炎德·英才大联考化学(一中版)-炎德·英才大联考长沙市一中2019届高三月考试卷(六)化 学

炎德·英才大联考长沙市一中2019届高三月考试卷(六)数 学(文科)长沙市一中高三文科数学备课组组稿(考试范围：集合、逻辑用语、算法、函数、导数、三角函数、立体几何、平面向量、复数、数列、不等式、概率统计、解析几何)本试题卷包括选择题、填空题和解答题三部分，共8页。

时量120分钟。

满分150分。

得分：一、选择题：本大题共8小题，每小题5分，共40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.若A ＝{x |x ＋1>0}，B ＝{x |x －3<0}，x ∈Z ，则A ∩B ＝ A.{1,2} B.{0,1,2} C.{1,2,3} D.{0,1,2,3}2.一组实验数据如下表，与两个变量之间的关系最接近的是下列关系式中的t 1.02 1.99 3.01 4.00 5.10 6.12 V 0.01 1.50 4.04 7.50 12.09 18.01A.V ＝log 2tB.V ＝－log 2tC.V ＝12(t 2－1) D.V ＝2t －23.已知α、β是不同的两个平面，直线a ⊂α，直线b ⊂β.命题p ：a 与b 没有公共点；命题q ：α∥β，则p 是q 的A.充要条件B.必要不充分条件C.充分不必要条件D.既不充分也不必要条件4.直线x sin2－y cos2＝0的倾斜角的大小是A.－12 B.－2C.12 D.25.在一次运动员的选拔中，测得到7名选手身高(单位：cm )分布的茎叶图如图.已知记录的平均身高为177cm ，但有一名候选人的身高记录不清楚，其末位数记为x ，那么x 的值为A.5B.6C.7D.86.执行如图所示的程序框图，若输出的n ＝6，则输入整数p 的最大值是A.32B.31C.15D.167.设双曲线x 2a 2- y 2b 2＝1(a>0，b>0)的离心率为54，抛物线y 2＝20x 的准线过双曲线的左焦点，则此双曲线的方程为A.x 24－y 23＝1B.x 23－y 24＝1 C.x 216－y 29＝1 D.x 29－y 216＝1 8.已知实系数一元二次方程x 2＋(1＋a )x ＋a ＋b ＋1＝0的两个实根为x 1、x 2，满足0<x 1<2，x 2>2.则ba －1的取值范围是A.(－1，－13) B.(－3，－1)C.(－3，－12)D.(－3，12)选择题答题卡题 号 1 2 3 4 5 6 7 8 答 案二、填空题：本大题共7小题，每小题5分，共35分，把答案填在答题卡中对应题号后的横线上.9.sin45°cos15°＋cos45°sin15°的值为 .10.若＝ad －bc ，则复数＝ .11.函数y ＝2cos 2x2－1的最小正周期是 .12.若直线l ：y ＋1＝k (x －2)被圆C ：x 2＋y 2－2x －24＝0截得的弦AB 最短，则直线AB 的方程是 .13.有一个底面圆半径为1、高为2的圆柱，点O 为这个圆柱底面圆的圆心，在这个圆柱内随机取一点P ，则点P 到点O 的距离大于1的概率为 .14.已知向量a ＝(3,4)，|a －b |＝1，则|b |的范围是 .15.某同学在研究函数f (x )＝x1＋|x |(x ∈R )时，分别给出下面几个结论：①等式f (－x )＋f (x )＝0对x ∈R 恒成立； ②函数f (x )的值域为(－1,1)；③若x 1≠x 2，则一定有f (x 1)≠f (x 2)；④函数g (x )＝f (x )－x 在R 上有三个零点.其中正确结论的序号有 .(请将你认为正确的结论的序号都填上)三、解答题：本大题共6小题，共75分.解答应写出文字说明，证明过程或演算步骤. 16.(本小题满分12分)在△ABC 中，角A 、B 、C 的对应边分别为a ，b ，c ，且满足a 2－ab ＋b 2＝c 2. (1)求角C ；(2)若△ABC 的面积为3，c ＝2，求a ＋b 的值.如图，边长为2的等边△PCD所在的平面垂直于矩形ABCD所在的平面，BC＝22，E、M分别是DC、BC的中点.(1)证明：AM⊥面PME；(2)求二面角P—AM—D的大小.已知：△ABC 为直角三角形，∠C 为直角，A (0，－8)，顶点C 在x 轴上运动，M 在y轴上，AM ＝12(AB ＋AC )，设B 的运动轨迹为曲线E .(1)求B 的运动轨迹曲线E 的方程；(2)过点P (2,4)的直线l 与曲线E 相交于不同的两点Q 、N ，且满足QP ＝PN ，求直线l 的方程.统计某校高三年级100名学生的数学月考成绩，得到样本频率分布直方图如下图所示，已知前4组的频数分别是等比数列{}a n 的前4项，后6组的频数分别是等差数列{}b n 的前6项，(1)求数列{}a n 、{}b n 的通项公式；(2)设m 、n 为该校学生的数学月考成绩，且已知m 、n ∈[)70，80∪[]140，150，求事件“||m －n >10”的概率.为了加快经济的发展，某省选择A、B两城市作为龙头带动周边城市的发展，决定在A、B两城市的周边修建城际轻轨，假设10km为一个单位距离，A、B两城市相距8个单位距离，设城际轻轨所在的曲线为E，使轻轨E上的点到A、B两市的距离之和为10个单位距离，(1)建立如图的直角坐标系，求城际轻轨所在曲线E的方程；(2)若要在曲线E上建一个加油站M与一个收费站N，使M、N、B三点在一条直线上，并且AM＋AN＝12个单位距离，求M、N之间的距离有多少个单位距离？(3)在A、B两城市之间有一条与AB所在直线成45°的笔直公路l，直线l与曲线E交于P，Q两点，求四边形P AQB的面积的最大值.定义在D上的函数f(x)，如果满足：对任意x∈D，存在常数M，都有f(x)≥M成立，则称f()x是D上的有界函数，其中M称为函数f()x的下界.已知函数f(x)＝(x2－3x＋3)·e x，其定义域为[－2，t](t>－2)，设f(－2)＝m，f(t)＝n.(1)试确定t的取值范围，使得函数f(x)在[－2，t]上为单调递增函数；(2)试判断m，n的大小，并说明理由；并判断函数f()x在定义域上是否为有界函数，请说明理由；(3)求证：对于任意的t>－2，总存在x0∈(－2，t)满足f′(x0)e x0＝23(t－1)2，并确定这样的x0的个数.炎德·英才大联考长沙市一中2019届高三月考试卷(六)文科数学参考答案一、选择题9.32 10.3＋i 11.2π 12.x －y －3＝0 13.23 14.[4,6] 15.①②③ 三、解答题16.解：(1)由cos C ＝a 2＋b 2－c 22ab ＝12，∴C ＝π3.(5分)(2)由S ＝12ab sin C ＝3，ab ＝4，(8分)故a 2＋b 2＝8，故a ＋b ＝(a ＋b)2＝a 2＋2ab ＋b 2＝8＋8＝4.(12分) 17.解：(1)连接EA ，∵△PCD 为正三角形，∴PE ⊥CD ，∵平面PCD ⊥平面ABCD ，∴PE ⊥平面ABCD ，∴PE ⊥AM.(3分)∵四边形ABCD 是矩形，∴△ADE 、△ECM 、△ABM 均为直角三角形，由勾股定理可求得EM ＝3，AM ＝6，AE ＝3，∴EM 2＋AM 2＝AE 2，∴∠AME ＝90°，∴AM ⊥EM.(4分) 又EM∩PE ＝E ，∴AM ⊥面PME.(6分)(2)∵AM ⊥平面PME ，∴PM ⊥AM ，∴∠PME 是二面角P —AM —D 的平面角，PE ＝PD sin 60°＝3，∴tan ∠PME ＝PE EM ＝33＝1，∴∠PME ＝45°，∴二面角P —AM —D 为45°.(12分)18.解：(1)由AM ＝12(AB ＋AC )，知M 为BC 中点，(2分)设B(x ，y)则M(0，y2)，C(－x,0).(4分)又∠C 为直角，故CB ·CA ＝0，∴x 2＝4y(5分) B 的运动轨迹曲线E 的方程为x 2＝4y.(x≠0)(6分) (2)∵QP ＝PN ，∴点P 是线段QN 的中点，设Q(x 1，y 1)、N(x 2，y 2)，线段QN 的中点P(2,4)，设l ：y －4＝k(x －2)方法一：则x 21＝4y 1，① x 22＝4y 2，②①－②得：4y 1－4y 2＝(x 1－x 2)(x 1＋x 2)，(8分)∴直线l 的斜率为k ＝y 1－y 2x 1－x 2＝14(x 1＋x 2)＝1.(11分)方法二：由{ y －4＝k(x －2)x 2＝4y ，消去y 得x 2－4kx ＋8k －16＝0，(*) 方程(*)中Δ＝16(k 2－2k ＋4)>0，显然方程(*)有两个不相等的实数根.(8分) 由x 1＋x 2＝4k ＝4⇒k ＝1.(11分)所以直线l 的方程为x －y ＋2＝0.(12分)19.解：(1)由已知：第2组的频数为3，第3组的频数为9，又前4组的频数是等比数列，所以a n ＝3n －1，(3分)又第4组的频数为27，后6组是首项为27，和是87的等差数列， 所以b n ＝－5n ＋32.(6分)(2)由(1)知成绩在[)70，80中的有3人，成绩在[]140，150中的有2人，分别记为：a 1，a 2，a 3和b 1，b 2，由||m －n >10知，这两人必来自两个不同的组，(8分)所以事件“||m －n >10”的概率为35.(13分)20.解：(1)以AB 为x 轴，以AB 中点为原点O 建立直角坐标系.设曲线E 上点P(x ，y)，∵|PA|＋|PB|＝10＞||AB ＝8∴动点轨迹为椭圆，且a ＝5，c ＝4，从而b ＝3.∴曲线E 的方程为x 225＋y 29＝1.(4分)(2)由|AM|＋|AN|＋|BM|＋|BN|＝20，|AM|＋|AN|＝12，所以|MN|＝8.(8分)(3)将y ＝x ＋t 代入x 225＋y 29＝1，得34y 2－18ty ＋9t 2－25×9＝0.设P(x 1，y 1)、Q(x 2，y 2)，则y 1＋y 2＝9t17，y 1y 2＝9t 2－25×934.||y 1－y 2＝(y 1＋y 2)2－4y 1y 2＝11750×9×17－9×25t 2，S ＝S △ABP ＋S △ABQ ＝12AB·||y 1－y 2＝83450×9×17－9×25t 2， 所以当t ＝0时，面积最大是601734，此时直线为l ：y ＝x.(13分)21.解：(1)f′(x)＝(x 2－3x ＋3)·e x ＋(2x －3)·e x ＝x(x －1)·e x . 由f′(x)>0⇒x>1或x<0；由f′(x)<0⇒0<x<1，所以f(x)在(－∞，0]，[1，＋∞)上单调递增，在[0,1]上单调递减， 要使f(x)在[－2，t]上为单调递增函数，则－2<t ≤0.(4分) (2)n>m.因为f(x)在(－∞，0]，[1，＋∞)上单调递增，在[0,1]上单调递减，所以f(x)在x ＝1处取极小值e .又f(－2)＝13e2<e ，所以f(x)在[－2，＋∞)上的最小值为f(－2)，从而当t>－2时，f(－2)<f(t)， 即m<n.(6分)由上知，因为f(x)在()－∞，0上递增，且恒大于0，f(x)在(0，＋∞)的最小值为e ， 所以函数f ()x 在(－∞，＋∞)上是有界函数，M ＝0.(8分)(3)因为f′(x 0)e x 0＝x 20－x 0，所以f′(x 0)e x 0＝23(t －1)2，即为x 20－x 0＝23(t －1)2. 令g(x)＝x 2－x －23(t －1)2，从而问题转化为证明方程g(x)＝x 2－x －23(t －1)2＝0在(－2，t)上有解，并讨论解的个数.因为g(－2)＝6－23(t －1)2＝－23(t ＋2)(t －4)，g(t)＝t(t －1)－23(t －1)2＝13(t ＋2)(t －1)，所以①当t>4或－2<t<1时，g(－2)·g(t)<0，所以g(x)＝0在(－2，t)上有解，且只有一解；②当1<t<4时，g(－2)>0且g(t)>0，但由于g(0)＝－23(t －1)2<0，所以g(x)＝0在(－2，t)上有解，且有两解；(10分) ③当t ＝1时，g(x)＝x 2－x ＝0⇒x ＝0或x ＝1， 所以g(x)＝0在(－2，t)上有且只有一解；(11分) ④当t ＝4时，g(x)＝x 2－x －6＝0⇒x ＝－2或x ＝3， 所以g(x)＝0在(－2,4)上有且只有一解.(12分)综上所述，对于任意t>－2，总存在x 0∈(－2，t)，满足f′(x 0)xx 0＝23(t －1)2，且当t ≥4或－2<t ≤1时，有唯一的x 0符合题意； 当1<t<4时，有两个x 0符合题意.(13分)。

炎德英才大联考长沙市一中2019届高三月考试卷(四)化学长沙市一中高三化学备课组组稿得分：本试题卷分选择题和非选择感网部分.共8页.时量90分钟,满分100分可能用到的相对原子质量H~1 C~12 N-14 0-16 Na-23 -S~32K~39 Ca~40 Cr--52-、选择题《本题有16个小题。

每小题3分，共48分。

每小题只有一个选项符合题意)1.化学与生产生活、社会密切相关。

下列有关说法正确的是A糖类、油脂,蛋白质均为有机高分子化合物B食品包装货中常有硅胶、生石灰还原铁粉等，其作用都是防止食品氧化变质C.洗涤剂除油污的原理与热碱液除油污的原理相同D.浓硫酸和浓硝酸在常温下都能用铝制容器盛装2.用NA表示阿伏加德罗常數的值，下列叙述正确的是A.用情性电极电解Cuso4,溶液后,若加人0.1 mol Cu(OH)2CO3,恰好使溶液复原,则电解过程中转移的电子数目为0.6N AB标准状况下,11.2 L.CH3CH2OH中含有的分子数为0.5N AC.在0.1 mol/L碳酸钠溶液中,阴离子总数大于0.1N AD.某密闭容器盛有0.1 mol N2和0. 3 mol H2,在一定条件下充分反应转移电子的数目为0. 6N A3.有一碘水和Fe(OH),胶体的颜色极为相似,能将它们区分开来的方法有①布朗运动②丁达尔现象③加热法④电泳实验法⑤加电解质法A①③⑤ B.①②④⑤ C.②③④⑤ D.全部4.在一定条件下,PbO2与Cr3+反应，产物是Cr2O72-和Pb2+ ,则与1 molCr3+反应所需PbO2的物质的量为A 3.0molB 1.5 mol C.1.0 mol D.0.75mol5.将一定量的Cl2通入一定浓度的苛性钾溶液中，两者恰好完全反应(已知反应过程放热),生成物中有三种含氯元素的离子，其中CIO-和CIO3-两种离子的物质的量(n)与反应时间(t)的变化示意图如图所示。

下列说法正确的是A.苛性钾溶液中KOH的质量是5.6gB.反应中转移电子的物质的量是0.18 molC.在酸性条件下,clo-和ClO-可生成Cl2D.有3.136 L.氯气参与反应化学试题(一中版)第1页(共8页)6.“工业上用铝土矿(主要成分为Al 2O 3,含Fe 2O 3杂质)为原料冶炼铝的工艺流程如下图所示:下列叙述正确的是 A 试剂X 可以是硫酸B 反应①过滤后所得沉淀1为氧化铁C 图中所示转化中.ALO AI 可选用热还原法D 反应②的离子方程式为2AIO 2 -+CO 2 +3H 2O- -2AI(OH)3,↓+C032- 7、短周期元素 M.N.X.Y.Z 的原子序数增大，它们组成的中学常见的单质或化合物存在如图所示转化关系。

炎德·英才大联考长沙市一中2019届高三月考试卷(六)英语长沙市一中高三英语备课组组稿(考试范围：全部内容)本试卷分为四个部分，包括听力、语言知识运用、阅读和书面表达。

时量120分钟。

满分150分。

得分：PART ONE LISTENING COMPREHENSION(30 marks)SECTION A(22.5 marks)Directions：In this section，you’ll hear six conversations between two speakers. For each conversation，there are several questions and each question is followed by three choices marked A，B and C.Listen carefully and then choose the best answer for each question.You will hear each conversation TWICE.Conversation 11. What does the man have to do today？A.Visit his lawyer.B.Go to a doctor.C.Make an appointment.2. What does the woman offer to do for the man？A.Answer his phones.B.Call his lawyer.C.Take notes at the meeting.Conversation 23. What are the speakers talking about？A.Flight timetable.B.The way to Union Street.C.Hiring a taxi.4. How much does each person need to pay？A.60 dollars.B.20 dollars.C.30 dollars.Conversation 35. Who may Alistair be？A.Bob’s girlfriend.B.Bill’s friend.C.Alistair’s sister.6. When would Bill go to Alistair’s house？A.In half an hour.B.In an hour.C.After he got some sugar from Marilyn.Conversation 47. Which kind of computer programming course does the man choose？A.Part-time course.B.Day course.C.Evening course.8. On which days can’t the man attend the data processing course？A.Mondays.B.Thursdays.C.Wednesdays.9. When does the data processing course end if it starts in October？A.November.B.December.C.January.Conversation 510. Why does old Jake look terribly depressed？A.Because he has just retired and lives alone.B.Because his wife divorced him.B.Because nobody likes him.11. What does the man say about Jake’s daughter？A.She is selfish.B.She is easy going.C.She is warm-hearted.12. Who is Jake’s doctor？A.The man.B.Johnson.C.Dorris.Conversation 613. What does the woman do？A.She is a housewife.B.She is a hostess.C.She is an actress.14. Why did James Dean move back to Indiana when he was young？A.Becausehis mother died.B.Becausehis father died.C.Because they run out of money.15. How many movies did James Dean have according to the man？A.One.B.Two.C.Three.SECTION B(7.5 marks)Directions：In this section，you will hear a short passage. Listen carefully and then fill in the numbered blanks with the information you have heard. Fill in each blank with NO MORE THAN THREE WORDS.You’ll hear the short passage TWICE.,Rosa,BradAge,16.,22Sports,17.,Long-distance runningRecords,5 world records,18.records for 5,000 and 10,000 metersTraining,Swims between15 and20 kilometers a day,Runs40 to50 kilometers everydayOccupation,19.,Used to be20.，but recently stopped to spend more time training.PART TWO LANGUAGE KNOWLEDGE (45 marks)SECTION A (15 marks)Directions：Beneath each of the following sentences there are four choices marked A，B，C and D. Choose the one answer that best completes the sentence.21. Shawn returned to Iowa after the 2019 Games，，as is known to us，she had been brought up and trained to be a gold medalist of gymnastics.A.whenB.thatC.thereD.where22. —Have you heard from Nelly recently？—Yes. I his letters and cards many times while I was in Italy.A.have receivedB.receivedC.had receivedD.would receive23. Now the Internet is a popular channel the public voice their opinions and show their strength.A.by thatB.by whichC.through thatD.through which24. after a whole day’s work that he could hardly stand it.A.So was tired and hungry heB.Wasso tired and hungry heC.So tired and hungry was heD.So tired and hungry he was25. Though to go to bed many times，the little boy just turned a deaf ear and fixed on his computer games.A.urgingB.being urgedC.urgedD.having urged26. When and where to go for the on-salary holiday yet.A.hasn’t been decidedB.is not being decidedC.are not decidedD.haven’t been decided27. Despite its center nowhere near the islands，Morakot(the typhoon) is being blamed for 25 deaths in the Philippines.A.wasB.beingC.isD.has been28. It’s unimaginable that such a top student as Jane cheat in the exam.A.mightB.canC.mayD.should29. The editor-in-chief asked me to write another article for them，about how to prevent bird flu.A.thatB.oneC.the oneD.those30. Some women a good salary in a job instead of staying home，but they decided not to work for the sake of the family.A.must makeB.should have madeC.would makeD.could have made31. I’m glad to say that she’s already finished50% of the book in thesedays.A.no less thanB.no more thanC.not more thanD.much less than32. —Did you go to Hainan Island for your vacation last month？—I to go，but I got sick at the last minute.A.planB.am planningC.have plannedD.had planned33. These surveys indicate that many crimes go by the police，mainly because not all victims report them.A.to be unrecordedB.to have beenunrecordedC.unrecordedD.unrecording34. I’m really hungry. Let’s eat at restaurant has a free table.A.whicheverB.whateverB.which D.what35. so much salt in the Dead Sea that people won’t get sunk.A.It existsB.There has existedC.There existsD.It has existedSECTION B (18 marks)Directions：For each blank in the following passage there are four words or phrases marked A，B， C and D.Fill in each blank with a word or phrase that best fits the context.“We’ve been good friends for so many years. And I don’t think you meant to do that ...”I said to myself，looking at Jack，my friend who was running across the36field.How I wish I could join them！But it was impossible because of the pain in my left foot，caused by Jack.I first met Jack in a football match in the elementary school. When my team looked as if we were37，Jack，who was watching，volunteered to join us. He was so confident and skilled that we won. From then on，Jack and I often played together and became best friends.But something happened before an important football match between Class Six and my class. My class had so many good players that we had to38the best ones. Jack and I were in the same team. The match was close in the first half. I saw my chance and was ready to score a goal. Suddenly，Jack39me. He slid to stop the ball，but collided with my left foot. I knew I had lost the chance to score and was40the field. But what really hurt me was that Jack didn’t say sorry. And when some of my teammates said he did it on purpose to41me from scoring，I felt even42.Now I stand here，with tears in my eyes. I don’t want to43those words but I don’t know how to persuade myself they are44. Then everything changes when Jack scores and wins！How excited I am！While I am still45in excitement，someone pats my shoulder. It is Jack，with a smile on his face. “I’m sorry that you can not join in because of my46. But you see，Jason，we beat them！No matter whether you joined in or not，you’ve made a contribution. Come on，let’s celebrate！”Suddenly，I am47by the players. The sunshine is so bright that I close my eyes. Riding high above my teammates，I feel so happy. And I know the friendship between Jack and me will last forever.36. A.basketball B.volleyball C.badminton D.football37. A.lost B.winning C.leading D.beaten38. A.replace B.award C.decide on D.call in39. A.ran into B.ran to C.ran across D.ran away40. A.sent away B.carried off C.stuck to D.hold on41. A.break B.interrupt C.make D.keep42. A.amused fortable C.depressed D.scared43. A.believe B.say C.deny D.hear44. A.right B.false C.true D.bad45. A.lost B.fallen C.caught D.drawn46. A.score B.pride C.reason D.carelessness47. A.raised up B.pulled away C.picked up D.pushed offSECTION C (12 marks)Directions：Complete the following passage by filling in each blank with one word that best fits the context.Healthy eating begins with learning how to“eat smart”. It’s not just what you eat，48. how you eat. Pay attention to what you eat and choosing foods that are both nourishing49. enjoyable helps support an overall healthy diet.Take time to chew your food：Chew your food slowly，savoring every bite. Wetend to rush through our meals，forgetting to actually taste the flavors and feel the textures(质地) of50. is in our mouths. Reconnect with 51.joy of eating.Avoid stress while eating：Avoid eating while working，driving，arguing，or watching TV. Try taking some deep breaths before beginning your meal，or light candles and play soothing music to create a relaxing atmosphere.Listen to your body：Ask 52.if you are really hungry. You may really be thirsty，so try drinking a glass of water first. During a meal，stop eating before you feel full. It actually takes a few minutes 53.your brain to tell your body that it has had 54.food，so eat slowly.Eat early：Starting your day55.a healthy breakfast can jumpstart your metabolism(新陈代谢)，and eating early in the day gives your body time to work those calories off.PART THREE READING COMPREHENSION (30 marks)Directions：Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A，B，C and D.Choosethe one that fits best according to the information given in the passage.AThe temperature is rising again in the Arctic. The sea ice area has dropped to one of the lowest levels on record，climate scientists reported last week.“The new Arctic Report Card tells a story of widespread and continued effects of a warming Arctic，”said Jackie Richter-Menge of the US’s Cold Regions Research and Engineering Laboratory.“This isn’t just a climatological (气候学的) effect. It impacts the people that live there，”she added.Scientists concerned about global warming focus on the Arctic because that is a region where the effects are expected to be felt first，and that has been the case in recent years.There was a slowdown in Arctic warming in 2019，but in the first half of 2019 warming was near a record pace. The monthly readings were over 4 degrees Celsius above normal in northern Canada，according to the report card. The report card was prepared by 69 researchers in eight countries.Researchers said last winter’s big snow storms that struck some Northern countries were tied to higher Arctic temperatures.“Normally the cold air is bottled up in the Arctic，” said Jim Overland of the US National Oceanic and Atmospheric Administration. “But last December and February，winds that normally blow west to east across the Arctic were instead bringing the colder air south，” he said.“As we lose more sea ice... warming in the atmosphere can create more of these winter storms，” Overland said.There is a powerful connection between ice cover and air temperatures，Richter-Menge explained. When temperatures warm，ice melts. When ice melts it shows darker surfaces underneath ，which absorb more heat. “That，in turn，causes more melting and on the cycle goes，” she said.In September the Arctic sea ice extent was the third smallest in the last 30 years，added Don Perovich of the US Army Laboratory. He said the three smallest ice covers have occurred in the last four years.56. Scientists care so much about the warming in the Arctic region because .A.the climate in the Arctic doesn’t change muchB.global warming effects are most serious in the Arctic regionC.there has been a major decrease of Arctic warming in recent yearsD.by studying the region they can make predictions about the future impact of global warming57. Which of the following shows that the Arctic is getting warmer？A.The surface of the sea ice in Arctic is getting darker and darker.B.The Arctic sea ice extent has disappeared over the last 30 years.C.The sea ice extent has increased to one of the highest levels on record.D.Winds that normally blow south across the Arctic didn’t come until last December and February.58. What does the underlined word “cycle” refer to？A.Ice giving off heat when it melts.B.Higher temperatures bringing more storms.C.The cause and the result of the melting.D.The life of the people living in the Arctic getting worse.59. According to researchers what led to big snow storms attacking some Northern countrieslast winter？A.Higher Arctic temperatures.B.The melting ice.C.The cold wind blowing west to east.D.Cold air bottled up in the Arctic.60. What is the main point of the article？st winter’s big snow-storms.B.Winds in the Arctic region.C.Arctic warming and its possible effects.D.Changes to the life of people living in the Arctic.BPeople with bigger brains ftend to score higher on standardized tests of intelligence，according to new study findings.However，the study author Dr Michael A.McDaniel of the Virginia Commonwealth University in Richmond emphasized that these findings represent a general trend，and people with small heads should not automatically believe they are less intelligent. For instance，Albert Einstein’s brain was “not particularly large”，McDaniel noted. “There’s some relationship between brain size and intelligence on the average，but there’s plenty of room for exceptions，”he said.Interest in the relationship between brain size and intelligence grew in the1830s，when German anatomist(解剖学家) Frederich Tiedmann wrote that he believed there was “an unquestionable connection between the size of the brain and the mental energy displayed by the individual man”. Since that statement，scientists have conducted numerous studies to determine if Tiedmann’s assertion was，in fact，correct. Most studies have looked into the link between head size and intelligence. More recently，however，researchers have published additional studies on brain size and intelligence，measured using MRI scan(核磁共振成像扫描).For his study，McDaniel analyzed more than 20 studies that looked into the relationship between brain size and intelligence in a total of 1,530 people. The studies showed that on the average，people with larger brain volume tended to be more intelligent. The relationship between brain volume and intelligence was stronger in women than men，and in adults than in children. McDaniel notes in the journal Intelligence.McDaniel is not sure why the relationship was stronger for adults and women. “Other research has shown that women，on the average，tend to have smaller brains than men，but score just as well—if not higher—in tests of intelligence，”he said.McDaniel insisted that the relationship between brain size and intelligence is not a “perfect”one. “One can certainly find lots of examples of smaller-sized people who are highly intelligent，”he said，“But，on the average，the relationship holds.”61. What does the text mainly talk about？A.MRI scans are applied to intelligence.B.On the average，a bigger brain means higher IQ.C.Dr McDaniel did well in his intelligence study.D.Scientists are interested in Tiedmann’s idea.62. By mentioning Albert Einstein，the writer wants to show.A.Albert Einstein was intelligentB.the result of intelligence test was falseC.being hard working is more important than intelligenceD.brain size doesn’t necessarily decide the level of intelligence63. The underlined word“assertion”in Para. 3 probably means“”.A.experimentB.statementC.proofD.demand64. After Frederich Tiedmann wrote his article，.A.many scientists agreed with himB.numerous studies have failed to prove his ideaC.MRI scan became popularly usedD.lots of researchers were interested in the connections between head size and intelligence65. According to the text，Dr McDaniel’s study.A.proves Tiedmann’s idea was completely trueB.shows women are smarter than menC.involves many studies and a lot of peopleD.explains why people with smaller brains are cleverCLEEDS，England ─ A Leeds University psychology professor is teaching a course to help dozens of Britons forgive their enemies.“The hatred we hold within us is a cancer，” Professor Ken Hart said，adding that holding in anger can lead to problems such as high blood pressure and heart disease.More than 70 people have become members in Hart’s first 20-week workshop in London─ａcourse he says is the first of its kind in the world.These are people who are sick and tired of living with a memory.They realize their bitternessis a poison they think they can pour out，but they end up drinking it themselves，said Canadian-born Hart.The students meet in groups of eight to ten for a two-hour workshop with an adviser every fortnight.The course，ending in July，is expected to get rid of the cancer of hatred in these people.“People have lots of negative attitudes towards forgiveness，” he said，“People confuse forgiveness with forgetting.Forgiveness means changing from a negative attitude to a positive one.”Hart and his team have created instructions to provide the training needed.“The main idea is to give you guidelines on how to look at various kinds of angers and howthey affect you，and how to change your attitudes towards the person you are angry with，” said Norman Claringbull， a senior expert on the forgiveness project.Hart said he believes forgiveness is a skill that can be taught，as these people “want to get free of the past”.66. From this passage we know that .A.high blood pressure and heart disease are caused by hatredB.high blood pressure can only be cured by psychology professorsC.without hatred，people will have less trouble connected with blood pressure and heartdiseaseD.people who suffer from high blood pressure and heart disease must have many enemies67. People going to Hart’s first 20-week workshop .A.enjoy the professor’s speechB.learn how to quarrel with othersC.are aware that their hatred is a poison that could finally end up harming themselvesD.meet in groups of eight to ten for a two-hour workshop every night and learn how to relax68. According to Professor Ken Hart，.A.most people are living with hatredB.people should attend his courses to forget the pastC.forgiveness means forgetting the bitternessD.people with a bitter memory can learn to have a positive attitude towards the past69. Which of the following is TRUE according to the passage？A.Hatred means living a positive life.B.People will be taught how to look at various kinds of angers in the workshop.C.Hart and his team enjoys high popularity among Londoners these days.D.People who are sick of living with a bitter memory have to pay a lot to Hart’s course.70. Which could be the best title for the passage？A.Britons learn to forgiveB.Hart and his teamC.Forgive and forgetD.Hatred， a poison to youPART FOUR WRITING (45 marks)SECTION A (10 marks)Directions：Read the following passage. Complete the diagram by using the information for the passage. Write NO MORE THAN THREE WORDS for each answer.At a primary school Manning，Carolina，second-grade teacher David Chadwell believed that segregating(隔离) elementary-age boys and girls produces immediate academic improvement—in both genders. “Although this is a tendency，we can teach boys and girls based on what we now know.”“They see differently. Literally，”he begins. Male and female eyesare not organized in the same way，he explains. The composition of the male eye makes it attuned(协调) to motion and direction. “Boys interpret the world as objects moving through space，”he says. “The teacher should move around the room constantly and be that object.”The male eye is also drawn to cooler colors like silver，blue，black，grey，and brown. It’s no accident boys tend to create pictures of moving objects like spaceships，cars，and trucks in dark colors instead of drawing the happy colorful family，like girls in their class.The female eye，on the other hand，is drawn to textures and colors. It’s also oriented toward warmer colors—reds，yellows，oranges—and visuals with more details，like faces. To engage girls，Chadwell says，the teacher doesn’t need to move as much，if at all. Girls work well in circles，facing each other. Using descriptive phrases and lots of color in overhead presentations or on the chalkboard gets their attention.Boys and girls also hear differently. “When someonespeaks in a loud tone，girls interpret it as yelling，”Chadwell says. “They think you’re mad and can shut down.”Girls have a more finely tuned aural structure；they can hear higher frequencies than boys and are more sensitive to sounds. He advises girls’teachers to watch the tone of their voices. Boys’teachers shouldsound matter of fact，even excited.A boy’s autonomic nervous system causes them to be more alert when they’re standing，moving，and the room temperature is around69 degrees. Stress in boys，he says，tends to increase blood flow to their brains，a process that helps them stay focused. This won’t work for girls，who are more focused seated in a warmer room around 75 degrees. Girls also respond to stress differently. When they are exposed to threat and confrontation，blood goes to their guts(内脏)，leaving them feeling nervous or anxious.“Boys will rise to a risk and tend to overestimate their abilities，”he says. “Teacherscan help them by getting them to be more realistic about results. Girls at this age shy away from risk，which is exactly why lots of girls’programs began in the private sector. Teachers can help them learn to take risks in an atmosphere where they feel confident about doing so.”Title：Primary students learn 71.David’s belief,Once we segregate elementary-age students，they will have the tendency to learn 72.. Differences between boys and girls,Sight,Boys’eyes are sensitive to 73. and are drawn to cooler colors.It is textures and74.of objects that attract girls.Hearing,Comparatively speaking，girls can hear75.and are more sensitive to sounds. They would interpret a loud tone as 76..Nervous system,Stressin boys tends to increase blood flow to their 77.，which helps them keep 78.. Boys often overestimate their abilities and are brave in face of the risk.When girls are exposed to79.，blood goes to their guts，leaving them feeling80.. Girls at this age in many cases will shyly avoid dealing with risk.SECTION B (10 marks)Directions：Read the following passage. Answer the questions according to the information given in the passage and required words limit. Write your answers on your answer sheet.Tsai Chin-chung is one of Taiwan’s most famous cartoonists，and his cartoons are enjoyed by people in many different countries in Asia. His books of cartoons have now become best sellers in Singapore，Malaysia，and even Japan.As soon as he could hold a pencil or a brush，Tsai Chin-chung lived only for drawing. Every day he practised drawing people and things around him as well as characters and scenesfrom his favorite stories.When he was only 15 years old，he left home to work for a publisher in Taibei. At first he was only 15 years old and he worked hard to draw pictures for books. So two years later he decided to leave his job as an artist who draws pictures for books and to work on drawing cartoon series. He made up his mind to succeed as a cartoonist even if it meant“living on instant noodles”in order to make himself famous.Now nearly 50 years old，Tsai Chin-chung has achieved something unusual for a modern cartoonist. He has become extraordinarily successful at changing Chinese literature and philosophy into humorous comic stories. In this way，he had made the Chinese classics known to thousands of people.In recognition of his great achievement，several years ago Tsai Chin-chung was given a prize as one of the 10 Outstanding Young People of Taiwan. Since then，he has won many prizes and his cartoons have become popular in countries and areas throughout Asia，America and Europe. Sofar，he has published more than 20 comic books. Ten of these are about ancient Chinese philosophers，and the remainder are based on Chinese historical and literary classics.Many of Tsai Chin-chung’s books of cartoons and comics have now been published in English in countries and areas like Singapore. His books have also been translated into several other languages，including Japanese，Korean and Thai. Even publishers in countries like France and Indonesia have recently signed agreements for permission to publish his cartoon series.81. What job did Tsai Chin-chung do when he was fifteen years old？(No more than 5 words) (2 marks)82. What does “living on instant noodles” mean in this passage？(No more than 4 words) (3 marks)83. How does he make the Chinese classics known to thousands of people？(No more than 10 words) (2 marks)84. Why was Tsai Chin-chung nominated one of the ten outstanding young people of Taiwan？(No more than 5 words) (3 marks)SECTION C (25 marks)Directions：Write an English composition according to the instructions given below in Chinese.The passage below“Let’s Live a Low-carbon Life(让我们低碳生活)”is about what is low-carbon living，why we should live a low-carbon life and how we can live a low-carbon life. Part of the article is written. Please finish the rest of it in over 120 words.Let’s Live a Low-carbon LifeLow-carbon everyday living means that men and women really should try their best to cut down resource consumption (资源消耗) to decrease discharge (排放) of carbon dioxide in order to lessen pollution to atmosphere and relieve deterioration (恶化) of eco-environment.炎德·英才大联考参考答案(一中版)－炎德·英才大联考长沙市一中2019届高三月考试卷(六)英语参考答案答题卡题序123456789101112131415答案 B A C B B C C B C A A B B A C 题序16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 答案 D B D C C A B D B D 题序313233343536373839404142434445答案A D C A C D D C A B D C A B A 题序464748495051525354555657585960答案D A D A C A C 题序61 62 63 64 65 66 67 68 69 70答案B D B D C C C D B A16. 1717. Swimming18. His country’s/National19. A school student20.a clerkPART TWO LANGUAGE KNOWLEDGESECTION C48. but49.and50. what51. the52. yourself/you53. for54. enough55. withPART FOUR WRITINGSECTION A71.differently72.better73.motion and direction74.warmer colors75.higherfrequencies76.yelling/shouting77.brains78.focused/attentive79.threat and confrontation80.nervous or anxiousSECTION B81.He drew pictures for books.82.It means working hard./It means hard work.83.By changing Chinese literature and philosophy into humorous comic stories.84.Because of his great achievement.SECTION COne possible version：Let’s Live a Low-carbon LifeLow-carbon everyday living means that men and women really should try their best to cut down resource consumption (资源消耗) to decrease discharge (排放) of carbon dioxide in order to lessenpollution to atmosphere and relieve deterioration (恶化) of eco-environment.How long our planet can support us is a hot issue nowadays. As a result，in order that we can make the earth a better place to live for the generations to come，the idea of low-carbon living is more and more popular in the world.How can we live a low-carbon life？First of all，when we go to school or some other places，let’s go by bike or on foot as much as possible instead of going by car. Furthermore，let’s economize on water，paper and electricity. Lastly，using environmentally friendly shopping bags instead of plastic bags will greatly cut down the amount of white garbage globally.Protecting the environment needs the efforts of every one of us and every small effort of us will make a big difference for making the earth a better place.。

长沙市一中2019届高三月考试卷(五)化学(考试范围：物质结构、反应热、化学反应速率与化学平衡)本试题卷分选择题和非选择题两部分，共6页。

时量90分钟，满分100分。

可能用到的相对原子质量：H－1C－12N－14O－16Na－23S－32Cl－35.5 Cu－64第Ⅰ卷选择题(共48分)一、选择题(单选题，每小题3分，共48分)1.下列叙述正确的是( )A.强电解质都是离子化合物，因此NaCl是离子化合物B.醋酸溶液的导电能力可能比稀硫酸强C.SO3溶于水，其水溶液能导电，SO3是电解质D.硫磺是单质，不导电，因此硫磺是非电解质2.俄罗斯科学家在利用回旋加速器进行的实验中，用含20个质子的钙元素的同位素反复轰击含95个质子的镅元素，结果4次成功制成4个第115号元素的原子。

这4个原子在生成数微秒后衰变成第113号元素。

前者的一种核素为288115X。

下列有关叙述正确的是( )A. X元素的核外电子数为288B.核素288115X的质量数与中子数之差为173C.113号元素属于非金属元素D.115号元素的最高正化合价是＋53.关于氢键，下列说法正确的是( )A.甲硫醇(CH3SH)比甲醇的熔点低的原因是甲醇分子间易形成氢键B.氯化钠易溶于水是因为形成了氢键C.氨易液化与氨分子间存在氢键无关D.H2O是一种非常稳定的化合物，这是由于氢键所致4.下列有关反应热的叙述正确的是( )A.已知2H2(g)＋O2(g)===2H2O(g)；ΔH＝－483.6kJ/mol，则氢气的燃烧热为241.8kJ/molB.C(石墨，s)===C(金刚石，s)；ΔH＞0，所以金刚石比石墨稳定C.已知碳的燃烧热为y kJ/mol，当7.2g的碳在12.8g的氧气中燃烧，至反应物耗尽并放出x kJ的热量，则可求出1mol碳与氧气反应生成一氧化碳时ΔH＝(0.5y－2.5x)kJ/molD.己知2C(s)＋2O2(g)===2CO2(g)；ΔH12C(s)＋O2(g)===2CO(g)；ΔH2，则ΔH1>ΔH25.R、M、T、G、J为原子序数依次递增的同一短周期主族元素，下列说法一定正确的是(m、n均为正整数)( )A.若M的最高正化合价为＋4，则五种元素都是非金属元素B.H n JO m为强酸，则G是位于ⅤA族以后的活泼非金属元素C.若T的最低化合价为－3，则J的最高正化合价为＋6D.若R、M的最高价氧化物的水化物R(OH)n、M(OH)n＋1均为碱，则R n＋的半径一定比M(n＋1)＋半径大6.下面元素周期表被分成a、b、c、d四个区域，下列有关说法正确的是( )A.元素周期表中b区域全部是金属元素B.X、Y两元素相比较，失电子能力较强的是X，可以验证该结论的实验是将在空气中放置已久的这两种元素的块状单质分别放入热水中C.Z元素代表的是Ca元素D.W元素是非金属元素，该元素对应的氢化物显酸性7.下列叙述正确的是( )A.168O2和188O2互为同位素，性质相似B.常温下，pH＝1的水溶液中Na＋、NO－3、HCO－3、Fe2＋可以大量共存C.明矾和漂白粉常用于自来水的净化和杀菌消毒，两者的作用原理相同D.硝酸铵溶于水是一个吸热过程，但常温下却能自发进行，说明ΔS＞08.下列各组离子能在指定溶液中共存的是( )①无色溶液中：K＋、Cl－、Na＋、H2PO－4、PO3－4、SO2－4②使pH试纸变深蓝的溶液中：CO2－3、NO－3、Na＋、S2－、AlO－2、SO2－3③水电离的c(H＋)＝10－12mol/L的溶液中：ClO－、HCO－3、NO－3、NH＋4、S2O2－3④加入Mg能放出H2的溶液中：Mg2＋、NH＋4、Cl－、Na＋、SO2－4⑤使甲基橙变红的溶液中：MnO－4、NO－3、SO2－4、Na＋、Fe3＋⑥pH＝0的溶液中：Fe2＋、Al3＋、NO－3、I－、Cl－、S2－A.①③B.②④⑤C.①②⑤D.③⑥9.叠氮酸(HN3)与醋酸酸性相似，下列叙述中一定错误的是( )A.HN3水溶液中微粒浓度大小顺序为：c(HN3)>c(H＋)>c(N－3)>c(OH－)B.HN3与NH3作用生成的叠氮酸铵是共价化合物C.NaN3水溶液中离子浓度大小顺序为：c(Na＋)>c(N－3)>c(OH－)>c(H＋)D.N－3与CO2含相等电子数10.通常人们把拆开1mol某化学键吸收的能量看成该化学键的键能。

炎德·英才大联考长沙市一中2019届高三月考试卷(六)数 学(理科)长沙市一中高三理科数学备课组组稿(考试范围：集合与逻辑、算法、函数、导数、三角函数、平面向量、复数、数列、推理与证明、不等式、计数原理、二项式定理、概率与统计、直线、平面、简单几何体、空间向量)本试题卷包括选择题、填空题和解答题三部分，共8页。

时量120分钟。

满分150分。

得分：一、选择题：本大题共8小题，每小题5分，共40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.若M ＝{x ||x －1|<2}，N ＝{x |x (x －3)<0}，则M ∩N ＝ A.{x |0<x <3} B.{x |－1<x <2} C.{x |－1<x <3} D.{x |－1<x <0}2.已知函数f (x )＝sin(2x －π4)，若存在α∈(0，π)，使得f (x ＋α)＝f (x ＋3α)恒成立，则α的值是A.π6B.π3C.π4D.π23.已知α，β是两个不同的平面，m ，n 是两条不同的直线，又知α∩β＝m ，且n ⊄α，n ⊄β，则“n ∥m ”是“n ∥α且n ∥β”的A.必要不充分条件B.充分不必要条件C.充要条件D.既不充分也不必要条件4.6名同学安排到3个宿舍，每个宿舍两人，其中甲必须在一号宿舍，乙和丙均不能到三号宿舍，则不同的安排方法种数为A.6B.9C.12D.185.若f (x )＝f 1(x )＝x1＋x ，f n(x )＝f n －1[f (x )](n ≥2，n ∈N *)，则f (1)＋f (2)＋…＋f (n )＋f 1(1)＋f 2(1)＋…＋f n (1)＝A.nB.9n ＋1C.nn ＋1D.16.已知m 是一个给定的正整数，如果两个整数a ，b 被m 除得的余数相同，则称a 与b 对模m 同余，记作a ≡b (mod m )，例如：5≡13(mod4).若22019≡r (mod7)，则r 可以为A.2019B.2019C.2019D.20197.在△ABC 所在的平面内有一点P ，满足P A ＋PB ＋PC ＝AB ，则△PBC 与△ABC 的面积之比是A.13B.12C.23D.348.若函数y ＝f (x )(x ∈R )满足f (x ＋2)＝f (x )，且x ∈(－1,1]时，f (x )＝1－x 2，函数g (x )＝{ lg|x |(x ≠0)1(x ＝0)，则函数h (x )＝f (x )－g (x )在区间[－5,10]内零点的个数为A.12B.14C.13D.8选择题答题卡二、填空题：本大题共7小题，每小题5分，共35分，把答案填在答题卡中对应题号后的横线上.9.已知a 是实数，(a －i)(1－i)i是纯虚数，则a 的值是 .10.若x 1，x 2，x 3，…，x 2019，x 2019的方差是2，则3(x 1－1),3(x 2－1)，…，3(x 2019－1),3(x 2019－1)的方差是 .11.已知某一几何体的正视图与侧视图如图所示，则在下列图形中，可以是该几何体的俯视图的图形为 (填你认为正确的图序号)12.已知函数f (x )＝－x 2＋ax －2b .若a ，b 都是区间[0,4]内的数，则使f (1)>0成立的概率是 .13.某机构对小学生作业负担的情况进行调查，设每个学生平均每天作业的时间为x (单位：分钟)，且x ～N (60,100)，已知P (x ≤50)＝0.159.现有1000名小学生接受了此项调查，下图是此次调查中某一项的流程图，则输出的结果大约是 .14.已知关于x 的方程9x －(4＋a )·3x ＋4＝0有两个实数解x 1，x 2，则x 21＋x 22x 1x 2的最小值是 .15.对有10个元素的总体{1,2,3，…，10}进行抽样，先将总体分成两个子总体A ＝{1,2,3,4}和B ＝{5,6,7,8,9,10}，再从A 和B 中分别随机抽取2个元素和3个元素组成样本，用P ij 表示元素i 和j 同时出现在样本中的概率，则P 15＝ ，所有P ij (1≤i <j ≤10)的和等于 .三、解答题：本大题共6小题，共75分.解答应写出文字说明，证明过程或演算步骤. 16.(本小题满分12分)已知向量m ＝(3sin x 4，1)，n ＝(cos x 4，cos 2x4)，f (x )＝m ·n .(1)若f (x )＝1，求cos(2π3－x )的值；(2)在△ABC 中，角A ，B ，C 的对边分别是a ，b ，c 且满足a cos C ＋12c ＝b ，求函数f (B )的取值范围.在高三年级某班组织的欢庆元旦活动中，有一项游戏规则如下：参与者最多有5次抽题并答题的机会.如果累计答对2道题，立即结束游戏，并获得纪念品；如果5次机会用完仍未累计答对2道题，也结束游戏，并不能获得纪念品.已知某参与者答对每道题答对的概率都是23，且每道题答对与否互不影响.(1)求该参与者获得纪念品的概率；(2)记该参与者游戏时答题的个数为ξ，求ξ的分布列及期望.如图，在体积为1的三棱柱ABC －A 1B 1C 1中，侧棱AA 1⊥底面ABC ，AB ⊥AC ，AC ＝AA 1＝1，P 为线段AB 上的动点.(1)求证：CA 1⊥C 1P ；(2)当AP 为何值时，二面角C 1－PB 1－A 1的大小为π6已知函数f (x )＝－x 2＋ax －ln x (a ∈R ).(1)求函数f (x )既有极大值又有极小值的充要条件；(2)当函数f (x )在[12，2]上单调时，求a 的取值范围.某旅游景区的观景台P 位于高(山顶到山脚水平面M 的垂直高度PO )为2km 的山峰上，山脚下有一段位于水平线上笔直的公路AB ，山坡面可近似地看作平面P AB ，且△P AB 为等腰三角形.山坡面与山脚所在水平面M 所成的二面角为α(0°＜α＜90°)，且sin α＝25.现从山脚的水平公路AB 某处C 0开始修建一条盘山公路，该公路的第一段、第二段、第三段…，第n －1段依次为C 0C 1，C 1C 2，C 2C 3，…，C n －1C n (如图所示)，且C 0C 1，C 1C 2，C 2C 3，…，C n －1C n 与AB 所成的角均为β，其中0＜β＜90°，sin β＝14.试问：(1)每修建盘山公路多少米，垂直高度就能升高100米.若修建盘山公路至半山腰(高度为山高的一半)，在半山腰的中心Q 处修建上山缆车索道站，索道PQ 依山而建(与山坡面平行，离坡面高度忽略不计)，问盘山公路的长度和索道的长度各是多少？(2)若修建x km 盘山公路，其造价为x 2＋100 a 万元.修建索道的造价为22a 万元/km.问修建盘山公路至多高时，再修建上山索道至观景台，总造价最少.已知正项数列{a n}的首项a1＝12，函数f(x)＝x1＋x，g(x)＝2x＋1x＋2.(1)若正项数列{a n}满足a n＋1＝f(a n)(n∈N*)，证明：{1a n}是等差数列，并求数列{a n}的通项公式；(2)若正项数列{a n}满足a n＋1≤f(a n)(n∈N*)，数列{b n}满足b n＝a nn＋1，证明：b1＋b2＋…＋b n<1；(3)若正项数列{a n}满足a n＋1＝g(a n)，求证：|a n＋1－a n|≤3 10·(37)n－1.炎德·英才大联考长沙市一中2019届高三月考试卷(六)数学(理科)参考答案一、选择题1.A2.D3.C4.B5.A6.C7.C 解：由P A ＋PB ＋PC ＝AB 得P A ＋PB ＋BA ＋PC ＝0，即PC ＝2AP ，所以点P 是CA 边上的三等分点，故S △PBC ∶S △ABC ＝2∶3.8.B 解：如图，当x ∈[0,5]时，结合图象知f (x )与g (x )共有5个交点，故在区间[－5,0]上共有5个交点；当x ∈(0,10]时，结合图象知共有9个交点，故函数h (x )＝f (x )－g (x )在区间[－5,10]上共有14个零点.二、填空题9.－1 10.18 11.①② 12.96413.15914.2 解：原方程可化为(3x )2－(4＋a )·3x ＋4＝0，∴3x 1·3x 2＝4，∴x 1＋x 2＝2log 32，∴x 1x 2≤(log 32)2.∴x 21＋x 22x 1x 2＝(x 1＋x 2)2－2x 1x 2x 1x 2＝4(log 32)2x 1x 2－2≥2. 15.1410 解：(1)由题意有：P 15＝C 13·C 25C 24·C 36＝14.(2)当1≤i <j ≤4时，P ij ＝1C 24＝16，这样的P ij 共有C 24个，故所有P ij (1≤i <j ≤4)的和为16·6＝1；当5≤i <j ≤10时，P ij ＝C 14·C 22C 36＝15.这样的P ij 共有C 26＝15个，故所有P ij (5≤i <j ≤10)的和为15·15＝3； 当1≤i ≤4,5≤j ≤10时，P ij ＝14，这样的P ij 共有4·6＝24，所有P ij (1≤i ≤4,5≤j ≤10)的和为24·14＝6，综上所述，所有P ij (1≤i <j ≤10)的和等于1＋3＋6＝10. 三、解答题16.解：(1)∵f (x )＝m ·n ＝3sin x 4cos x 4＋cos 2x 4＝32sin x 2＋12cos x 2＋12＝sin(x 2＋π6)＋12，而f (x )＝1，∴sin(x 2＋π6)＝12.(4分)又∵2π3－x ＝π－2(x 2＋π6)，∴cos(2π3－x )＝－cos2(x 2＋π6)＝－1＋2sin 2(x 2＋π6)＝－12.(6分)(2)∵a cos C ＋12c ＝b ，∴a ·a 2＋b 2－c 22ab ＋12c ＝b ，即b 2＋c 2－a 2＝bc ，∴cos A ＝12.又∵A ∈(0，π)，∴A ＝π3.(10分)又∵0<B <2π3，∴π6<B 2＋π6<π2，∴f (B )∈(1，32).(12分)17.解：(1)设“参与者获得纪念品”为事件A ，则P (A )＝1－P (A )＝1－[(13)5＋C 15(13)4(23)]＝232243.(4分) 故该参与者获得纪念品的概率为232243.(5分)(2)ξ的可能取值为2,3,4,5，P (ξ＝2)＝(23)2＝49；P (ξ＝3)＝C 1223·13·23＝827； P (ξ＝4)＝C 1323(13)223＝427；P (ξ＝5)＝C 14(23)(13)3＋C 04(13)4＝19.(8分) 故ξ(10分)Eξ＝2×49＋3×827＋4×427＋5×19＝7927.(12分)18.解：(1)证明：∵AA 1⊥底面ABC ，∴AA 1⊥AC ，AA 1⊥AB . 又∵AB ⊥AC ，∴以A 为原点，AC ，AB ，AA 1所在的直线分别为x 轴，y 轴，z 轴建立直角坐标系.又∵VABC －A 1B 1C 1＝12AB ×AC ×AA 1＝1，∴AB ＝2.(2分)设AP ＝m ，则P (0，m,0)，而C 1(1,0,1)，C (1,0,0)，A 1(0,0,1)， ∴CA 1＝(－1,0,1)，C 1P ＝(－1，m ，－1)， ∴CA 1·C 1P ＝(－1)×(－1)＋0×m ＋1×(－1)＝0， ∴CA 1⊥C 1P .(6分)(2)设平面C 1PB 1的一个法向量n ＝(x ，y ，z )，则{n ·B 1C1＝0n ·C 1P ＝0，即{ x －2y ＝0－x ＋my －z ＝0.令y ＝1，则n ＝(2,1，m －2)，(9分) 而平面A 1B 1P 的一个法向量AC ＝(1,0,0)， 依题意可知cos π6＝|n ·AC ||n ||AC |＝2(m －2)2＋5＝32，∴m ＝2＋33(舍去)或m ＝2－33. ∴当AP ＝2－33时，二面角C 1－PB 1－A 1的大小为π6.(12分)19.解：(1)∵f ′(x )＝－2x ＋a －1x ＝－2x 2＋ax －1x(x >0)，∴f (x )既有极大值又有极小值⇔方程2x 2－ax ＋1＝0有两个不等的正实数根x 1，x 2. (3分)∴⎩⎨⎧Δ＝a 2－8>0x 1＋x 2＝a 2>0x 1·x 2＝12>0，∴a >22， ∴函数f (x )既有极大值又有极小值的充要条件是a >2 2.(6分)(2)f ′(x )＝－2x ＋a －1x ，令g (x )＝2x ＋1x ，则g ′(x )＝2－1x 2，g (x )在[12，22)上递减，在(22，2]上递增.(8分)又g (12)＝3，g (2)＝92，g (22)＝22，∴g (x )max ＝92，g (x )min ＝2 2.(10分)若f (x )在[12，2]单调递增，则f ′(x )≥0即a ≥g (x )，∴a ≥92.若f (x )在[12，2]单调递减，则f ′(x )≤0，即a ≤g (x )，∴a ≤2 2.所以f (x )在[12，2]上单调时，则a ≤22或a ≥92.(13分)20.解：(1)在盘山公路C 0C 1上任选一点D ，作DE ⊥平面M 交平面M 于E ，过E 作EF ⊥AB 交AB 于F ，连结DF ，易知DF ⊥C 0F .sin∠DFE ＝25，sin ∠DC 0F ＝14.∵DF ＝14C 0D ，DE ＝25DF ，∴DE ＝110C 0D ，所以盘山公路长度是山高的10倍，索道长是山高的52倍，所以每修建盘山公路1000米，垂直高度升高100米.从山脚至半山腰，盘山公路为10km.从半山腰至山顶，索道长2.5km.(6分)(2)设盘山公路修至山高x (0＜x ＜2)km ，则盘山公路长为10x km ，索道长52(2－x )km.设总造价为y 万元，则y ＝(10x )2＋100a ＋52(2－x )·22a ＝(10x 2＋1－52x )a ＋102a .令y ′＝10axx 2＋1－52a ＝0，则x ＝1.当x ∈(0,1)时，y ′＜0，函数y 单调递减；当x ∈(1,2)时，y ′>0，函数y 单调递增，∴x ＝1，y 有最小值，即修建盘山公路至山高1km 时，总造价最小，最小值为152a 万元.(13分)21.证明：(1)∵a n ＋1＝f (a n )＝a n 1＋a n ，∴1a n ＋1＝1＋a n a n ＝1a n ＋1，即1a n ＋1－1a n＝1，∴{1a n }是以2为首项，1为公差的等差数列. ∴1a n ＝2＋(n －1)，即a n ＝1n ＋1.(3分) (2)证明：∵a n ＋1≤a n 1＋a n ，a n >0，∴1a n ＋1≥1＋a n a n ，即1a n ＋1－1a n≥1.当n ≥2时，1a n －1a 1＝(1a 2－1a 1)＋(1a 3－1a 2)＋…＋(1a n －1a n －1)≥n －1，∴1a n ≥n ＋1，∴a n ≤1n ＋1. 当n ＝1时，上式也成立，∴a n ≤1n ＋1(n ∈N *)，∴b n ＝a n n ＋1≤1(n ＋1)2<1n (n ＋1)＝1n －1n ＋1， ∴b 1＋b 2＋…＋b n <(1－12)＋(12－13)＋…＋(1n －1n ＋1)＝1－1n ＋1<1.(8分)(3)∵a 1＝12，a 2＝g (a 1)＝45，a 2－a 1＝45－12＝310>0.又∵a n ＋1－a n ＝2a n ＋12＋a n －2a n －1＋12＋a n －1＝3(a n －a n －1)(a n ＋2)(a n －1＋2)，由迭代关系可知，a n ＋1－a n >0，∴a n ≥a 1＝12. 又∵(2＋a n )(2＋a n －1)＝(2＋2a n －1＋12＋a n －1)(2＋a n －1)＝5＋4a n －1≥7， ∴3(2＋a n )(2＋a n －1)≤37， ∴|a n ＋1－a n |＝3(2＋a n )(2＋a n －1)|a n －a n －1|≤37|a n －a n －1|， ∴|a n ＋1－a n |≤37|a n －a n －1|≤(37)2|a n －1－a n －2|≤…≤(37)n －1|a 2－a 1|＝310(37)n －1.(13分)。

炎德·英才大联考长沙市一中2019届高三月考试卷(六)生物长沙市一中高三生物备课组组稿(考试主要范围：必修2第6、7章、必修3第1章、选修3专题1) 本试题卷包括选择题、非选择题两部分，共8页。

时量90分钟。

满分90分。

得分：第Ⅰ卷选择题(共36分)一、选择题(选出正确答案填写在答题卡上。

每小题1分，共36分)1.下列实验试剂或材料与相应的实验名称不相符合的是A.甲基绿吡罗红——观察DNA和RNA在细胞中的分布B.澄清石灰水——探究酵母菌培养液中CO2的产生情况C.马蛔虫受精卵卵裂的固定装片——观察有丝分裂D.斐林试剂——探究温度对唾液淀粉酶活性的影响2.下列物质可以在人体同一个细胞中合成的是A.胰岛素和呼吸酶B.胰岛素和胰高血糖素C.雄激素和促性腺激素D.胰岛素和胰蛋白酶3.下列关于生物膜蛋白的叙述，错误的是A.都与物质的跨膜运输有关B.能与糖类结合，形成细胞与细胞间联络的“文字”C.能与神经递质结合，引起神经元的兴奋或抑制D.膜蛋白的结构和功能具有特异性4.下列有关细胞结构和功能的叙述，正确的是A.有内质网的细胞不一定是真核细胞B.有高尔基体的细胞不一定具有分泌功能C.有线粒体的细胞不能进行无氧呼吸D.有核糖体的细胞一定能合成分泌蛋白5.下列关于ATP的描述中，正确的是A.1摩尔ATP中含61.08kJ的能量B.噬菌体以ATP作为直接能源物质，其产生ATP的结构只有细胞质基质C.对于动物、真菌和大多数细菌来说，A TP合成所需要的能量均来自细胞呼吸D.绿色植物光合作用合成的ATP与细胞呼吸产生的ATP相等，以有利于维持其体内ATP 的平衡6.右图A、B、C、D分别表示某个雄性动物(2n)在精子形成过程中不同阶段的细胞，a、b分别表示每个细胞中染色体和DNA的数量变化。

根据a和b的变化，细胞出现的先后顺序是A.ABCDB.BCDAC.DBCAD.CBDA7.下列人体的细胞中，可以找到两条X染色体的是①精原细胞②卵原细胞③初级精母细胞④初级卵母细胞⑤次级精母细胞⑥次级卵母细胞A.①③⑤B.②④⑤C.②④⑥D.②④⑤⑥8.下列关于细胞的分裂、分化、癌变、衰老和凋亡等描述中，正确的是A.细胞分化过程中，形态、功能不同的细胞中所含有的信使RNA都不相同B.环境中的致癌因子会损伤细胞中的DNA分子，使原癌基因和抑癌基因发生突变，导致正常细胞的生长和分裂失控而变成癌细胞C.衰老细胞呼吸速率减慢，细胞核体积变小，核膜内折，染色质收缩、染色加深D.成熟生物体内，被病原体感染的细胞的清除，不是通过细胞凋亡来完成的9.基因D、d和T、t是分别位于两对同源染色体上的等位基因，下列叙述正确的是A.DDtt和ddTT杂交，则F2双显性性状的个体中能稳定遗传的个体占1/16B.后代的表现型数量比为1∶1∶1∶1，则两个亲本的基因型一定为DdTt和ddttC.基因型分别为DDTT、ddtt的豌豆间行种植后，具有隐性性状的一行植株上所产生的F1既有显性个体又有隐性个体D.基因型为DdTt的个体，如果产生的配子中有dd的类型，则可能是在减数第二次分裂过程中发生了染色体变异10.下列有关利用基因型为DdTt的二倍体植株育种的说法中，正确的是A.杂交育种过程中，此植株需自交多代后才能筛选出具有优良性状的个体B.对该植株诱变处理后一定会出现更多的优良性状C.基因型为DdTt的植株进行单倍体育种所得到的植株自交后代1/4为纯合子D.基因型为DdTt的植株进行多倍体育种所得到的四倍体植株与原植株之间产生了生殖隔离11.下列有关叙述错误的是A.转基因技术产生的变异属于定向的基因重组B.体细胞杂交技术是人为造成染色体变异的方法，它打破了自然界生殖隔离的限制C.人工诱变能提高突变率，但没有改变基因的结构D.经过诱变处理和人工选择的作用后的生物可变得更适合人类的需要12.现以3种不同的限制性内切酶对6.2kb大小的线状DNA进行剪切后，用凝胶电泳分离各核酸片段，实验结果如图所示：请问：3种不同的限制性内切酶在此DNA片段上相应切点的位置是13.上海医学遗传研究所成功培育出第一头携带人白蛋白基因的转基因牛。

湖南省长沙市一中2019届高三第一次月考化学试题及答案第I卷选择题（共54分）一、选择题（本题包括18小题，第小题3分，共54分，每小题只有一个选项符合题意）1．以N A表示阿伏加德罗常数，下列说法正确的是A．0.1 mol Fe与足量盐酸反应，转移的电子数为0.3 N AB．28 g CO中所含的原子数为2 N ACO 数为0.1 N AC．0.1 mol·L-1 Na2CO3溶液中，含有23D．标准状况下，22.4 L苯的分子数为N A【答案】B2．室温时，两个容积相同的烧瓶中分别盛有M和N两种气体（同温同压），取下弹簧夹A，使两烧瓶内的气体接触（如图），容器内的压强由大到小的顺序是编号①②③④气体M H2S H2N H2NO气体N SO2Cl2HCl O2A．①②③④ B．②④①③ C．④①②③ D．①④③②【答案】B3．右图是某学校实验室从化学试剂商店买回的硫酸试剂标签上的部分内容。

据此下列说法正确的是A．该硫酸的物质的量浓度为9.2 mol·L-1B．1 mol 铁加入到足量的该硫酸中，可产生2 g H2C．该硫酸与等质量的水混合所得溶液的物质的量浓度大于9.2 mol·L-1D．配制200 mL，4.6 mol·L-1的硫酸溶液需取该硫酸50 mL【答案】D4．分类方法在化A．根据纯净物的元素组成，将纯净物分为单质和化合物B．根据溶液导电能力强弱，将电解质分为强电解质、弱电解质C．根据是否具有丁达尔效应，将分散系分为溶液、浊液和胶体D．根据反应中的能量变化，将化学反应分为“化合、分解、复分解、置换”四类【答案】A5．下列物质性质中，可以证明某化合物内一定存在离子键的是A．水溶液能导电B．由金属和非金属元素的原子组成C．熔融状态能导电D．可以溶于水【答案】C6．下列各组离子在指定的溶液中能大量共存的是SO-①无色溶液中：K＋、Cu2＋、Na＋、24CO-、Na＋、AlO2－、NO3－②pH＝11的溶液中：23③加入Al能放出H2的溶液中：Cl－、HCO3－、NO3－、NH4＋④在由水电离出的c（OH－）＝10－13 mol·L－1的溶液中：Na＋、Ba2＋、Cl－、I－⑤能使红色石蕊试纸变为蓝色的溶液：Na＋、Cl－、S2－、ClO2－⑥酸性溶液中：Fe2＋、Al3＋、NO3－、Cl－A．①②⑤ B．③⑤⑥ C．②④ D．②④⑥【答案】C7．将ag Fe2O3、Al2O3样品溶解在过量的200 mL 0.05 mol/L的硫酸溶液中然后向其中加入NaOH溶液使Fe3＋、Al3＋刚好完全沉淀，用去NaOH溶液100 mL，则NaOH溶液的浓度为A．0.1 mol·L－1 B．0.2 mol·L－1 C．0.4 mol·L－1 D．0.8 mol·L－1【答案】B8．有一澄清透明的溶液，只可能含有大量的Fe3＋、Fe2＋、H＋、AlO2－、Al3＋、CO32－、NO3－七种离子中的几种，向该溶液中逐滴加入一定量1 mol·L－1 NaOH溶液的过程中，开始没有沉淀，而后才有沉淀。

2019—2020学年度长沙市第一中学高三第四次月考高中化学化学试卷可能用到的相对原子质量：H-1 C-12 O-16 Si-28 S-32 Cl-35.5 Ar-40 Na-23 Fe-56 Ba-137一、选择题〔每题2分，共40分〕1．以下表达正确的选项是 ..................〔〕A．除零族元素外，短周期元素的最高化合价在数值上都等于该元素所属的族序数B．X、Y均为短周期元素，其简单离子m X a＋与n Y b－的电子层结构相同，那么m＋a=n －b。

C．F、Cl、Br的最外层电子数差不多上7，次外层电子数差不多上8D．结合质子〔H+〕能力：OH-＞CH3COO-＞Cl-2．依照表1信息，判定以下表达正确的选项是 ..................〔〕表1部分短周期元素的原子半径及要紧化合价元素代号L M Q R T原子半径／nm 0.160 0.143 0.112 0.104 0.066要紧化合价＋2 ＋3 ＋2 ＋6、－2 －2 A．热稳固性：H2T＜H2R B．单质与稀盐酸反应的速率为L＜Q C．M与T形成的化合物具有两性D．L2＋与R2－的核外电子数相等3．最近媒体报道了一些化学物质，如:爆炸力极强的N5、比黄金还贵的18O2、太空中的甲醇气团等。

以下讲法中，正确的选项是〔〕A．18O2和16O2是两种不同的核素B、甲醇〔CH3OH〕属于离子化合物C．N5分子中含有极性共价键D．2N5=== 5N2是化学变化4．从以下事实所列出的相应结论正确的选项是〔〕实验事实结论A Cl2的水溶液能够导电Cl2是电解质Ra作为标准，居里夫人〔Marie Curie〕因对Ra元素的5．居室装修用石材的放射性常用22688研究两度获得诺贝尔奖，以下表达中正确的选项是〔〕A．Ra元素位于元素周期表中第六周期ⅡA族Ra原子中含有88个中子B．一个22688C．RaCl2在熔融状态下可导电D．Ra〔OH〕2是一种两性氢氧化物6．以下各组离子一定能大量共存的是〔〕 A．在含大量Fe3＋的溶液中：NH4＋、Na＋、Cl—、SCN—B．在强碱溶液中：Na＋、K＋、AlO2—、CO32—C．在c〔H＋〕＝10—13 mol/L的溶液中：NH4＋、Al3＋、SO42—、NO3—D．在pH＝1的溶液中：K＋、Fe2＋、Cl—、NO3—7．以下变化中，属于物理变化的是〔〕①加热氨水可得到氨气②氯化铵晶体受热后由试管底部移到试管上部③固体碘受热变成紫红色气体④液氨气化⑤浓硝酸从无色液体变成黄色液体A．①③④B．③④C．②③④D．③④⑤8．砷〔As〕的原子结构为那么以下表达中正确的选项是〔〕A．在AsCl3分子中，As的最外电子为8个B．As的氢化物为AsH3，是一种强氧化剂C．As的相对原子质量为74.92,由此可知As中子数为42D．H3AsO4是强酸9．以下图所示对实验仪器名称的标注或实验操作正确的选项是〔〕10．在给定条件下，以下加点的物质在化学反应中能被完全消耗的是〔〕A．用浓硫酸．．与足量Cu反应B．标准状况下，将1g铝片．．投入到20mL18mo1／L的硫酸中C．向100mL 3mo1／L的硝酸中加入5.6g铁．D．在5×107Pa、500℃和铁触媒催化的条件下，用氮气．．和足量氢气合成氨11．如图是元素周期表的一部分，关于元素X、Y、Z的表达正确的选项是〔〕①X的气态氢化物与Y的最高价氧化物对应的水化物能发生反应生成盐②Y的氢化物沸点比它上一周期同族元素的氢化物沸点低③Z的单质在常温下是液体④Z的原子序数比Y大19⑤Z所在的周期中含有32种元素A．①②③④B．①②③④⑤C．只有③D．只有①④12．在汽车尾气净化装置里，气体在催化剂表面吸附与解吸作用的过程如下图。