【www.guakaob.com--高三】
四川省成都市
2015届高三摸底（零诊）考试
物 理 试 题
第I卷（选择题，共42分）
一、本题包括6小题，每小题3分，共18分。每小题只有一个选项符合题意。 1关于物理学史，下列说法正确的是
A奥斯特发现了电磁感应现象
B麦克斯韦提出了狭义相对论
C赫兹首次用实验证实了电磁波的存在
D伦琴利用射线拍摄了首张人体骨骼照片
2关于光现象，下列说法正确的是
A水面上的油膜呈现彩色，这是光的干涉现象
B一束白光通过三棱镜后形成彩色光带，这是光的全反射现象
C．用光导纤维传播信号，利用了光的衍射
D用透明的标准样板和单色光检查平面的平整度，利用了光的偏振
3下列说法正确的是
A穿过线圈的磁通量变化越大，线圈上产生的感应电动势越大
B通过线圈的电流变化越快，线圈的自感系数越大
C．电场总是由变化的磁场产生的
D．真空中的光速在任何惯性系中测得的数值都相同
4做简谐运动的弹簧振子，每次通过平衡位置与最大位移处之间的某点时，下列哪组物理量完全相同
A回复力、加速度、速度 B回复力、加速度、动能 C回复力、速度、弹性势能 D加速度、速度、机械能 5如图所示．L1和L2是输电线，甲、乙是两个互感器，通过观测接在甲、乙中的电表读数，可以间接得到输电线两端电压和通过输电线的电流。若已知图中n1：n2=100：1，n3：n4=1：10,V表示散为220V，A表示数为l．0A，则下列判断正确的是
A甲是电压互感器，输电线两端电压是2 2×104V
B乙是电压互感器，输电线两端电压是2 2×103 v
C甲是电流互感器，通过输电线的电流是100 A
D乙是电流互感器，通过输电线的电流是0．1A
6图为学校自备发电机在停电时为教学楼教室输电的示意图，发电机输出电压恒为220 V，发电机到教学楼的输电线电阻用图中r等效替代。若使用中，在原来工作着的日光灯的基础上再增加教室开灯的盏数，则
A整个电路的电阻特增大，干路电流蒋减小
B因为发电机输出电压恒定，所以原来工作着的日光灯的
亮度将不变
C发电机的输出功率将减小
D．输电过程中的损失功率（即输电线路消耗的功率）将增大
二、本题包括6小题，每小题4分，共24分。每小题给出的四个选项中，有的只有一个选
项正确，有的有多个选项正确，全部选对的得4分，选对但不全的得2分，有选错的得0分。
7图甲是一台小型发电机的构造示意图，线圈逆时针转动，产生
的电动势e随时间t变化的正弦规律图像如图乙所示。发电
机线圈的内电阻不计，外接灯泡的电阻为12Ω。则
A．在t=0．01 s时刻，穿过线圈的磁通量为零 B
电压表的示数为 C灯泡消耗的电功率为3W
D若其它条件不变，仅将线圈的转速提高一倍，则线圈电动势
的表达式
t（V）
8一列简谐横波在t=0．4 s时刻的波形如图甲所示，波传播方向
上质点A的振动图像如图乙所示。则
A该波沿x轴负方向传播
B该波的波速是25 m／s
C任意0 ．4 s内，质点A通过的路程均
为10m
D从此时刻起，质点P将比质点Q先
回到平衡位置
9 2014年3月8日，“马航”一架飞往北京的飞机与地面失去联系。人们根据赤道上同步
卫星接收到的该飞机飞行时发出的“握手”电磁波信号频率的变化，利用电磁渡的多普勒效应，确定了该飞机是在向南航线而非向北航线上失踪、井最终在南印度洋坠毁的。若该飞机发出的“握手”电磁波信号频率为fo,且飞机黑匣子能够在飞机坠毁后发出37．5 MHz的电磁波信号，则以下说法正确的是
A．飞机由北向正南方向飞向赤道的过程中，同步卫星接收到的“握手”电磁波频率小
于fo
B．飞机由北向正南方向飞向赤道的过程中，同步卫星接收到的“握手”电磁波频率大
于fo
C．黑匣子发出的电磁波信号在由海水传到空气中时，频率将变大
D．黑匣子发出的电磁渡信号在由海水传到空气中时，波长将变长
10如图所示，块上、下表面平行的玻璃砖的厚度为L，玻璃砖的折射率
n=
表面AB射入的人射角i=60°，光在真空中的光速为c，则
A折射角r=30°
B
光在玻璃中传播的时间为
C光在玻璃中传播的时为L 3c2L c
D改变入射角i，光在下表面CD可能发生全发射
11甲图中a、b是电流相等的两直线电流，乙图中c，d是电荷量相同的两正点电荷，O为
两电流（或电荷）连线的中点，在o点正上方有一电子，“较小的速度v射向O点，不计重力。关于电子的运动，下列说法正确的是
A甲图中的电子将做变速运动
B乙图中的电子将做往复运动
C乙图中的电子在向O点运动的过程
中，加速度一定在减小
D．乙图中的电于在。点动能最大，电势能最小
12．如图甲所示，虚线右侧存在匀强磁场，磁场方向垂直纸面向外，正方形金属框电阻为R，
边长为L，t=0时刻，线框在外力作用下由静止开始、以垂直于磁场边界的恒定加速度a进人磁场区域，t1时刻线框全部进入磁场。规定顺时针方向为感应电流i的正方向，安培力大小为F，线框中电功率的瞬时值为P，通过导体横截面的电荷量为q，其中P—t图线为抛物线。则图乙所示i、F、P、q随时间t变化的关系图线正确的是
第Ⅱ卷（非选择题，共58分）
三、本题共2小题，共15分。
13（4分）下列说法正确的是____和____。（填选项序号字母）
A利用双缝干涉相邻两亮条纹的间距△x与双缝间距离d及光的波长的关系式△
x
l，可以测量光的波长 d
a计算相邻亮条纹间距 nB在“用双缝干涉测量光的波长”实验中，为了减小相邻条纹间距的测量误差，应测出从第1依次至第n条亮条纹间的距离a，然后利用公式△x
C在“用单摆测重力加速度”实验中，计时的起点应该选在摆球运动到最高处，因为此
时摆球速度最小
D．在“用单摆测重力加速度”实验中，若摆长的长度只考虑了摆线的长度，则加速度
的测量值较真实值偏小
14．（11分）欲测量只G表的内阻rg和一个电源的电动势E内阻r。要求：测量尽量准确、能测多组数据且滑动变阻器调节方便，电表最大读数不得小于量程的1/3。待测元件及提供的其他实验器材有
A待测电源E：电动势约l．5V，内阻在0．4—0．7Ω间
B待测G表：量程500 μA，内阻在150～250Ω间
C电流表V:量程2A，内阻约0 1Ω
D电压表v：量程300 mV，内阻约500Ω
E定值电阻R0：R0=300Ω；
F滑动变阻器R1：最大阻值10Ω，额定电流lA
H电阻箱R2:0~9999Ω
J开关S一个，导线若干
（1）小亮先利用伏安法测量G表内阻ra。 ①图甲是小亮设计的实验电路图，其中虚线框中的元件是；（填元件序号字母） ②说明实验所要测量的物理量 ; ③写出G表内阻的计算表达式rg
（2）测出rg=200Ω后，小聪把G表和电阻箱R2串联、并将R2接入电路的阻值调到
2800Ω，使其等效为一只电压表，接着利用伏安法测量电源的电动势E及内阻r。 ①请你在图乙中用笔画线，将各元件连接成测量电路图，
②若利用测量的数据，作出的G表示IG．与通过滑动变阻器R1的电流I的关系图像如
图丙所示，则可得到电源的电动势E= v,内阻r= Ω。
四、本题共4小墨，共43分。解答应写出必要的文字说明、方程式和重要演算步骤·只写
出最后答案的不能得分，有数值运算的题，答案中必须明确写出数值和单位。
15（8分）如图所示，电荷量Q=2×l0-7C的正点电荷A固定在空间中O点，将质量m=2×
10-4 kg、电荷量q=1×l0-7 C的另一正点电荷B从O点正上方高于0 5m的某处由静止释放，B运动过程中速度最大位置在P。若静电力常量k=9×109 N．m2／C2，重力加速度g=10 m／s2。求
（1）B运动到距O点l=0．5 m处的加速度大小；
（2）P、O间的距离L。
16（8分）图甲所示的电视机显像管能够通过磁场来控制电子的偏转，显像管内磁场可视为圆心为O、半径为r的匀强磁场。若电子枪垂直于磁场方向射出速度为vo的电子，由P点正对圆心O射入磁场，要让电子射出磁场时的速度方向与射入时的速度方向成θ角（图乙）．已知电子的质量为m，电荷量为e，不计电子的重力。求：
（1）磁感应强度大小；
（2）电子在磁场中运动的时间。
（结果用m、e、r、θ、vo表示）
17．（13分）如图所示，MN和PQ是平行、光滑、间距L=0．l m、足够长且不计电阻的两
根竖直固定金属杆，其最上端通过电阻R相连接，R=0．5 Ω．R两端通过导线与平行板电容器连接，电容器上下两板距离d=l m。在R下方一定距离有方向相反、无缝对接的两个沿水平方向的匀强磁场区域I和Ⅱ，磁感应强度均为B=2 T，其中区域I的高度差h1=3m，区域Ⅱ的高度差h2=lm。
现将一阻值r=0．5Ω、长l=0．l m的金属棒a紧贴MN和PQ，从距离区域I上边缘h=5
m处由静止释放;a进入区域I后即刻做匀速直线运动，在a进入区域I的同时，从紧贴电容器下板中心处由静止释放一带正电微粒A。微粒的比荷q20C/kg,重力加速度m
g=10 m/s2．求
（1）金属棒a的质量M，
（2）在a穿越磁场的整十过程中，微粒发生的位移大小x。
（不考虑电容器充、放电对电路的影响及充、放电时间）
成都市2013级高中毕业班摸底测试
英语
本试卷分选择题和非选择题两部分。第I卷（选择题）1至8页，第II卷（非选择题）第9至10页，共10页；满分150分，考试时间120分钟。
注意事项：
1. 答题前，务必将自己的姓名、考籍号填写在答题卡规定的位置上。
2. 答选择题时，务必使用2B铅笔将答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦擦干净
后，再选涂其他答案标号。
3. 答非选择题时，务必使用0.5毫米黑色签字笔，将答案书写在答题卡规定位置上。
4. 所有题目必须在答题卡上作答，在试卷上答题无效。
5. 考试结束后，只将答题卡交回。
第I卷（100分）
第一部分 听力（共两节，满分30分）
做题时，先将答案标在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节 （共5个小题；每小题1.5分，满分7.5分）
听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。
1. What was the original price of the T-shirt?
A. $ 14. B. $ 28. C. $ 40.
2. What will Jessica do on the weekend?
A. Work on her paper. B. Make some plans. C. Go shopping.
3. What has the man decided to do on Saturdays?
A. To meet a friend. B. To visit an exhibition C. To attend a wedding.
4. Where are the two speakers?
A. In a classroom. B. At a hotel. C. In a store.
5. When does the bank close on Saturday?
A. At 9:00 pm. B. At 5:00 pm C. At 4:00 pm.
第二节 （共15个小题；每小题1.5分，满分22.5分）
听下面5段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟。听完后，各小题给出5秒钟的作答时间。每段对话或独白读两遍。
听第6段材料，回答第6至第7题。
6. What do we know about Nora?
A. She lives near the central bus station.
B. She likes to work with other girls.
C. She prefers a room of her own.
7. What is good about the flat?
A. It has a big kitchen.
B. It has good furniture.
C. It has a large sitting room.
听第7段材料，回答第8至第9题。
8. Where has Barbara been?
A. Florence. B. Milan. C. Rome.
9. What has Barbara got in her suitcase?
A. Stones. B. Books. C. gifts.
听第8段材料，回答第10至第12题。
l0. Who is making the telephone call?
A. Jack Cooper. B. Thomas Jerry. C. Leman Brothers.
11. What is the message about?
A. A visit to England. B. The date for a trip. C. A business meeting.
12. What relation is the woman to Mr. Cooper?
A. His secretary. B. His boss. C. His wife.
听第9段材料，回答第13至第16题。
13. What color was the small car?
A. Orange. B. Green. C. yellow.
14. What was Mrs. Franks doing when the accident took place?
A. Getting ready to cross the road.
B. Walking along York Avenue.
C. Standing outside a hotel.
15. How did the accident happen?
A. A bank clerk rushed into the street.
B. A car ran into a lorry.
C. A lorry hit a car.
16. Who could the man speaker most probably be?
A. A police officer.
B. The driver of the lorry.
C. A person who saw the accident.
听第10段材料，回答第17至第20题。
17. What is the talk mainly about?
A. The plan for the day.
B. The history of the school.
C. The courses for the term.
18. Where can the visitors learn about the subjects for new students?
A. In the school hall.
B. In the classrooms.
C. In the science labs.
19. What can students do in the practical areas?
A. Attend workshops.
B. Take science courses.
C. Enjoy excellent meals.
20. When are the visitors expected to ask questions?
A. After the welcome speech.
B. Before the tour of the labs.
C. During the lunch hour.
第二部分 阅读理解（共两节，满分40分）
第一节 （共15小题；每小题2分，满分30分）
阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上将该项涂黑。
A
Thanks for signing up for the 2014 Black Friday Turkey Trot! This email will provide some basics about the race and some great news!
First, your race packet (参赛物品包) is ready and can be picked up at the Fleet Feet Sports Tulsa location you‟ve specified during registration.
Hours for pickup.
Tuesday, 10 am to 8 pm (Fleet Feet Kings Point)
Tuesday, 10 am to 7 pm (Fleet Feet Blue Dome)
Wednesday, 10 am to 5 pm (both stores, closing early for Thanksgiving)
Packets can also be picked up on the race day at BOK Center, beginning at 8:30 am.
Race Start Times
1) 5 mile, 8:30 am 2) 1 mile fun run, 9:30 am
Parking
There is surface parking to the east of the BOK Center, and some surface parking to the west of the Convention Center. Many lots will be pay-lots. Please pay attention to the signs. We suggest arriving early to find parking. Racing Timing
The 5 km run will be timed using the BIB-TAG system. Your race number will have a timing device attached to the back of the race number; don‟t remove or bend this device. Simply wear the Bib on the front of your body on the outside of your clothing so it is visible and facing forward. You don‟t need to return the Bib, which is disposable.
The Turkey Trot is also a kick-off event for our weekend long “FITNATIC” celebration---we also have a huge number of events and specials all weekend. For more information, please visit .
See you on Friday.
21. Where should a runner go to pick up his packet at 8:30 am on Friday?
A. Kings Point. B. Convention Center. C. Blue Dome D. BOK Center
22. How long will the FITNATIC celebration last?
A. Seven days. B. Five days C. Two days D. One day.
23. What is the purpose of the passage?
A. To attract sports fans to apply for the activity.
B. To inform the race participants of the activity.
C. To describe details related to the activity.
D. To collect money for the parking-lots.
B
More than 2.25 billion cups of coffee are drunk throughout the world each day, and it‟s likely that many taste bitter. Now, a new study suggests that coffee fans can make their drink sweeter by changing the color of their cups.
Researchers from Oxford set out to prove whether the claim that coffee drunk from a white cup tastes biter was true. They used 36 volunteers and three different colored cups---blue, white and transparent glass--- to examine the claim.
In one experiment, the white cup increased the intensity (浓度) of the coffee taste relative to the transparent cup. Then, in a second experiment, coffee drunk from the white cup was found to taste less sweet when compared to the other colored cups, while the blue cup made the coffee taste the sweetest.
The scientists believe that the color brown may be associated with bitterness, and coffee in a white cup appears the brownest.
“Our study clearly shows that the color of a cup does influence our sense of the coffee taste,” leading author Dr.
George Doorn, wrote in an article for The Conversation. “The effect of the color of the cup on the taste of the coffee reported here suggests that cafe owners should carefully consider the color of their cups,” he said. “The potential effects may spell the difference between a one-time purchase and a return customer.”
Actually, the idea that color can change the food and drink taste came out many years ago. A study published last year reported that red, strawberry-flavored cake served on a white plate was rated as 10 percent sweeter than the same food presented on a black plate.
24. The passage is mainly about _____.
A. the popularity of sweet coffee. B. an experiment made in Oxford.
C. the effect of cup color on coffee‟s taste D. useful tips on how to make coffee.
25. In which cup will coffee taste the sweetest?
A. A white cup. B. A blue cup. C. A transparent cup D. A brown cup
26. Café owners should consider their cups‟ color in order to ______.
A. reduce the daily expenses B. show their taste in coffee
C. appeal to more customers D. make their café different.
27. We learn from the passage that_____.
A. coffee in a white cup tastes sweeter than that in a transparent glass
B. over 2 billion cups of sweet coffee are drunk worldwide each year.
C. Dr. George Doorn wrote an article about making conversations.【2016年成都零诊试题及答案】
D. the idea that color could affect the taste of drink is not new.
C
We should feel grateful in our heart when we accept anything others sacrifice for us. However, we often unconsciously do the opposite, which may not be regarded as returning kindness with ingratitude, but have the equal power to harm each other. In particular, the closer the relationship is, the more determined we are.
Jennifer, my friend Randy‟s mother, is already over 70, poor eyesight and weak legs. But due to her character, she chose to live alone in the suburbs. No matter how busily Randy works, he would go there to visit her once or twice every week.
That day as soon as he parked his car, Randy smelt the delicious smell of meat coming from her mother‟s house. His mother said, “Your birthday is coming next week, so I‟m preparing pork trotters (猪蹄) for you!” Seeing the steaming delicious trotters, he couldn‟t help complaining, “I don‟t like these things at all, so fatty.”
On his way back, he called me, saying that he felt sorry. In fact, he longed to thank his mother and eat up that bowl of trotters. But he felt sorry that it took her too much time and energy. If he didn‟t stop her strictly, he was afraid the same thing would continue. He would rather not eat trotters any more than have his mother overwork. I understand how he felt exactly. Each of us has done like that. Because of feeling sorry for others‟ sacrifice, we purposely harden our heart against accepting others‟ favor and even criticize them severely in order to frighten their goodness away and make them never do that again.
This method may work, but it will hurt each other‟s feelings. It‟s not wrong logically, but we always neglect another sound deep in our heart: because we‟re afraid we can‟t repay them, we‟re unwilling to shoulder others‟ goodness. So we reduce its value and refuse it severely. But to destroy others‟ goodness is also to deny you.
28. Randy refuse to eat the pork trotters his mother cooked because ____.
A. he disliked them at all B. they were really very fatty.
C. they weren‟t his favorite taste D. he didn‟t want her to overwork.
29. Randy telephoned the author to _____.
A. express his apology to his mother B. complain about his mother
C. apologize for his rudeness D. ask for a bowl of trotters.
30. According to the author, we sometimes say “no” to others‟ favor so that ______.
A. they can be frightened away B. they won‟t continue doing that
C. we needn‟t repay them later D. we won‟t feel sorry for their sacrifice
31. In the last paragraph, the author implies that we should ____.
A. refuse others‟ favor immediately B. deal with others‟ favor wisely
C. repay others‟ goodness actively D. shoulder others‟ goodness completely.
D
For a while, I wrote a “Tuesday tip” on my blog Lyonsdenmom.com. It was about easy week-night dinners, organizing parties or perhaps finding time out for friends.
About a year ago, I ran out of tips.
The truth? As a busy working mom with five busy kids, I probably do have a few tips to share. But honestly, the bar is set pretty low---on a recent day when I was walking our dog, a stranger who knew I had five kids said, “Wow! You have a dog, too?! And it even looks like you showered today!” Yes, it‟s true, I shower. Not every day, but most days. See, I‟m telling the truth. Honestly, in this cold winter, I‟m probably taking a shower more to warm up than to clean up.
Other funny truths? I‟m tired. In fact, for the past year, I‟ve been too tired to type up any update on our life here in Lyons Den. It‟s hard to arrange a career with all these kids. Although folks just believe that it must be so much easier now since all the kids are in school, I‟m here to tell you, it‟s not. It‟s really not. When I get home from work, I‟m often tearfully greeted by five kids and five homework folders filled with math facts, invitations, notices and artwork.
All those happy smiling faces I share on Facebook are real. We are a happy family---thank God for that! But we‟re not always smiling, and even in those rare best times when I can get all five kids looking at the camera, the would be that one of them isn‟t wearing underwear, one is pinching (捏) someone behind the scenes and one is just perfectly pronouncing “Damn!” So, less perfectly-posed pictures, but more telling the truth. Even if only on Tuesday.
32. It seems that the author‟s life used to be _____.
A. tiring B. busy C. relaxing D. funny
33. Which of the following is true about the author?
A. She can‟t get along well with her neighbors.
B. She‟s living a happy life with her family
C. She likes to have a shower every day.
D. She has already closed her blog now.
34. Which of the following words can best take the place of the word ?
A. answers. B. chances. C. solutions D. ways.
35. The passage mainly talks about _____.
A. the happiness of a working mother B. the worry of a working mother
C. the hardship of a working mother D. the bittersweet of a working mother
第二节 （共5小题；每小题2分，满分10分）
根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。
People tend to become more personal and hide less of themselves when using email. Some Britain researchers have found in a recent study that there are good reasons for this.
The team of researchers asked 83 pairs of students, all strangers to each other, to solve a problem. They had to discuss this question: ___36____ The pairs of students had to talk over the problem either face to face or by computers. Dr. Johnson said, “They told their partners four times as much about themselves when they talked over the Internet as when they talked face to face. When the computers were fitted with cameras so that students could see each other, this limited the personal side of the conversation.”
___37___ It was mainly about things such as where they went to school, or where they used to live. But some students discussed their love stories, and personal childhood experiences.
Dr. Johnson believes that emailing encourages people to focus on themselves. __38__ “If you cannot see the
成都市零诊考试（文科数学）复习（二）：解答题训练
【基础训练】
17．（本小题满分12分）在ABC中，角A、B、C所对的边为a、b、c，且满足
cos2Acos2B2cosAcosA
66
（1）求角B的值； （2）若b
1
且ba，求ac的取值范围．
2
19．（本小题满分12分）如图，在底面为梯形的四棱锥SABCD中，已知AD//BC，
ASC60
，ADDCSASCSD2．
（Ⅰ）求证：ACSD； （Ⅱ）求三棱锥BSAD的体积．
A
S
23．（本小题满分10分）选修4－4：坐标系与参数方程 以直角坐标系的原点O为极点，以x轴正半轴为极轴，
B
C
D
建
立极坐标系，曲线C1的极坐标方程为4cos(0)，曲线C2的参数方程为
xmtcos
0（为参数），已知射线，，与曲线C1t
ytsin44
分别交于（不包括极点O）点A,B,C.
（Ⅰ）求证：OBOC（Ⅱ）当
.
12
时，B,C都恰在曲线C2上，求m与的值.
【压轴题训练：导数及其应用】
21．（本小题满分12分）已知aR，函数f(x)
131
x(a2)x2b，g(x)2alnx. 62
（Ⅰ）若曲线yf(x)与曲线yg(x)在它们的交点(1,c)处的切线互相垂直，求a,b的值； （Ⅱ）设F(x)f(x)g(x)，若对任意的x1,x2(0,)，且x1x2，都有
F(x1)F(x2)a(x1x2)，求a的取值范围．
【参考答案】
17． 解：（1）由已知cos2Acos2B2cos
AcosA 66
得2sin2B2sin2A2cos2A（2）因为ba，所以B
3
4
12sin4
2
化简得sinB 故B或． A ，
33
3
，
由正弦定理
acb
sinAsinCsinB
2，得a=2sinA,c=2sinC，
12ac2sinAsinC2sinAsinA
23
3sinAAA26
因为ba，所以
3
A
2
,A，
3662
所以a
1
cA． 26
19．解：（Ⅰ）设O为AC的中点，连接OS,OD，SASC,OSAC
DADC,DOAC,
又OS,OD平面SOD，且OSDOO，
AC平面SOD，又SD平面SOD ACSD
（Ⅱ）连接BD，在ASC中，SASC,ASC60，O为AC的中点，
ASC为正三角形，且AC2,OS【2016年成都零诊试题及答案】
在ASC中，DA2DC24AC2，O为AC的中点， ADC900，且OD1，
在SOD中，OS2OD2SD2 SOD为直角三角形，且SOD900 SOOD又OSAC，且ACDOO
SO平面ABCD
1
VBSADVSBADSBADSO
3
1111ADCDSO3232
23.解：（Ⅰ）依题意OA4cos，OB4cos(
)，OC4cos()；
44
OBOC4cos()4cos()
44
sin)sin) （Ⅱ）当
12
时，B,C
两点的极坐标为(2,
),化为直角坐标为36
(1
所以经过点B，C
的直线方程为yx1)，而曲线C2是经过点(m,0)且倾斜角为的直线，故m2,21．解 (1)f(x)
2
。 3
123x(a2)x，f(1)a 22
g(x)
2a
，g(1)2a x
依题意有f(1)g(1)1，且f(1)g(1)，
32a(a)11172可得，解得a1,b，或a,b.
113212(a2)b062
(2) F(x)
12
x(a2)x2alnx. 2
不妨设x1x2,F(x1)F(x2)a(x1x2) ， 等价于F(x2)ax2F(x1)ax1. 设G(x)F(x)ax，
则对任意的对任意的x1,x2(0,)，且x1x2，都有
F(x2)F(x1)
a，
x2x1
等价于G(x)F(x)ax在(0,)上是增函数．
G(x)
12
x2alnx2x， 2
2ax22x2a2可得G(x)x， xx
依题意有，对任意x0，有x22x2a0恒成立． 由2ax22x(x1)21，可得a
1
. 2
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