．川藏铁路被称为“最难建设的铁路”，目前川藏铁路建设的最大制约因素是( ) A．高寒 B．冻土 C．成本 D．缺氧 解析：4.C 5.A 6.C 第4题，结合图示可明显看出，旅客和货物周转并非逐年增长；旅客周转量2007年增长最快。货物周转增长幅度超过旅客周转增长幅度。旅客周转总量与货物周转总量不具有可比性。第5题，成本不属于交通运输的意义。第6题，因为“青藏铁路已成功运营十多年”，意味着其当年所面临的高寒、缺氧、冻土等问题均已得到成功解决。由题中“预估算投资超过2 000亿元”可知，目前川藏铁路建设的最大制约因素是成本。 课时跟踪检测（二十六）经济建设的发展和曲折 一、选择题(每小题3分，共45分) 1．中国“一五”计划国家财政预算支出中，工业建设占58.2%，交通、邮政和通讯占19.2%，农业、林业和水利占7.6%，文化、教育和卫生事业占7.2%。以此推知，“一五”计划的核心目标是() A．建立计划经济体制B．发展经济改善民生 C．建立工业化的基础D．平衡发展国民经济 解析：选C此时中国积极进行“一五”计划，“一五”计划并不完全等于计划经济体制，故A项错误；根据材料“文化、教育和卫生事业占7.2%”可知，民生的内容只占一小部分，故B项错误；根据材料“工业建设占58.2%”可知，“一五”计划重点是发展重工业，建立工业化的基础，故C项正确；从材料中的数据可看出，国民经济比例发展不平衡，故D项错误。 2．新中国成立初期某一时期“全国工业总产值平均每年递增19.6%，农业总产值平均每年递增4.8%。经济发展比较快，经济效果比较好，重要经济部门之间的比例比较协调。市场繁荣，物价稳定，人民生活显著改善”。由此，可以推测出当时中国() A．经济政策深受苏联影响 B．经济建设出现浮夸风 C．市场经济体制已经建立 D．工农业比重严重失调 解析：选A依据题干材料“全国工业总产值平均每年递增19.6%，农业总产值平均每年递增4.8%。经济发展比较快，经济效果比较好”，可以看出工业总产值递增快于农业总产值，符合新中国成立初期中国向苏联学习的模式，故A项正确。 3．1960年9月7日，中共中央发出指示：淮河以南直到珠江流域地区，应当维持平均每人每年原粮三百六十斤，遭灾的地方应当更低些；淮河以北地区口粮标准应当压低到平均每人每年原粮三百斤左右，东北等一部分严寒地区可以稍高一点。这种普遍降低口粮标准的指示意在() A．最大限度地缓解经济困难压力 B．优先满足重工业发展的需要 C．解决自然灾害带来的市场压力 D．为恢复农业提供充足劳动力 课时跟踪检测二十七难溶电解质的溶解平衡 (时间：45分钟满分：100分) 一、选择题(每小题6分，共60分) 1．下列对沉淀溶解平衡的描述正确的是( ) A．反应开始时，溶液中各离子浓度相等 B．沉淀溶解达到平衡时，生成沉淀的速率和沉淀溶解的速率相等 C．沉淀溶解达到平衡时，溶液中溶质的离子浓度相等，且保持不变 D．沉淀溶解达到平衡时，如果再加入难溶性的该沉淀物，将促进溶解 解析：沉淀溶解平衡符合一般平衡的特点，反应开始时，各离子的浓度没有必然的关系，A项错误；平衡时，沉淀的生成速率与溶解速率相等，B项正确；平衡时，离子浓度不再变化，但不一定相等，C项错误；沉淀溶解达到平衡时，如果再加入难溶性的该沉淀物，由于固体的浓度为常数，故平衡不移动，D 项错误。 答案：B 2．(2017届保定市高阳中学月考)对饱和AgCl溶液(有AgCl固体存在)进行下列操作后c(Ag＋)减小而K sp(AgCl)均保持不变的是( ) A．加热B．加水稀释 C．滴加少量1 mol/L盐酸D．滴加少量1 mol/L AgNO3溶液 解析：含AgCl饱和溶液中，存在＋(aq)＋Cl－(aq) ΔH>0，加热沉淀溶解平衡正向移动，c(Ag＋)增大，K sp(AgCl)也增大，A项不符合题意；加水稀释，由于饱和AgCl溶液中有AgCl固体存在，加水AgCl固体溶解，该溶液仍为饱和溶液，c(Ag＋)不变，B项不符合题意；滴加少量1 mol/L盐酸，c(Cl －)增大，沉淀溶解平衡逆向移动，c(Ag＋)减小，由于温度不变，K sp(AgCl)保持不变，C项符合题意；滴加少量1 mol/L AgNO3，溶液c(Ag＋)增大，D项不符合题意。 答案：C 3．(2017届玉溪第一中学月考)物质间的反应有时存在竞争反应，几种溶液的反应情况如下： (1)CuSO4＋Na2CO3 主要：Cu2＋＋CO2－3＋H2O―→Cu(OH)2↓＋CO2↑ 次要：Cu2＋＋CO2－3―→CuCO3↓ (2)CuSO4＋Na2S 主要：Cu2＋＋S2－―→CuS↓ 次要：Cu2＋＋S2－＋2H2O―→Cu(OH)2↓＋H2S↑ 下列几种物质的溶解度大小的比较中，正确的是( ) A．Cu(OH)2>CuCO3>CuS B．CuS>Cu(OH)2>CuCO3 C．CuS 课时跟踪检测 (二十九) 等差数列及其前n 项和 一抓基础，多练小题做到眼疾手快 1．(2017·桂林调研)等差数列{a n }中，a 4＋a 8＝10，a 10＝6，则公差d ＝( ) A ．1 4 B ．12 C ．2 D ．－12 解析：选A 由a 4＋a 8＝2a 6＝10，得a 6＝5，所以4d ＝a 10－a 6＝1，解得d ＝1 4，故选A ． 2．等差数列{a n }的前n 项之和为S n ，若a 5＝6，则S 9为( ) A ．45 B ．54 C ．63 D ．27 解析：选B 法一：∵S 9＝9(a 1＋a 9) 2＝9a 5＝9×6＝54．故选B ． 法二：由a 5＝6，得a 1＋4d ＝6， ∴S 9＝9a 1＋9×8 2 d ＝9(a 1＋4d )＝9×6＝54，故选B ． 3．(2017·陕西质量监测)已知数列{a n }满足a 1＝15，且3a n ＋1＝3a n －2．若a k ·a k ＋1<0，则正整数k ＝( ) A ．21 B ．22 C ．23 D ．24 解析：选C 3a n ＋1＝3a n －2?a n ＋1＝a n －23?{a n }是等差数列，则a n ＝473－2 3n ．∵a k ＋ 1· a k <0， ∴????473－23k ????453－23k <0，∴452 课时跟踪检测(二十八)种群的特征与数量的变化 一、选择题 1．下列关于种群数量变化的叙述中，不．正确的是() A．在理想条件下，种群数量增长可用一定的数学模型表示 B．一个物种引入新的地区后，一定呈“J”型增长 C．对家鼠等有害动物的控制，要尽量降低其K值 D．研究一个呈“S”型增长的种群的增长速率可预测其K值 2．利用人工合成的性引诱剂诱杀害虫的雄性个体，该害虫的种群密度将明显减小，其原因是() A．雄性个体数量减小使雌虫生殖能力下降 B．成虫个体数量大量迁出使幼虫个体数量减少 C．受人工合成的性引诱剂的影响，雌性个体也减少 D．种群的性别比例失调使种群的出生率下降 3．下列有关种群增长的“S”型曲线的叙述，错误的是() A．通常自然界中的种群增长曲线最终呈“S”型 B．达到K值后种群的增长速率也可能为负值 C．种群增长的开始阶段不受自身密度的影响 D．相同的种群K值也可能不同 4．社鼠是主要生活在山地环境中的植食性鼠类。下列有关叙述正确的是() A．社鼠与其天敌黄鼬的种群数量波动是不同步的 B．社鼠的种群数量总是处在环境容纳量之下 C．生活一段时间后，社鼠种群就会从增长型转变为衰退型 D．在食物十分充足的条件下，社鼠的种群数量一定呈“J”型增长 5．(2014·青岛模拟)自然条件下，种群增长曲线呈“S”型。假设种群的K值为200，N表示种群数量，据表分析不．正确的是() A．环境阻力对种群增长的明显影响出现在S4点之后 B．防治蝗虫应在蝗虫数量达到S3点之前进行 C．渔业捕捞后需控制剩余量在S3点 D．(K－N)/K值为0.50 时，种群增长速率最大 6．下列对探究酵母菌种群数量变化规律实验的叙述，正确的是() A．用血球计数板计数酵母菌个数时，取适量培养液直接滴加到计数室内 B．对于压在一个方格界限上的酵母菌的处理方法是计数四条边及其顶角的酵母菌数C．已知血球计数板的方格为2 mm×2 mm，若盖玻片下经稀释10倍的培养液厚度为0.1 mm，计数时观察值为M，则10 mL培养液中酵母菌的总数约为2.5 M×105个 D．与一般的生物实验一样，该探究实验也需要单独设置对照组 7.右图中曲线Ⅰ表示某种群的出生率，曲线Ⅱ表示其死亡 率。则() A．种群在c点之前呈“J”型曲线增长，c点之后呈“S”型曲 线增长 B．种群数量增长最快的时期是a点对应的时期 C．c点时此种群的个体总数达到环境容纳量 D．曲线表明种群数量变化受食物的影响 8.生态学家对某地区两个生物种群(Ⅰ和Ⅱ)的存活 率进行了调查，结果如右图所示。下列关于对种群Ⅰ和 Ⅱ实施重点保护时期的叙述正确的是() A．种群Ⅰ和Ⅱ都为7～10岁 B．种群Ⅰ和Ⅱ都为1～10岁 C．种群Ⅰ为0～1岁，种群Ⅱ为6～7岁 D．种群Ⅰ为1岁以后各年龄期，种群Ⅱ为7岁以后各年龄期 9．(2012·海南高考)某小组用样方法调查草地中某种双子叶植物的种群密度。下列做法错误的是() A．随机取样 B．选择植物生长茂盛处取样 C．根据调查数据估算该种群密度 D．根据地段的形状确定取样方法 10．(2014·深圳模拟)某小组进行“探究培养液中酵母菌种群数量的动态变化”实验时，同样实验条件下分别在4个试管中进行培养(如下图)，均获得了“S”型增长曲线。下列有关该实验的说法错误的是() 课时跟踪检测（二十六） “专题六”补短增分（综合练） A 组——易错清零练 1．(2018·山东日照联考)已知函数f (x )＝ln ????2x 1＋x ＋a 是奇函数，则实数a 的值为( ) A ．1 B ．－1 C ．1或－1 D ．4 解析：选B 由题意知f (－x )＝－f (x )恒成立，则ln ? ?? ??－2x 1－x ＋a ＝－ln ????2x 1＋x ＋a ，即－2x 1－x ＋a ＝ 1 2x 1＋x ＋a ，解得a ＝－1.故选B. 2．已知f (x )是奇函数，且f (2－x )＝f (x )，当x ∈(2,3)时，f (x )＝log 2(x －1)，则当x ∈(1,2)时，f (x )＝( ) A ．－log 2(4－x ) B ．log 2(4－x ) C ．－log 2(3－x ) D ．log 2(3－x ) 解析：选C 依题意得f (x ＋2)＝f (－x )＝－f (x )，f (x ＋4)＝－f (x ＋2)＝f (x )．当x ∈(1,2)时，x －4∈(－3，－2)，－(x －4)∈(2,3)，故f (x )＝f (x －4)＝－f (4－x )＝－log 2(4－x －1)＝－log 2(3－x )，选C. 3．已知函数f (x )为R 上的奇函数，且当x ≥0时，f (x )＝－e x ＋e － x －m cos x ，记a ＝－2f (－2)，b ＝－f (－1)，c ＝3f (3)，则a ，b ，c 的大小关系是( ) A ．b 0)，若关于x 的方程f 2(x )－(a ＋2)f (x )＋3＝0恰好有六个不 同的实数解，则实数a 的取值范围为( ) A ．(－23－2,23－2) B ．? ???23－2，3 2 课时跟踪检测（二十七）通过神经系统的调节 一、选择题 1．下列关于神经调节的说法正确的是() A．在反射弧完整的情况下，只要给感受器一个刺激，就会引起感受器的兴奋 B．将灵敏电流计的电极均接在一离体神经纤维膜内，在某处给予一有效刺激，电流计一定会发生两次方向相反的偏转 C．将一离体神经纤维置于较高浓度的NaCl溶液中，对测定的静息电位影响不大 D．在反射弧某一部位给以适当刺激，效应器产生相应的反应，说明发生了反射 解析：选C给感受器一个适宜刺激、且达到一定的刺激量，才会引起感受器的兴奋，A错误；将灵敏电流计的电极均接在一离体神经纤维膜内，若给予的一有效刺激部位位于灵敏电流计的两电极之间、且距离两电极相等，则产生的兴奋同时到达电流计的两极，灵敏电流计不会发生偏转，B错误；静息电位产生的机理是K＋外流，因此将一离体神经纤维置于较高浓度的NaCl溶液中，对测定的静息电位影响不大，C正确；在反射弧某一部位给以适当刺激，效应器产生相应的反应，若没有经过完整的反射弧，则没有发生反射，D错误。 2．(2019·潍坊期末)下列有关神经调节的叙述，正确的是() A．反射是机体神经调节的结构基础 B．机体受刺激后产生神经冲动与胞外Na＋内流有关 C．神经递质与突触后膜上的受体结合，一定引起突触后神经元兴奋 D．神经系统可支配某些内分泌腺的分泌，故神经系统的发育和功能不受激素的影响解析：选B反射弧是机体神经调节的结构基础，A错误；胞外Na＋内流产生了动作电位，B正确；神经递质与突触后膜上的受体结合，引起突触后神经元兴奋或抑制，C错误；神经系统的发育和功能受激素的影响，D错误。 3．(2019·济南重点中学联考)下列关于神经调节的说法错误的是() A．静息状态下，神经纤维膜外带正电、膜内带负电 B．神经纤维受到一定强度的刺激后，细胞膜对Na＋的通透性增加，Na＋内流 C．反射过程中，突触小体内会发生电信号→化学信号→电信号的转变 D．只有保持完整的反射弧结构才能完成反射活动 解析：选C静息电位表现为外正内负，A正确；神经纤维受到一定强度的刺激后，细胞膜对Na＋的通透性增加，Na＋内流，产生动作电位，B正确；反射过程中，突触小体内会发生电信号→化学信号的转变，C错误；反射的结构基础是反射弧，只有反射弧完整，反射 课时跟踪检测（二十九） 数列的概念与简单表示法 (二)重点高中适用作业 A 级——保分题目巧做快做 1．已知数列1,2，7，10，13，…，则219在这个数列中的项数是( ) A ．16 B ．24 C ．26 D ．28 解析：选C 因为a 1＝1＝1，a 2＝2＝4，a 3＝7，a 4＝10，a 5＝13，…，所以a n ＝3n －2.令a n ＝3n －2＝219＝76，解得n ＝26. 2.(2018·郑州模拟)已知数列{a n }满足a 1＝1，a n ＋2－a n ＝6，则a 11的值为( ) A ．31 B ．32 C ．61 D ．62 解析：选A ∵数列{a n }满足a 1＝1，a n ＋2－a n ＝6， ∴a 3＝6＋1＝7，a 5＝6＋7＝13，a 7＝6＋13＝19， a 9＝6＋19＝25，a 11＝6＋25＝31. 3．数列{a n }的前n 项和S n ＝2n 2－3n (n ∈N *)，若p －q ＝5，则a p －a q ＝( ) A ．10 B ．15 C ．－5 D ．20 解析：选D 当n ≥2时，a n ＝S n －S n －1＝2n 2－3n －[2(n －1)2－3(n －1)]＝4n －5，当n ＝1时，a 1＝S 1＝－1，符合上式，所以a n ＝4n －5，所以a p －a q ＝4(p －q )＝20. 4．(2018·湖南湘潭一中、长沙一中等六校联考)已知数列{a n }满足：?m ，n ∈N *，都有 a n ·a m ＝a n ＋m ，且a 1＝12 ，那么a 5＝( ) A.132 B.116 C.14 D.12 解析：选A ∵数列{a n }满足：?m ，n ∈N *，都有a n ·a m ＝a n ＋m ，且a 1＝12 ，∴a 2＝a 1a 1＝14，a 3＝a 1·a 2＝18，∴a 5＝a 3·a 2＝132 . 5．若数列{a n }满足：a 1＝19，a n ＋1＝a n －3(n ∈N *)，则数列{a n }的前n 项和最大时，n 的值为( ) A ．6 B ．7 课时跟踪检测（二十八）原子的核式结构模型 一、单项选择题 1．对α粒子散射实验装置的描述，你认为正确的有( ) A．实验器材有放射源、金箔、带有荧光屏的放大镜 B．金箔的厚度对实验无影响 C．如果不用金箔改用铝箔，就不会发生散射现象 D．实验装置放在空气中和真空中都可以 解析：选A 若金箔的厚度过大，α粒子穿过金箔时必然受较大的阻碍而影响实验效果，B错；若改用铝箔，铝核的质量仍远大于α粒子的质量，散射现象仍能发生，C错；若放置在空气中，空气中的尘埃对α粒子的运动会产生影响，故D错。只有A对。 2．卢瑟福利用α粒子轰击金箔的实验研究原子结构，正确反映实验结果的示意图是( ) 解析：选D 卢瑟福利用α粒子轰击金箔的实验研究原子结构，即α粒子散射实验，实验结果显示：绝大多数α粒子穿过金箔后基本上仍沿原来的方向前进，但是有少数α粒子发生了较大角度的偏转，极少数α粒子的偏转角超过90°，有的几乎达到180°，也就是说它们几乎被“撞了回来”。能正确反映该实验结果的是选项D。 3．在卢瑟福的α粒子散射实验中，某一α粒子经过某一原子核附近时的轨迹如图中 实线所示。图中P、Q为轨迹上的点，虚线是过P、Q两点并与轨 迹相切的直线，两虚线和轨迹将平面分为四个区域。不考虑其他 原子核对该α粒子的作用，那么关于该原子核的位置，下列说法 中正确的是( ) A．可能在①区域 B．可能在②区域 C．可能在③区域 D．可能在④区域 解析：选A α粒子带正电，原子核也带正电，对靠近它的α粒子产生斥力，故原子核不会在④区域；若原子核在②、③区域，α粒子会向①区域偏；若原子核在①区域，可能会出现题图所示的轨迹，故应选A。 4．(福建高考)在卢瑟福α粒子散射实验中，金箔中的原子核可以看作静止不动，下列各图画出的是其中两个α粒子经历金箔散射过程的径迹，其中正确的是( ) 2019-2020年高考数学二轮复习课时跟踪检测二十六理 一、选择题 1．已知直线ax ＋by ＝1经过点(1,2)，则2a ＋4b 的最小值为( ) A. 2 B ．2 2 C ．4 D ．4 2 解析：选B 因为直线ax ＋by ＝1经过点(1,2)，所以a ＋2b ＝1，则2a ＋4b ≥22a ·22b ＝22 a ＋2b ＝22，当且仅当a ＝2b ＝1 2 时等号成立． 2．(xx 届高三·湖南五市十校联考)已知函数f (x )＝x ＋sin x (x ∈R)，且f (y 2 －2y ＋3)＋f (x 2 －4x ＋1)≤0，则当y ≥1时， y x ＋1 的取值范围是( ) A.???? ??14，34 B.??????14，1 C ．[1,32－3] D.???? ??13，＋∞ 解析：选A 函数f (x )＝x ＋sin x (x ∈R)为奇函数，又f ′(x )＝ 1＋cos x ≥0，所以函数f (x )在其定义域内单调递增，则f (x 2 －4x ＋1)≤f (－y 2 ＋2y －3)，即x 2 －4x ＋1≤－y 2 ＋2y －3，化简得(x －2)2 ＋(y －1)2 ≤1，当y ≥1时表示的区域为上半圆及其内部，如图所示．令 k ＝y x ＋1＝ y x －－ ，其几何意义为过点(－1,0)与半圆相交或相切的直线的斜率，斜率最 小时直线过点(3,1)，此时k min ＝ 1 3－－ ＝1 4 ，斜率最大时直线刚好与半圆相切，圆心到直线的距离d ＝|2k －1＋k |k 2＋1 ＝1(k >0)，解得k max ＝3 4，故选A. 3．(xx·石家庄质检)在平面直角坐标系中，不等式组???? ? x ＋y ≤0，x －y ≤0， x 2＋y 2≤r 2 (r 为常数)表示 的平面区域的面积为π，若x ，y 满足上述约束条件，则z ＝ x ＋y ＋1 x ＋3 的最小值为( ) A ．－1 B ．－52＋1 7 C.1 3 D ．－7 5 解析：选 D 作出不等式组表示的平面区域，如图中阴影部分所示，由题意，知14πr 2 ＝π，解得r ＝2.z ＝x ＋y ＋1x ＋3＝1＋y －2x ＋3 ，表 课时跟踪检测(十)短文三篇 (时间：40分钟满分：45分) 一、基础巩固(15分，每小题3分) 1．下列词语中，加点字的注音全都正确的一组是() A．迸．发(bìnɡ)苇．草(wěi) 聚苯乙烯．(xī) 培养皿．(mǐn) B．针灸．(jiù) 畜．牧(xù) 赋．予(fù) 厚赐．(cì) C．不堪．(kān) 惋．惜(wǎn) 弥．补(mí) 囊．括(náng) D．推衍．(yǎn) 轮廓．(ɡuō) 清晰．(xī) 囿．于成见(yòu) 解析：选C A项，“迸”应读bèng；B项，“灸”应读jiǔ；D项，“廓”应读kuò。 2．下列各组词语中，有错别字的一组是() A．消磨禀赋枯燥无味垂暮之年 B．婉约短暂稍纵即逝一衣带水 C．顽石脆弱具有优势一头畜生 D．苦恼磨难基本政策帖近真实 解析：选D D项，帖—贴。 3．下列各句中加点成语的使用，全都不正确的一项是() ①许多事情的真相稍纵即逝 ．．．．，如果无法追索，紧随其后的将是一场近于残酷的良心较量。 ②“五一”小长假第一天，天公作美，风和日丽 ．．．．，不少市民选择中短途旅程，开启愉快的3天假期。 ③事实无情，曾经受消费者爱戴，被人们寄予厚望的，也是“老三样”中年纪最轻的 富康轿车，如今也进入了垂暮之年 ．．．．。 ④从高铁、核电到“一带一路”，中国的国家战略已从韬光养晦 ．．．．转变为“走出去”的负责任大国战略，中国正在为疲软的世界经济贡献力量。 ⑤这次中秋灯展中，我们以灯光营造出满月造型，就像是把钟灵毓秀 ．．．．的月亮搬到家中一样，瞬间让家庭增添了几分童话色彩。 ⑥在中国新诗发展史上，徐志摩的诗可谓独树一帜 ．．．．，他的诗富于想象，意境清新，风格柔美飘逸。 A．①②④B．②③⑥ 高中历史课时跟踪检测（二十八）第3课百日维新（含解析）新 人教版选修1 一、选择题(每小题4分，共24分) 1．晚清有御史上奏称：“近日人心浮动，民主民权之说日益猖獗。若准各省纷纷立会，恐会匪闻风而起，其患不可胜言。”这奏折针对的是( ) A．太平军B．洋务派 C．维新派 D．义和团 解析：选C 解题关键是明确材料的含义，认真分析材料中的信息：“民主民权之说日益猖獗”“若准各省纷纷立会”“其患不可胜言”等，明确民主民权之说是民族资产阶级的主张，故选C项。 2．19世纪末，梁启超呼吁中国应“合汉合满合蒙合回合苗合藏，组成一大民族”。下列维新派在维新变法时期的活动中，体现了此观点的是( ) A．发起“公车上书” B．改革旧的官僚制度 C．组建强学会 D．成立保国会 解析：选D “合汉合满合蒙合回合苗合藏，组成一大民族”体现的是保国思想，D项符合题意。其余各项不符合材料信息。 3．某和约批准后，光绪帝下罪己诏：“去岁仓促开衅……水陆交绥，战无一胜……嗣后我君臣上下，惟当坚苦一心，痛除积弊，详筹兴革。”之后清政府采取的变革措施之一是( ) A．“整理国故，尊孔复古” B．“改革科举，废除八股” C．“立行宪法，大开国会” D．“设置内阁，厘清官制” 解析：选B 戊戌变法改革科举，废除八股，与材料中“嗣后我君臣上下……痛除积弊，详筹兴革”相符，故B项正确。 4．在维新变法高潮时期，光绪帝曾说：“国家振兴庶政，兼采西法，诚以为民立政，中西所同，而西法可补我所未及。”这反映了光绪帝( ) A．同顽固派斗争的决心 B．向西方学习的思想 C．变更国体的主张 D．大兴民权的意向 解析：选B 光绪帝是大清的皇帝，其支持推行变法的目的是为了维护清朝统治权和富国强兵，用西学器物来为大清所用是其本意。 5．戊戌变法将使大小官员连带关系“因之失职失业者将及万人”，这是因为变法规定( ) 课时跟踪检测 （二十） 指 数 层级(一) “四基”落实练 1．计算： －x 3＝( ) A ．x －x B ．－x x C ．－x －x D ．x x 解析：选C 由已知，得－x 3≥0，所以x ≤0，所以－x 3＝ (－x )·x 2＝ －x ·x 2＝ －x ·|x |＝－x －x ，选C. 2．设2a ＝5b ＝m ，且1a ＋1 b ＝2，则m 等于( ) A.10 B ．10 C ．20 D ．100 解析：选A ∵2a ＝m,5b ＝m ，∴2＝m 1a ，5＝m 1b ，∵2×5＝m 1a ·m 1b ＝m 1a ＋1b ，∴m 2＝10，∴m ＝10.故选A. 3．已知a ＞0，将 a 2a ·3 a 2 表示成分数指数幂，其结果是( ) A ．a 12 B ．a 56 C ．a 7 6 D ．a 3 2 解析：选C a 2 a ·3 a 2 ＝a 2÷23·a a ?? ???1 2＝a 526 －＝a 76，故选C. 4．计算(2n ＋1)2·??? ?122n ＋14n ·8 －2 (n ∈N *)的结果为( ) A.1 6 4 B ．22n ＋ 5 C ．2n 2－2n ＋6 D ．????122n － 7 解析：选D 原式＝22n ＋2·2－2n －1(22)n ·(23)－2＝21 22n －6＝27－2n ＝????122n －7. 5．(多选)下列式子中，正确的是( ) A ．(27a 3) 1 3 ÷0.3a － 1＝10a 2 B.2233a b ?? ???－÷1133a b ?? ??? ＋＝a 13 －b 1 3 C.[]()22＋32(22－3)2 1 2 ＝－1 D.4 a 3 a 2a ＝24 a 11 解析：选ABD 对于 A ，原式＝3a ÷0.3a －1＝ 3a 2 0.3 ＝10a 2，A 正确；对于B ，原式＝1111 3333113 3 a b a b a b ???? ???????－＋＋＝a 13－b 13，B 正确；对于C ，原式＝[(3＋22)2(3－22)2] 12＝(3＋ 22)(3－22)＝1.这里注意3＞22，a 12 (a ≥0)是正数，C 错误；对于D ，原式＝ ＝ a 1124 ＝ 24 a 11，D 正确． 6．使等式 (x －2)(x 2－4)＝(x －2)x ＋2成立的x 的取值范围为________． 解析：若要等式成立．需满足x ≥2. 答案：[2，＋∞) 7．计算：(0.008 1) 14 －－????3×????560×130.2527818? ????? ????? ?? －－＋1 2 － －10×(0.027) 13 ＝ ________. 解析：原式＝103－3×????13＋231 2－－3＝－83. 答案：－8 3 8．若a ＝2，b ＞0，则 12 2 12 a b a a b ＋＋(a 12 －b 13 － )(a ＋a 12 b 13 － ＋b 23 － )的值为________． 解析：原式＝a 3 2 ＋b －1＋12a ?? ???3－13b ?? ??? －3＝a 32＋b －1＋a 32－b －1＝2a 32＝2×232＝4 2. 答案：4 2 9．计算下列各式： (1)(－x 13 y 13 －)(3x 12 － y 23)(－2x 16y 23 )； 课时跟踪检测（二十七） 函数的零点与方程的解 A 级——学考合格性考试达标练 1．函数f (x )＝2x 2－3x ＋1的零点是( ) A ．－1 2，－1 B ．12，1 C ．1 2 ，－1 D ．－12 ，1 解析：选B 方程2x 2－3x ＋1＝0的两根分别为x 1＝1，x 2＝1 2，所以函数f (x )＝2x 2－3x ＋1的零点是1 2 ，1. 2．函数y ＝x 2－bx ＋1有一个零点，则b 的值为( ) A ．2 B ．－2 C ．±2 D ．3 解析：选C 因为函数有一个零点，所以Δ＝b 2－4＝0，所以b ＝±2. 3．若函数f (x )的图象是一条连续不断的曲线，且f (0)>0，f (1)>0，f (2)<0，则y ＝f (x )有唯一零点需满足的条件是( ) A ．f (3)<0 B ．函数f (x )在定义域内是增函数 C ．f (3)>0 D ．函数f (x )在定义域内是减函数 解析：选D 因为f (1)>0，f (2)<0，所以函数f (x )在区间(1，2)上一定有零点．若要保证只有一个零点，则函数f (x )在定义域内必须是减函数． 4．在下列区间中，函数f (x )＝e x ＋4x －3的零点所在的区间为( ) A ．(－2，－1) B ．(－1，0) C ．??? ?0，1 2 D ．???? 12，1 解析：选C 因为f (0)＝e 0－3<0，f ????12＝e 1 2 ＋2－3>0，所以函数的零点所在的区间为2020版高考地理课时跟踪检测二十八交通运输方式和布局含解析
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