清华大学中学生标准学术能力诊断性测试2020年5月诊断性测试英语试题

中学生标准学术能力诊断性测试2020年5月测试英语试卷本试卷共150分，考试时间100分钟。

第一部分阅读理解（共两节，满分60分）第一节（共15小题；每小题3分，满分45分）ASummer is that time of this year 2019 when everyone looks to escape from the boring activities of life. So bring your kids to join us to have fun in the summer camp.Outdoor Word Game:All you need to do is setting up many huge letters that can be easily moved. These letters will help kids spell out certain words. Teenagers would also love something like this as it gives them the opportunity to invest their time in learning new words.Spray Painting:To bring out the creativity in a person, an activity centered on spray painting is the perfect way to get those creative juices flowing. All you need to do is providing plain white T-shirts and some cans of colored spray paint. It will be quite surprising to see some of the original ideas that will flow from individuals.Outdoor Twister:A person will be in charge of monitoring the game and will call out colors which can be placed outdoors. Participants have the task of placing either their hands or legs on the same color. A fun and exciting game focuses on hand-eye coordination（协调）.The Maze（迷宫）:One of the funniest games is the hallway maze game where a maze is constructed from either toilet paper or strings of paper. The chosen participant is then asked to make his way through the maze within a limited time without touching paper. This is one of the best and entertaining summer camp ideas for kids and adults also.1．Which activity most probably needs some imagination?A．Outdoor Word Game. B．Spray Painting.C．Outdoor Twister. D．The Maze.2．Which of the following is TRUE according to the passage?A．The maze is made of toilet paper in The Maze.B．You have to spray juice on your T-shirt in Spray Painting.C．Outdoors Twister tests whether you are good at controlling your body movement.D．You have to bring some huge letters to play in Outdoor Word Games.3．Who is the article intended for?A．Parents. B．Children. C．Teachers. D．Teenagers.BWhat makes a person sexy? Looks, talent, public image and how we accordingly view their personality all play into why we find ourselves attracted to certain celebrities and public figures.Every year, People put it all together when they name their “Sexiest Man Alive”. This year, the magazine decided that United States musician John Roger Stephens, better known as John Legend, has the full package.The title comes following some impressive achievements for the 40-year-old. He is among the youngest people to win an Emmy, Grammy, Oscar and Tony award, and the first African-American man to win all four of them. With numerous awards and nominations, an Ivy-League degree, and a handsome face, Legend has gained huge popularity worldwide. However, his dedication to family life maybe what wins over many.After getting married to US model Chrissy Teigen in 2013, Legend is the father of one son and one daughter. He’s not shy about telling the world their love is permanent. On the inside of Legend’s arm, there is a tattoo that says “Chrissy Luna Miles”, the names of his wife and children. In fact, Legend has gained strength from his family since childhood. He still remembers the days when his family would gather around his grandmother’s piano to sing Christmas songs. This inspired his passion for music. His best-known single, All of Me, is a love song to his wife. When he performed it at the 2014 Grammy Awards, many were touched by his delicate voice and the deep love beneath. “The more you know someone, the more you’re inspired by your relationship,” Legend told LA Confidential Magazine. “You have to grow enough to be able to write that song with sincerity and authenticity.”Despite his onstage confidence, Legend had to work to become a legend. As a teenager, he was the smallest kid in class. “I was always less mature, less at ease socially. I had plenty of awkward times,” he told People. “Most of your teenage years, into your twenties, you’re still figuring out who you are, how you present yourself to the world ... Eventually, I think you get more at ease with yourself.” Indeed, knowing who you are and be yourself could be the real key to attractiveness.4．What plays the biggest part in making Legend popular worldwide?A．High-level education. B．Handsome look.C．Efforts put in family. D．Talent in music.5．What does the third paragraph mainly talk about?A．L egend’s hobby as a boy.B．L egend’s family members.C．The secret behind Legend’s success.D．Composing background of the song All of Me.6．What can you infer from the passage?A．Legend is proud of his success in music.B．Legend’s interest in music originates from his family.C．Legend is the first black singer who won the Grammy award.D．Legend received the title “Sexiest Man Alive” before he got married.7．What is essential to attractiveness according to Legend?A．Being more mature.B．Being true to yourself.C．Having onstage confidence.D．Having attractive appearance.CWhat makes people trustworthy? Do they always tell the truth? Do they always keep their promises? In the near future, voluntary blood donations might be used as a clue to prove someone’s trustworthiness.On Nov 19, the National Health Commission (NHC) and other departments jointly released a document urging the social credit system to include voluntary blood donations. An incentive mechanism（激励机制）is also recommended, to provide donors with more conveniences and rewards like preferential treatment in using public facilities or visiting government-run p arks, China Daily reported. “We need to show we care about donors so they feel honored,” Liu Jiang, director of Beijing’s blood donation office, told CCTV.Indeed, donating blood is key to saving many lives. Due to blood’s very limited shelf life, regular blood donations are needed from a sufficient number of healthy people. This ensures that safe blood will be available whenever and wherever it is needed, according to the World Health Organization. However, the notice received mixed reviews on social media, with some people questioning whether it was necessary to include voluntary blood donation in the social credit system, according to the South China Morning Post. The system records things like a person’s career information, and payments for credit cards or other debt expenses are used to tell whether a person or company is trustworthy. People who cannot pay debts on time would have a worse credit score, resulting in more difficulties borrowing money from banks, reported the People’s Daily.Many Sina Weibo users believe that blood donations should be voluntary. They say it has little to do with social credit. Others doubt whether it is appropriate to reward this action because some people would donate blood for reasons other than helping save people’s lives. Guangming Daily commented that only acts closely linked to personal credit should be included in the social credit system. A voluntary blood donor might refuse to pay his or her debts, while someone who doesn’t donate blood might have a perfect credit re cord, it noted.8．What benefit can voluntary blood donors get according to the 2nd paragraph?A．Free park tour. B．Free treatment in hospitals.C．Running in government parks. D．Priority in using public facilities.9．Why are blood donations regularly needed?A．Blood can’t be stored for long.B．Some donated blood is not healthy.C．Fewer people are willing to donate blood.D．More and more people need blood to get treated.10．What can you learn from the last paragraph?A．Many blood donors refuse to pay his or her debts.B．Whoever donates blood will have a perfect credit record.C．It’s right to reward blood donators for they save people’s lives.D．Some people agree that voluntary blood donation shouldn’t be linked to social credit. 11．What’s the author’s attitude to using voluntary blood donations to prove trustworthiness?A．Positive. B．Objective. C．Indifferent D．Negative.DFive years ago, UK schools began to learn Shanghai’s math teaching methods on account of top scores produced by Chinese teenagers in a global academic evaluation. This test is called the Program for International Student Assessment (PISA), run by the organization for Economic Cooperation and Development (OECD). Taking around three hours on computers, it mainly focuses on 15-year-olds’ reading, math and science abilities. Earlier this month, the latest test results were published.Students from Beijing and Shanghai, as well as Jiangsu and Zhejiang provinces, outperformed students from the other 78 participating education systems in mathematics and science by a wide margin. In reading comprehension scores, only Singapore came close. Chinese mainland students first took the tests in 2009, with Shanghai topping the scores. The city claimed the top spot again in 2012.The PISA rankings aroused global interest in Chinese teaching methods and as a result, Britain increased exchanges with Chinese schools to improve its math education. Nearly 600 teachers from Britain and China, mainly from primary schools, have taken part in the ex change since 2014, and around 5,000 of Britain’s 16,000 primary schools have adopted the Shanghai math teaching method. In the latest PISA test, Chinese mainland students averaged 591 points in math —more than 100 points higher than the OECD average. British students averaged 502, jumping from 27th place three years ago to 18th in the math rankings.Philip Avery, director of education for the Bohunt Education Trust, UK, said, “We’ve benefited fromworking with Chinese partners for the high quality of lesson planning and teaching for memorization in China. Our Chinese partners have benefited from our approach to the development of character, focus on innovation and application of knowledge.”However, Zhang Xuanmin, who is in charge of the PISA project in Shanghai, points out that besides basic education, Chinese students still need to improve their social and emotional competencies. 12．Which of the following is TRUE according to the passage?A．UK teenagers are poorly-educated.B．UK schools’ teaching methods are out of fashion.C．Teenagers in Shanghai got higher scores in PISA.D．Teenagers in Shanghai are the best students in the world.13．What does the underlined word mean in the 2nd paragraph?A．Laugh at. B．Look up to. C．get along with. D．be superior to. 14．What’s probably the average math point of OECD in the latest PISA test?A．302. B．490. C．502. D．591.15．What can be indicated by Philip Avery’s words?A．The exchange program is a win-win situation.B．Chinese students still have a long way to go in education.C．UK schools get more benefits from the exchange program.D．UK teenagers have gained a lot of improvement in math learning.第二节（共5小题；每小题3分，满分15分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

标准学术能力诊断性测试2024年9月测试数学试卷（A 卷）本试卷共150分，考试时间90分钟.一､单项选择题：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.设,a b ∈R ，则“22log log a b >”是“1122b a ⎛⎫⎛⎫> ⎪ ⎪⎝⎭⎝⎭”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2.集合(){}{}22ln 23,23,A x y x x B y y x x x A ==--==-+∈∣∣，则A B ⋂=R ð（）A.(),1∞-- B.()(],13,6∞--⋃C.()3,∞+ D.()[),16,∞∞--⋃+3.已知复数z 满足5z z ⋅=，则24i z -+的最大值为（）C. D.4.已知非零向量,a b 满足3a b = ，向量a 在向量b 方向上的投影向量是9b - ，则a 与b 夹角的余弦值为（） A.33 B.13 C.33- D.13-5.设函数()f x 的定义域为R ，且()()()()42,2f x f x f x f x -++=+=-，当[]1,2x ∈时，()()()2,303f x ax x b f f =+++=-，则b a -=（）A.9-B.6-C.6D.96.班级里有50名学生，在一次考试中统计出平均分为80分，方差为70，后来发现有3名同学的分数登错了，甲实际得60分却记成了75分，乙实际得80分却记成了90分，丙实际得90分却记成了65分，则关于更正后的平均分和方差分别是（）A.82，73 B.80，73 C.82，67D.80，677.已知()sin 404cos50cos40cos θθ-=⋅⋅ ，且ππ,22θ⎛⎫∈- ⎪⎝⎭，则θ=（）A.π3- B.π6- C.π6 D.π38.已知函数()2221x f x x =-++，则不等式()()2232f t f t +->的解集为（）A.()(),13,∞∞--⋃+ B.()1,3- C.()(),31,∞∞--⋃+ D.()3,1-二､多项选择题：本题共3小题，每小题6分，共18分.在每小题给出的四个选项中，有多项符合题目要求.全部选对得6分，部分选对但不全得3分，有错选的得0分.9.已知实数,,a b c 满足0a b c <<<，则下列结论正确的是（）A.11a c b c>-- B.a a c b b c +<+C.b c a c a b --> D.2ac b bc ab+<+10.已知函数()sin3cos3f x a x x =-，且()3π4f x f ⎛⎫≤⎪⎝⎭对任意的x ∈R 恒成立，则下列结论正确的是（）A.1a =±B.()f x 的图象关于点π,04⎛⎫ ⎪⎝⎭对称C.将()f x 的图象向左移π12个单位，得到的图象关于y 轴对称D.当π23π,1236x ⎡⎤∈-⎢⎥⎣⎦时，满足()2f x ≤-成立的x 的取值范围是π7π,3636⎡⎤-⎢⎥⎣⎦11.在长方体1111ABCD A B C D -中，已知4,2AB BC ==，13,AA M N =､分别为1111B C A B ､的中点，则下列结论正确的是（）A.异面直线BM 与AC 所成角的余弦值为7210B.点T 为长方形ABCD 内一点，满足1D T ∥平面BMN 时，1D T的最小值为5C.三棱锥1B B MN -的外接球的体积为14πD.过点,,D M N 的平面截长方体1111ABCD A B C D -所得的截面周长为+三､填空题：本题共3小题，每小题5分，共15分.12.若实数,x y 满足1232,34x y x y ≤+≤≤-+≤，则x y +的取值范围是__________.13.如图所示，在梯形ABCD 中，1,3AE AB AD =∥,3,BC BC AD CE =与BD 交于点O ，若AO x AD y AB =+ ，则x y -=__________.14.在四面体ABCD 中，3,,CD AD CD BC CD =⊥⊥，且AD 与BC 所成的角为30 .若四面体ABCD 的体积为2，则它的外接球表面积的最小值为__________.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.（13分）已知复数12213i z =-+=--.（1）若12z z z =，求z ；（2）在复平面内，复数12,z z 对应的向量分别是,OA OB ，其中O 是原点，求AOB ∠的大小.16.（15分）在ABC 中，角,,A B C 的对边分别是,,a b c ，且cos cos 1a C b A c -+=.（1）求角A ；（2）已知b D =为BC 边上一点，且2,BD BAC ADC ∠∠==，求AD 的长.17.（15分）如图所示，在四棱锥P ABCD -中，底面ABCD 为平行四边形，PA ⊥平面ABCD ，点Q 为PA 的三等分点，满足13PQ PA =.（1）设平面QCD 与直线PB 相交于点S ，求证：QS ∥CD ；（2）若3,2,60,AB AD DAB PA ∠==== ，求直线CQ 与平面PAD 所成角的大小.18.（17分）甲､乙两位同学进行投篮训练，每个人投3次，甲同学投篮的命中率为p ，乙同学投篮的命中率为()q p q >，且在投篮中每人每次是否命中的结果互不影响.已知每次投篮甲､乙同时命中的概率为15，恰有一人命中的概率为815.（1）求,p q 的值；（2）求甲､乙两人投篮总共命中两次的概率.19.（17分）已知函数()233x x f x a --=⋅+是偶函数，()246h x x x =-+.（1）求函数()e 2x y h a =-的零点；（2）当[],x m n ∈时，函数(()h f x 与()f x 的值域相同，求n m -的最大值.标准学术能力诊断性测试2024年9月测试数学（A卷）参考答案一､单项选择题：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.12345678A B C C D B A C二､多项选择题：本题共3小题，每小题6分，共18分.在每小题给出的四个选项中，有多项符合题目要求.全部选对的得6分，部分选对但不全的得3分，有错选的得0分.91011AD BC BD三､填空题：本题共3小题，每小题5分，共15分.12.21,55⎡⎤-⎢⎥⎣⎦13.11114.73π-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.（13分）解：（1）()() ()()12224i13i24i26i4i127i13i13i13i19i5 zzz-+---++-++ =====-+-+---5z∴==（2）依题意向量()()2,4,1,3OA OB=-=--于是有()()()214310OA OB⋅=-⨯-+⨯-=-OA OB====AOB∠为OA 与OB 的夹角，2cos2OA OBAOBOA OB∠⋅∴==-[]0,πAOB∠∈，3π4AOB∠∴=16.（15分）解：（1）由正弦定理可得：cos sin cos sin cos 1sin a C b A C B A c C--+==()cos 1sin sin cos sin A C A C B ∴+=-，由()sin sin B A C =+可得：()cos sin sin sin cos sin A C C A C A C ⋅+=-+，cos sin sin sin cos sin cos cos sin A C C A C A C A C ⋅+=--，cos sin sin cos sin A C C A C∴⋅+=-sin 0C ≠ 可得：cos 1cos A A +=-，1cos 2A ∴=-，()0,πA ∈ ，2π3A ∴=（2）,BAC ADC BCA ACD ∠∠∠∠== ，BAC ∴ 与ADC 相似，满足：AC BC CD AC =，设CD x =，则有3x =解得：1,3x x ==-（舍去），即：1CD =2π3ADC BAC ∠∠== ，在ADC 中，由余弦定理可得：2222πcos 32AD CD AC AD CD+-=⋅⋅，即：211221AD AD +--=⨯⨯解得：1,2AD AD ==-（舍去），AD ∴的长为117.（15分）解：（1）证明：因为平面QCD 与直线PB 相交于点S ，所以平面QCD ⋂平面PAB QS=因为四边形ABCD 为平行四边形，AB ∴∥CD ，AB ⊄ 平面,QCD CD ⊂平面,QCD AB ∴∥平面QCDAB ⊂ 平面PAB ，平面QCD ⋂平面,PAB QS AB =∴∥QS ，AB ∥,CD QS ∴∥CD（2）过点C 作CH AD ⊥于点H ，PA ⊥ 平面,ABCD PA ⊂平面PAD ，所以平面PAD ⊥平面ABCD ，因为平面PAD ⋂平面ABCD AD =，且CH AD ⊥，CH ∴⊥平面PAD连接,QH CQH ∠∴是直线CQ 与平面PAD 所成的角因为点Q 为PA 的三等分点，232,223PA QA PA =∴==，在Rt DCH 中，333sin602CH =⋅= 在ACD 中，利用余弦定理可得：222223cos120,19223AC AC +-=∴=⨯⨯ ，在Rt QAC 中，222(22)1933QC QA AC =+=+=在Rt QCH 中，3312sin 233CH CQH CQ ∠===，可得π6CQH ∠=，即直线CQ 与平面PAD 所成的角等于π618.（17分）解：（1）设事件A ：甲投篮命中，事件B ：乙投篮命中，甲､乙投篮同时命中的事件为C ，则C AB =，恰有一人命中的事件为D ，则D AB AB =⋃，由于两人投篮互不影响，且在投篮中每人每次是否命中的结果互不影响，所以A 与B 相互独立，,AB AB 互斥，所以：()()()()P C P AB P A P B ==⋅()(()()(()()()P D P AB AB P AB P AB P A P B P A P B =⋃=+=⋅+⋅可得：()()1581115pq p q p q ⎧=⎪⎪⎨⎪-+-=⎪⎩解得：1335p q ⎧=⎪⎪⎨⎪=⎪⎩或3315,,,1533p p q p q q ⎧=⎪⎪>∴==⎨⎪=⎪⎩（2）设i A ：甲投篮命中了i 次；j B ：乙投篮命中了j 次，,0,1,2,3i j =，()30285125P A ⎛⎫== ⎪⎝⎭()2213223223365555555125P A ⎛⎫⎛⎫=⨯+⨯⨯+⨯= ⎪ ⎪⎝⎭⎝⎭()2223232323545555555125P A ⎛⎫⎛⎫=⨯+⨯⨯+⨯= ⎪ ⎪⎝⎭⎝⎭()3028327P B ⎛⎫== ⎪⎝⎭()2211221221433333339P B ⎛⎫⎛⎫=⨯+⨯⨯+⨯= ⎪ ⎪⎝⎭⎝⎭()2222112112233333339P B ⎛⎫⎛⎫=⨯+⨯⨯+⨯= ⎪ ⎪⎝⎭⎝⎭设E ：甲､乙两人投篮总共命中两次，则021120E A B A B A B =++由于i A 与j B 相互独立，021120,,A B A B A B 互斥，()()()()()()()()021*********P E P A B A B A B P A P B P A P B P A P B ∴=++=⋅+⋅+⋅8236454830412591259125271125=⨯+⨯+⨯=19.（17分）解：（1）()233x x f x a --=⋅+ 是偶函数，则()()f x f x -=，即11333399x x x x a a --⋅+=⋅+，()113309x x a -⎛⎫∴--= ⎪⎝⎭，由x 的任意性得119a =，即9a =()246h x x x =-+ ，()()()()()22e 2e 4e 618e 4e 12e 6e 2x xx x x x x y h a ∴=-=-⋅+-=-⋅-=-+，令()()e 6e 20x x -+=，则e 6x =或e 2x =-（舍去），即ln6x =，()e 2x y h a ∴=-有一个零点，为ln6（2）设当[],x m n ∈时，函数()f x 的值域为[],s t ，则函数()()h f x 的值域也为[],s t ，由（1）知()2933332x x x x f x ---=⋅+=+≥=当且仅当33x x -=，即0x =时等号成立，令()p f x =，则2p ≥，()2246(2)2h x x x x =-+=-+ 在区间[)2,∞+上单调递增，所以当[],p s t ∈时，()2,s h p ≥的值域为()(),h s h t ⎡⎤⎣⎦，即()()h s s h t t ⎧=⎪⎨=⎪⎩，则224646s s s t t t ⎧-+=⎨-+=⎩，即,s t 为方程246x x x -+=的两个根，解得23s t =⎧⎨=⎩，所以当[],x m n ∈时，()f x 的值域为[]2,3令()30x x λ=>，则()133,1x x y f x λλλ-==+=+>，3x λ= 在()0,∞+上单调递增，对勾函数1y λλ=+在()1,∞+上单调递增，由复合函数的单调性知，()f x 在()0,∞+上单调递增，()f x 是偶函数，()f x ∴在(),0∞-上单调递减令()3f x =，即333x x -+=，解得332x +=或332x =，即33log 2x +=或33log 2x -=，故n m -的最大值为3333535735log log log 222-+-=答案解析1.A【解析】由22log log a b >可得0a b >>，由1122b a⎛⎫⎛⎫> ⎪ ⎪⎝⎭⎝⎭可得a b >，由a b >得不到0a b >>，故必要性不成立；由0a b >>可以得到a b >，故充分性成立，则“22log log a b >”是“1122b a ⎛⎫⎛⎫> ⎪ ⎪⎝⎭⎝⎭”的充分不必要条件.2.B 【解析】集合(){}{}22ln 23230A x y x x x x x ==--=-->∣∣()(){}310{13},x x x x x x =-+>=<->∣∣或集合{}{}223,6B yy x x x A y y ==-+∈=>∣∣，{}()(]6,,13,6B y y A B ∞=≤∴⋂=--⋃R R ∣3.C【解析】复数z 满足5z z ⋅=，设22i,5z a b z z a b =+⋅=+=，()()2224i 24i (2)(4)z a b a b -+=-++=-++，则点()2,4-到圆225a b +=+=4.C【解析】设非零向量,a b 夹角为θ，向量a 在向量b 方向上的投影向量是39b - ，则cos ,39b a a b b θ⨯=-= ∣，解得3cos 3θ=-.5.D【解析】()()42f x f x -++= ，取()()1,312x f f =+=，()()()321211f f a b a b =-=-++=--，()()2f x f x +=- ，取()()0,2042x f f a b ===++，()()303,1423,2f f a b a b a +=---+++=-=- ，()()42f x f x -++= ，取2x =，则()21f =，则7b =，则729b a -=+=.6.B【解析】设更正前甲，乙，丙 的成绩依次为12350,,,,a a a a ，则12505080a a a +++=⨯ ，即507590655080a ++++=⨯ ，()222250(7580)(9080)(6580)807050a -+-+-++-=⨯ ，更正后平均分：()5016080908050x a =++++= ，()22222501(6080)(8080)(9080)807350s a ⎡⎤=-+-+-++-=⎣⎦ .7.A 【解析】()sin 40sin40cos cos40sin θθθ-=- 4cos50cos40cos 4sin40cos40cos θθ=⋅⋅=⋅⋅ 1cot40tan 4cos40θ⇒-=14cos40tan cot40θ-⇒=sin404sin40cos40cos40-=()sin 30102sin80cos40+-= 13cos102cos1022cos40+-=3313sin10cos10sin10cos102222cos40cos40--==()()sin 1060sin 50cos40cos40--===πππ,,223θθ⎛⎫∈-∴=- ⎪⎝⎭.8.C【解析】设()()21121x g x f x x =-=-++，()()2221112121x x x g x f x x x -⋅-=--=--+=--+++，()()2221102121x x x g x g x x x ⎛⎫⋅+-=-++--+= ⎪++⎝⎭，设()()1212121222,112121x x x x g x g x x x ⎛⎫⎛⎫>-=-+--+ ⎪ ⎪++⎝⎭⎝⎭()()()()()122121121222222021212121x x x x x x x x x x -⎛⎫=-+-=-+> ⎪++++⎝⎭，故()g x 为奇函数，且单调递增，()()()()()()22223212310230f t f t f t f t g t g t +->⇒-+-->⇒+->，()()()()()222302332g t g t g t g t g t +->⇒>--=-，故232t t >-，解得()(),31,t ∞∞∈--⋃+.9.AD【解析】A.0a b c <<<，可得a c b c -<-，故11a c b c>--，A 正确；B.设不等式成立，则()()a a c b c b b c b b b c++<++，可得ab ac ab bc +<+，即ac bc <，由0a b c <<<可得ac bc >，故假设不成立，B 错误；C.不妨假设211313210,,1332b c a c a b c a b --+--+=-<=-<=-<====--，故,C b c a c a b --<错误；D.设不等式成立，()()22,,,0ac b bc ab ac bc ab b a b c a b b a b c +<+-<--<-<<< ，()()a b c a b b -<-成立，故2ac b bc ab +<+成立，D 正确.10.BC【解析】A.()()sin3cos33sin 0,cos πf x a x x x ϕϕϕϕ⎛⎫=-=+=-=≤ ⎪⎝⎭()3π4f x f ⎛⎫≤ ⎪⎝⎭对任意x ∈R 恒成立，()f x ∴在3π4x =处取得极值，即3ππ3π42k ϕ⨯+=+，解得7π3ππ,sin 0,π,,sin 4422k ϕϕϕϕϕϕ=-+=-≤∴=-=-=- ，可求得1a =-，A 错误；B.()()3ππ3,0,44f x x f f x ⎛⎫⎛⎫=-=∴ ⎪ ⎪⎝⎭⎝⎭的图象关于点π,04⎛⎫ ⎪⎝⎭对称，B 正确；C.将()f x 的图象向左平移π12个单位，得到()π3ππ3331242g x x x x ⎛⎫⎛⎫=+⨯-=-=- ⎪ ⎪⎝⎭⎝⎭，函数图象关于y 轴对称，C 正确；D.()3π2342f x x ⎛⎫=-≤- ⎪⎝⎭，即3π1sin 342x ⎛⎫-≤- ⎪⎝⎭，7π3π11π2π32π646k x k ∴+≤-≤+，解得23π231π2ππ363363k x k +≤≤+，由题意知π23π,1236x ⎡⎤∈-⎢⎥⎣⎦，符合条件的k 的取值为1,0-，当1k =-时，π7π3636x -≤≤，均在定义域内，满足条件，当0k =时，23π31π3636x ≤≤，此时仅有23π36x =满足条件，所以满足()22f x ≤-成立的x 的取值范围为π7π23π,363636⎡⎤⎧⎫-⋃⎨⎬⎢⎣⎦⎩⎭，D 错误.11.BD【解析】A.MN ∥,AC BMN ∠∴为直线MN 与AC 所成角，在BMN 中，根据余弦定理可知222cos 2BM MN BN BMN BM MN∠+-=⋅，422BM MN BN ======，代入求得cos 10BMN A ∠=错误；B.取AD 的中点E ，取CD F ，取11A D 的中点S ，连接11,,,,EF D E D F AS SM ，SM ∥,AB AS ∥BM ，所以四边形ABMS 是平行四边形，AS ∥BM 且AS ∥11,D E D E ∴∥1BM D E ∴∥平面BMN ，同理可得1D F ∥平面BMN ，1DT ∥平面,BMN T ∈平面ABCD ，所以点T 的运动轨迹为线段EF ，在1ΔD EF 中，过点1D 作1D T EF ⊥，此时1D T 取得最小值，由题意可知，11D E D F EF ===，1111sin sin sin 105D EF BMN D T D E D EF ∠∠∠====，B 正确；C.取MN 的中点1O ，连接11B O ，则1111O N O M O B ==，过点1O 作1OO ∥1BB ，且111322OO BB ==，OM ∴为外接球的半径，在1Rt MB N 中，MN =，2R OM ∴==，34ππ,33V R C ∴==球错误；D.由平面11AA D D ∥平面11BB C C 得，过点,,D M N 的平面必与11,AA C C 有交点，设过点,,D M N 的平面与平面11AA D D 和平面11BB C C 分别交于,DO PM DO ∴∥,PM 同理可得DP ∥,ON 过点,,D M N 的平面截长方体1111ABCD A B C D -所得的截面图形为五边形DPMNO ，如图所示，以D 为坐标原点，以1,,DA DC DD 所在直线分别为,,x y z 轴建立空间直角坐标系，设,AO m CP n ==，则()()()()()0,0,0,2,0,,0,4,,1,4,3,2,2,3D O m P n M N ，()()()()0,2,3,1,0,3,2,0,,0,4,ON m PM n DO m DP n ∴=-=-== ，DP ∥,ON DO ∥PM ，()()2323m n n m ⎧=-⎪∴⎨=-⎪⎩，解得2m n ==，DO DP ∴==ON PM MN ====，所以五边形DPMNO 的周长为DO DP ON PM MN ++++==+，D 正确.12.21,55⎡⎤-⎢⎥⎣⎦【解析】令()()()()2323x y m x y n x y m n x m n y +=++-+=-++，2131m n m n -=⎧∴⎨+=⎩，解得()()2121,,235555m n x y x y x y ==-∴+=+--+，1232,34x y x y ≤+≤≤-+≤ ，则()()22441323,555555x y x y ≤+≤-≤--+≤-，24435555x y ∴-≤+≤-，即21,55x y ⎡⎤+∈-⎢⎣⎦.13.111【解析】建立如图所示的平面直角坐标系，设1AD =，则3BC =，()()()()220,0,3,0,,,1,,,33B C A m n D m n E m n ⎛⎫∴+ ⎪⎝⎭，所以直线BD 的方程为1n y x m =+，直线CE 的方程为()2329n y x m =--，联立两直线方程求得()()666655,,,,1,0,,11111111m n m n O AO AD AB m n +-⎛⎫⎛⎫∴=-==-- ⎪ ⎝⎭⎝⎭ ，6511,511m x my AO xAD y AB n ny -⎧=-⎪⎪=+∴⎨⎪-=-⎪⎩ ，解得651,,111111x y x y ==∴-=.14.73π-【解析】依题意，可将四面体ABCD 补形为如图所示的直三棱柱ADE FCB -，AD 与BC 所成的角为30 ，30BCF ∠∴= 或150，设,CB x CF y ==，外接球半径记为R ，外接球的球心如图点O ，11113sin 23324ABCD CBF V DC S xy BCF xy ∠⎛⎫∴=⋅⋅=⨯⨯== ⎪⎝⎭ ，解得8xy =，在2Rt OCO 中，2222222223922sin 4BF R OC OO CO BF BCF ∠⎛⎫⎛⎫==+=+=+ ⎪ ⎪⎝⎭⎝⎭，在BCF 中，由余弦定理可得2222cos BF BC CF BC CF BCF ∠=+-⋅⋅，要使外接球表面积最小，则R 要尽可能小，则BCF ∠应取30 ，(2222BF x y xy ∴=+≥-，当且仅当x y =时取等，(22min 99732444R BF xy ∴=+=+=-所以外接球表面积的最小值2min min 4π73πS R ==-.。

中学生标准学术能力诊断性测试2020年5月测试7．化学与生活生产密切相关，下列说法正确的是A．我国海洋开发走向深蓝，大型舰船的底部常镶嵌锌块做正极，防止船底腐蚀B．补铁酱油中含有三价铁，可补充人体缺乏的铁元素C．采用“燃煤固硫”、“煤的气化液化”、“静电除尘”、“汽车尾气催化净化”等方法，提高了空气质量，使我们的生活环境更美好D．“歼-20”飞机上使用的碳纤维被誉为“新材料之王”，是我国打破其他国家技术垄断，自主研发和生产的一种新型有机高分子材料8．下列说法正确的是A．14C与12C 60互为同位素B．14C60与12C60是具有相同质子数的不同核素C．CH3COOH与HCOOCH3互为同素异形体D．硝基苯与互为同分异构体9．用N A表示阿伏伽德罗常数的值，下列叙述不正确的是A．常温常压下，0.1mol的Na2O和Na2O2，混合物中阴离子总数为0.1N AB．常温下，46g的NO2和N2O4混合气体中含有的氮原子数为N AC．标准状况下，22.4L C3H6分子中含有N A个碳碳双键D．100mL0.1 mol·L−1CH3COONa溶液中阴离子总数大于0.01N A10．下列实验操作及现象和结论均正确的是11．向10mL 0.2mol·L−1的KIO3 溶液中逐渐加入NaHSO3 粉末，生成的I2的物质的量随所加NaHSO3的物质的量变化如右图所示，下列说法不正确的是A．A点对应的I 的物质的量为1.0×10−3molB．0a:ab=5:1C．当溶液中的n(I2)=5×10−4mol时，加入NaHSO3的物质的量可能为2.5×10−3mol或4.5×10−3mol D．由ab段反应可知，氧化性I2>HSO3−12．A、B、C、D为石墨电极，E、F分别为短周期相邻的两种活泼金属中的一种，且E能与NaOH 溶液反应。

按图接通线路，反应一段时间，当电路中通过1.0×10−3mol电子时，下列叙述正确的是A．U型管中的D端先变红，b烧杯中的溶液会变蓝B．a烧杯中最多有0.127gI2(KI足量)生成，甲池中的质量会减少0.04g(CuSO4溶液足量)C．A极产生气体的体积为5.6mL，甲池溶液的pH值为2D．E电极附近的溶液无明显现象产生13．常温下，将0.1mol·L−1的NaOH溶液逐渐加到5mL0.1mol·L−1的一元酸HA溶液中，测得混合溶液的BG(BG=-lg)与所加NaOH的体积的变化关系如图所示。

中学生标准学术能力诊断性测试2020年5月测试理科数学试卷（一卷）本试卷共150分，考试时间120分钟。

一、选择题：本大题共12小题，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．已知集合{}2log (2)0A x x =->，{}245,B y y x x x A ==-+∈，则A B ⋃=（ ） A ．[)3,∞B ．[)2,∞C ．()2,∞D ．()3,∞2．在复平面内，复数231ii+-的虚部为（ ）A B C ．D ． 3．已知单位向量a ，b 满足22a b a b +=-，则()()3a b a b -⋅+=（ ） A ．1B ．2C ．3D ．44．下列程序框图的算法思想源于我国古代数学名著《九章算术》中的“更相减损术”．执行该程序框图，若输入16a =，10b =，则程序中需要做减法的次数为（ ）A ．6B ．5C ．4D ．35．在()()252211x x x ++-的展开式中，4x 的系数为（ ）A ．6-B ．6C ．10D ．46．在三角形ABC 中，a ，b ，c 分别为角A ，B ，C 的对边，且满足22265b c a bc +=+，则sin 2B C +⎛⎫=⎪⎝⎭（ ）A ．2B C ．5D7．函数()32x e f x x -=-的部分图像大致是（ ）A ．B ．C ．D ．8．已知函数()31663x x f x x x e e -=--+-，若211011f f a a ⎛⎫⎛⎫+≤ ⎪ ⎪+-⎝⎭⎝⎭，则a 的取值范围为（ ） A ．(][),12,-∞-⋃+∞ B ．()1,2- C ．()()1,00,1-⋃ D ．()[)1,1$2,-⋃+∞9．已知等差数列{}n a 满足：11a =，4164a a +=，则1912222a a a⨯⨯⋅⋅⋅⨯=（ ）A ．382B ．192C ．162D ．76210．已知椭圆()222210x y a b a b +=>>21y x =+相切，则a =（ ）A ．2BCD ．111．设()f x 为定义于[]1,1-上的偶函数，当[]0,1x ∈时，()12f x x =-，则方程()()22x f f x =的实数解的个数为（ ） A ．8B ．6C ．4D ．212．已知当[]0,1x ∈时，不等式()()22cos 11sin 0x x x x θθ--+->恒成立，则θ的取值范围为（ ） A ．π5πππ1212k k θ+<<+（k 为任意整数） B ．π5πππ66k k θ+<<+（k 为任意整数） C ．π5π2π2π1212k k θ+<<+（k 为任意整数） D ．π5π2π2π66k k θ+<<+（k 为任意整数） 二、填空题：本大题共4小题．13．设数列{}n a 满足14a =，210a =，215n n a a -=，3n ∀≥，则201920181ln ln 2a a -=______． 14．设实数x ，y 满足02203x y x y x -≥⎧⎪++≥⎨⎪≤⎩，则22x y +的最大值为______．15．假设抛一枚质地均匀的色子，若抛出的点数为1、2或3，我们称为“小”，否则，若抛出的点数为4、5或6，则称为“大”。

2020年5月清华大学中学生标准学术能力理科综合诊断性测试一卷本试卷共300分，考试时间150分钟。

可能用到的相对原子质量：H 1 O 16 C 12 N 14 Fe 56 Cr 52 S 32 I 127 Ba 137一、选择题：本题共13小题，每小题6分，共78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。

1．2019年诺贝尔生理医学奖授予了揭示“细胞如何感知和适应氧气”机理的三位科学家。

他们研究发现肾脏中有专门的细胞可以感受氧气水平的变化，当氧气供应不充足时，低氧诱导因子（HIF-1α）不被降解，细胞内积累的HIF-1α可促进促红细胞生成素（EPO）的合成；氧气供应充足时，HIF-1α合成后很快被降解，具体调节途径如下图所示。

请据图分析下列说法错误的是A．低氧时，HIF-1α进入细胞核联合ARNT与EPO基因调控序列结合，增强EPO基因的表达，使细胞合成更多的EPOB．若将细胞中的脯氨酸酰羟化酶基因敲除，EPO基因的表达水平会下降，细胞合成的EPO量减少C．正常条件下，人体细胞内HIF-1α的含量较低，在医学上可尝试通过提高HIF-1α的含量来治疗人类的贫血症D．高原反应时，EPO 会刺激骨髓中的造血干细胞，使其增殖分化生成大量红细胞，提高氧气的运输能力，该调节方式属于激素调节2．双脱氧核苷三磷酸（ddNTP）属于非天然核苷酸，是桑格-库森法测定DNA 序列的底物。

ddNTP 与脱氧核苷三磷酸（dNTP）的结构如下图所示，根据所学知识判断下列选项错误的是A．若X表示OH，该结构代表的物质dNTP可作为体内DNA分子复制的原料B．若将ddNTP加到正在复制的DNA反应体系中，ddNTP结合到子链后，子链的延伸会立即终止C．ddNTP、dNTP以及磷脂分子的元素组成都为C、H、O、N、PD．若X表示OH，碱基为A时，该物质可为细胞的各项生命活动直接提供能量3．细胞自噬有助于人类更好地了解细胞如何实现自身的循环利用，帮助细胞适应饥饿和应对感染等不良环境。

中学生标准学术能力诊断性测试2020 年 5 月测试英语试卷本试卷共150 分，考试时间100 分钟。

第一部分阅读理解（共两节，满分60 分）第一节（共15 小题；每小题 3 分，满分45 分）ASummer is that time of this year 2019 when everyone looks to escape from the boring activities of life. So bring your kids to join us to have fun in the summer camp.Outdoor Word Game:All you need to do is setting up many huge letters that can be easily moved. These letters will help kids spell out certain words. Teenagers would also love something like this as it gives them the opportunity to invest their time in learning new words.Spray Painting:To bring out the creativity in a person, an activity centered on spray painting is the perfect way to get those creative juices flowing. All you need to do is providing plain white T-shirts and some cans of colored spray paint. It will be quite surprising to see some of the original ideas that will flow from individuals.Outdoor Twister:A person will be in charge of monitoring the game and will call out colors which can be placed outdoors. Participants have the task of placing either their hands or legs on the same color. A fun and exciting game focuses on hand-eye coordination（协调）.The Maze（迷宫）:One of the funniest games is the hallway maze game where a maze is constructed from either toilet paper or strings of paper. The chosen participant is then asked to make his way through the maze within a limited time without touching paper. This is one of the best and entertaining summer camp ideas for kids and adults also.1.Which activity most probably needs some imagination?A．Outdoor Word Game. B．Spray Painting.C．Outdoor Twister. D．The Maze.2.Which of the following is TRUE according to the passage?A.The maze is made of toilet paper in The Maze.B.You have to spray juice on your T-shirt in Spray Painting.C.Outdoors Twister tests whether you are good at controlling your body movement.D.You have to bring some huge letters to play in Outdoor Word Games.3.Who is the article intended for?A.Parents. B．Children. C．Teachers. D．Teenagers.BWhat makes a person sexy? Looks, talent, public image and how we accordingly view their personality all play into why we find ourselves attracted to certain celebrities and public figures. Every year, People put it all together when they name their “Sexiest Man Alive”. This year, the magazine decided that United States musician John Roger Stephens, better known as John Legend, has the full package.The title comes following some impressive achievements for the 40-year-old. He is among the youngest people to win an Emmy, Grammy, Oscar and Tony award, and the first African-American man to win all four of them. With numerous awards and nominations, an Ivy-League degree, and a handsome face, Legend has gained huge popularity worldwide. However, his dedication to family life maybe what wins over many.After getting married to US model Chrissy Teigen in 2013, Legend is the father of one son and one daughter. He’s not shy about telling the world their love is permanent. On the inside of Legend’s arm, there is a tattoo that says “Chrissy Luna Miles”, the names of his wife and children. In fact, Legend has gained strength from his family since childhood. He still remembers the days when his family would gather around his grandmoth er’s piano to sing Christmas songs. This inspired his passion for music. His best-known single, All of Me, is a love song to his wife. When he performed it at the 2014 Grammy Awards, many were touched by his delicate voice and the deep love beneath. “The more you know someone, the more you’re inspired by your relationship,” Legend told LA Confidential Magazine. “You have to grow enough to be able to write that song with sincerity and authenticity.”Despite his onstage confidence, Legend had to work to become a legend. As a teenager, he was the smallest kid in class. “I was always less mature, less at ease socially. I had plenty of awkward times,” he told People. “Most of your teenage years, into your twenties, you’re still figuring out who you are, how you present yourself to the world ... Eventually, I think you get more at ease with yourself.” Indeed, knowing who you are and be yourself could be the real key to attractiveness.4.What plays the biggest part in making Legend popular worldwide?A．High-level education. B．Handsome look.C．Efforts put in family. D．Talent in music.5.What does the third paragraph mainly talk about?A.Legend’s hobby as a boy.B.Legend’s family members.C.The secret behind Legend’s success.D．Composing background of the song All of Me.6.What can you infer from the passage?A.Legend is proud of his success in music.B.Legend’s interest in music originates from his family.C.Legend is the first black singer who won the Grammy award.D.Legend received the title “Sexiest Man Alive” before he got married.7.What is essential to attractiveness according to Legend?A.Being more mature.B.Being true to yourself.C.Having onstage confidence.D.Having attractive appearance.CWhat makes people trustworthy? Do they always tell the truth? Do they always keep their promises? In the near future, voluntary blood donations might be used as a clue to prove someone’s trustworthiness.On Nov 19, the National Health Commission (NHC) and other departments jointly released a document urging the social credit system to include voluntary blood donations. An incentive mechanism（激励机制）is also recommended, to provide donors with more conveniences and rewards like preferential treatment in using public facilities or visiting government-run parks, China Daily reported. “We need to show we care about donors so they feel honored,” Liu Jiang, director of Beijing’s blood donation office, told CCTV.Indeed, donating blood is key to saving many lives. Due to blood’s very limited shelf life, regular blood donations are needed from a sufficient number of healthy people. This ensures that safe blood will be available whenever and wherever it is needed, according to the World Health Organization. However, the notice received mixed reviews on social media, with some people questioning whether it was necessary to include voluntary blood donation in the social credit system, according to the South China Morning Post. The system records things like a person’s career information, and payments for credit cards or other debt expenses are used to tell whether a person or company is trustworthy. People who cannot pay debts on time would have a worse credit score, resulting in more difficulties borrowing money from banks, reported the P eople’s Daily.Many Sina Weibo users believe that blood donations should be voluntary. They say it has little to do with social credit. Others doubt whether it is appropriate to reward this action because some people would donate blood for reasons other than helping save people’s lives. Guangming Daily commented that only acts closely linked to personal credit should be included in the social credit system. A voluntary blood donor might refuse to pay his or her debts, while someone who doesn’t donate blood might have a perfect credit record, it noted.8.What benefit can voluntary blood donors get according to the 2nd paragraph?A．Free park tour. B．Free treatment in hospitals.C．Running in government parks. D．Priority in using public facilities.9.Why are blood donations regularly needed?A.Blood can’t be stored for long.B.Some donated blood is not healthy.C.Fewer people are willing to donate blood.D.More and more people need blood to get treated.10.What can you learn from the last paragraph?A.Many blood donors refuse to pay his or her debts.B.Whoever donates blood will have a perfect credit record.C.It’s right to reward blood donators for they save people’s lives.D.Some people agree that voluntary blood donation shouldn’t be linked to social credit. 11．What’s the author’s attitude to using voluntary blood donations to prove trustworthiness?A．Positive. B．Objective. C．Indifferent D．Negative.DFive years ago, UK schools began to learn Shanghai’s math teaching methods on account of top scores produced by Chinese teenagers in a global academic evaluation. This test is called the Program for International Student Assessment (PISA), run by the organization for Economic Cooperation and Development (OECD). Taking around three hours on computers, it mainly focuses on 15-year-olds’ reading, math and science abilities. Earlier this month, the latest test results were published.Students from Beijing and Shanghai, as well as Jiangsu and Zhejiang provinces, outperformed students from the other 78 participating education systems in mathematics and science by a wide margin. In reading comprehension scores, only Singapore came close. Chinese mainland students first took the tests in 2009, with Shanghai topping the scores. The city claimed the top spot again in 2012.The PISA rankings aroused global interest in Chinese teaching methods and as a result, Britain increased exchanges with Chinese schools to improve its math education. Nearly 600 teachers from Britain and China, mainly from primary schools, have taken part in the exchange since 2014, and around 5,000 of Britain’s 16,000 primary schools have adopted the Shanghai math teaching method. In the latest PISA test, Chinese mainland students averaged 591 points in math —more than 100 points higher than the OECD average. British students averaged 502, jumping from 27th place three years ago to 18th in the math rankings.Philip Avery, director of education for the Bohunt Education Trust, UK, said, “We’ve benefited fromworking with Chinese partners for the high quality of lesson planning and teaching for memorization in China. Our Chinese partners have benefited from our approach to the development of character, focus on innovation and application of knowledge.”However, Zhang Xuanmin, who is in charge of the PISA project in Shanghai, points out that besides basic education, Chinese students still need to improve their social and emotional competencies.12.Which of the following is TRUE according to the passage?A．UK teenagers are poorly-educated.B．UK schools’ teaching methods are out of fashion.C．Teenagers in Shanghai got higher scores in PISA.D．Teenagers in Shanghai are the best students in the world.13.What does the underlined word mean in the 2nd paragraph?14.What’s probably the average math point of OECD in the latest PISA test?15．What can be indicated by Philip Avery’s words?A.The exchange program is a win-win situation.B.Chinese students still have a long way to go in education.C．UK schools get more benefits from the exchange program.D．UK teenagers have gained a lot of improvement in math learning.第二节（共 5 小题；每小题 3 分，满分15 分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

中学生标准学术能力诊断性测试2020 年 5 月测试英语试卷本试卷共150 分，考试时间100 分钟。

第一部分阅读理解（共两节，满分60 分）第一节（共15 小题；每小题 3 分，满分45 分）ASummer is that time of this year 2019 when everyone looks to escape from the boring activities of life. So bring your kids to join us to have fun in the summer camp.Outdoor Word Game:All you need to do is setting up many huge letters that can be easily moved. These letters will help kids spell out certain words. Teenagers would also love something like this as it gives them the opportunity to invest their time in learning new words.Spray Painting:To bring out the creativity in a person, an activity centered on spray painting is the perfect way to get those creative juices flowing. All you need to do is providing plain white T-shirts and some cans of colored spray paint. It will be quite surprising to see some of the original ideas that will flow from individuals.Outdoor Twister:A person will be in charge of monitoring the game and will call out colors which can be placed outdoors. Participants have the task of placing either their hands or legs on the same color. A fun and exciting game focuses on hand-eye coordination（协调）.The Maze（迷宫）:One of the funniest games is the hallway maze game where a maze is constructed from either toilet paper or strings of paper. The chosen participant is then asked to make his way through the maze within a limited time without touching paper. This is one of the best and entertaining summer camp ideas for kids and adults also.1.Which activity most probably needs some imagination?A．Outdoor Word Game. B．Spray Painting.C．Outdoor Twister. D．The Maze.2.Which of the following is TRUE according to the passage?A.The maze is made of toilet paper in The Maze.B.You have to spray juice on your T-shirt in Spray Painting.C.Outdoors Twister tests whether you are good at controlling your body movement.D.You have to bring some huge letters to play in Outdoor Word Games.3.Who is the article intended for?A.Parents. B．Children. C．Teachers. D．Teenagers.BWhat makes a person sexy? Looks, talent, public image and how we accordingly view their personality all play into why we find ourselves attracted to certain celebrities and public figures. Every year, People put it all together when they name their “Sexiest Man Alive”. This year, the magazine decided that United States musician John Roger Stephens, better known as John Legend, has the full package.The title comes following some impressive achievements for the 40-year-old. He is among the youngest people to win an Emmy, Grammy, Oscar and Tony award, and the first African-American man to win all four of them. With numerous awards and nominations, an Ivy-League degree, and a handsome face, Legend has gained huge popularity worldwide. However, his dedication to family life maybe what wins over many.After getting married to US model Chrissy Teigen in 2013, Legend is the father of one son and one daughter. He’s not shy about telling the world their love is permanent. On the inside of Legend’s arm, there is a tattoo that says “Chrissy Luna Miles”, the names of his wife and children. In fact, Legend has gained strength from his family since childhood. He still remembers the days when his family would gather around his grandmother’s piano to sing Christmas songs. This inspired his passion for music. His best-known single, All of Me, is a love song to his wife. When he performed it at the 2014 Grammy Awards, many were touched by his delicate voice and the deep love beneath. “The more you know someone, the more you’re inspired by your relati onship,” Legend told LA Confidential Magazine. “You have to grow enough to be able to write that song with sincerity and authenticity.”Despite his onstage confidence, Legend had to work to become a legend. As a teenager, he was the smallest kid in class. “I was always less mature, less at ease socially. I had plenty of awkward times,” he told People. “Most of your teenage years, into your twenties, you’re still figuring out who you are, how you present yourself to the world ... Eventually, I think you get more at ease with yourself.” Indeed, knowing who you are and be yourself could be the real key to attractiveness.4.What plays the biggest part in making Legend popular worldwide?A．High-level education. B．Handsome look.C．Efforts put in family. D．Talent in music.5.What does the third paragraph mainly talk about?A.Legend’s hobby as a boy.B.Legend’s family members.C.The secret behind Legend’s success.D．Composing background of the song All of Me.6.What can you infer from the passage?A.Legend is proud of his success in music.B.Legend’s interest in music originates from his family.C.Legend is the first black singer who won the Grammy award.D.Legend received the title “Sexiest Man Alive” before he got married.7.What is essential to attractiveness according to Legend?A.Being more mature.B.Being true to yourself.C.Having onstage confidence.D.Having attractive appearance.CWhat makes people trustworthy? Do they always tell the truth? Do they always keep their promises? In the near future, voluntary blood donations might be used a s a clue to prove someone’s trustworthiness.On Nov 19, the National Health Commission (NHC) and other departments jointly released a document urging the social credit system to include voluntary blood donations. An incentive mechanism（激励机制）is also recommended, to provide donors with more conveniences and rewards like preferential treatment in using public facilities or visiting government-run parks, China Daily reported. “We need to show we care about donors so they feel honored,” Liu Jiang, director of Beijing’s blood donation office, told CCTV.Indeed, donating blood is key to saving many lives. Due to blood’s very limited shelf life, regular blood donations are needed from a sufficient number of healthy people. This ensures that safe blood will be available whenever and wherever it is needed, according to the World Health Organization. However, the notice received mixed reviews on social media, with some people questioning whether it was necessary to include voluntary blood donation in the social credit system, according to the South China Morning Post. The system records things like a person’s career information, and payments for credit cards or other debt expenses are used to tell whether a person or company is trustworthy. People who cannot pay debts on time would have a worse credit score, resulting in more difficulties borrowing money from banks, reported the P eople’s Daily.Many Sina Weibo users believe that blood donations should be voluntary. They say it has little to do with social credit. Others doubt whether it is appropriate to reward this action because some people would donate blood for reasons other than helping save people’s lives. Guangming Daily commented that only acts closely linked to personal credit should be included in the social credit system. A voluntary blood donor might refuse to pay his or her debts, while someone who doesn’t donate blood might have a perfect credit record, it noted.8.What benefit can voluntary blood donors get according to the 2nd paragraph?A．Free park tour. B．Free treatment in hospitals.C．Running in government parks. D．Priority in using public facilities.9.Why are blood donations regularly needed?A.Blood can’t be stored for long.B.Some donated blood is not healthy.C.Fewer people are willing to donate blood.D.More and more people need blood to get treated.10.What can you learn from the last paragraph?A.Many blood donors refuse to pay his or her debts.B.Whoever donates blood will have a perfect credit record.C.It’s right to reward blood donators for th ey save people’s lives.D.Some people agree that voluntary blood donation shouldn’t be linked to social credit. 11．What’s the author’s attitude to using voluntary blood donations to prove trustworthiness?A．Positive. B．Objective. C．Indifferent D．Negative.DFive years ago, UK schools began to learn Shanghai’s math teaching methods on account of top scores produced by Chinese teenagers in a global academic evaluation. This test is called the Program for International Student Assessment (PISA), run by the organization for Economic Cooperation and Development (OECD). Taking around three hours on computers, it mainly focuses on 15-year-olds’ reading, math and science abilities. Earlier this month, the latest test results were published.Students from Beijing and Shanghai, as well as Jiangsu and Zhejiang provinces, outperformed students from the other 78 participating education systems in mathematics and science by a wide margin. In reading comprehension scores, only Singapore came close. Chinese mainland students first took the tests in 2009, with Shanghai topping the scores. The city claimed the top spot again in 2012.The PISA rankings aroused global interest in Chinese teaching methods and as a result, Britain increased exchanges with Chinese schools to improve its math education. Nearly 600 teachers from Britain and China, mainly from primary schools, have taken part in the exchange since 2014, and around 5,000 of Britain’s 16,000 primary schools have adopted the Shanghai math teaching method. In the latest PISA test, Chinese mainland students averaged 591 points in math —more than 100 points higher than the OECD average. British students averaged 502, jumping from 27th place three years ago to 18th in the math rankings.Philip Avery, director of education for the Bohunt Education Trust, UK, said, “We’ve benefited fromworking with Chinese partners for the high quality of lesson planning and teaching for memorization in China. Our Chinese partners have benefited from our approach to the development of character, focus on innovation and application of knowledge.”However, Zhang Xuanmin, who is in charge of the PISA project in Shanghai, points out that besides basic education, Chinese students still need to improve their social and emotional competencies.12.Which of the following is TRUE according to the passage?A．UK teenagers are poorly-educated.B．UK schools’ teaching methods are out of fashion.C．Teenagers in Shanghai got higher scores in PISA.D．Teenagers in Shanghai are the best students in the world.13.What does the underlined word mean in the 2nd paragraph?14.What’s probably the average math point of OECD in the latest PISA test?15．What can be indicated by Philip Avery’s words?A.The exchange program is a win-win situation.B.Chinese students still have a long way to go in education.C．UK schools get more benefits from the exchange program.D．UK teenagers have gained a lot of improvement in math learning.第二节（共 5 小题；每小题 3 分，满分15 分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

中学生标准学术能力测试中学生标准学术能力诊断性测试2020年5月测试理科综合-物理参考答案(一卷)二、选择题：本题共8小题，每小题6分，共48分。

在每小题给出的四个选项中，第14~18题只有一项符合题目要求，第19～21题有多项符合题目要求。

全部选对的得6分，选对但不全的得3分，有选错的得0分。

14 15 16 17 18 19 20 21B D D DC BD AD CD三、非选择题：共62分。

(一)必考题：共47分。

22 . (6分)答案：(1)1.050 (2分) (2)23 . (9分)答案：(2分) (3) (2分)(1)5409 ( 3 分)(2)实验电路如图所示，(3分)(3) (3分)24. (14分)解析：(1)设粒子不从MN 边界飞出的入射速度最小值为vmn, 对应的粒子在两个区域中做圆周运动的半径分别为r₁和r₂。

两圆心的连线与MN 的夹角为θ。

中学生标准学术能力测 试庄(x+2)sin θ=r ₂五+7cOS θ=h(1分)( 2 分 )( 1 分 )( 1 分 )( 1 分 )( 1 分 )(2)设粒子入射速度为v, 粒子在两区域中的运动半径分别为r ₁ 和 r ₂, 粒子第一次通过AB 时距离A 点为x ,由题意有(n=1,2,3 … …)x=√P²-(h-x)²可 得n<2.9则 n=1 时n=2 时25 . (18分)(1 分)( 1 分 )( 1 分 )( 1 分 )( 1 分 )( 1 分 )( 1 分 )解析：(1)由动能定理得：解得： d=8m( 1 分 )( 1 分 )②①THUSSAT中学生标准学术能力测试小物块通过D 点时，③( 1分)从C点至D 点，由机械能守恒定律得：④ ( 1 分)解得：R=2m ⑤( 1分)(2)由动能定理得：⑥( 1 分)由牛顿第二定律得：F-μmg=ma₁⑦(1分)μ₂mg- μ₃(M+m)g=Ma₂⑧( 1 分)设小物块从B点运动至C点所需时间为t,则vc=vg+at₁⑨(1分)木板到达凹槽右端时的速度v=a₂T₁⑩( 1 分)由题意可知v<vc 且a₂>0 ⑪( 1 分)解得②( 1 分)(3)当M=0.1kg时，由⑧得a₂=9m/s²设木板的长度为L, 则⑬( 1 分)解得L=3.5m ① ( 1 分)小物块离开D 点后做平抛运动，竖直方向 2 ⑮(1分)水平方向x=vo¹2 ⑩( 1 分)解得x = 4m ⑪( 1 分)由于x >L, 故小物块不能落在木板上⑩( 1 分)(二)选考题：共15分。

绝密★启用前2020届清华大学中学生标准学术能力诊断性测试高三5月测试数学（文）试题（一卷）学校：___________姓名：___________班级：___________考号：___________注意事项：1、答题前填写好自己的姓名、班级、考号等信息 2、请将答案正确填写在答题卡上一、单选题1．已知集合{}{}14,2P x x Q x x =-<<=<，那么()R P C Q ⋂=（）A ．[)2,4B ．()1,-+∞C ．[)2,+∞D ．(]1,2- 答案：A {}2R C Q x x =≥，所以()[)2,4R P C Q ⋂=，选A.2．已知复数z 满足4z i i =-（其中i 为虚数单位），则z 的虚部为（） A ．4iB ．4C ．1D ．1- 答案：B把已知等式变形，再由复数代数形式的乘除运算化简得答案．解： 由4z i i=-，得2(4)414z i i i i i =-=-=+． ∴复数z 的虚部是4．故选：B ．点评：本题考查复数代数形式的乘除运算，考查复数的基本概念，是基础题．3．已知实数x ，y 满足约束条件222y x y x ≤⎧⎪+≥⎨⎪≤⎩，则3x y +的最大值为（）A ．2B ．6C ．8D ．12答案：C先根据约束条件画出可行域，再利用几何意义求最值，3z x y =+表示直线在y 轴上的截距，只需求出可行域直线在y 轴上的截距最大值即可．解：先根据约束条件画出可行域，作直线30x y +=，讲直线30x y +=平移，当过点(2,2)时，3x y +取得最大值 ()max 33228x y +=⨯+=故选：C ．点评：本题主要考查线性规划问题，以及利用几何意义求最值，属于基础题．4．已知实数a ，b 满足5a b +=，23log log a b =，则ab =（）A ．2B ．3C ．5D ．6 答案：D设23log log a b k ==，则2k a =，3k b =，再利用5a b +=即可求出k 的值，进而求出a ，b 的值．解：设23log log a b k ==，则2k a =，3k b =，235k k a b ∴+=+=，1k ∴=，2a ∴=，3b =，∴236ab =⨯=故选：D ．点评：本题主要考查了对数式与指数式的互化，以及对数的运算性质，是基础题．5．已知向量a r ，b r 满足1a =r ，2a b -=r r 且a b ⊥r r ，则向量a r 与a b -r r 的夹角为（）A ．2π3B ．π3C ．5π6D ．π6答案：B根据()a b b -⊥r r r 即可得出()0a b b -=r r r g ，从而得出·1a b =r r ，进而得出1cos ,2a b <>=r r ，根据向量夹角的范围即可求出夹角．解：Q a b ⊥r r ，∴0a b ⋅=r r∴()21a a b a a b ⋅-=-⋅=r r r r r r 设向量a r 与a b -r r 的夹角为θ∴()1cos 2a a b a a b θ⋅-==-r r r r r r ∵()0,θπ∈∴3πθ=故选：B ．点评：考查向量垂直的充要条件，以及向量数量积的运算，向量夹角的余弦公式，属于中档题．6．已知函数()ln f x x x =，则函数()f x 的单调递增区间为（）A ．RB ．()0,∞+C ．1,e ⎛⎫+∞ ⎪⎝⎭D ．(),e +∞答案：C 求()ln f x x x =的导数()f x '，由()0f x '>，即可求得答案．解：()ln 1f x x '=+Q ，令()0f x '>得：ln 1x >-，11x e e-∴>=． ∴函数()ln f x x x =的单调递增区间为1,e ⎛⎫+∞ ⎪⎝⎭． 故选：C ．点评：本题考查利用导数研究函数的单调性，易错点在于忽视函数的定义域，属于中档题．7．数列{}n a 的前n 项和()2*23n S n n n =-∈N ，若5p q +=()*,p q ∈N ，则p q a a +=（）A ．6B ．8C ．9D ．10答案：D 当1n =时，可得1a ，当2n …时，1n n n a S S -=-，验证1n =时是否适合可得通项公式，代入通项公式求解可得结果．解：当1n =时，11231a S ==-=-，当2n …时，221232(1)3(1)45n n n a S S n n n n n -=-=---+-=-， 当1n =时，上式也适合，∴数列{}n a 的通项公式为：45n a n =-∴()454541010p q a a p q p q +=-+-=+-=故选：D ．点评：本题考查等差数列的前n 项和公式和通项公式的关系，属中档题．8．已知x ，y ∈R ，“1x y +≤且1x y -≤”是“1x y +≤”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：C作出不等式组对应的平面区域，利用区域关系结合充分条件和必要条件的定义进行判断即可．解： 1x y +≤且1x y -≤等价于1111x y x y -≤+≤⎧⎨-≤-≤⎩ 1x y +≤等价于()()()()10,010,010,010,0x y x y x y x y x y x y x y x y ⎧+≤≥≥⎪-≤≥≤⎪⎨-+≤≤≥⎪⎪--≤≤≤⎩作出两个不等式组对应的平面区域都是以()1,0，()0,1，()1,0-，()0,1-为顶点的正方形∴“1x y +≤且1x y -≤”是“1x y +≤”的充要条件，故选：C ．点评：本题主要考查充分条件和必要条件的判断，结合充分条件和必要条件结合平面区域的关系是解决本题的关键．9．已知实数0a ≠，则函数()1sin f x ax a ⎛⎫=+ ⎪⎝⎭的图象一定不可能的是（） A ．B ．C ．D ．答案：A求函数的导数，判断()0f '的正负情况，即可得出答案.解：∵()1sin f x ax a ⎛⎫=+ ⎪⎝⎭∴()1cos f x a ax a ⎛⎫'=+ ⎪⎝⎭ ∴()10cos f a a'=， 观察各选项的图象，判断()0f '的正负情况，得：观察A 选项的图象，得()10sin 0f a=>，34T <<，故234a π<< ∴223a ππ<<，3122a ππ<<，()10cos 0f a a'=> 故A 选项的图象不符合观察B 选项的图象，得()10sin 0f a=>，67T <<，故267a π<< ∴273a ππ<<，3172a ππ<<，()10cos 0f a a'=> 故B 选项的图象符合观察C 选项的图象，得()10sin 0f a=>，69T <<，故269a π<< ∴293a ππ<<，3192a ππ<<，()10cos 0f a a'=> 故C 选项的图象符合观察D 选项的图象，得()10sin 0f a=>，24T <<，故224a π<< ∴2a ππ<<，112a ππ<<，()10cos 0f a a'=> 故D 选项的图象符合故选：A.点评：本题考查了函数的图象的识别，利用导数判断函数的性质，属于中档题．10．已知x ，y ∈R ，则方程组21y =⎪=+⎩的解(),x y 的个。

中学生标准学术能力诊断性测试2020 年5 月测试英语参考答案1-5 BCACC 6-10 BBDAD 11-15 BCDBA 16-20 CGAEF21-25 ACDBC 26-30 BDADB 31-35 CCBAD 36-40 DAACB41．truly 42．themselves 43．that/which 44．based 45．was called46．friends 47．Another 48．how 49．to convey 50．knew短文改错We’ve all experienced positive and negative mood. The emotions we feel every day play amoods animportant role in how you think and behave. For one thing, people who are often in a positive moodwein their everyday life tends to be happier, healthier and get along better with others. For other, a badtend anothermood can ruin our day, as well the day of the people around us. However, there are many things weascan do to turn our bad mood into a good one. As far as I’m concerning, exercise is one of the keys toconcernedgetting rid from a bad mood. Meanwhile, the simple act of sharing time in others is a great way to release of withstress and anxiety. So next time we’re feeling down, and call up a friend or visit a neighbor.书面表达Dear editor,I’m so honore d to introduce the great changes that have taken place in my hometown for the last ten years. Ten years ago, my hometown was a small and poor city, which had fewer factories. And people had very limited choices on the daily diets and transportation. However, nowadays my hometown has taken on a brand-new look with rapid development of culture and economy. People have confidence when walking on the clean and busy street. Also, there are so many tall buildings standing around the city. When it comes to the transportation, private cars can be seen easily. Besides, people can have dinner in various restaurants.From my point of view, I really appreciate the life at present and I do believe our city will become more and more prosperous.Thank you for your reading.Yours,Li Hua。