华师导航教育港澳台联考周考三
港澳台华侨生联考试题：数学基础练习30套：第22套：三角函数基础(含答案)
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2021年华师附属高级中学高三英语第三次联考试卷及参考答案
2021年华师附属高级中学高三英语第三次联考试卷及参考答案第一部分阅读（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A、B、C、D四个选项中选出最佳选项AFour Truly Unique Canadian Camping ExperiencesMount Robson Provincial Park,British ColumbiaNamed after the highest mountain in the Canadian Rockies, this park gives you breathtaking views of mountain landscapes along with lakes, waterfalls, canyons, and caves. The Berg Lake campground is located right at the northern base of the 3, 954-meter peak (山巅), which is about a day's hike in.Fundy National Park,New BrunswickIf you've grown tired of the tent or RV, this park is one of the few national parks offering yurt (蒙古包) rentals. Make sure you visit theBay of Fundywhere the world's highest tides make for some great surfing. You also can't miss the amazing Acadian forest waterfall. If you're looking for even more entertainment, the park also hostsmusic and cultural festivals each summer and has its own golf course.KluaneNational Parkand ReserveYukonFrom May to September, theKathleenLakecampground sees visitors come from far and wide to camp, hike and fish. Mountaineering is especially popular as Kluane is home to 17 of Canada's 20 highest peaks. Flightseeing over the park's glaciers and rafting (漂流) the winding Alsek River will also keep you out enjoying the wilderness.Prince Edward Island National Park,Prince Edward IslandIf you're looking for a family-friendly park, this one is wonderful. Between the seven beaches and more than 50 kilometersof hiking and cycling trails, you'll certainly be kept busy. Literature lovers, you can see what inspired L.M. Montgomery'sAnne of Green Gables at the nearby Green Gables Heritage Place and even explore the original house.1. Where is the park offering yurt rentals located?A. InBritish Columbia.B. InNew Brunswick.C. InYukon.D. InPrince Edward Island.2. What can you do inKluaneNational Parkand Reserve?A. Climb the highest mountain inCanada.B. Experience the highest tides.C. Raft the windingAlsekRiver.D. Attend music and cultural festivals.3. Which will you choose if you are a fan of Anne of Green Gables?A.Mount RobsonProvincialPark.B. Fundy National Park.C.KluaneNational Parkand Reserve.D.Prince Edward IslandNational Park.BIsraeli Paintings—Israeli artist Menashe Kadishman will hold a personal show named "Flock of Sheep" from November 26 to December 20 at the China National Art Museum On show are 550 colourful oil paintings of sheep heads.His works have been on show inthe Metropolitan Museum in New York and Tate Gallery in London over the past 30 years.Time: 9: 00 a.m.—4: 00 p.m., November 26—December 20.Place: China National Art Museum, 1 Wusi Dajie, Dongcheng District, Beijing.Tel: 6401-2252Russian Ballet—The Kremlin Ballet from Russia will perform two immortal classical ballets—"Swan Lake" and "The Nutcracker"—at the Beijing Beizhan Theatre. Set up in 1990, the theatre has a number of first-class ballet dancers. Most of their performances are classical.Time: 7: 15 p.m., December 5 and 6 ("Swan Lake"); 7: 15 p.m., December 7 ("The Nutcracker")Place: Beizhan Theatre, Xiwai Dajie, Xicheng District, Beijing.Tel: 6605-3388Folk Concert—The Central Conservatory of Music will hold a folk concert in memory of the late musician Situ Huacheng.On the programme are many popular folks such as "Moon Night on the Bamboo Tower", "Celebrating Harvest", "Deep and Lasting Friendship", "Golden Snake Dances Wildly" and "Children's Holiday".Time: 7: 30 p.m., November 25.Place: Beijing Concert Hall, 1 Beixinhuajie, Xicheng District, Beijing.Tel: 6605-58124.If a child is very fond of dancing, his parents should take him to ________.A.China National Art MuseumB.Beizhan TheatreC.Beijing Concert HallD.1 Wusi Dajie5.Menashe Kadishman is well known for painting ________.A.deerB.birdsC.sheepD.flowers6.Which of the following is TRUE?A.The folk concert will last three days.B.The ballet "The Nutcracker" will be put on once.C.The Israeli paintings will be on show for a month.D.China National Art Museum lies in Xicheng District.7.If you dial the telephone number 6605-3388 on Dec. 8, you can ________.A.go to the folk concertB.visit the Art MuseumC.watch the balletD.none of the aboveCI cried the first time I saw the Notre Dame（巴黎圣母院）years ago. I'd waited my entire life to see this great French architecture, and experienced it in its full glory on a bright sunny day. Last night, I again cried for the centuries-old church while watching it burn.I hadn't expected to spend my evening that way. My friend and I were having dinner at a cafe a block or so away from the Notre Dame, choosing to skip going inside with the intention to go back the next day.However, we heard that it caught fire, so we left the cafe and ran towards the church, following heavy smoke from it, and soon we joined a nearly silent crowd. Some were praying, some were crying, but most were staring in disbelief at the disaster happening before us. The fire continued to get worse. About 400 firefighters were working to control the fire. We could see their flashlights shining as they inspected the front from a balcony.The Notre Dame is part of the heartbeat ofParis, I reflected on the experiences I've had there, from attending a bread market out front to admiring the beautiful windows and architecture inside. It is a spot that helps makeParismagical. And here we were, watching it burn down. It was too much to handle, but it was impossible to look away.About 9：30 pm, the gathered crowd spontaneously（自发地）began to sing Hymns（圣歌）to the church. We sang along with the group, feeling at once less like tourists and more like members of them. I hadn't imagined all that before.For hundreds of years, the Notre Dame hasseen the most joyous and the most terrible moments in the lives of both France and her people. And when everyone was able to become one emotional force, it showed that even in her darkest hour, the Notre Dame was still there to bring us all together.8. Why did the author cry for the Notre Dame for the first time?A. She was touched by its greatness.B. She was sorrowful to watch it burn.C. She was regretful for missing its glory.D. She was excited about French cultures.9. What was the author doing when the Notre Dame caught fire?A. Heading for a faraway cafe.B. Visiting a church with a friend.C. Eating nearby with a friend.D. Wandering along the street alone.10. What can we know about the fire scene?A. People expressed their sadness in different ways.B. People were nervously rushing in different directions.C. Hundreds of volunteers joined in putting out the fire.D. Firefighters kept people away with shining flashlights.11. What impressed the author most?A. The church allowed visitors to gaingreat experiences.B. Many foreign tourists became members of the church.C. The church survived disasters for hundreds of years.D. People were brought together to sing to the church.DAmerica---that glorious symbol of multiculturalism, the great melting pot---qualifies as part of the developed world, right? Not quite, if we consider the state of second language learning in schools across the country. According to a 2018 study, Europe often tops the U.S. in foreign language education in school. 92% of European students are learning a foreign language in school. In America it’s only 20%. In more than 20 European countries, studying a foreign language for at least one year is compulsory. In comparison, only 10 states and D.C. require learning a foreign language for graduation.I went to a public school in Pennsylvania that ranked onNewsweek’s list of America’s top high schools in 2015. Foreign language learning was not a graduation requirement. A common response to such stories and statistics is: So what? Why should Americans care about learning another language when English has recently seemed to dominate as the official language of the world?The world is globalizing faster than we can imagine. More than half of the world’s population speaks more than one language. It is also increasingly becoming the need for success in this globalizing world. Having the ability to speak a second language opens up the possibility of travelling and immersing yourself in another part of the world. This means people can feel other cultures, and traditions in places you were previously kept away because you could not communicate in the language.The teaching of foreign languages can be instrumental in bringing about peace and unity in the country we live in. Learning a second language can be an efficient vehicle to help to bridge communities. To speak another language means having access to a universe of different experiences and world views of another community of people.12. Why does the writer mention Europe?A. America makes studying a foreign language compulsory.B. America is the glorious symbol of multiculturalism.C. America isn’t really qualified as the developed world.D. America doesn’t focus on foreign language education13. What is American’s attitude towards education of foreign languages?A. Less concerned.B. More worried.C. Quite doubtful.D. Very supportive.14. What can visiting people do if they can speak the language where they visit?A. Make the world globalizing.B. Achieve success in business.C. Experience people’s real life there.D. Keep away their own culture.15. What is the main idea of the last paragraph?A. Using a second language can bring harmony.B. Communities of people enjoy the great views.C. Speaking another language is reallynecessary.D. Learning a second language can be difficult.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
港澳台联招辅导班考前综合试题：数学3含答案
1 2 3 2 n n 1 3. 设 n N ,则 C n Cn 6 Cn 6 Cn 6
4. 函数 f ( x) sin x 2 | sin x |, x 0,2 的图象与直线 y k 有且仅有两个不同的交点，则 k 的取值范 围是__________。 1 k 3 5. PA⊥平面 ABC，∠ACB=90°且 PA=AC=BC=a，则异面直线 PB 与 AC 所成角的正切值等于 2 ．
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由此得 cos B
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广东省华南师范大学附属中学2021届高三数学月考试题(三)理(含解析).doc
广东省华南师范大学附属中学2021届高三数学月考试题（三）理（含解析）本试卷分选择题和非选择题两部分，共4页，满分150分，考试用时120分钟. 注意事项：1.本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分.答卷前，考生务必将自己的姓名和考生号、试室号、座位号等填写在答题卡上，并用2B 铅笔在答题卡上的相应位置填涂考生号.2.回答第Ⅰ卷时，选出每小题答案后，用2B 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，再选涂其它答案标号.3.回答第Ⅱ卷时，用黑色钢笔或签字笔将答案写在答卷上.第Ⅰ卷一、选择题：本大题共12小题，每小题5分，共60分.每小题给出的四个选项中，只有一项符合题目要求.1.已知复数14z i =-，24z i =+，则12z z i等于（ ） A. 15i B. 15i -C. 17iD. 17i -【答案】D 【解析】 【分析】根据复数乘法和除法运算法则可求得结果. 【详解】()()12441717i i z z i i i i-+===- 故选：D【点睛】本题考查复数的乘法和除法混合运算，属于基础题. 2.设集合A ={5，ba，a -b }，B ={b ，a +b ，-1}，若A ∩B ={2，-1}，则A ∪B =（ ） A. {}2,3B. {1,-2，5}C. {2,3，5}D. {1,-2，3，5}【答案】D【解析】 【分析】根据A∩B＝{2，－1}，得21b a a b ⎧=⎪⎨⎪-=-⎩或12ba ab ⎧=-⎪⎨⎪-=⎩，求得a b 、代入集合B 中检验，即可求得结果. 【详解】A∩B＝{2，－1}，{}5,2,1A ∴=-，21b a a b ⎧=⎪⎨⎪-=-⎩或12b a a b ⎧=-⎪⎨⎪-=⎩，解得12a b =⎧⎨=⎩或11a b =⎧⎨=-⎩（1）当12a b ==，时，{}2,3,1B =-满足题意，{}1,2,3,5A B ⋃=- （2）当11a b ==-，时，{}1,0,1B =--不满足集合元素的特征，舍去 综上{}1,2,3,5A B ⋃=- 故选D.【点睛】本题考查集合中元素的特征，根据题意由其中一个集合条件解出未知数，代入另一个集合检验是常用的解题思路，考查了分类讨论思想，属于基础题.3.设平面α与平面β相交于直线m ，直线a 在平面α内，直线b 在平面β内，且b m ⊥，则“a b ⊥”是“αβ⊥”的( ) A. 充分不必要条件 B. 必要不充分条件 C. 充要条件 D. 既不充分也不必要条件【答案】B 【解析】试题分析：因为直线a 在平面α内，直线b 在平面β内，且b l ⊥，若αβ⊥，根据面面垂直的性质定理，,b α⊥一定有b a ⊥；反之，当b a ⊥，若a l 时，αβ⊥不一定成立，所以“a b ⊥”是“αβ⊥”的必要不充分条件，故选B. 考点：1、充分条件与必要条件；2、面面垂直的判定与性质. 4.若110a b<<，则下列四个不等式恒成立的是（ ）A. ||||a b >B. a b <C. 33a b <D.a b ab +<【答案】D 【解析】 【分析】由不等式可得0b a <<，依次验证各个选项可得结果. 【详解】110a b<< 0b a ∴<< a b ∴<，a b <，33b a <，可知,,A B C 错误；0ab >，0a b +< a b ab ∴+<，D 正确.故选：D【点睛】本题考查根据不等式的性质比较大小的问题，属于基础题.5.过抛物线22y x =的焦点作一条直线与抛物线交于,A B 两点，它们的横坐标之和等于1，则这样的直线（ ） A. 有且仅有零条 B. 有且仅有一条C. 有且仅有两条D. 有且仅有四条 【答案】B 【解析】 【分析】根据AB 与抛物线的通径长相等可确定这样的直线有且仅有一条. 【详解】由抛物线方程知其通径长为：22p =由抛物线焦点弦公式可知：12112AB x x p =++=+=，与通径长相等∴这样的直线有且仅有一条故选：B【点睛】本题考查抛物线中焦点弦的相关问题，涉及到抛物线焦点弦长的求解，需明确焦点弦中最短的为通径.6.如图，在三棱锥O ABC -中，1OA OB OC ===，90AOB ︒∠=，OC ⊥平面AOB ，D 为AB 中点，则OD 与平面OBC 所成的角为（ ）A.4π B.3π C.2π D.34π 【答案】A 【解析】 【分析】取OB 中点E ，由线面垂直性质可得DE OC ⊥，由三角形中位线性质可得DE OB ⊥，从而根据线面垂直判定定理证得DE ⊥平面OBC ，由线面角定义可知DOE ∠为所求角；利用等腰三角形性质可求得结果.【详解】取OB 中点E ，连接DEOC ⊥平面OAB ，DF ⊂平面OAB DE OC ∴⊥,D E 分别为,AB OB 中点 //DE OA ∴，又AOB 90∠= DE OB ∴⊥,OB OC ⊂平面OBC ，OB OC O = DE ∴⊥平面OBCDOE ∴∠即为OD 与平面OBC 所成角OA OB =，D 为AB 中点 1452DOE AOB ∴∠=∠=，即4π OD ∴与平面OBC 所成角为4π故选：A【点睛】本题考查直线与平面所成角的求解问题，关键是能够结合线面垂直性质与判定定理、三角形中位线的性质，在图形中找到垂直关系，从而确定直线与平面所成角. 7.函数sin sin 122xxy =+的部分图象大致是（ ）A. B.C. D.【答案】D 【解析】 因为()sin()sin sin()sin 11()2222x x x xf x y f x ---=+==+=，所以函数sin sin 122xxy =+是定义在R 上的偶函数，排除A 、B 项；又sin2sin2115()222222f πππ=+=+=，排除C ，综上，函数sin sin 122xxy =+大致的图象应为D 项，故选D.8.若f(x)=21ln(2)2x b x -++∞在(-1,+)上是减函数，则b 的取值范围是( ) A. [-1，+∞] B. （-1，+∞）C. （-∞，-1]D. （-∞，-1）【答案】C 【解析】由题意可知()02bf x x x +'=-<+，在(1,)x ∈-+∞上恒成立，即(2)b x x <+在(1,)x ∈-+∞上恒成立，由于1x ≠-，所以1b ≤-，故Ｃ为正确答案．9.已知,αβ为锐角，11sin(2),cos 53αββ+==，则sin()αβ+的值为（ ）【答案】D 【解析】 【分析】 根据cos cos3πβ<可得到32ππβ<<，从而确定23232ππαβ<+<，由同角三角函数可求解出sin β和()cos 2αβ+，利用两角和差正弦公式可求得结果.【详解】11cos cos 323πβ=<=且β锐角 32ππβ∴<<sin β∴=又02πα<<23232ππαβ∴<+<，又()1sin 25αβ+= ()cos 25αβ∴+=-()()()()sin sin 2sin 2cos cos 2sin αβαββαββαββ∴+=+-=+-+⎡⎤⎣⎦111535315⎛⎫+=⨯--⨯= ⎪ ⎪⎝⎭ 故选：D【点睛】本题考查利用两角和差正弦公式求解三角函数值的问题，关键是能将所求角利用已知角配凑出来，进而利用公式进行求解；易错点是在求解同角三角函数值时，未将角的范围确定准确，造成三角函数值的符号求解错误.10.在ABC ∆中，内角A ，B ，C 所对的边分别为a ，b ，c ，若sin 1sin 2B C =，22(3)cos a b C CA CB -=⋅，则角C =（ ）A.6π B.3π C.2π或6π D.3π或2π 【答案】D 【解析】分析：由正弦定理得12b c =，即2c b =，又由22(3)cos a b C CA CB -=⋅，得22(3)cos cos a b C ab C -=，所以cos 0C =或223a b ab -=，分类讨论即可求解C 角的大小.详解：因为sin 1sin 2B C =，由正弦定理得12b c =，即2c b =， 由22(3)cos a b C CA CB -=⋅，得22(3)cos cos a b C ab C -=， 所以cos 0C =或223a b ab -=， 当cos 0C =时，2C π=；当223a b ab -=时，由余弦定理得222222222222(2)31cos 22(3)2(3)2a b c a b b a b C ab a b a b +-+--====--，所以3C π=， 综上所述：2C π=或3C π=.点睛：本题主要考查了利用正弦定理和三角函数的恒等变换求解三角形问题，对于解三角形问题，通常利用正弦定理进行“边转角”寻求角的关系，利用“角转边”寻求边的关系，利用余弦定理借助三边关系求角，利用两角和差公式及二倍角公式求三角函数值. 利用正、余弦定理解三角形问题是高考高频考点，经常利用三角形内角和定理，三角形面积公式，结合正、余弦定理解题.11.如图所示，已知EAB ∆所在的平面与矩形ABCD 所在的平面互相垂直，3,2,60EA EB AD AEB ︒===∠=，则多面体E ABCD -的外接球的表面积为（ ）A.163πB. 8πC. 16πD. 64π【答案】C 【解析】 【分析】取AB 中点F ，由等腰三角形三线合一和面面垂直的性质可确定EF ⊥平面ABCD ，取,AC BD 交点G ，可知球心O 与G 的连线OG ⊥平面ABCD ；作//OM FG ，假设OG MF x ==，分别在Rt EOM ∆和Rt OGB ∆中利用勾股定理可构造关于x 和球的半径R的方程组，解方程组求得R ，代入球的表面积公式即可求得结果.【详解】取AB 中点F ，连接EF ；连接,AC BD ，交于点G ，连接FG ； 设O 为E ABCD -外接球球心，连接OG ，过O 作//OM FG ，交EF 于点M四边形ABCD 为矩形 G ∴为四边形ABCD 的外接圆圆心 由球的性质可知：OG ⊥平面ABCDEA EB =，F AB 中点 EF AB ∴⊥平面EAB ⊥平面ABCD ，平面EAB ⋂平面ABCD AB = EF ∴⊥平面ABCD//OG EF ∴，又//OM FG ∴四边形OMFG 为平行四边形 112OM FG AD ∴===，OG MF = 60AEB ∠=，EA EB = EAB ∴∆为等边三角形 3AB ∴=又933942EF =-=，11139422BG BD ==+= 设OG MF x ==，E ABCD -外接球半径为R则222222331132x R x R ⎧⎫⎪-+=⎪⎪⎪⎪⎝⎭⎨⎛⎫⎪+= ⎪⎪ ⎪⎪⎝⎭⎩，解得：24R = ∴多面体E ABCD -的外接球的表面积2416S R ππ==故选：C【点睛】本题考查棱锥外接球表面积的求解问题，关键是能够根据垂直关系以及球的性质确定球心的位置，通过直角三角形勾股定理来构造出关于球的半径的方程，解方程求得球的半径，进而求得结果.12.正项数列{}n a 的前n 项和为n S ，且()2*2n n n S a a n N =+∈，设()2112nn n na c s +=-，则数列{}n c 的前2021项的和为（ ） A. 20192020-B. 20202019-C. 20202021-D. 20212020-【答案】C 【解析】 【分析】先根据和项与通项关系得11n n a a --=，再根据等差数列定义与通项公式、求和公式得,n n a S ，代入化简n c ，最后利用分组求和法求结果. 【详解】因为()2*2,0n n n nS a a n Na=+∈>，所以当1n =时，21112a a a =+，解得11a =，当2n ≥时，()()2211122n n n n n n n a S S a a a a ---=-=+-+，所以 ()()1110n n n n a a a a --+--=， 因0n a >，所以11n n a a --=，所以数列{}n a 是等差数列，公差为1，首项为1， 所以()()111,2n n n n a n n S +=+-==， 所以()()()2121111112(1)1nn n n n n a n c s n n n n ++⎛⎫=-=-=-+ ⎪++⎝⎭， 则数列{}n c 的前2021项的和11111111202011223342020202120212021⎛⎫⎛⎫⎛⎫⎛⎫=-+++-++++=-+=- ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭. 故选：C【点睛】本题考查根据和项求通项、等差数列定义、等差数列通项公式与求和公式以及分组求和法，考查基本分析求解能力，属中档题.第Ⅱ卷二、填空题（每小题5分，满分20分）13.己知函数23()21x x a f x ⋅+=-在定义域内为奇函数，则实数a=_______．【答案】3 【解析】 【分析】由题得f(-x)+f(x)=0,由此化简求出a 的值.【详解】由题得f(-x)+f(x)=0,所以323232320,0,121212112xxx x xx x x a a a a --+⋅+⋅+⋅++=∴+=---- 322332230,0122121x x x x x x x a a a a +⋅⋅+--⋅+⋅+∴+=∴=---，32230,2(3)(3)0,x x x a a a a ∴--⋅+⋅+=∴---= (21)(3)0,3x a a ∴--=∴=.故答案为3【点睛】本题主要考查奇偶性的性质和指数的运算，意在考查学生对这些知识的掌握水平和分析推理计算能力.14.等差数列{}n a 的前n 项和为n S ，918S =-，1352S =-，等比数列{}n b 中，55b a =，77b a =，则15b 的值为___________.【答案】64-. 【解析】 【分析】根据等差数列前n 项和公式，利用1a 和d 表示出913,S S ，解方程组可求得1a 和d ，由等差数列通项公式求得57,a a ，即57,b b ，进而求得等比数列的2q ，根据等比数列通项公式可求得结果.【详解】设等差数列{}n a 公差为d则91113119899361821312131378522S a d a d S a d a d ⨯⎧=+=+=-⎪⎪⎨⨯⎪=+=+=-⎪⎩，解得：121a d =⎧⎨=-⎩5514242b a a d ∴==+=-=-，77164b a a d ==+=-设等比数列{}n b 公比为q ，则2752b q b == 841574264b b q ∴==-⨯=- 故答案为：64-【点睛】本题考查等差和等比数列的综合应用问题，涉及到等差数列和等比数列的通项公式、等差数列前n 项和公式的应用，属于基础公式的应用问题.15.已知过点()2,2P 的直线与圆()2215x y -+=相切，且与直线10ax y -+=垂直，则a =__________．【答案】2 【解析】设切线为0x ay m ++=，因为过()2,2P ，故22m a =--，所以切线为220x ay a +--=，又圆心到它的距离为d r ===2a =，故填2．16.若关于x 的方程2||2x kx x =+恰有四个不同的实根，则实数k 的取值范围是________. 【答案】(1,)+∞. 【解析】 【分析】将所给方程有四个不同的实根转化为函数1y k =的图象和函数()()()2,02,0x x x g x x x x ⎧+>⎪=⎨-+<⎪⎩的图象有3个交点，通过数形结合的方式来确定1k的范围，进而求得结果. 【详解】关于x 的方程22x kx x =+有四个不同的实根，且0x =是此方程的一个根∴关于x 的方程12k x x =+有3个不同的非零的实数解∴方程()()2,012,0x x x x x x k ⎧+>⎪=⎨-+<⎪⎩有3个不同的非零的实数解，即函数1y k =的图象和函数()()()2,02,0x x x g x x x x ⎧+>⎪=⎨-+<⎪⎩的图象有3个交点画出函数()g x 图象，如图所示：∴当101k <<，即1k >时，函数1y k =和函数()()()2,02,0x x x g x x x x ⎧+>⎪=⎨-+<⎪⎩有3个交点即当()1,k ∈+∞时，方程22x kx x =+恰有四个不同的实根故答案为：()1,+∞【点睛】本题考查根据方程根的个数求解参数范围的问题，关键是能够将问题转化为两函数的交点个数的问题，通过数形结合的方式，结合函数图象可确定参数的取值范围.三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17-21题为必考题，每个试题考生都须作答.第22、23题为选考题，考生根据要求作答. （一）必考题：共60分. 17.若向量()3sin ,sin a x x ωω=，()cos ,sin b x x ωω=，其中0>ω，记函数()12f x a b =⋅-，若函数()f x 216π+. （I ）求()f x 的表达式；（II ）设ABC ∆三内角,,A B C 的对应边分别为,,a b c ，若3a b +=，3c =，()1f C =，求ABC ∆的面积.【答案】（Ⅰ）()sin 26f x x π⎛⎫=-⎪⎝⎭；3【解析】 【分析】（I ）利用平面向量数量积运算、二倍角和辅助角公式将函数化为()sin 26f x x πω⎛⎫=-⎪⎝⎭，根据两相邻极值点之间距离可构造方程求得函数的最小正周期，由此可求得ω，进而得到函数解析式；（II ）根据C 的范围和()1f C =可求得3C π=，利用余弦定理可构造方程求得ab ，代入三角形面积公式即可求得结果. 【详解】（I ）()211cos sin sin 2cos 2sin 22226f x x x x x x x πωωωωωω⎛⎫=+-=-=- ⎪⎝⎭()f x 相邻两个极值点之间距离为2，即2=T π∴=，即22ππω=，解得：1ω= ()sin 26f x x π⎛⎫∴=- ⎪⎝⎭（II ）由()1f C =得：sin 216C π⎛⎫-= ⎪⎝⎭ 0C π<< 112666C πππ∴-<-< 262C ππ∴-=，解得：3C π=3a b +=，c =2222cos3c a b ab π=+-()233a b ab +-=∴，即：2ab =ABC ∆∴的面积1sin 22S ab C ==【点睛】本题考查三角函数和解三角形的综合应用问题，涉及到平面向量数量积运算、利用二倍角和辅助角公式化简三角函数、正弦型函数周期性的应用、余弦定理和三角形面积公式的应用等知识，属于常考题型.18.如图，在三棱锥P ABC -中，平面PAB ⊥平面ABC ，AP BP ⊥，AC BC ⊥，60PAB ∠=，45ABC ∠=，D 是AB 中点，,E F 分别为,PD PC 的中点.（Ⅰ）求二面角B PA C --的余弦值；（Ⅱ）在棱PB 上是否存在点M ，使得//CM 平面AEF ？若存在，求PMPB的值；若不存在，说明理由. 【答案】（Ⅰ）217；（Ⅱ）存在，23.【解析】 【分析】（Ⅰ）取AD 中点O ，连接PO ，根据直角三角形性质和等腰三角形三线合一可证得PO AB ⊥，由面面垂直性质知PO ⊥平面ABC ；作//OG CD ，由等腰三角形三线合一和平行关系可知OG AB ⊥，从而可得到,,PO OG AB 两两互相垂直，可建立起空间直角坐标系；利用二面角的向量求法可求得结果；（Ⅱ）设PM PB λ=，可表示出M 坐标；根据线面垂直的判定定理可证得PD ⊥平面AEF ，进而得到平面AEF 的法向量PD ，若线面平行关系成立，则0CM PD ⋅=，由此构造方程可求得λ，进而求得结果.【详解】（Ⅰ）在PAB ∆中，取AD 中点O ，连接POAP BP ⊥，D 为AB 中点 PD AD ∴=又60PAB ∠= PAD ∴∆为等边三角形 PO AB ∴⊥ 在平面ABC 中，过O 作CD 的平行线，交AC 于GAC BC ⊥，45ABC ∠= AC BC ∴=，又D 为AB 中点 CD AB ∴⊥又//OG CD OG AB ∴⊥平面PAB ⊥平面ABC ，平面PAB ⋂平面ABC AB =，PO ⊂平面PABPO ∴⊥平面ABC ，又OG ⊂平面ABC PO OG ∴⊥,,OG OB OP 两两垂直，如图可建立空间直角坐标系O xyz -设4AB a =，则()0,,0A a -，()0,3,0B a ，()2,,0C a a ，()3P a ，()0,,0D a ，30,,22a E a ⎛⎫ ⎪ ⎪⎝⎭，3,,22a F a a ⎛⎫ ⎪ ⎪⎝⎭则()2,2,0AC a a =，()0,,3PA a a =-- 设平面PAC 的法向量(),,n x y z =则00n AC n PA ⎧⋅=⎨⋅=⎩，即030x y y z +=⎧⎪⎨+=⎪⎩，令1z =，则3y =3x ()3,3,1n ∴=-又平面PAB 的一个法向量为()2,0,0DC a =2321cos ,72n DC a n DC an DC⋅∴===⨯⋅二面角B PA C --为锐二面角 ∴二面角B PA C --的余弦值为217（Ⅱ）设M 是棱PB 上一点，则存在[]0,1λ∈使得：PM PB λ=∴点()()0,331M a a λλ-，则()()()2,3131CM a a a λλ=---由（Ⅰ）知：CD ⊥平面PAB CD PD ∴⊥ //EF CD EF PD ∴⊥又PAD ∆为等边三角形，E 为PD 中点 AE PD ∴⊥,EF AE ⊂平面AEF ，EF AE E = PD ∴⊥平面AEF∴平面AEF 的一个法向量为()0,,3PD a a =-CM ⊄平面AEF //CM ∴平面AEF 当且仅当0CM PD ⋅=时成立即()()()()()()222,31,310,,331310a a a a a a a λλλλ---⋅-=---=解得：23λ=∴在棱PB 上存在点M ，使得//CM 平面AEF ，此时23PM PB λ== 【点睛】本题考查空间向量法在立体几何中的应用问题，涉及到二面角的求解、存在性问题的求解；求解存在性问题的关键是能够通过共线向量将未知数减少为一个，进而根据线面平行关系可确定所证向量与平面法向量垂直，由此构造方程求得结果.19.人耳的听力情况可以用电子测听器检测，正常人听力的等级为025db -（分贝），并规定测试值在区间(0,5]为非常优秀，测试值在区间(5,10]为优秀，某班50名同学都进行了听力测试，所得测试值制成频率分布直方图：（Ⅰ）现从听力等级为(0,10]的同学中任意抽取出4人，记听力非常优秀的同学人数为X ，求X 的分布列与数学期望：（Ⅱ）现选出一名同学参加另一项测试，测试规则如下：四个音叉的发生情况不同，由强到弱的次序分别为1，2，3，4.测试前将音叉随机排列，被测试的同学依次听完后给四个音叉按发音的强弱标出一组序号1234,,,a a a a （其中1234,,,a a a a 为1，2，3，4的一个排列），记12341234Y a a a a =-+-+-+-，可用Y 描述两次排序的偏离程度，求2Y ≤的概率.【答案】（Ⅰ）分布列见解析，1.6；（Ⅱ）16.【解析】 【分析】（Ⅰ）根据频率分布直方图可得到听力等级分别为(]0,5和(]5,10的人数，根据超几何分布的概率公式可分别求得X 所有可能的取值对应的概率，从而得到分布列；根据数学期望的计算公式可求得期望；（Ⅱ）首先确定所有排列总数，利用列举法列出Y 0=和2Y =的所有可能的情况，根据古典概型概率公式求得结果.【详解】（Ⅰ）听力等级为(]0,5的有0.0165504⨯⨯=人；为(]5,10的有0.0245506⨯⨯=人 则X 的所有可能取值为：0,1,2,3,4()46410151021014C P X C ====；()1346410808121021C C P X C ====；()224641*********C C P X C ====，()3146410244321035C C P X C ====；()4441014210C P X C ===X ∴的分布列为：()341471********* 1.621210E X ∴=⨯+⨯+⨯+⨯+⨯=. （Ⅱ）序号1234,,,a a a a 的排列总数为4424A =种当Y 0=时，11a =，22a =，33a =，44a = 当123412342Y a a a a =-+-+-+-=时，1234,,,a a a a 的取值为11a =，22a =，34a =，43a =或11a =，23a =，32a =，44a =或12a =，21a =，33a =，44a =()412246P Y ∴≤== 【点睛】本题考查超几何分布的分布列与数学期望的求解、古典概型概率问题的求解，涉及到频率分布直方图的应用等知识；求解分布列问题的关键是能够结合频率分布直方图确定随机变量所有可能的取值，进而计算得到每个取值所对应的的概率，属于常考题型.20.已知椭圆2222C :1(0)y x a b a b+=>>的上下两个焦点分别为12,F F 过点1F 与y 轴垂直的直线交椭C 于,M N 两点，2MNF ∆C 的离心率为2. （Ⅰ）求椭圆C 的标准方程；（Ⅱ）已知O 为坐标原点，直线y kx m =+与y 轴交于点P ，与椭圆交于,A B 两个不同的点，若存在m 使得34OA OB OP +=，求m 的取值范围.【答案】（Ⅰ）2214y x +=；（Ⅱ）()()2,11,2--⋃. 【解析】 【分析】（Ⅰ）令y c =可求得MN ，进而表示出2MNF ∆的面积，与离心率和椭圆,,a b c 关系一起可构成方程组求得22,a b ，进而得到椭圆方程；（Ⅱ）由向量线性运算可知3AP PB =，从而得到,A B 横坐标之间关系为123x x =-；将直线方程与椭圆方程联立可得韦达定理的形式，利用123x x =-，即()21212340x x x x ++=可求得22241m k m -=-，根据联立后的二次方程>0∆可构造出关于m 的不等式，解不等式求得结果. 【详解】（Ⅰ）设椭圆的焦距2c当y c =时，2122b MN x x a=-=2MNF ∴∆的面积为212122b cMN F F c MN a⨯⨯===又c e a ==222a b c =+，解得：21b =，24a = ∴椭圆C 的标准方程为：2214y x +=（Ⅱ）由34OA OB OP +=得：1344OP OA OB =+ 3AP PB ∴= 设()11,A x y ，()22,B x y 由22440y kx m x y =+⎧⎨+-=⎩得：()2224240k x mkx m +++-= 则()()222244440m k k m ∆=-+->，即2240k m -+>12224x km x k -∴+=+，212244m x x k -=+由3AP PB =得：123x x =- ()21212340x x x x ∴++=()()2222224412044m k m k k-∴+=++ 222240m k m k ∴+--=显然21m =不成立 22241m k m -∴=-2240k m -+> 2224401m m m -∴-+>-，即()222401m m m ->- 解得：21m -<<-或12m <<m ∴的取值范围为()()2,11,2--⋃【点睛】本题考查直线与椭圆综合应用问题，涉及到平面向量在椭圆中的应用；解题关键是能够根据平面向量的线性运算得到比例关系，从而得到横坐标之间的关系，利用韦达定理和判别式来构造方程和不等式求得结果.21.设函数()()2ln 11f x x ax x =-+++，()()21xg x x e ax =-+，a R ∈.（1）当1a =时，求函数()f x 在点()()22f ,处的切线方程； （2）若函数()g x 有两个零点，试求a 的取值范围； （3）证明()()f x g x ≤.【答案】（1）65y x =-（2）0,（3）见解析【解析】 试题分析： （1）求出导数'()f x ，计算'(2)f 得切线斜率，由点斜式写出直线方程，整理成一般式即可；（2）函数()g x 有两个零点，首先用导数来研究函数的性质：单调性、极值，然后由零点存在定理进行判断，求出'()(2)xg x x e a =+，按a 分类讨论，0a =时，()(1)xg x x e =-只有一个零点；0a >时，20x e a +>，这样易判断'()g x 的正负，从而得()g x 的单调区间和极值，由零点存在定理可判断符合题意；在0a <时，'()0g x =有两个解10x =和2ln(2)x a =-，又要按12,x x 的大小分类研究'()g x 的正负得()g x 的单调性，从而确定零点个数，最后综合可得；（3）证明函数不等式()()f x g x ≤，可证()()0f x g x -≤，设()()()h x f x g x =-，利用导数)'(h x 求出()h x 的最大值，只要最大值小于等于0，即证． 试题解析：（1）函数()f x 的定义域是()1,+∞，()()2211x ax a f x x -+'=-.当1a =时，()2426f a +'==，()2437f a =+=.所以函数()f x 在点()()2,2f 处的切线方程为()762y x -=-. 即65y x =-.（2）函数()g x 的定义域为R ，由已知得()()2xg x x e a '=+.①当0a =时，函数()()1xg x x e =-只有一个零点；②当0a >，因为20x e a +>，当(),0x ∈-∞时，()0g x '<；当()0,x ∈+∞时，()0g x '>. 所以函数()g x 在(),0-∞上单调递减，在()0,+∞上单调递增. 又()01g =-，()1g a =，因为0x <，所以10x -<，1x e <所以()11x ex x ->-，所以()21g x ax x >+- 取01142a x a--+=，显然00x <且()00g x > 所以()()010g g <，()()000g x g <.由零点存在性定理及函数的单调性知，函数有两个零点.③当0a <时，由()()20x g x x e a =+='，得0x =，或()2x ln a =-. )i 当12a <-，则()20ln a ->. 当x 变化时，()g x '，()g x 变化情况如下表：注意到()01g =-，所以函数()g x 至多有一个零点，不符合题意.)ii 当12a =-，则()20ln a -=，()g x 在(),-∞+∞单调递增，函数()g x 至多有一个零点，不符合题意.若12a >-，则()20ln a -≤. 当x 变化时，()g x '，()g x 变化情况如下表：注意到当0x <，0a <时，()()210x g x x e ax =-+<，()01g =-，所以函数()g x 至多有一个零点，不符合题意.综上，a 的取值范围是()0,+∞.（3）证明：()()()()111xg x f x x e ln x x -=-----. 设()()()111xh x x e ln x x =-----，其定义域为()1,+∞，则证明()0h x ≥即可. 因为();111x x x h x xe x e x x ⎛⎫=-=- ⎪--⎝⎭，取311x e -=+，则()()1310x h x x e e =-<'，且()20h '>.又因为()()()21101x h x x e x =++-'>'，所以函数()h x '在()1,+∞上单增.所以()0h x '=有唯一的实根()01,2x ∈，且0011x e x =-. 当01x x <<时，()0t h x <；当0x x >时，()0h x '>.所以函数()h x 的最小值为()0h x .所以()()()()0000000111110xh x h x x e ln x x x x ≥=-----=+--=. 所以()()f x g x ≤.点睛：利用导数证明不等式的技巧：（1）树立服务意识．利用给定函数的某些性质岧函数的单调性、最值等，服务于要证明的不等式．（2）强化变形技巧．对于给出的不等式直接证明无法下手，可考虑对不等式进行必要的等价变形后，再去证明．例如采用两边取对数（指数），移项通分等等，要注意变形的方向，因为要利用函数的性质，力求变形后不等式一边出现需要的函数关系式．（3）巧妙构造函数，．根据不等式的结构特征构造函数，利用函数的最值进行解决，在构造函数的时候灵活多样，注意积累经验．（4）证明操作过程：①构造函数()x ϕ，转化为证明()0x ϕ>或()0x ϕ<；②利用导数求函数()x ϕ的单调区间；③利用定义域内()x ϕ与0的大小关系，证明不等式．（二）选考题：共10分.请考生在第22、23题中任选一题作答.如果多做，则按所做的第一22.在直角坐标系xOy 中，曲线1C ：cos sin x r y r θθ=⎧⎨=⎩（θ为参数，常数0r >），以原点为极点，x 轴非负半轴为极轴建立极坐标系，曲线2C 的极坐标方程为28sin 150ρρθ-+=.（1）若曲线1C 与2C 有公共点，求r 的取值范围；（2）若1r =，过曲线1C 上任意一点P 作曲线2C 的切线，切点为Q ，求PQ 的最大值. 【答案】（1）35r ≤≤（2）26【解析】【分析】（1）根据三角函数同角三角函数关系消元得曲线1C 的普通方程，将曲线2C 的极坐标方程化为直角坐标方程，最后根据两圆位置关系列不等式，解得r 的取值范围；（2）先根据切线长公式得2PQ ，再根据三角函数有界性得最大值.【详解】解：（1）曲线1C 的普通方程为222(0)x y r r +=>，曲线2C 的普通方程为()2241x y +-=若1C 与2C 有公共点，则()()22100401r r -≤-+-≤+，所以35r ≤≤. （2）设()cos ,sin P αα，由22222221PQ PC C Q PC =-=- ， 得()222cos sin 41PQ αα=+-- 168sin 18824α=-≤+=.当且仅当sin 1α=-时取最大值，故PQ 的最大值为26.【点睛】本题考查参数方程化普通方程、极坐标方程化直角坐标方程以及两圆位置关系、切线长公式等，考查基本分析求解能力，属基本题.23.已知函数()|1|||f x x x a =+-+．（1）若0a =，求不等式()0f x ≥的解集；（2）若方程()f x x =有三个不同的解，求a 的取值范围．【答案】（1）；（2）10a -<<.【详解】（1）0a =时，1,1,()1{21,10,1,0.x f x x x x x x -<-=+-=+-≤<≥∴当1x <-时，()10f x =-<不合题意；当10x -≤<时，()210f x x =+≥，解得102x -≤<； 当0x ≥时，()1f x =0>符合题意．综上，()0f x ≥的解集为1[,)2-+∞． （2）设()1u x x x =+-，()y u x =的图象和y x =的图象如图，易知()y u x =的图象向下平移1个单位以内（不包括1个单位）与y x =的图象始终有3个交点，从而10a -<<．。
最新港澳台华侨生联考：数学三轮复习：综合练习5(含答案)
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华师导航教育港澳台联考周考三
华师导航教育港澳台联考周考三地理一、选择题：本大题攻20小题，每题3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。
图1示意某地气温和降水资料。
读图1，完成1-2题.1、该地的地带性植被是（）A、亚寒带针叶林B、针阔叶混交林C、温带森林草原D、落叶阔叶林2、该地可能位于（）A、印度B、俄罗斯C、挪威D、智利图2为某人口超过1亿的国家不同年份人口年龄和性别结构变化。
读图2，完成3-4题。
3、根据图示信息判断，该国（）A、1950年劳动力最充足B、1970年人口增长最快C、2005年老年女性人口超过老年男性人口D、人口自然增长率持续增高4、当前，该国人口面临的主要问题是（）A、数量急剧增加B、老龄化严重C、新生儿男女比例失衡D、有大量剩余劳动力5、下列大河中，流向大致与地球自传方向一致的是（）A、尼罗河B、亚马孙河C、刚果河D、密西西比河6、可能由地震直接引发的自然灾害是（）A、台风B、寒潮C、海啸D、龙卷风图3为某国能源消费构成的变化。
读图3，完成7-8题。
7、1950-2009年，该国（）A、煤炭比重持续下降B、能源消费构成渐趋多元化C、石油消费量大幅下降D、水能渐趋枯竭8、该国可能是（）A、印度B、巴西C、日本D、中国9、下列钢铁工业企业中，原理原料、燃料产地而临近市场布局的是（）A、鞍钢B、攀钢C、唐钢D、宝钢10、我国在甘肃酒泉建设的有“陆上三峡”之称的大型能源基地，开发的能源是（）A、风能B、谁能C、太阳能D、核能11、世界很多国家共同签订的《京都议定书》，应对的全球性环境问题时（）A、生物多样性锐减B、环境污染C、南极“臭氧空洞”D、全球变暖12、下列各组地貌景观中，形成景观的主要作用力相同的一组是（）A、长白山天池、杭州西湖B、黄山怪石、野柳怪石C、云南石林、桂林山水D、长江三峡、东非大裂谷13、下列国家天然气产量最多的是（）A、俄罗斯B、美国C、中国D、英国14地中海沿岸典型的经济作物是（）A、大豆B、花生C、油橄榄D、甜菜15、下列国家中，是世界重要稻米出口国的是（）A、孟加拉国B、泰国C、土耳其D、委内瑞拉16、与北半球信风风向相同的是（）A、亚欧大陆东岸的夏季风B、北印度洋的冬季风C、越过赤道的南半球信风D、南极地区的极地东风17、下列城市中，一年内太阳升起的方位变化最大的是（）A、柏林B、罗马C、开罗D、科伦坡18、在北方冬季，人们常说“雪后寒”。
2021年华南师范大学附属中学高三英语第三次联考试卷及答案解析
2021年华南师范大学附属中学高三英语第三次联考试卷及答案解析第一部分阅读（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A、B、C、D四个选项中选出最佳选项ACome and enjoy Vivaldi's TheFour Seasonsperformed by live musicians!Tickets△Zone A Sating (Excellent Visibility, $75)△Zone B Seating (Great Visibility, $60)△Zone C Seating (Good Visibility, $45)△Zone D Seating (Restricted Visibility, 30)Zone A and Zone B audiences will get the chance to take pictures with the performers on the stage after the show.Highlights* A beautiful venue bathed in candlelight.*Classical music performance by the Angel Strings quartet*A safe and socially-distanced event, ensuring you are comfortable and at ease.General Info*Dates and times: Various dates, at 6:30 pm and 8:30 pm (select during purchase).*How long: 65 minutes. Doors open 45 minutes before the start time. We recommend you arrive at least 30 minutes before the start of the event, as late entry is not permitted.*Where: Events on Oxlade*Age requirement: Must be 8 years old or older to attend. Anyone under the age of 16 must be accompanied by an adult.*Please note: The 6:30 pm seating will take place during daylight hours outdoors, and the space will not be that dark. In the case of rain, the event will be moved to the indoor area of the venue.DescriptionWhether you're looking for a beautifully unique classical music performance or a romantic candlelit experience, this performance is for you. You don't need to know all things about Vivaldi to enjoy the evening; simply sit back and admire the wonderful atmosphere and the pieces you'll hear.Join our musicians for an evening under the stars, and prepare to be taken into the clouds with Vivaldi' s most treasured masterpieces!1.What can someone with a $45 ticket do?A.Perform on the stage.B.Enjoy good visibility.C.Select a seat in Zone B.D.Take photos with the musicians.2.What should potential audiences keep in mind?A.Arrive at the venue on time.B.Learn about Vivaldi in advance.C.The performance lasts 45 minutes.D.The event will be canceled if it rains.3.What do we know about the 8:30 p.m. performance?A.It welcomes children under the age of 8.B.Its performers differ on different dates.C.Its stage will be decorated with candles.D.It will be shown in the indoor area of the venue.BFrom skateboarding to Fleetwood Mac, TikTok users got creative in a pandemic (流行病) year with new songs, dances and shows in 60 seconds or less.The social mediavideo app on Wednesday shared its list of top 100 videos, creators and trends in America during 2020. “These videos brought joy and inspiration to millions of Americans in the rough year,” said Kudzi Chikumbu, director of creator community at TikTok.The platform has been widely associated with Generation Z (people born after 1996), millennials (people born in the 1980s or 1990s) and influencers who have started careers based on the shared videos.The Weeknd'sBlinding Lightsand Jason Derulo's Savage Loveinspired TikTok dance challenges that made them among the top songs used on the app.For some TikTok creators, the pandemic itself became inspiration to create a connection with other users. Comedian Caitlin Reilly used the app during quarantine (隔离) to make fun of those annoying coworkers for one of the top liked videos. And singer Curtis Roach made an song for the endless days at home with his song Bored in the House.The second most popular video was an Idaho man named Nathan Apodaca who shot to fame after coolly singing Dreams by Fleetwood Mac, while skateboarding on a highway.But the most liked TikTok video was awarded to Bella Poarch with 45 million followers, who created a simplebut interesting video with a few seconds of well-timed head nods and eye rolls.While the app might be designed for youth, Chikumbu said that the growth of TikTok this year has pushed it more into mainstream culture. “You're seeing everyone from the teenager to the college students with their parents and then their grandparents all making videos,” said Chikumbu. “And now TikTok trulytranscendsgenerations, particularly in this year when people had a lot of time to dig in and not only watch, but try.”4. What do we know about The Weeknd?A. He created the famous song Dreams.B. He started a career based on shared videos.C. He is probably a popular singer on TikTok.D. He organized the TikTok dance challenges.5. What did Curtis Roach think of his life during quarantine?A. Meaningful.B. Peaceful.C. Content.D. Uninteresting.6. The most popular TikTok video in 2020 was created by ______.A. Caitlin ReillyB. Curtis RoachC. Nathan ApodacaD. Bella Poarch7. What does the underlined word “transcends” in the last paragraph mean?A. Makes use of.B. Goes beyond.C. Calls on.D. Takes charge of.CAn anti-obesity program for Australian girls didn’t lead to any improvements in their diet, physical activities or body weight a year later, according to a new report.Findings from the school-based intervention (介入), which involved exercise sessions and nutrition workshops for lower-income girls, are the latest disappointment in a lot of research attempting tohead offadult obesity and the disease risks that come with it.Especially during the middle-and high-school years, girls’ physical activity reduces obviously, according to lead researcher David Lubans, from theUniversityofNewcastleinNew South Wales,Australia. He said, “In the future we need to make the programs more interesting and exciting and present information in a way that is meaningful to adolescent girl.”Lubans and his workmates conducted their study in 12 schools in low-income areas ofNew South Wales. At the start of the study, girls in both groups weighed an average of close to 130pounds, with about four in ten considered overweight. Over the next year, adolescents in the intervention group were given pedometers (计步器) to encourage walking and running and invited to nutrition workshops and regular exercise sessions during the schoolday and at lunchtime. Participation in some of those activities were less than ideal. For example, the girls went to only one-quarter of lunchtime exercise sessions, and less than one in ten completed at-home physical activity or nutrition challenges, the researchers reported. At the end of the year, girls in both groups had gained a similar amount of weight and there was no difference in their average body fat.Preventive medicine researcher Robert Klesges said that although some anti-obesity programs have helped adults lose weight, the teen population has always been a source of failure for researchers. “The common belief is: nothing works,” he said. “And we have got to get beyond that.”“We need to think outside the box,” said Klesges, who wasn’t involved in the new study. “That could include learning from what has worked in adult studies, such as giving meal replacement drinks or prepared foods to teens who have trouble making changes to their diet. Or, it could mean using a “step-care” method — rather than researchers or their doctor telling them to keep doing the same thing.” Klesges said.8. The underlined words “head off” in Paragraph 2 can best be replaced by “________”.A. damageB. defendC. preventD. affect9. The methods used in the program to stop obesity don’t include ________.A. walking and runningB. inviting them to nutrition workshopsC. joining exercise sessions regularlyD. giving meal replacement drinks10. The main reason for the failure of the anti-obesity program is probably that ________.A. the participants didn’t take an active part in itB. the program was not interesting and exciting to participantsC. the participants didn’t get extra nutrition or exercise helpD. the program didn’t pay attention to healthy exercise11. What can be inferred from the last paragraph?A. As researchers, it is important to have creative research methods.B. Researchers need to give meals or prepare foods to participants.C. Teen girls have no difficulty in making changes to their diet.D. Some ant-obesity programs have not helped adults lose weight.DAlthough computer technology is often necessary today, using a pen or pencil activates more areas of your brain than a keyboard does. You can potentially remember more by handwriting, according to a new study.The potential benefits of handwriting for memory have been debated for some time. The new study set out to answer one question: How does handwriting compare to using a keyboard when it comes to remembering new information?In all,24 participants took part. Researchers asked each of them to write with a pen and then each was also asked to type on a keyboard. While performing these tasks, each volunteer wore a cap that held electrodes next to their head. It looked somewhat like a hair net fitted with 256 sensors. Those sensors recorded the participants' brainwaves. The electrodes noted which parts of the brain turned on during each task. And they showed that writing turned on memory areas in the brain while typing didn't.Audrey van der Meer, the new study's leader, says this suggests that when we write by hand, we remember better. “This is because writing involves complex movements that activate more areas of the brain. The increased brain activity gives the brain more ‘hooks’ to hang your memories on,” she explains. Van der Meer also points out that writing by hand is related to visual notetaking. “Rather than typing blindly, the visual notetaker has to think about what is important to write down. Then, key words can be interlinked by boxes, arrows and small drawings,” she adds.This study does not recommend banning digital devices. In fact, its authors point out, computers and other devices with keyboards have become necessary in modern society. Keyboarding can especially benefit those with certain special needs (such as if they have trouble using their hands) and typing beats writing when it comes to speed, they add.12. Why were participants asked to wear caps in the study?A. To record their brainwavesB. To inform them of their tasksC. To allow them to focus on writingD. To protect their heads like hair nets13. What does Audrey van der Meer try to explain?A. Why handwriting is more complex than typingB. Why the brain works when it comes to learningC. Why handwriting helps remember informationD. Why key words are helpful to visual notetaking14. What is the study's authors' view on typing?A. It relieves people's handsB. It remains vital and helpfulC. It is not worth recommendingD. It is more challenging than writing15. Which of the following can be a suitable title for the text?A. How Can You Remember New Information?B. Handwriting Benefits Health in the LongRunC. Should Typing Take the Place of Handwriting?D. Handwriting Is Better for Memory Than Typing第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2021届华师附属高级中学高三英语第三次联考试卷及参考答案
2021届华师附属高级中学高三英语第三次联考试卷及参考答案第一部分阅读（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A、B、C、D四个选项中选出最佳选项AExperts say that if food were a country, it would rank second behind theUSas one of the biggest greenhouse gas polluters. The reason is the rising demand for meat. Animal farming is responsible for 14.5 percent of global methane emissions. While cowsare the worst contributors, pigs, sheep, donkeys and other animals play a part as well.Animal agriculture also causes land to become damaged, water to be polluted and forests to get destroyed. With the world population forecast to rise to 9.8 billion by 2050, things are only looking worse for our already decreasing natural resources. While going vegetarian would help, meat consumption is too deep-rooted in most Western diets to allow for such a sharp, permanent change. That is why experts are advocating substituting some of the beef, chicken, or pork with ordinary insects!Insects, which grow into adults within a matter of months, if not weeks, are ready for consumption much faster than domestic animals. They also require much less room, use less water and food, and produce far less greenhouse gas than animals.Of the 1.1 million insect species worldwide, scientists have identified 1,700 as eatable. Among them are ants, grasshoppers, grubs, and earthworms. Just like animals, each insect has a different taste. Tree worms taste just like pork, and grubs are similar to smoked meat.While eating insects might be a new concept for Western people, over 2 billion people worldwide consume insects as a regular part of their diet. Besides being delicious, insects are high in protein, have very few calories, and are free of the saturated fat found in animal meat. Insects can be prepared in many ways. Creative cooks can use them to cook protein-rich soup, make baked treats, and even fry a few with vegetables. So eat insects--- both your body and Mother Earth will thank you for it!1. Which of the following animals contribute the most to global methane emissions?A. Sheep.B. Donkeys.C. Cows.D. Pigs.2. How is the third paragraph developed?A. By making comparisons.B. By providing examples.C. By listing data.D. By asking questions.3. What can be inferred from the last paragraph?A.Few people eat insects regularly.B. Ordinary insects are high in fat.C. Insects contain various vitamins.D. Saturated fat is harmful to health.BIf you’ve ever had a dog, you know just how deep a connection you can develop with “man’s best friend”. But a dog has a much shorter life span — about 12 to 15 years long — than humans, which means every dog owner has to go through the heartbreaking moment when their loving pet passes away.Why not make a clone of that dog then? This is the solution offered by a South Korean company, Sooam Biotech Research Foundation. The company has successfully cloned at least 400 dogs, mostly for US customers, ever since it pioneered the technique in 2005. Now, Sooam Biotech is planning to introduce their business toUKdog owners, offering them dogs that look just like their lost ones.Meanwhile, another dog is selected to supply an egg.Researchers then replace the DNA in the egg with that from the skin cell and implant the egg into the womb (子宫) of a female dog. The egg grows into a puppy over the following two months. To clone a dog, researchers first need to take a skin cell from a living dog or one that has just died.The whole process takes less than a day, but it comes at a shockingly high price — around £63,000 (614,000 yuan). But if you can’t afford it now, you can also save the cells in a laboratory and access them at a later date. Just like identical twins of humans, they share the exact same DNA but there will still be small differences between them. “The spots on a Dalmatian clone will be different, for example,” Insung Hwang, head of Sooam Biotech, toldThe Guardian. However, as magical as cloning might sound, there is no guarantee that the cloned dog will be a perfect replica of the original one.Dog owners will also have to accept the fact that personality is not “clone-able”. Apart from genes, personality is also determined by upbringing and environment, which are both “random elements [that] cloning technologies simply cannot overcome”, Professor Tom Kirkwood atNewcastle University,UK, toldThe Telegraph.Perhaps bringing our dogs back with cloning is not the best way to remember them after all.Kirkwood, a dog owner himself, pointed out: “An important aspect of our relationship with them is coming to terms with the pain of letting go.”4. According to the article, Sooam Biotech Research Foundation is ______.A. working on plans to help dog owners enjoy their pets longerB. offering a way to help dogs give birth to more puppiesC. providing a service that will make copies of pet dogsD. introducing a completely new technique to clone dogs5. Which of the following statements about dog cloning is TRUE according to the article?A. Dog cloning technology hadn’t been put into practice until recently.B. Dog cloning is very expensive and usually takes several months to complete.C. Dog cloning is very popular among US andUKpet owners.D. Cloned dogs might develop different habits and characteristics even though they look very similar.6. Which of the following shows the correct order of the dog cloning process?a. an egg is taken from another dogb. a skin cell is taken from the pet dog and saved in a laboratoryc. the egg is placed in the womb of a female dogd. the DNA of the egg is replaced by the DNA from the skin celle. the egg grows into a puppy in two monthsA. acbde.B. adbce.C. bacde.D. badce.7. We can learn from the article thatKirkwood______ dog cloning.A. disapproves ofB. supportsC. is afraid ofD. is curious aboutCWe've all heard it before：to be successful, get out of bed early. After all, Apple CEO Tim Cook gets up at 3：45 am, Fiat CEO Sergio Marchionne at 3：30 am and Richard Branson at 5：45 am﹣and, as we all know, "the early bird's catches the worm. "But just because some successful people wake up early, does that mean it's a trait most of them share？And if the idea of having exercised, planned your day, eaten breakfast, visualized and done one task before 8 am makes you want to roll over and hit snooze till next Saturday, are you really doomed to a less successful life？For about half of us, this isn't really an issue. It's estimated that some 50% of the population isn't really morning or evening﹣oriented, but somewhere in the middle. Roughly one in four of us, though, tend more toward bright﹣eyed early risers, and another one in four are night owls. For them, the effects can go beyond falling asleep in front of the TV at 10 pm or being regularly late for work.Numerous studies have found that morning people are more self﹣directed and agreeable. And compared tonight owls, they plan for the future more and have a better sense of well﹣being.Although morning types may achieve more academically, night owls tend to perform better on measures of memory, processing speed and cognitive（认知）ability, even when they have to perform those tasks in the morning. Night﹣time people are also more open and more creative. And one study shows that night owls areas healthy and wise as morning types﹣and a little bit wealthier.Still think the morning people sound more like CEO material？Don't set your alarm for 5 am Just yet. As it turns out, overhauling（全面改革）your sleep time may not have much effect"If people are left to their naturally preferred time, they feel much better. They say that they are much more productive. The mental capacity they have is much broader, " says Oxford University biologist Katharina Wulff. On the other hand, she says, pushing people too far out of their natural preference can be harmful. When they wake early, for example, night owls are still producing melatonin（褪黑素）. "Then you disrupt it and push the body to be in the daytime mode. That can have lots of negative physiological consequence. " Wulff says, like a different sensitivity to insulin and glucose（葡萄糖）which can cause weight gain.8. What does the authordo in the first three paragraph？A. raising the problem→analyzing the problem → solving the problemB. leading in the topic→challenging a viewpoint → discussing about the topicC. presenting a viewpoint → providing supporting proofs→making a conclusionD. introducing a viewpoint →raising the question→presenting author's viewpoint9. What can we know from the 4th and 5th paragraph？A. Morning types tend to have clear goals and better mood.B. To beat night﹣time people ask them to do math calculation in themorning.C. Night owls tend to sacrifice their health for their wealth.D. Neither night owls nor morning persons perform better than the middle ones.10. Which of the following does Katharina Wulff support？A. Don't fall sleep in front of the TV.B. Avoid being regularly late for work.C. Stop setting your alarm for 5 am.D. Better not overhaul your sleep time.11. Why does the author write this article？A. To explain why some people are more successful.B.To compare the differences between early risersand night owls.C. To advise people to get up neither too early nor too late.D. To argue against this view that the Carly bird catches the worm.DIt was very cold and I had been watching a homeless man make himself comfortable in a “shelter” on the river bank. His “shelter” was a tarpaulin (油布)tied to rocks to keep the wind from blowing it away. He had been living there for over a month. I never saw him with warm clothing or food. I knew what I wanted to do.When I told my parents what I wanted to do they werealarmed. They said I could be putting myself at risk, taking a box to a homeless person at night! But I knew, in my deep heart, that I would be safe.I got a box. My parents watched as I added warm gloves, a heavy blanket ... into the box until it was full! Then, I put a Christmas card on top. It said, “Even though we hardly know each other, I want to wish you a Merry Christmas!” I put ten one-dollar bills inside it as well.My father insisted he went there with me as it was 10 pm on Christmas Eve. I said he could drive me but he had to stay in the car. He agreed.I took the box and walked towards his “house”. I called, “Sir, I have a Christmas box for you!”“Go away!” he shouted.“Sir,” I repeated.“Go away!” he shouted.“Why?” I asked him.He walked over and I expected to see an angry face. Instead I saw two of the most beautiful, gentle, blue eyes I have ever seen.“Merry Christmas!” I said.“Why are you doing this?” he asked.“Because you matter to me,” I said. With that I gave him the box.Tears came to his eyes and he thanked me. I got back to the car and watched him carry the box like it was filled with gold. I didn’t want to embarrass (使困窘) him by watching him any more so Dad and I left.12. The underlined word “alarmed” can best be replaced by _____.A. pleasedB. worriedC. disappointedD. surprised13. Why did the author ask his father to stay in the car?A. Because he wanted to prove he was brave.B. Because he believed the homeless man was bad.C. Because he wanted to protect his father from being hurt.D. Because he didn’t want the homeless man to feel bad.14. When the homeless man saw the author first, he was _____.A. quite angryB. very excitedC. quite puzzledD. very curious15. The author’s purpose in writing the text is to tell readers that _____.A. it is easier said than doneB. poverty is the mother of healthC. where there is a will, there is a wayD. a willing helper doesnot wait until he is asked第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
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华师导航教育港澳台联考周考三
历史试卷
1、商朝都城遗址“殷墟”出土了大量篆刻有卜辞德甲骨，“殷墟”位于今河南（）
A、郑州
B、洛阳
C、商丘
D、安阳
2、秦朝在全国统一使用的货币是（）
3、230年，东吴派遣将军卫温率军进入台湾，台湾当时被称作（）
A、夷陵
B、澎湖
C、夷洲
D、琉球
4、唐中期，为解决财政困难，唐德宗任用杨炎改革赋税制度，实行（）
A、两税法
B、一条鞭法
C、租庸调制
D、摊丁入亩
5、1127年金军南下，攻破北宋都城汴京，俘获徽、钦二帝，北宋灭亡，史称（）
A、靖康之变
B、靖难之役
C、土木之变
D、陈桥兵变
6、明朝统治者为了加强皇权，授权“锦衣卫”掌管缉捕、刑狱之事，监视、侦察官民行为。
负责指挥锦衣卫的是（）
A、宦官
B、皇帝
C、内阁大学士
D、刑部尚书
7、一位清代官员在信中说：“旧党之阻挠，八股试贴之无用、部议之因循守旧，大臣之不明新学，上皆言之。
”信中所说的“上”是指（）
A、咸丰皇帝
B、同治皇帝
C、光绪皇帝
D、宣统皇帝
8、1879年，康有为游历设有租界的上海等地后说：“彼族宫室桥梁道路之整，巡役狱囚之肃、舟车器艺之精，而我首善之区一切及与相反。
”这句话反映出（）
A、康有为维新变法的主要思想已经形成
B、一些知识分子认识到中西之间的差距
C、近代知识分子对西方文明有了更加理性的认识
D、租界是西方列强侵华的桥头堡和基地
9、1927年，日本在“东方会议”上确立了“把满洲从中国本土分裂出来，自成一区，置日本势力之下”的侵略方针。
为实现这一方针，日本制造了（）
A、九一八事变
B、华北事变
C、卢沟桥事变
D、八一三事变
10、抗日战争时期，中国政府对外关系方面取得的重要成果是（）
A、改定新约，实现关税自主
B、废除了英美等国在华治外法权等特权
C、收回汉口、九江英租界
D、中国政府代表团出席日本无条件投降仪式
11、抗日战争胜利以后，中国民族党派成为重要的政治力量，其中主要以海外人士为主的民族党派是（）
A、中国民族同盟
B、中国民主建国会
C、九三学社
D、中国致公党
12、毛泽东与美国记者安娜.露易丝.斯特朗的谈话中提出“一切反动派都是纸老虎”的论断，这次谈话是在（）
A、北伐战争时期
B、土地改革时期
C、抗日战争时期
D、解放战争时期
13、新中国成立初期，毛泽东形象的说：“现在我们能造些什么？能造桌子、椅子，能造茶碗茶壶，能种粮食，还能磨成面粉，还能造纸。
但是，一辆汽车、一架飞机、一辆坦克、一辆拖拉机都不能造。
”由此可见，我国当时（）
A、轻工业比较发达
B、农业有较大进步
C、重工业十分落后
D、工农业发展失调
14、一份《新闻简报》中写道：“广东连县星子乡田北社水稻亩产6万多斤的大卫星，广西环县又放出13万斤的卫星来。
”这则报道反映的时期应是（）
A、农业合作化时期
B、“大跃进”时期
C、国民经济调整时期
D、“文化大革命”时期
15、18世纪末，法国军民高唱《马赛曲》，走上前线抗击外敌入侵，取得瓦尔密战役的胜利。
这次战役发生在（）
A、几轮特派统治时期
B、君主立宪派统治时期
C、雅各宾派统治时期
D、拿破仑统治时期
16、每个人，只要他不违反正义法则，就可以完全自由的以自己的方式追求自身利益，就可以完全自由的以自己的勤奋和资本与其他任何人即任何阶层的人的勤奋和资本相竞争。
提出上述自由放任主义的是（）
A、弗兰西斯.培根
B、亚当.斯密
C、霍布斯
D、伏尔泰
17、第二次工业革命后形成的新的工业群包括（）
A、电力工业、电器工业、化学工业、汽车工业
B、纺织工业、机器制造业、铁路运输、煤炭工业
C、纺织工业、电力工业、汽车工业、石油工业
D、机器制造业、铁路运输业、电器工业、石油工业
18、1830年，原棉几乎占美国出口的50%，其中大部分运往英国，而在运往英国的原棉中76%来自美国南方各州。
棉织品一般占英国出口的48%，其中输往美国的占33%。
据此可知（）
A、棉花是内战前美国经济的支柱
B、奴隶制是南方棉花种植园的基础
C、对外贸易是英国经济的生命线
D、英国工业革命与美国南部种植园经济又密切关系
19、华盛顿会议对第一次世界大战后太平洋地区的国际关系进行了调整，下列关于华盛顿会议的表述，正确的是（）
A、中国的国际地位得到提高
B、战胜国与战败国之间矛盾加剧
C、对军备竞赛有所限制
D、美日同盟得到加强
20、“和平、发展和保护环境是相互依存和密不可分的”。
下列各项中，能够充分体现这一思想宗旨的是（）
A、1961年不结盟国家和政府首脑会议宣言
B、1989年亚太经合组织成立
C、1991年《马斯特里赫特条约》
D、1992年里约热内卢宣言
二、材料分析题：本大题共2小题，每小题15分，共30 分
21、阅读下列材料，并结合所学知识回答问题
材料：抗日战争开始时，一种抵抗敌人到底的民族感和决心的浪潮弥漫了全中国。
统一战线口号首先克服了一切中国国内的纠纷。
国民党政府监狱中所有的因共产主义或左派活动而被拘禁的人都被释放了，其他逃亡国外的人也回国为民族事业而听从分配……因此，中国人对进犯的敌人所作的抵抗超出了日本人最初的一切预料。
______傅吾康《一百年来的中国革命》（1851—1949）回答：根据材料及所学知识，概述抗日战争之前中国人民同仇敌忾进行抗战的表现。
22、阅读下列材料，并结合所学知识回答问题
材料一：
实际上，探险的不同动机交织在一起，并彼此强化……当葡萄牙航海家达伽马在1498年到达印度的卡里库特港时，当地的统治者问他想要什么，他答道：“基督教和香料”。
材料二：
第一，作为上述海洋的宗主和统治者的两位陛下今后对哥伦布阁下赐以他个人以及靠自己的技巧在这实现而且获得的一切岛屿和大陆的海军司令。
其次，国王和女王陛下对哥伦布阁下赐以上述他在海中所发现或获得的一切大陆和岛屿的钦差和最高总督；要他总辖其中每个地方以及任何地方并指派充任各种官职的人员，而两位陛下则享有遴选他们认为最合适者的权力。
再次，在此后赐予哥伦布的上述海军司令辖境内从一切购买、交换、发现或得到的珍珠或宝石、金银及其他任何种类、形式和名称的货物上，同意都归他管并自留十分之一，即计算在这方面的一切费用，在从整个的纯利益中把其余的九成交给两位陛下后，同意他自己留下的这十分之一并随意来使用这一部分。
_____西班牙统治者与哥伦布签署的《圣塔菲协定》（1498年4月17日）回答：
（1）根据材料并结合所学知识，概括西班牙和葡萄牙开辟新航路的动因。
（6分）（2）根据材料二，指出西班牙统治新发现土地的基本原则。
（9分）
三、问答题：本大题共3小题，每小题30分，任选2题作答。
共60分
23、说明宋元时期内地棉纺织业的发展情况，评价黄道婆的贡献以及历史作用。
（30分）
24、简述20实际30年代前期国民政府实行的经济政策和措施的内容以及作用。
（30分）
25、第二次世界大战中。
反法西斯同盟国取得斯大林格勒保卫战、阿拉曼战役、中途岛海战的胜利，完成了战略转折。
从战争双方的角度，结合具体史实，指出战略转折得到实现的政治、军事条件。