2019届湖南省长沙市铁路一中高三上学期第三次阶段性测试5科6套.docx

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1、2019届湖南省长沙市铁路一中高三上学期第三次阶段性测试理科数学试题审题：高二数学组时量：120分钟总分值：150分一、填空题（共12小题，每题5分）1.设集合A = 2nx = %,假设Ac5 = 0,那么y的值为（）A. 0 B. 1 C. e D. 22.2.复数Z满足z =-（，为虚数单位），那么复数Z所对应的点所在象限为（）A.第一象限l + iB.第二象限C.3 .以下命题中，是假命题的是A. X/x O, x In xC. w R, sin xo + cos x（）=第三象限D.第四象限（ ）B. tan = 201 6D.X/x三开蛤）,jr4,以下函数中，最小正周期为兀，且图

2、象关于直线工=2对称 3的是（）jrX TTA y - sin（2x + ） B y - sin（+ ）62 3JTTTC y = sin（2x） D y = sin（2x）365 .如右图，给出了一个程序框图，其作用是输入工的值，输出 相应的y的值,假设要使输入的x的值与输出的y的值相等，那么这 样的工的值的集合为（）A.0 B.1,3 C.0,l,3 D.0,36 .直线。与直线垂直，。平行于平面那么 与平面a的位置关系是（）A. bllaB. buaC. 6与平面。相交D.以上都有可能7.某几何体三视图如右，其中三角形的三边长与圆的 直径均为2,那么该几何体体积为（）人 32 + 863

3、2 + V3A. 71B. 713322.解：(1)由 y = 3 + Jf+8x 15 得(y 3=1(x-4)2(yN3),即(x_4+(y_3)2=l(yN3),故曲线。的一个参数方程为f = 4 + cos。(。为参数，且夕40,司).y = 3 + sin。L (2)由(1)可知点 P的坐标为(4 + cos6 , 3 + sin0) , 0eO 9 司,那么矩形QAPB 的周长为C = 2(4 + cos6 + 3 + sine) = 14 + 2虚sin，+ wj，A Cg12 , 14+2V2 八八 1八兀 兀 57r . (n Ji /271 9 0 g ， 9 sin 0H

4、G9 1L 4 144(4j223.解：因为该函数的定义域为R,所以|x+l| + |x3|一论0恒成立.设函数g(x) = |x+ l|+|x3|,那么m不大于函数g(x)的最小值,又|x+l| + |x3闫Q+l)Q3)|=4,即g(x)的最小值为4,所以2二4.2所以7日+4方=所以7日+4方=(7白+48), (-+ 十D/、， 21 、(6打+28+&+2匕)(；7工+一T7I) Ja-r b a-r Zb4. 2 (3占+方), 2 (a+2b)a+ 2b 3a+ b5 + 4 9 4 0nn3 1 士 r、当且仅当a+2b=3a+b,即方=2后寸，等号成立.9所以7好的最小值为*

5、2019届湖南省长沙市铁路一中高三上学期第三次阶段性测试文科数学试题命题人:霍菁琰审题人哨雅文时量：120分钟总分：150分一、选择题：本大题共12个小题，每题5分，共60分.在每题给出的四个选项中，只有一项为哪一项符合题目要求的.1-集合A = 九_4。,B = x-1x O, x In xC. e 7?, sin X。+ cos = 3B.3jco e 2?, tan jvo = 2016 DWx e R 2 O4. x3”是 ln(x2)0）的右顶点人作斜率为-1的直线/,该直线与双曲线的两条渐近线的 1 交点分别为民C,假设A8 = BC,那么此双曲线的离心率是（） 2A.叵 B. V

6、3 C. 2 D. V52实数机的值为二、填空题：本大题共4小题，每题5分，共20分.设向量2 = （2,根），B = （l, 1）,假设BJL0 + 2B）,那么x+ y5.假设实数满足 xe J, x 1,.设函数= 1 i那么使得/（x）W2成立的x的取值范围是.%*一. 1,41r-I16、假设两个正实数满足一方+刀=1,且 6 +N疗一6加恒成立，那么实数机的最大值是.三、解答题（本大题共6小题，共70分，解容许写出文字说明，证明过程或演算步骤）17.(本小题总分值 12 分)函数/(x) = 2cos? x + J5sin2x + Q (xR).假设/(%)有最大值2,求实数a的值

7、；求函数/(%)的单调递增区间.18.(本小题总分值12分) 是等差数列，其前项和为包是等比数列，且 % = b、= 2 , % + % = 27 , S4 Z?4 = 10 .(1)求数列4与的通项公式;(2)求北+。2b2 +。也的值19.(本小题总分值12分) ABC的内角A , B ,C的对边分别为a, b ,ccsinFeos=221 + e C e (0, ), a cos B + bsin A = 2 22(1)求 ABC的外接圆的而积S； (2)求a+b的取值范围。22二十与 =1(。人0)的离心率为 a b20.(本小题总分值12分)点A(0,2),椭圆：,尸是椭圆的右焦点，

8、直线Ab的斜率为空，O 23(1)求椭圆的标准方程；(2)设过点A的动直线/与椭圆E相交于P,Q两点，当AP。的面积最大时，求直线/的方程.为坐标原点.21.(本小题总分值12分)函数 /(%) =(6Z-)x2 +ln x(a e R).（1）当 =1时，求函数/（x）在区间l,e上的最大值和最小值；（2）假设在区间（1,”）内，函数/（x）的图象恒在直线y = 2狈下方，求实数。的取值范围.22.（本小题总分值10分）在直角坐标系X0V中，曲线G的参数方程为卜= 6csa，（a为参数）,以坐标原点为极点，以工轴的y = sin a,正半轴为极轴，建立极坐标系，曲线。2的极坐标方程为夕sin

9、（6 + ；） = 2夜.（I ）写出G的普通方程和G的直角坐标方程；（H）设点P在C上，点Q在C,上，求|PQ|的最小值及此时P的直角坐标.长铁一中2018下期高三第三次阶段性测试数学（文科）试卷答案题号123456789101112答案CACBADCBCBCD二、填空题2013. 614.15. x816.8三、解答题17.解：(D/(x) = 2cos2 x + 6sin2x + a = l + cos2x + Vsin2x + a = 2sin(2x + ) + l +(7 ,6TT TT当2xd=卜2k/i (kZ)时，/(x)有最大值，6 2JT即x = k兀(kZ)时，/(x)有

10、最大值为3 + a, .3 + a=2,解得。=1； 6令一三+ 2左左 2x +上 + 2左，26 2JT7T解得人乃 x 4 = (t? + /?)2 - 3ab?(a + /?)2 -3(a-rb, i71V Ce 0, - , ：.C = -2)由正弦定理知：2Rsin Acos B + 27?sin Bcos A = 27?sin(A + B) = 2/?sin C = c = 2 ,.上=2=迪=2心毡 sin C c = 2 ,另解:由正弦定理知 =嘉=华一券si,笄inB,4J3/. q + b = (sin A + sin B),而 sin A + sin B = sin A

11、 + sin1时.，从而I PQ1= ViTF |x,-x9|= 4芈 二 -4% +12又点。到直线PQ的距离d= /.，左2 + 114、4k2 .3 AOPQ 的面积为 S.PQ =-PQd= J，乙J K I 1设,4/3 =1(),4?444那么 Sopq- = -(), 2.当AOP。的面积最大时，/的方程为y =2或丁 =1 0 . 1(1)当 a = 10寸，/Xx) = x+lnx , f (x) = x + = 2xx - 2 2x2+lX对于xwl,0,有f(x)0, /(x)在区间1,0上为增函数,e1，/(X)min = /=；(2)令 g(x) = /(x) - 2

12、ax -a- -)x2 -2ax + nx ,那么 g(x)的定义域为(0,+oc).在区间(l,+oo)上，函数于(x)的图象恒在直线y = 2以下方等价于g(x) 0在区间(1,+8)上恒成立.，/、 I、 c 1(26z-1)x2-2 + 1(-1)(26z-1)x-1g (x) = (2a-l)x-2a + - = -=-假设a/ 2假设a/ 2，令g(x)=。，得极值点为=1, %2 =!2a-1当 2斗=1，即时，在(%2，+)上有 g(X)0 .此时，g。)在区间(,+8)上是增函数，并且在该区间上有g(X)(g(X2)，+8)，不合题意;当入2西=1，即时，同理可知，g(X)在

13、区间(1,收)上，有g(X)(g(l),+8),也不合题意;假设那么有2a 140,此时在区间(l,+oo)上恒有g(x)0.从而g(X)在区间(1,+00)上是减函数.要使g(x) 0在此区间上恒成立，只需满足g(l) = -a-由此求得。的范围是2 2综合可知，当时，函数/(x)的图象恒在直线y = 2以下方.2X2 922 ( I)g的普通方程为一+y =1，G的直角坐标方程为%+y4 =。.(II)由题意，可设点尸的直角坐标为(百cosa,sina),因为G是直线，所以| PQ |的最小值即为P到G的距离d(。)的最小值，d(a) =G的距离d(。)的最小值，d(a) =| a/3 c

14、os a + sin。- 41=a/2 I sin( + )-2|.3绝密启用前长铁一中2019届高三第三次阶段性测试考前须知:4 + V304 + 373C.兀D, 兀338、曲线y = /和曲线丫 =五围成一个叶形图(如下图阴影局部)，其面积是()1A. 1B. tC.乎D. 1.分配4名水暖工去3个不同的居民家里检查暖气管道.要求4名水暖工都分配出去，并每名水暖工只去 一个居民家，且每个居民家都要有人去检查，那么分配的方案共有()A. 种 B. 种 C. 种 D. 种.抛物线x2 = -4y的准线与双曲线二二二1(。 0/ 0)的两条渐近线围成一个等腰直角三角 cr b形，那么该双曲线的

15、离心率是()A. V5B. 5C. V2D. 29 .如图，在AA8C中，AD AB.BC = 3BD.AD = 1 ,那么 恁而 的值为()A. 1B. 2C. 3D. 4.定义在R上的函数/(x)满足/(4) = 1, /(x)为函数/(x)的导函数，已Z? +1知/(x)的图像如下图，假设两个正数满足/(2。+31,那么 的 a + 1取值范围是()A 4,5) B. (J!)C(-8!55,+8)D(f,3)二、填空题：(此题共4小题，每题5分，共20分)TT 7T10 .假设函数/(x) = cos2x + asinx在区间(一,一)是减函数，那么。的取值范围是6 211 .假设(x

16、 + 工)展开式的二项式系数之和为64,那么展开式的常数项为 x1 .答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。2 .回答选择题时，选出每题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦 干净后，再选涂其他答案标号。回答非选择题时，将答案写在答题卡上，写在本试卷上无效。3 .考试结束后，将本试卷和答题卡一并交回。第一局部听力（共两节，总分值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小题；每题1.5分，总分值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三个选项中选出最正

17、确选项。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 time is it in New York?C. Its 10:00 pm.A. Its 5:00 pm.B. Its 7:00 pm.2. What do we know about the man?A. He dialed the wrong number.B. He was looking for Philips.C. He invited the woman to have ice cream.3. What does the man think is important?A

18、. To be unexpected.B. To enjoy every song.4. What may lead to the man finding no job?A. His age.B. His living address.5. Why isnt the mans brother bringing Jennifer to the party?A. They are divorced now.B. They live very far away.第二节（共15小题；每题1.5分，总分值22.5分）C. To get what you expect.C. His email addre

19、ss.C. Jennifer broke her leg.C.C.C. They are lovers.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三个选项中选出最正确选项, 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，每题5秒钟;听完后各小题将给出 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、7题。6. Where might the woman usually study?A. In the library.B. At home.In the lab.7. What is the mans major?A. Psycho

20、logy.B. Physics.Maths.听第7段材料，回答第8、9题。8. What is the relationship between the speakers?A. They are brother and sister.B. They are roommates.9. Why didnt the man invite the woman at first?A. He was embarrassed about her presence.B. He thought she had other plans.C. He wanted her to go out with her fri

21、ends. 听第8段材料，回答第10至12题。10. What is the name of the cat?A. Alice.B. Lola.C. Jenny.11. What is Alices advice for the pregnant woman?A. Name her baby what she wants.B. Make her sister get another cat.C. Find another name for her baby.12. Why does the woman read the advice page?A. To feel better about h

22、erself.B. To get good advice.C. To be entertained.听第9段材料，回答第13至16题。13. How many people went on the trip together?A. Four.B. Twelve.C. Eighteen.14. According to the man, what is most important on family trips?A. Having some privacy.B. Spending time with the children.C. Visiting as many places as poss

23、ible.15. What is the closest city to where the man stayed?A. Cordoba.B. Madrid.C. Sevilla.16. How does the man feel about the trip now?A. Quite tired.B. Very grateful.C. A littledisappointed. 听第10段材料，回答第17至20题。17. Who is the intended audience of this announcement?A. Staff at childrens organizations.

24、B. Young people who want to volunteer.C. People who have given money in the past.18. How much money of the donations will go to services this year?A. 85 %.B. 95 %.C.100%.19. Which program would be funded by this foundation?A. After-school programs.B. Future career planning.C. Computers for preschool

25、 students.20. What type of support does the foundation want?A. Equipment only.B. Both volunteers and equipment.C. Both financial donations and volunteers.第二局部 阅读理解（共两节，总分值40分） 第一节（共15小题；每题2分，总分值30分）阅读以下短文，从每题所给的A、B、C和D四个选项中，选出最正确选项。AMore than great drinks, great rewardsEnjoy all the benefits and mor

26、e with your membership to our Loyalty Program! Whenever you pay with your membership account, you,ll earn a Star.Collect more Stars, earn more rewards.Three ways to join usBuy a Starbucks Card handy to create an account.Track your Stars online or through the mobile app, and well send an email when y

27、ouve earned a reward.You can also join from your phone.Download the Starbucks9 App.One of the most exciting benefits of being a member is using our mobile app to pay for purchases; view your Stars and rewards; access iTunes Pick of the Week; see current offers.Or you can join with specially marked c

28、offee purchased at the grocery store.Enter your Starcode （limit 2 per day）.Look fbr the Starcode symbol on specially marked Starbucks products where you buy groceries.Three levels with increasingly greater rewardsTo reach each level in our Loyalty Program, you need to collect more Stars. （ Remember,

29、 to earn a Star you must pay with a registered Starbucks Card.）Welcome levelTo earn your first rewards, just register a Starbucks Card.Birthday drink or treat on us; birthday coupon （优惠券）for 15% off a purchase at StarbucksStore .Green levelCollect 5 Stars within 12 months and youll be in the Green l

30、evel.What is included in the Welcome level plus早 Free in-store refills （续杯）on hot or iced brewed coffee or teaGold levelCollect 30 Stars within 12 months and youre at the Gold level.What is included in the Green level plus早 A free food or drink item after another 12 Stars earned Personalized Gold Ca

31、rd21. Which of the following is a way you can apply for membership?A. To enter a Starcode from specially marked Starbucks products.B. To buy a Starbucks Card over the phone.C. To update the Starbucks9 App from the official website.D. To buy a drink at a Starbucks on weekends.22. With the Starbucks9

32、App, you can.A. change the pricesB. earn a StarC. pay for rewardsD. view current offers23. With a Starbucks Card of Green level, you will get.A. a free cakeB. personalized Green CardC. free in-store refills D. all purchases 15% offBFor years I have had no idea what I have been doing with my life. I

33、was a 30-year-old lawyer in New York. But being a lawyer was never my dream or goal in life. I honestly wanted to be a writer. I have a great imagination and would write amazing stories in my head. But I always knew that being a writer was never possible for me because it was a better financial deci

34、sion to stay a lawyer.Recently, I couldnt fall asleep at my usual time of 10 p. m. and when I did fall asleep I had the same dream over and over again. The dream starts with me in the ocean trying to go for a swim and Im searching for something, but I start to drown and have no control over my body.

35、 Then a light shines through the waters and when I look up all I can see is myself in a bright white room writing a novel. Then I hear a voice say repeatedly, Now is the time to try something new!”It wasnt just a dream; it was my opportunity to make something good out of my life. That afternoon, I q

36、uit my job at the law firm and I couldnt have been any happier. My life started at 30, and every day since that point I havent stopped enjoying life. I started to write and have been on the best-sellers list for the last two months. Things have definitely turned around.Change is a good thing; it giv

37、es us an opportunity to take a chance. So my two favorite words I live by and so should you are “change and chance”.24. From the first paragraph, we can know that.A. the author is now 30 years oldB. It is impossible for the author to become a writerC. a lawyer can be likely to earn more than a write

38、rD. the author prefers to be a lawyer rather than a writer25. The second paragraph mainly talks about the authors.A. difficulty in sleeping at night. B. strong desire to become a writerC. wish to have a swim in the waters D. terrible swimming experience in the ocean.26. The underlined part in the 3r

39、d paragraph probably means the author.A. regretted having quitted his job as a lawyerB. was unhappy after giving up his job as a lawyerC. was upset because he had to give up his job as a lawyerD. was pretty happy when he quitted his job as a lawyer27. The best title of the text might be.A. Lawyer or Writer B. Change and ChanceC. Change and Regret D. Risk or OpportunityCAs free as they make us, mobile phones still need to stay close to a power source. Soon that may change with green power.Three Chilean students got the idea for a plant-powered device（装置）to charge their cel