清华大学中学生标准学术能力诊断性测试2020年5月诊断性测试英语答案

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。

中学生标准学术能力诊断性测试2020年5月测试文科数学试卷（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，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．已知集合{}14P x x =-<<，{}2Q x x =<，则()R P Q ⋂=ð（ ） A ．[)2,4 B ．()1,-+∞ C ．[)2,+∞ D ．(]1,2- 2．已知复数z 满足4zi i=-（其中i 为虚数单位），则z 的虚部为（ ） A ．4iB ．4C ．1D ．1-3．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 ．124．已知实数a ，b 满足5a b +=，23log log a b =，则ab =（ ） A ．2B ．3C ．5D ．65．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 ．π66．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 +∞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 ．108．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 ．10．已知x ，y ∈R ，则方程组21y =⎪=+⎩的解(),x y 的个数（ ）A ．0B ．1C ．2D ．411．已知ABC △中，角A ，B ，C 所对的边分别是a ，b ，c ．若4cos a b C b a +=，且()1cos 6A B -=，则cos C =（ ） A ．23B ．34C ．23或34- D ．不存在12．已知m ，n ，p ∈R ，若三次函数()32f x x mx nx p =+++有三个零点a ，b ，c ，且满足()()3112f f -=<，()()022f f =>，则111a b c++的取值范围是（ ） A ．1,13⎛⎫⎪⎝⎭B ．11,43⎛⎫⎪⎝⎭C ．11,42⎛⎫⎪⎝⎭D ．11,32⎛⎫⎪⎝⎭二、填空题：13．已知1F 和2F 是椭圆2213x y +=的两个焦点，则12F F =______． 14．将1名同学和2名老师随机地排成一排，则该名学生恰好在2名老师中间的概率为______． 15．定义在R 上的偶函数()f x 满足()184f x +=，则()2020f =______．16．已知ABC △中，π2A ∠=，3AB =，4AC =．如图，点D 为斜边BC 上一个动点，将ABD △沿AD 翻折，使得平面AB D '⊥平面ACD ．当BD =______时，B C '取到最小值．三、解答题：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，每道试题考生都必须作答．第22、23题为选考题，考生根据要求作答． （一）必考题：17．如图，点0P 是锐角α的终边与单位圆的交点，0OP 逆时针旋转π3得1OP ，1OP 逆时针旋转π3得2OP ，…，1n OP -逆时针旋转π3得n OP ．（1）若0P 的坐标为34,55⎛⎫⎪⎝⎭，求点1P 的横坐标； （2）若点2020P 的横坐标为45，求2πsin 23α⎛⎫+ ⎪⎝⎭的值．18．某高中某班共有40个学生，将学生的身高分成4组：平频率/组距[)150,160，[)160,170，[)170,180，[)180,190进行统计，作成如图所示的频率分布直方图．（1）求频率分布直方图中a 的值和身高在[)160,170内的人数；（2）求这40个学生平均身高的估计值（同一组中的数据用该组区间的中点值为代表）（精确到0.01）．19．如图，四棱锥P ABCD -中，PAB △是边长为2的等边三角形．梯形ABCD 满足：1BC CD ==，AB CD ∥，AB BC ⊥．（1）求证：PD AB ⊥；（2）若2PD =，求点D 到平面PBC 的距离．20．如图，已知抛物线C ：24x y =，过直线1y =上一点M 作直线l 交抛物线C 于A ，B 两点，且点M 为AB 中点、作直线MN AB ⊥交y 轴于点N ．（1）求点N 的坐标；（2）求NAB △面积的最大值． 21．已知函数()()1ln f x x x =+． （1）求()y f x =在1x =处的切线方程：（2）已知实数2k >时，求证：函数()y f x =的图象与直线l ：()1y k x =-有3个交点．（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，则按所做的第一题计分．作答时请写清题号．22．[选修4-4：坐标系与参数方程选讲] 在极坐标系中，已知曲线C ：2221sin ρθ=+，过点()1,0F -引倾斜角为α的直线l ，交曲线C 于P ，Q 两点．（1）求曲线C 的直角坐标方程；（2）若直线l 分别交直线2x =±于A ，B 两点，且PQ 、AF BF -、AB 成等比数列，求cos α的值． 23．[选修4-5：不等式选讲] 已知实数a ，b 满足：22a b +=． （1）求证：2821ca b b c +++≥+；（2）若对任意的a ，*b ∈R ，1211c c b a++-≤+恒成立，求c 的取值范围．中学生标准学术能力测试诊断性测试2020年5月测试文科数学（一卷）答案一．选择题：本大题共12小题，每小题5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．二．填空题：本大题共4小题，每小题5分．13．14．1315．38+ 16．157三、解答题：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，每个试题考生都必须作答．第22、23题为选考题，考生根据要求作答． （一）必考题 17．解：（1）因为点034,55P ⎛⎫ ⎪⎝⎭，根据三角函数的定义可得4sin 5α=，3cos 5α= 根据题意可知点1P 的横坐标为πππ314cos cos cos sin sin 333525ααα⎛⎫+=-=⨯-=⎪⎝⎭ （2）根据题意可知点2020P 的横坐标为2020π4π4cos cos 335αα⎛⎫⎛⎫+=+= ⎪ ⎪⎝⎭⎝⎭ 所以π4cos 35α⎛⎫+=- ⎪⎝⎭又因为π0,2α⎛⎫∈ ⎪⎝⎭，所以ππ5π,336α⎛⎫+∈ ⎪⎝⎭，所以π3sin 35α⎛⎫+= ⎪⎝⎭所以2πππ24sin 22sin cos 33325ααα⎛⎫⎛⎫⎛⎫+=++=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭． 18．解：（1）由图可得[)150,160，[)160,170，[)170,180，[)180,190三组的频率分别为0.1250，0.3000，0.1250，可得人数分别为5，12，5， 所以身高在[)160,170内的共有18人， 所以180.04504010a ==⨯；（2）这40个学生平均身高的估计值为()1155516518175121855169.2540⨯⨯+⨯+⨯+⨯= 所以这40个学生平均身高的估计值为169.25cm ． 19．解（1）取AB 的中点O ，连接OP ，OD ，因为PAB △为边长为2的等边三角形， 所以PO AB ⊥，因为1BO CD ==，AB CD ∥， 所以四边形OBCD 为平行四边形， 又因为AB BC ⊥，所以DO AB ⊥． 因为DO PO O ⋂=，所以AB ⊥平面POD ， 所以PD AB ⊥；（2）设点D 到平面PBC 的距离为h ，因为1BC DO ==，PO =，2PD =，所以DO PO ⊥，又因为DO AB ⊥，所以DO ⊥平面PAB ． 由D PBC P DBC V V --=可得，11113232h BC PB PO BC DC ⨯⨯⨯⨯=⨯⨯⨯⨯，所以2h =． 20．解：设点()11,A x y ，()22,B x y ，中点(),1M t ，直线AB 的斜率为k ，（k 斜率显然存在且不为0）．由21122244x y x y ⎧=⎨=⎩可得()()()1212124x x x x y y -+=-， 所以1212124y y x x x x -+=⨯-，故24t k =，（1）直线MN ：()11y x t k -=--，即()112y x k k-=--，解得点()0,3N ． （2）因为直线AB 经过点(),1M t ，直线AB 的斜率为k ， 所以可得直线AB 的方程是：221y kx k =-+，由22421x y y kx k ⎧=⎨=-+⎩联立可得224840x kx k -+-=， 所以1221224,84,16160,x x k x x k k +=⎧⎪=-⎨⎪∆=-+>⎩，所以12AB x =-=|2k2＋2|又因为点N 到直线AB的距离为d =，所以NAB △的面积21S=+=≤=当213k=时，NAB△的面积取到最大值9．21．解：（1）因为()()1lnf x x x=+，所以()1lnxf x xx+'=+，所以()12f'=，又因为()10f=，所以()f x在1x=处的切线方程22y x=-；（2）证明：当2k>时，函数()y f x=的图象与直线l交点的个数等价于函数()()1ln1k xh x xx-=-+的零点个数，因为()()()()222121211x kxkh xx x x x+-'=-=++，()0,x∈+∞，设()()2221g x x k x=+-+，因为二次函数()g x在x∈R时，()010g=>，()1420g k=-<，所以存在()10,1x∈，()21,x∈+∞，使得()10g x=，()20g x=，所以()h x在()10,x单调递增，()12,x x单调递减，()2,x+∞单调递增．因为()10h=，所以()()110h x h>=，()()210h x h<=，因此()h x在()12,x x存在一个零点1x=；又因为当kx e-=，()()()1211k kkk kk e k eh e ke e-------=--=<++，所以()h x在()1,k e x-存在一个零点；当kx e=时，()()1211kkk kk eh e k ke e-⎛⎫=-=>⎪++⎝⎭，所以()h x在()2,kx e存在一个零点；所以，函数()y f x=的图象与直线l：()1y k x=-有3个交点．（二）选考题：请考生在第22，23题中任选一题作答，如果多做，则按所做的第一题计分．作答时请写清题号．22．[选修4-4：坐标系与参数方程]解：（1）曲线C 的方程可化为2212x y +=； （2）设直线l 的参数方程为1cos ,sin x t y t αα=-+⎧⎨=⎩（t 为参数），代入椭圆C 方程得()221sin 2cos 10t t αα+--=，所以1222cos 1sin t t αα+=+，12211sin t t α-=+，故12PQ t t =-=， 又因为4cos AB α=，2=cos AF BF α-，所以244cos cos αα= 当cos 0α≥时，2cos 20αα+-=，解得cos 2α=， 当cos 0α<时，2cos20αα--=，解得cos 2α=，所以cos 2α=2．∴曲线2C的直角坐标方程为20x -+=或100x -=．23．[选修4-5：不等式选讲]（1）解：（1）证明：因为2224a b b a b +++≥++=， 若0c ≤，不等式显然成立;． 若0c >，则288411c c c c=≤=++， 所以2821ca b b c +++≥+， 当()()20a b b +⨯+≥，且1c =取到等号； 综上2821ca b b c +++≥+．（2）因为122222422a b a b a b b a b a b a+++=+=++≥， 所以114c c ++-≤，解得22c -≤≤．。

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”。

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年5月清华大学2020届高三毕业班中学生标准学术能力诊断性测试英语试题本试卷共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.。