2018届安徽省六安市第一中学高三上学期第五次月考英语试题

六安一中2025届高三年级第四次月考数学试卷时间：120分钟 满分：150分一､选择题：本题共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.已知是两个不同的平面，是两条不同的直线，下列命题不正确的是（ ）A.若，则B.若，则C.若，则D.若，则2.如图所示，在四棱锥中，底面是正方形，为中点，若，则（ ）A. B.C. D.3.某学校高二年级选择“物化生”，“物化地”和“史地政”组合的同学人数分别为240，90和120.现采用分层抽样的方法选出30位同学进行某项调查研究，则“史地政”组合中选出的同学人数为（ ）A.8B.12C.16D.64.已知数列的首项，则（ ）A.48B.80C.63D.655.已知等差数列满足，前项和为，若，则与最接近的整数是（ ）A.5B.4C.2D.16.已知数列满足，若对于任意都有，则实数的取值范围是（）,αβ,m n m ∥,n m α⊥n α⊥,m m αβ⊥⊥α∥β,m m αβ⊥⊂αβ⊥m ∥,n ααβ⋂=m ∥nP ABCD -ABCD E PD ,,PA a PB b PC c === BE =111222a b c -+ 111222a b c -- 131222a b c -+ 113222a b c -+ {}n a 110,1n n a a a +==++8a ={}n a 131,3a a ==n n S 12111n nT S S S =+⋯+9T {}n a *712,8,2,8n n a n n a n a n -⎧⎛⎫-+>⎪ ⎪=∈⎝⎭⎨⎪≤⎩N *n ∈N 1n n a a +>aA. B. C. D.7.在棱长为2的正方体中，是线段上一个动点，则下列结论正确的有（）A.不存在点使得异面直线与所成角为B.存在点使得异面直线与所成角为C.存在点使得二面角的平面角为D.当时，平面截正方体所得的截面面积为8.已知一圆柱的轴截面为正方形，母线长为，在该圆柱内放置一个棱长为的正四面体，并且正四面体在该圆柱内可以任意转动，则的最大值为（）A.1B.2C.D.4二､多选题：本题共3小题，每小题6分，共18分.在每小题给出的选项中，有多项符合题目要求.全部选对的得6分，部分选对的得部分分，有选错的得0分.9.如图的形状出现在南宋数学家杨辉所著的《详解九章算法∙商功》中，后人称为“三角垛”.“三角垛”最上层有1个球，第二层有3个球，第三层有6个球，，设第层有个球，从上往下层球的总数为，则（ ）A. B.C. D.1,12⎛⎫⎪⎝⎭113,220⎛⎫ ⎪⎝⎭13,120⎛⎫ ⎪⎝⎭31,2⎛⎫ ⎪⎝⎭1111ABCD A B C D -M 11A C M BM AC 90 M BM AC 30 M M BD C --451114A M AC =BDM 92a a ⋯n n a n n S 34S a =132n n n a a ++-=11n n a a n +-=+1055a =10.在边长为6的菱形中，，现将沿折起到的位置，使得二面角是锐角，则三棱锥的外接球的表面积可以是（ ）A.B.C.D.11.对于棱长为1（单位：）的正方体容器（容器壁厚度忽略不计），下列说法正确的是（ ）A.底面半径为高为的圆锥形罩子（无底面）能够罩住水平放置的该正方体B.C.该正方体内能同时整体放入两个底面半径为高为的圆锥D.的圆锥三､填空题：本题共3小题，每小题5分，共15分.12.已知一组数据的平均数是1，则这组数据的中位数为__________.13.已知四棱锥平面，底面是为直角，的直角梯形，如图所示，且为的中点，则到直线的距离为__________.14.若在长方体中，.则四面体与四面体公共部分的体积为__________.四､解答题：本题共5小题，共77分.解答应写出文字说明､证明过程或演算步骤.15.（本小题满分13分）设三角形的内角的对边分别为且.（1）求角的大小；（2）若，求三角形的周长.16.（本小题满分15分）已知无穷等比数列的前项和为（1）求的值；ABCD π3A ∠=ABD V BD PBD V P BD C --P BCD -58π45π48π55πm 1m,1m 0.5m,0.8m 31,2,0,1,,1x -,A EBCD AE -⊥BCDE EBCD E ∠EB ∥DC 224,CD EB AE DE ====F AD F BC 1111ABCD A B C D -13,2,4AB BC AA ===11ABB C 11AC BD ABC A B C ､､a b c ､､()2sin 2AB C +=A 3,b BC =ABC {}n a n 3nn S b=+1,b a（2）设，求数列的前项和.17.（本小题满分15分）如图所示，在三棱柱中，平面，点是的中点（1）证明：；（2）求与平面所成角的正弦值.18.（本小题满分17分）如图1，在等腰梯形中，，点在以为直径的半圆上，且，将半圆沿翻折如图2.（1）求证：平面；（2）当多面体的体积为32时，求平面与平面夹角的余弦值.19.（本小题满分17分）若存在非零常数，使得数列满足，则称数列为“数列”.（1）判断数列：是否为“数列”，并说明理由；（2）若数列是首项为1的“数列”，数列是等比数列，且与满足，求的值和数列的通项公式；（3）若数列是“数列”，为数列的前项和，，证明：221,1,2,3,n n c a n n =+-= {}n c n n T 111ABC A B C -112,AC BC AB AB ===⊥ABC 1,AC AC D ⊥AC 11AC B C ⊥1A D 11BB C C ABCD AD ∥,8,4,60BC AD BC DAB ∠===,E F AD »»»AE EFFD ==AD EF ∥ABCD ABE DCF -ABE CDF t {}n a ()11231,n n a a a a a t n n +-=≥∈N {}n a ()H t 1,3,5,11,152()2H {}n a ()H t {}n b {}n a {}n b 212321log ni n n i aa a a ab ==+∑ t {}n b {}n a ()H t n S {}n a n 11,0a t >>1e n S nn n t S S -+>--六安一中2025届高三年级第四次月考数学试卷参考答案1.D2.C3.A4.C5.C6.C7.D8.D9.ACD 10.AD 11.BD 12.【答案】114.15.（1）因为为的内角，所以，因为，所以可化为：，即，即解得：，即.（另解：由；得.）（2）由三角形面积公式得代入得：，所以，故为正三角形，，周长等于16.（1）当时，，因为是等比数列，所以，又因为，所以（2）由（1）知，43,,A B C ABC V ()sin sin B C A +=21cos sin22A A -=()2sin 2A B C +=)sin 1cos A A =-sin A A =πππ4πsin ,3333A A ⎛⎫⎛⎫+=+∈ ⎪ ⎪⎝⎭⎝⎭π2π33A +=π3A =2sin 2sincos 222A A A A =⋅=πtan 226A A ==11sin ,322b c A b ⋅==1π13sin 232c ⨯⋅=a c =ABC V 3a b c ===9.2n ≥1123n n n n a S S --=-=⨯{}n a 12a =113a S b ==+1b =-123n n a -=⨯因为，且，所以是以6为首项，9为公比的等比数列，.17.解析：（1）由题意，平面平面，所以，又，且平面，所以平面，因为平面，所以.（2）法一（坐标法）：由（1）知，又，所以，以为原点建立如图所示的空间直角坐标系，则，，所以，，设平面的法向量为，则，所以，从而故直线与平面法二（几何法）：取中点，则，26a =2229n na a +={}2n a ()()2421321n n T a a a n ⎡⎤=+++++++-⎣⎦()291236919124n n n n n -⋅=⨯+=-+-1AB ⊥,ABC AC ⊂ABC 1AC AB ⊥1AC AC ⊥11AB AC ⊂､1111,AB C AB AC A ⋂=AC ⊥11AB C 11B C ⊂11AB C 11AC B C ⊥11AC B C ⊥BC ∥11B C AC BC ⊥C ()()()()10,0,0,2,0,0,0,2,2,0,2,0C B B A ()0,1,0D ()()()12,0,0,2,2,2,0,1,0CB BB DA ==-=()()()1110,1,02,2,22,3,2DA DA AA DA BB =+=+=+-=-11BC C C (),,n x y z =1202220n CB x n BB x y z ⎧⋅==⎪⎨⋅=-++=⎪⎩ ()0,1,1n =- 111cos ,DA n DA n DA n⋅===⋅1A D 11BB C C 11C A M CM ∥1A D记与面所成角为，则由知解得，又，所以18.（1）连由等边三角形可知分布在同一个圆周上，且，则六边形为正六边形，面面（2）在图1中连交于，则，连交于，则，故在图2中面面记面与面所成角为，则故，即面面法一（几何法）：延长交于延长交于则为面与面交线且取中点，连接，则即为面与面所成角在中，，故，故面与面所成角的余弦值为法二（坐标法）：以为坐标原点，所在的直线为轴，建立空间直角坐标系，则，CM 11BB C C θ1111112sin A CC B BM CC B Bd d CMCMθ--==111111A B C C C A B C V V --=11111111133B C C A A B C S d S AB ⋅=⋅1A d =CM ===sin θ=OB OC ､A B C D F E ､､､､､AE EF FD DC CB BA =====ABCDFE EF ∴∥AD ∥,BC EF ⊄ABCD,BC ⊂ABCD EF ∴∥ABCDEB AD 1O AD EB ⊥FC AD 2O AD FC ⊥AD ⊥1,EO B AD ⊥2FO CABE CDF θ1212,6sin EO B FO C EO B FO C S S ∠∠θθ====V 1221ABE DCF EO B FO C D FO CA EOB V V V V ----=++锥112121132sin 3233EO B EO B FO C S AO S EF S DO θ=⨯+⨯+⨯==V πsin 1,2θθ==AEFD ⊥ABCDAB DC ､,Q F AE D ､,P PQ ABE CDF 8,8AP AQ PD QD ====PQ M AM DM ､AMD ∠ABE CDF AMD V 8AM DM AD ===1cos 5AMD ∠==ABE CDF 151O 111,,O B O D O E ,,x y z ()()(()()(0,2,0,,0,0,,4,0,0,6,0,0,4,A B E C D F -，有令得同理可得面法向量，设面与面所成角为，故19.【详解】（1）根据”数列“的定义，则，故，因为成立，成立，不成立，所以不是”数列“.（2）由是首项为2的”数列“，则，由是等比数列，设公比为，由，则.两式作差可得，即，由是”数列“，则，对于恒成立，所以，即对于恒成立，则，即，因为解得，，又由，则，即，故所求的，数列的通项公式.（3）设函数，则，令，解得，当时，，则在区间单调递减，且，又由是”数列"，即，对于恒成立，()(2,0,0,2,AB AE ==2020AB n y AE n y ⎧⋅=+=⎪⎨⋅=+=⎪⎩1,x=()1,n =CDF ()m =ABE CDF α1cos 5m n m n α⋅==⋅ ()H t 2t =11232n n a a a a a +-= 212a a -=3212a a a -=43211113542a a a a -=-⨯⨯=-≠1,3,5,11,152()2H {}n a ()H t 231,21a t a t =+=+{}n b q 212321log nn n i iaa a a ab ==+∑ 121231211log n i n n n i a a a a a a b +++==+∑ ()2112312121log log n n n n n a a a a a a b b +++=-+- ()21123121log n n n a a a a a a q ++=-+ {}n a ()H t 1123n n a a a a a t +-= 1,n n ≥∈N ()()211121log n n n a a t a q +++=--+()12121log log n n n t a t b b +++=+-1,n n ≥∈N ()()22321log 1log t a t q t a t q ⎧+-=⎪⎨+-=⎪⎩()()222(1)log 121log t t qt t t q ⎧+-=⎪⎨++-=⎪⎩0t ≠1,2t q =-=2111211,log a a a b ==+11b =12n n b -=1t =-{}n b 12n n b -=()ln 1f x x x =-+()11f x x'=-()0f x '=1x =1x >()0f x '<()ln 1f x x x =-+()1,∞+()1ln1110f =-+={}n a ()H t 1123n n a a a a a t +-= 1,n n ≥∈N因为，则，再结合，反复利用，可得对于任意的，则，即，则，即，相加可得，则，又因为在上单调递增，所以，又，所以，即，故.11,0a t >>211a a t =+>121,0,1a t a >>>1123n n a a a a a t +=+ 1,,1n n n a ≥∈>N ()()10n f a f <=ln 10n n a a -+<ln 1n n a a <-1122ln 1,ln 1,,ln 1n n a a a a a a <-<-⋯<-1212ln ln ln n n a a a a a a n +++<+++- ()12ln n n a a a S n <- ln y x =()0,x ∞∈+12en S nn a a a -< 1123n n a a a a a t +-= 1e n S nn a t -+-<1en S nn n S S t -+--<1en S nn n t S S -+>--。

安徽省六安市2018届高三英语上学期第三次月考试题第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest the woman do?A. Close her eyes to relax for a while.B. Make an appointment at once.C. Get a calendar soon.2. What is Tim doing?A. Locking the door.B. Walking a dog.C. Knocking at the door.3. What’s the man’s favorite subject?A. English.B. Math.C. Both English and math.4. What has the woman been doing?A. Doing the garden.B. Working at her office.C. Taking a long shower.5. Where did the woman finally put her desk?A. Behind the door.B. Under the big window.C. Under the little window opposite the door.第二节（共15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，各小题将给出5秒钟的作答时间。

安徽省六安市第一中学2017-2018学年高二9月月考英语试题第二部分阅读理解（共15小题，每题2分，满分30分）第一节（共10小题；每小题2分，满分20分)阅读下面三篇短文，从每题所给的四个选项(A、B、C、D)中，选出最佳选项，并在答题卡上将该项涂黑。

AAunt Karen always had a special place in my heart. When I was growing up, I knew I could count on her to have room for me on her lap and words of love and encouragement when I needed to hear them. When she died five years ago，I was devastated. The whole family was still in shock when her husband, Uncle Ronnie, died a week later. I longed to have a small item o f Aunt Karen’s to remember her by, but seeing her children and grandchildren overcome by the grief of this double loss made me shy away from asking.A few months after Aunt Karen’s death, I was on my way to work when I saw Rescued Treasures, a local second-hand store. I only had a couple of dollars on me and didn’t really intend to buy anything, but I stopped anyway just to look inside. I had been shopping around for a few minutes when a small, black handbag caught my eye. It wasn’t fancy or special. I didn’t really need a handbag and continued to look around the store, but something kept drawing me back to that handbag. Finally, I checked the price tag (标签). It was just one dollar.The handbag stayed in the back of my car for weeks until I came upon it during a car clean-up. I opened it up. I couldn’t believe it. They hadn’t even cleaned it out. It was still full of junk, old candy wrappers, old receipts (收据) and used paper. Usually the store emptied things inside, so there wouldn’t be any surprises for a new owner.I threw away some wastes, and sorted through the receipts, when I found one item in the small inside pocket. It was an insurance card with the name “Karen Stair”written on it. I began to cry. My beloved Aunt Karen. This was her handbag.1. What do we know from the passage?A. Karen’s husband survived her by five years.B. Karen’s children refused to give any item to the author.C. The author was very shy when she was young.D. Karen had been very kind to the author.2. The underlined word “devastated” in Paragraph 1 probably means “”.A. very worriedB. a little lonelyC. extremely sadD. slightly disappointed3. The author made up her mind to buy the handbag because .A. she just needed to buy a handbagB. the bag looked strange and was worth the priceC. it happened that she could afford itD. someone else persuaded her to buy it4. As soon as the author opened the handbag, she felt very .A. surprisedB. excitedC. sickD. nervous【答案】1. D 2. C 3. C 4. A【解析】本文是记叙文。

安徽省六安市2018届高三英语上学期第三次月考试题第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest the woman do?A. Close her eyes to relax for a while.B. Make an appointment at once.C. Get a calendar soon.2. What is Tim doing?A. Locking the door.B. Walking a dog.C. Knocking at the door.3. What’s the man’s favorite subject?A. English.B. Math.C. Both English and math.4. What has the woman been doing?A. Doing the garden.B. Working at her office.C. Taking a long shower.5. Where did the woman finally put her desk?A. Behind the door.B. Under the big window.C. Under the little window opposite the door.第二节（共15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，各小题将给出5秒钟的作答时间。

安徽省六安市第一中学2018届高三上学期第五次月考英语试题时间：120分钟总分：150分第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest doing?A. Buying a road map.B. Driving to the beach.C. Going back home.2. What day is it today?A. Tuesday.B. Thursday.C. Friday.3. What is the weather probably like today?A. HotB. Cold.C. Cool.4. Where does conversation probably take place?A. At home.B. In a restaurantC. In a furniture shop.5. How will the woman mainly deal with the money?A. Save most of it.B. Buy a lot of clothes.C. Give it to her parents.第二节（共15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分钟；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。

听下面一段对话，回答第6和第7两个小题。

6. What does the woman plan to do this weekend?A. Work overtime.B. Attend a festival.C. His cousin.7. Whom will the man probably ask for help?A. His auntB. His sisterC. His cousin听下面一段对话，回答第8至第9三个小题。

安徽省六安市第一中学2018届高三上学期第三次月考英语试题第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest the woman do?A. Close her eyes to relax for a while.B. Make an appointment at once.C. Get a calendar soon.2. What is Tim doing?A. Locking the door.B. Walking a dog.C. Knocking at the door.3. What’s the man’s favorite subject?A. English.B. Math.C. Both English and math.4. What has the woman been doing?A. Doing the garden.B. Working at her office.C. Taking a long shower.5. Where did the woman finally put her desk?A. Behind the door.B. Under the big window.C. Under the little window opposite the door.第二节（共15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，各小题将给出5秒钟的作答时间。

第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest the woman do?A. Close her eyes to relax for a while.B. Make an appointment at once.C. Get a calendar soon.2. What is Tim doing?A. Locking the door.B. Walking a dog.C. Knocking at the door.3. What’s the man’s favorite subject?A. English.B. Math.C. Both English and math.4. What has the woman been doing?A. Doing the garden.B. Working at her office.C. Taking a long shower.5. Where did the woman finally put her desk?A. Behind the door.B. Under the big window.C. Under the little window opposite the door.第二节（共15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，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

六安一中2025 届高三年级第四次月考英语试卷时间：120 分钟总分：150 分第一部分听力(共两节，满分30 分)第一节(共 5 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。

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. When did Mr Smith expect the man to call?A. Before 10:15.B. Before 10:30.C. Before 10:45.2. What will the man do next?A. Go back home.B. Take off his coat.C. Turn on the lights.3. What is the man?A. A driver.B. A model.C. A salesman.4. Why does the woman want to lose weight?A. To keep healthy.B. To take wedding photographs.C. To attend her friend’s wedding.5. Where is the woman going?A. The park.B. The office.C. The supermarket.第二节(共15 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，各个小题将给出 5 秒钟的作答时间。

每段对话或独白读两遍。

听下面一段对话，回答第 6 至第7 两个小题。

6. What is the probable relationship between the speakers?A. Husband and wife.B. Mother and son.C. Brother and sister.7. What caused the death of the goldfish probably?A. Too much fish food.B. The small fishbowl.C. Lack of water.听下面一段对话，回答第8 至第10 三个小题。

六安市第一中学2018届高三上学期第五次月考英语试题时间：120分钟总分：150分第I卷第一部分：听力（共两节，满分30分）第一节（共5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 does the man suggest doing?A. Buying a road map.B. Driving to the beach.C. Going back home.2. What day is it today?A. Tuesday.B. Thursday.C. Friday.3. What is the weather probably like today?A. HotB. Cold.C. Cool.4. Where does conversation probably take place?A. At home.B. In a restaurantC. In a furniture shop.5. How will the woman mainly deal with the money?A. Save most of it.B. Buy a lot of clothes.C. Give it to her parents.第二节（共15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分钟；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。

听下面一段对话，回答第6和第7两个小题。

6. What does the woman plan to do this weekend?A. Work overtime.B. Attend a festival.C. His cousin.7. Whom will the man probably ask for help?A. His auntB. His sisterC. His cousin听下面一段对话，回答第8至第9三个小题。