为x轴、y轴、之轴建立空间直角坐标系（图略），则则A(-1,1,0),C(1,0,0),G(2,0w3),DA1=(2,0,2),DE=(0,2,1),则面A1DE的一个法所以CG=(1,0W3),AC=(2,-1,0).向量为n=(2,1,-2).设M(x,2,x),则AM=(x一2,2，设面ACGD的法向量为n=(x,y,z),z).由AM·n=0,得2(x-2)十2-2z=0→x-之=1，故点M的轨迹为以BC,BB,的中点为端点的线段，长为交n=0'即z+5x=0,则AC.n=0,2x-y=0.√1+1=√2.故选B.所以可取n=(3,6,-3).9②xD2解析：如图，连接B1D1,又面BCGE的法向量可取m=(0,1,0),A易知△B1CD1为正三角形，所n·m√3所以cosn,m〉=nm=2以BD1=CD1=2.分别取因此面ACGD与面BCGE夹角的大小为30°B1C1,BB1,CC1的中点M,G,【方法导航】折叠问题中的行与垂直关系的处理关键H,连接D1M,D1G,D1H,则A是结合图形弄清折叠前后变与不变的关系，尤其是隐含易得D1G=D1H=√22+1=√5，DM⊥B,C1,且的垂直关系.一般地，翻折后还在同一个面上的性质D1M=√3.由题意知G,H分别是BB1,CC1与球面的交不发生变化，不在同一面上的性质发生变化点.在侧面BCCB1内任取一点P,使MP=√2，连接11.解：(1)证明：因为PD⊥底面ABCD,所以PD⊥AD.又底面ABCD为正方形，所以AD⊥DC,DP,则DP=√DM+MP=√(W3)2+(W2)2=√5，因此AD⊥面PDC.连接MG,MH,易得MG=MH=√2，故可知以M为圆因为AD∥BC,AD中面PBC,所以AD∥面PBC心，√2为半径的圆弧GH为球面与侧面BCC,B,的交由已知得L∥AD,线.由∠B1MG=∠C,MH=45°知∠GMH=90°，所以因此l⊥面PDCG升的长为}×2xX2-=(2)以D为坐标原点，DA的方ZA2向为x轴正方向，建立如图所示【方法导航】立体几何中空间动，点轨迹的判断或求轨迹的的空间直角坐标系Dxyz,则D长度，一般是根据线、面行，线、面垂直的判定定理和性(0,0,0),C(0,1,0),B(1,1,0),质定理，结合圆或圆锥曲线的定义推断出动点的轨迹（还P(0,0,1),DC=(0,1,0),可以利用空间向量的坐标运算求出动，点的轨迹方程).PB=(1,1,-1).10.解：(1)证明：由已知得AD/BE,CG∥BE,所以AD/CG,由(1)可设Q(a,0,1),所以AD,CG确定一个面，则DQ=(a,0,1).从而A,C,G,D四点共面.n·DQ=0,由已知得AB⊥BE,AB⊥BC,且BE∩BC=B,设n=(x,y,z)是面QCD的法向量，则n·Dd=0,所以AB⊥面BCGE.又ABC面ABC,所以面ABC⊥面BCGE即/ax+z=0可取n=(-1,0,a),y=0,(2)作EH⊥BC,垂足为H.-1-a因为面BCGE⊥面ABC,面BCGE∩面所以cosn,Pi)=n·P响n|PB1√5.√1+aABC=BC,所以EH⊥面ABC.设PB与面QCD所成角为，由已知，菱形BCGE的边长为2，∠EBC=60°，可求得则sin9=5.la+1L_53h+2aBH=1,EH=3.3√1+aa2+1以H为坐标原点，元的方向为x轴的正方向，建立如图所示的空间直角坐标系Hxyz,因为识月十年1≤3，当且仅当a=1时，等号成立，1+DZA所以PB与面QCD所成角的正弦值的最大值为53【方法导航】利用向量求线面角的两种方法(I)分别求出斜线和它所在面内的射影直线的方向向量，转化为求两个方向向量的夹角（或其补角）；教学笔记数学·参考答案/67

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6x4-V6)x=5当且仅当34,即时，等号成立x-y4×2V6-33y 2xy=5故选：C【点睛】关键点睛：解题的关键是由己知条件求出a,6c后，再由4P,8三点共线，得+子-1，所以化简后结合基本不等式可求出其最小值，8.C【分析】分别作出函数y=c,y=nx,y=gx图像，根据三个图像分别与函数y=图像交点情况比较大小【详解】由ae°=blnb=clgc=1,a分别作函数y=e,y=lnx,y=lgx图像，如图所示，.y=Inxy=lgx它们与函数y=二图像交点的横坐标分别为Q,b,c,有图像可得a

答案与详解0.06=0.5,解得x≈86.67.所以估计这部分人的s甲2>s乙2.D正确.故选B.测试成绩的均数和中位数分别是86.75,86.67.6.AB由题意，+十…+2=五，故选B.n4.A设7个数为x1,x2,x3,x4,x5,x6,x7,则[,-z列+，-a++u.-门，x1十x2十x十x,十x十6十x1=4,对于A,ax1,ax2,…,axm的均数为7(x1-402+(x2-4)2+(x3-4)2+z4-40)2+(x-4)2+x6-4)2+x,-4ax1十ax2十…十axn=a(x1十x2十十xn）nax,A正确；对于B,ax1十b,ax2+b,…,axm+b=2,所以x1十x2+x3十x4十x5+x6十x7=28,所以(x1-4)2+(x2-4)2+(x-4)2+(x4-4)2+的均数为+6+az+6十+a,+b=an(x-4)2+(x6一4)2+(x7-4)2=14,则这8个数的均数为云-名红，十：十云，+：十红，十：计+6,其方差为([a+b)-ar+b]+[(a.x2十b)-(ax+b)]+…+[(axn+b)-(a元十b)]x,+4)=日×(28+4)=4，方差为2=日×11[(ax,-ax)2+(ax2-ax)2+…+n[(x1-4)2+(x2-4)2+(x3-4)2+(x4-4)2+(ax,-az)2](x,-4)2+(x6-4)2+(x,-4)2+(4-4)2]==a27[(x1-a)2+(x,-z)2+.+日×14+0)=子

第二节（满分25分）阅读下面材料，根据其内容和所给段落开头语续写两段，使之构成一篇完整的短文。Micah,a 17-year-old with special needs,was last seen at the family's River Oaks apart-ment in Westheimer,Houston on December 10.His mother Kate told her son,"You have todo your housework..You have to get along with your siblings(兄弟姐妹).”Micah then wentout for a walk at around 10 pm,and then disappeared.8Within 15 minutes,Kate and her husband started looking for Micah.They lookedthrough both ways and across the street.Micah left his phone;he left his shoes;he left in ex-actly what he was wearing-black basketball shorts and a navy T-shirt.bnsAlerted to his disappearance,family,friends,and the whole community began searchingcrazily for the teen.Kate and Brandon,Micah's father,and Micah's four siblings postedsigns,looked for clues on surveillance (videos,and checked his online gaming chatro-oms for information.Houston Police Department,Texas Center for the Missing,Texas EquuSearch,and plen-ty of people online shared the post and called nearby businesses,hospitals,and shelters,all学hoping to find Micah,who had multiple learning disabilities.What worried Kate was that Micah could have easily gotten lost since he was still unfa-等miliar with the area.The family was fairly new to Houston,having just moved from TexasCity in June so Kate could be closer to her cancer treatments.&About three weeks into the search,Kate received a photo and a text that gave her hope.The picture showed a young man on the street,holding up a sign and asking for food.HKate said,"Someone on the neighborhood app had been following our posts,and he justtexted me.He was not sure that's him,but I was!That's my son!"烟Following the information,Kate and Brandon immediately rushed to the area,which wasjust five miles away in southeast Houston.There they miraculously found Micah,safe and吟sound.》注意：霄1.续写词数应为150左右；2.请按如下格式在答题卡的相应位置作答。It turned out that on the day when Micah disappeared,a homeless couple took him in.After three weeks away,Micah was just happy to be back home.【高一英语第10页（共10页）】·23-404A·

2.所使用语法结构和词汇较为丰富、准确，可能有些许错误，但不影响意义表达。3.比较有效地使用了语句间的连接成分，使所续写短文结构紧凑。第三档：(11一15分)1.与所给短文关系较为密切，与所提供各段落开头语有一定程度的衔接。2.应用的语法结构和词汇能满足任务的要求，虽有一些错误，但不影响意义表达。3.应用简单的语句间连接成分，使全文内容连贯。第二档：(6一10分)1.与所给短文有一定的关系，与所提供各段落开头语有一定程度的衔接。2.语法结构单调，词汇项目有限，有些语法结构和词汇方面的错误，影响了意义的表达。3.较少使用语句间的连接成分，全文内容缺少连贯性。第一档：(1一5分)1.与所提供短文和开头语的衔接较差。2.语法结构单调，词汇项目很有限，有较多语法结构和词汇方面的错误，严重影响了意义的表达。3.缺乏语句间的连接成分，全文内容不连贯。不得分：(0分)白卷、内容太少无法评判或所写内容与所提供内容无关。天一文化TIANYI CULTURE一9

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55.D他们的团队在一起学会了全身心地投入到他们的任务和旅程中。语法填空56.eventually 57.with 58.going 59.to develop 60.created 61.information62.was grown 63.longer 64.after 65.who/that写作第一节One possible version:Good afternoon,everyone!As we all know,oceans play an important role in our daily life.In a way,human beingscan't live without oceans.Then,what can we do to protect them?First of all,we should limit the use of plastic,so as not to put sea creatures at risk.Sec-ondly,saving energy is essential.We may use energy efficient electrical appliances.Thirdly,keeping beaches and waterways clean is also of great importance.Lastly,we must tell othersabout ocean conservation.Each person can make a difference.In conclusion,as long as we alltry hard,we'll protect oceans well.第二节One possible version:The next morning,Anna went to Mrs Smith's house again."I think you overpaid me lastnight,"she said and handed the twenty-dollar bill to her.Mrs Smith looked surprised."Ididn't know where that money had gone!I knew that I had put it in my purse.Then thismorning,I couldn't find it.She started to cry."It's the last payment for something my hus-band needed.I made a mistake of giving you the twenty dollars,but you are such an honestand kind girl that you did not keep it.Mrs Smith opened her purse and counted out six dollars."I hope you'll baby-sit for usagain.Our children think you're the best baby-sitter they've ever had,and so do I.I thinkthey will be proud of having such a great sister baby-sit them!"Anna said yes and went backhome happily.When she gave her mother the six dollars,the best gift for her,she felt veryproud because she thought she did a great job.附：听力部分录音材料(Text 1)M:How about these shirts in brown or in dark blue?These two colors are coming in this·13太【23新教材·DY·英语·参考答案一WYB一选择性必修第四册一QG】