2019-2020年广州市质检二：广东省广州市2019届高三教学质量检测(二)数学(文)word-附详细答案

亲爱的同学：这份试卷将再次记录你的自信、沉着、智慧和收获，我们一直投给你信任的目光……2019高三教学质量检测考试（二）理综-化学试题1. 生活离不开化学。

某种金属制成的器皿，放置于空气中，其表面会逐渐变黑，如将表面变黑的上述器皿放入盛有食盐水的铝制容器中浸泡，一段时间后，黑色完全褪去。

下列成语与该金属有关的是A. 衣紫腰银B. 点石成金C. 铜鸵荆棘D. 铁柞成针【答案】A【解析】某种金属制成的器皿，放置于空气中，其表面会逐渐变黑，如将表面变黑的上述器皿放入盛有食盐水的铝制容器中浸泡，一段时间后，黑色完全褪去，该金属是银，表面会逐渐变黑是生成了Ag2S。

银器放在铝制容器中，由于铝的活泼性大于银，故铝为负极，失电子，银为正极，银表面的Ag2S得电子，析出单质银。

A. 衣紫腰银涉及金属银，故A正确；B. 点石成金涉及金属金，故B错误；C. 铜鸵荆棘涉及金属铜，故C错误；D. 铁柞成针涉及金属铁，故D错误；故选A。

2. N A表示阿伏加德罗常数的值。

俗名为“臭碱”的硫化钠广泛应用于冶金染料、皮革、电镀等工业。

硫化钠的一种制备方法是Na2SO4+2C Na2S+2CO2↑。

下列有关说法正确的是A. 1mol/LNa2SO4溶液中含氧原子的数目一定大于4N AB. 1L0.1mol/LNa2S溶液中含阴离子的数目小于0.1N AC. 生成1mol氧化产物时转移电子数为4N AD. 通常状况下11.2LCO2中含质子的数目为11N A【答案】C【解析】A. 未注明溶液的体积，无法判断1mol/LNa2SO4溶液中含氧原子的数目，故A错误；B. 1L0.1mol/LNa2S溶液中含有0.1molNa2S，硫离子水解生成HS-和氢氧根离子，阴离子的数目大于0.1N A，故B错误；C. 根据方程式，氧化产物为二氧化碳，生成1mol氧化产物时转移电子数为4N A，故C正确；D. 通常状况下，气体摩尔体积不是22.4L/mol ，故11.2LCO2的物质的量不是0.5mol，故D错误；故选C。

试卷类型： A2019年广州市普通高中毕业班综合测试（二）语文试题本试卷共10页，22小题，满分150分。

考试用时150分钟。

注意事项：1．答题前，考生先将自已所在县（市、区）、姓名、试室号、座位号和考生号填写清楚，将条形码粘贴在指定区域。

2．选择题每小题选出答案后，用2B铅笔把答题卷上对应题目的答案标号涂黑，如需改动请先用橡皮擦擦干净，再选涂其他答案标号。

主观题请用黑色墨水签字笔在答题卷上作答。

3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

4．考试结束，监考人员将试卷、答题卷一并收回。

5．保持答题卷清洁，不要折叠、不要弄破。

一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）阅读下面的文字，完成1～3题。

“天下”是中国传统文化对世界秩序的一种原初想象，“天下主义”是以“天下”理念为核心，由具有普遍性和开放性的世界秩序、价值规范与理想人格构成的思想体系。

在当今全球化语境之下，中国文化理念和文化战略的自觉自信体现的正是“天下主义”的精神内核。

文化自信首先是一种“以天下观天下”的世界观的自信。

《道德经》有云：“修之于天下，其德乃普。

故以身观身，以家观家，以乡观乡，以国观国，以天下观天下。

”“天下”是中国文化特有的思维尺度，是一个最宏大、最完备的分析单位，具有最广阔的容纳力。

面对差异性的多元文化格局，西方文化多以民族国家为基本单位，文化视域限于国家、民族内部，虽然也有关于世界的思考，比如斯多葛学派的“世界主义”等，但其思考方式是“以国家观世界”，与中国文化的立足点和尺度不同。

中国文化的“天下”蕴含了“天下无外”的理想，各个民族的历史文化在世界内部是平等共存的；中国文化依循“修身、齐家、治国、平天下”的进路，从“身-家-国”逻辑同构的角度，最终达到“天下大同”的境界。

与西方文化相较，“天下”的世界观更具有开放性和包容性。

文化自信的核心是“以天下为一家”的价值观的自信。

秘密★启用前2019年广州市普通高中毕业班综合测试（二）语文参考答案与评分标准一、现代文阅读（36分）（一）（9分）1．【内容理解】（3分）A（B项，“‘以天下为一家’的价值观把‘他者’融入‘自我’”并非“旨在达到家庭利益的最大化”；C项，不是“君子的理想人格塑造了中国人独特的精神气质”；D项，“中庸之道”不可以消除文化冲突。

）2.【论证分析】（3分）B（文章不是“以‘天下’理念为核心”。

）3.【分析推断】（3分）C（西方的“世界观不具开放性和包容性”推断不当。

）（二）（12分）4．【内容理解】（3分）C（A项，“A企业在这三家企业中业务量一直稳居第一”不正确；B项，C企业“都处于劣势”不正确；D项，“B企业的发展几乎与中国快递业的发展同步”不正确。

）5.【概括分析】（3分）D（“智能产品创新研发的大量投入”并非“可循环包装在当下难以推广的主要因素”。

）6.【分析综合】（6分）快递企业：①保证消费者信息安全；②建立更规范、更专业的物流体系；③提升自动化智能化水平；④推动绿色配送。

消费者：改变消费观念，支持快递包装绿色化。

[“快递企业”4分，“消费者”2分。

意思对即可。

]（三）（15分）7.【分析鉴赏】（3分）C（“追求生态效益而牺牲经济效益”不正确。

）8.【分析鉴赏】（6分）纪实性：①作者亲历；②材料真实；③情感真挚。

文学性：①多用修辞，形象生动；②化用名句，典雅隽永；③间用口语，具有生活气息。

[“纪实性”3分，“文学性”3分。

意思对即可。

]9.【鉴赏评价】（6分）①含意丰富，既指高林树在库布齐大沙漠种下的第一棵柳树，又指高林树本人，还指生活的火种、生命的希望。

②突显主题，赞美“高林树们”用辛勤的劳动改造沙漠、改变生活的奋斗精神。

③强化效果，通过“沙海”之“大”和“一苗树”之“小”的对比，引起读者关注。

[每点2分。

意思对即可。

]二、古代诗文阅读（34分）（一）（19分）10.【文言断句】（3分）A（以风恙拜章乞骸，改刑部尚书致仕。

专业资料word完美格式试卷类型：B2019年广州市普通高中毕业班综合测试（二）语文2018.4 本试卷共8页，24小题，满分为150分。

考试用时150分钟。

注意事项：1．答卷前，考生务必用2B铅笔在“考生号”处填涂考生号。

用黑色字迹的钢笔或签字笔将自己所在的市、县／区、学校以及自己的姓名和考生号、试室号、座位号填写在答题卡上。

用2B铅笔将试卷类型（A）填涂在答题卡相应位置上。

2．选择题每小题选出答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其他答案。

答案不能答在试卷上。

3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液。

不按以上要求作答的答案无效。

4．作答选做题时，请先用2B铅笔填涂选做题的题组号对应的信息点，再作答。

漏涂、错涂、多涂的，答案无效。

5．考生必须保持答题卡的整洁。

考试结束后，将试卷和答题卡一并交回。

一、本大题4小题，每题3分，共12分。

1．下列词语中加点的字，每对读音都不相同．．．．的一组是A．瓦砾．／闪烁．哽咽．／谒．见供．职／供．稿B．慑．服／蹑．足侪．辈／颀．长碑帖．／熨帖．C．吭．声／高亢．敕．令／叱．咤起哄．／哄．堂大笑D．巢．穴／窠．臼鼾．声／酣．梦拖沓．／一沓．报纸2．下列各句中加点的词语，使用恰当的一项是A．本届国际诗歌节将先后举办采风创作、中国诗歌论坛、诗歌朗诵会、筹建诗歌碑林长廊等活动，中国诗歌论坛是整个诗歌节的压轴戏．．．。

B．国产26集三维英雄动画片《戚继光》由国内明史专家全程把关，从道具场景到人物活动都反复推导．．，力求最大程度保持对史实的尊重。

C．根据最新报告，近年媒体报道的未成年人遭受家庭暴力的案件数量一日千里．．．．，2008至2019年有300例，2018-2019年则有397例。

D．两年来反腐败实践无禁区、全覆盖、零容忍已经初见成效，但我们也不能满足现有成绩，毕竟开创廉政新局面不可能毕其功于一役．．．．．．。

2019届市普通高中毕业班综合测试（二）理科综合本试卷共15 页，38小题，满分300分。

考试用时150分钟。

注意事项：1．答卷前，考生务必将自己的、市县/区、学校、班级、学生号、试室号和座位号填写在答题卡上，并用2B铅笔在答题卡的相应位置填涂考生号。

2．作答选择题时，选出每小题答案后，用2B铅笔在答题卡上把对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其他答案。

写在本试卷上无效。

3．非选择题必须用黑色字迹的钢笔或签字作答，答案必须写在答题卡各题目指定区域的相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔或涂改液。

不按以上要求作答无效。

4．考生必须保持答题卡的整洁。

考试结束后，将答题卡交回。

可能用到的相对原子质量：H 1 B 11 C 12 N 14 O 16 S 32 Cl 35.5 K 39 Ti 48Fe 56 Zn 65一、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．下列关于细胞与其产生的物质的叙述，正确的是A．细胞多数无机盐以离子的形式存在，对维持生命活动有重要作用B．同一个体不同细胞功能的差异主要是因为不同细胞携带不同遗传信息C．再次接触到同种抗原时，抗体能迅速通过分裂增殖产生大量新的抗体D．血糖下降时，肌细胞中的糖原能被分解成葡萄糖，从而维持血糖平衡2．青霉素药理作用是干扰细菌细胞壁的形成，万古霉素是一种新型的抗生素，其结构与作用原理类似于青霉素。

以下分析错误的是A．万古霉素因干扰细菌增殖而发挥抗菌功效B．万古霉素的使用使细菌产生抗万古霉素变异C．青霉素过敏者不适合使用万古霉素D．万古霉素的使用会使细菌群体中抗万古霉素个体比例上升3．下列关于细胞癌变的说法，错误的是A．癌症的发生是细胞中多个基因发生突变的结果B．癌变细胞的表面物质、形态结构会发生一定的变化C．香烟烟雾中只有尼古丁这一种化学致癌因子D．提高免疫系统的监控和清除功能是治疗癌症的一种思路4．某学习小组用光学显微镜对有关实验材料进行观察和研究,结果记录如下，正确的是实验材料观察到的结构或现象A 人的口腔上皮细胞经健那绿染色后可观察到线粒体的嵴B 小鼠的肝细胞在30%蔗糖溶液中发生质壁分离C 洋葱鳞片叶外表皮经龙胆紫染色细胞中出现多条染色体D 黑藻叶片椭球形的叶绿体在细胞质中移动5．“调控植物生长--代平衡实现可持续农业发展”入选2018年度中国科学十大进展，其研究证实DELLA蛋白通过阻遏某些基因的转录从而抑制植物生长发育，而赤霉素能解除细胞中已经存在的DELLA蛋白的阻遏效果。

2019年广州市普通高中业班综合测试（二）英语2019.4 本试卷10页,满分120分，考试用时120分钟。

注意事项：1.本试卷分第I卷(选择题)和和第卷(非选择题)两部分。

答卷前，考生务必将自己的姓名、考生号、考场号和座位号填写在答题卡上。

用2B铅笔将试卷类型(A)填涂在答题卡相应位置上。

用2B铅笔在“考生号”处填涂考生号信息点，修改时须用橡皮擦干净。

因笔试不考听力，第I卷从第二部分的“阅读理解”开始,试题题序号从“21”开始。

2.作答第I卷时,选出每小题答案后,用2B铅笔在答题卡上对应题目选项的答案信息点涂黑；如需要改动，用橡皮擦干净后,再选涂其他答案。

答案不能答在试卷上。

3.第卷必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案,然后再写上新答案；不准使用铅笔和涂改液不按以上要求作答无效。

4.考生必须保证答题卡的整洁。

考试结束后,将试卷和答题卡一并并交回。

第二部分阅读理解(共两节，满分40分)第一节(共15小题:每小题2分，满分30分)阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项。

AThe country is India. A large dinner party is being given in an up-country station by acolonial official and his wife. The guests are army and government officers and their wives, and anAmerican naturalist.At one side of the long table, a spirited discussion springs up between a young girl and an armyofficer. The girl insists women have long outgrown the jumping-on-a-chair-at-the-sight-of-a-mouseera, and that they are not as anxious as their grandmothers were. The officer says they are,arguing women haven't the actual nerve control of men.“A woman's reaction in any crisis," the officer says,“is to scream. And while a man mayfeel like it, he has that ounce more of control than a woman has."The American scientist does not join in the argument but sits and watches the faces of theother guests. As he stares, he sees a slight, though strange look of anxiety come over the face of thehostess. With a small gesture she summons the servant standing behind her chair. She whispers tohim. The servant's eyes widen. He turns quickly and leaves the room. No one else sees this, nor theservant when he puts a bowl of milk on the balcony outside the glass doors.The American understands. In India, milk in a bowl means only one thing. It is bait fora snake. He realizes there is a cobra in the room. The American's eyes move across the roombut he sees nothing. He realizes the snake can only be in one place - under the table.His first reaction is to jump back and warn the others. But he knows any sudden movementwill frighten the cobra and it will strike. He speaks quickly, the quality of his voice so arrestingthat it quietens everyone.“I want to know just what control everyone at this table has. I will countthree hundred - that's five minutes - and not one of you is to move a single muscle. Now! Ready!"The 20 people sit like stone images while he counts. He is saying ..o.. hundred andeighty.."when, out of the corner of his eye, he sees the snake emerge and make for the bowl of milk. Four orfive screams ring out as he jumps to slam shut the balcony doors.“There is your proof!" the host says.“A man has just shown us real control."“Just a minute," the American says, turning to his hostess,“How did you know that cobrawas in the room?"A faint smile comes across the woman's face as she repli es. “Because it was lying across myfoot.""21.What is the argument between the army officer and the young girl about?A. Whether women are afraid of mice.B. Whether men are calmer than women.C. Whether men are cleverer than women.D. Whether women would make suitable soldiers.22. Why is the servant asked to put out some milk?A. To play a trick.B. To serve the guests.C. To attract the snake .D. To feed the hostess's pet.23. Why does the scientist suggest the guests play a game?A. He doesn't want anyone to panic.B. He intends to test the officer's theory.C. He sees there was a snake in the room.D. He wants to entertain the other guests.24. What does the author imply through the hostess's final statement?A. The army officer's opinion is wrong.B. The hostess understood the American's intention.C. The American was surprised by the snake's presence.D. The hostess has had previous experience dealing with snakes.B25. What caused musicals to move in a new direction during the 1930's?A. The development of new musical instruments.B. The audience s demand for more realistic art forms.C. The rising popularity of other types of entertainment.D. The greater acceptance of black performers by white audiences.26. In which period did musical theatre become more complex and dramatic?A. Pre - 1900.B. 1900- 1929.C.1940- 1949.D.1950- 1959.27. What can be reasonably inferred about the musical West Side Story?A. It told its story in a new way.B. It was based on a true story.C. It was a non-Broadway show.D. It was not very successful at first.CIn 1874 Francis Galton, a British professor, analysed a sample of English scientists and foundthe vast majority to be first-born sons. This led him to theorise that first-born children enjoyed aspecial level of attention from their parents that allowed them to advance intellctually. Half acentury later Alfred Adler, an Austrian psychologist, made a similar argument relating to personality.First-born children, he suggested, were more diligent, while the later-born were more outgoing andemotionally stable. Many subsequent studies have explored these ideas, but their findings have beenvaried - some supporting and some rejecting the original conclusions.The main problem with the previous studies is that they were too small - often limited to afew dozen individuals. This would be true even if the statistical methods needed to analyse the datawere simple, but they are not. Distinguishing birth-order effects from those caused by family sizecomplicates matters, meaning still bigger samples must be analysed to obtain meaningful results.To overcome the limitation of these earlier studies, German social scientist Dr. HelmetSchmukle and his colleagues analysed three huge sets of data from America, Britain and Germany.These data sets, though collected for other purposes, included personality and intelligence tests on20, 186 people at different stages of their lives. The American tests were on individuals aged between29 and 35. The British tests were conducted on 50-year-olds. The German tests ran the whole span ofadult life, from 18 to 98.Birth order, they found, had no effect on personality: first-borns were no more, nor less,likely than their younger siblings to be hardworking, outgoing or anxious. But it did affectintelligence. In a family with two children, the first child was more intelligent than the second60% of the time, rather than the 50% that would be expected by chance. On average, thistranslated to a difference of 1.5 IQ points between first and second siblings. That figure agreeswith previous studies, and thus looks confirmed.It is, nevertheless, quite a small difference - and whether it is enough to account for Galton'soriginal observation is unclear. In any event, it is certainly not deterministic. Galton was theyoungest of nine.28. Alfred Adler concluded that first-born children were.A. more stableB. more sociableC. more intelligentD. more hardworking29. What does the underlined“they" in paragraph 2 refer to?A. The data.B. The analyses.C. The previous studies.D. The statistical methods.30. Why was Schmukle's study considered superior to previous research?A. It involved a wider age range.B. It had a much larger sample size.C. It included a larger number of countries.D. It was conducted over a longer period of time.31. Why does the author mention Galton's family background in the last paragraph?A. To confirm Galton's difficult upbringing.B. To suggest Galton's theory may not be correct.C. To compare his experience with Galton's parents.D. To explain why Galton was interested in birth order.DPhotography has opened our eyes to a multitude of beauties, things we literally could nothave seen before the invention of the frozen image. It has greatly expanded our notion of whatis beautiful, what is aesthetically(审美上) pleasing. Items formerly considered trivial, and notworth an artist's paint, have been revealed and honored by the photograph: things as ordinary as afence post, a chair, a vegetable. And as technology has developed, photographers have exploredcompletely new points of view: those of the microscope, the eagle, the cosmos.What is it that delights the human eye and allows us to claim that a photograph is beautiful?Photography depends on the trinity of light, composition, and moment. Light literally makes therecording of an image possible, but in the right hands, light in a photograph can make the image soar. The same is true with composition. What the photographer chooses to keep in or out of theframe is all that we will ever see - but that combination is vital. And the moment that the shutter ispressed, when an instant is frozen in time, provides the whole image with meaning. When thethree - light, composition, and moment - are in balance, there is visual magic.Light, composition, and moment come together in a photograph to bring us the ultimatereality: a view of the world unknown prior to the invention of the camera. Before photography, thebasic artistic rules of painting were rarely broken. Images were made to please, not to capturereality. But as photography evolved, painterly rules were often reacted in the pursuit of fresh vision.Photographers became interested in the real world, good and bad, and it was the accidental detail thatwas celebrated. Photography invited the world to see with new eyes - to see photographically - andall of the arts have drawn new inspiration from this change.With these basic aesthetic tools, photographers have evolved from scientists longing to“fix"an image - any image - to artistic revolutionaries. Photographs have created a new way of seeing,changed our ideas of beauty and, most importantly, made art more democratic. They have given usvisual proof that the world is grander than we imagined, and that there is beauty, often overlooked, in nearly everything.32. Before the invention of photography, which of the following was least likely to appear in an artistic work?A. A great person.B. A lovely insect.C. A grand building.D. A beautiful landscape.33. What is the function of paragraph 2?A. To argue that photographic beauty is subjective.B. To explain the evolution of the concept of beauty.C. To describe the elements that make a successful photo.D. To illustrate different types of photographic techniques.34. How has photography affected other art forms?A. It has reduced their popularity.B. It has forced them to change their rules.C. It has changed their methods of composition.D. It has provided them with new points of view.35. What does the author mean by saying photography has“made art more demo cratic" ?A. It has expanded the concept of artistic beauty.B. It has challenged the status of traditional art forms.C. It has enabled the development of new artistic tools.D. It has allowed more people to take part in creative activities.第二节(共5小题;每小题2分，满分10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。

2019年广州市普通高中业班综合测试（二）英语2019.4 本试卷10页,满分120分，考试用时120分钟。

注意事项：1.本试卷分第I卷(选择题)和和第卷(非选择题)两部分。

答卷前，考生务必将自己的姓名、考生号、考场号和座位号填写在答题卡上。

用2B铅笔将试卷类型(A)填涂在答题卡相应位置上。

用2B铅笔在“考生号”处填涂考生号信息点，修改时须用橡皮擦干净。

因笔试不考听力，第I卷从第二部分的“阅读理解”开始,试题题序号从“21”开始。

2.作答第I卷时,选出每小题答案后,用2B铅笔在答题卡上对应题目选项的答案信息点涂黑；如需要改动，用橡皮擦干净后,再选涂其他答案。

答案不能答在试卷上。

3.第卷必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案,然后再写上新答案；不准使用铅笔和涂改液不按以上要求作答无效。

4.考生必须保证答题卡的整洁。

考试结束后,将试卷和答题卡一并并交回。

第二部分阅读理解(共两节，满分40分)第一节(共15小题:每小题2分，满分30分)阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项。

AThe country is India. A large dinner party is being given in an up-country station by acolonial official and his wife. The guests are army and government officers and their wives, and anAmerican naturalist.At one side of the long table, a spirited discussion springs up between a young girl and an armyofficer. The girl insists women have long outgrown the jumping-on-a-chair-at-the-sight-of-a-mouseera, and that they are not as anxious as their grandmothers were. The officer says they are,arguing women haven't the actual nerve control of men.“A woman's reaction in any crisis," the officer says,“is to scream. And while a man mayfeel like it, he has that ounce more of control than a woman has."The American scientist does not join in the argument but sits and watches the faces of theother guests. As he stares, he sees a slight, though strange look of anxiety come over the face of thehostess. With a small gesture she summons the servant standing behind her chair. She whispers tohim. The servant's eyes widen. He turns quickly and leaves the room. No one else sees this, nor theservant when he puts a bowl of milk on the balcony outside the glass doors.The American understands. In India, milk in a bowl means only one thing. It is bait fora snake. He realizes there is a cobra in the room. The American's eyes move across the roombut he sees nothing. He realizes the snake can only be in one place - under the table.His first reaction is to jump back and warn the others. But he knows any sudden movementwill frighten the cobra and it will strike. He speaks quickly, the quality of his voice so arrestingthat it quietens everyone.“I want to know just what control everyone at this table has. I will countthree hundred - that's five minutes - and not one of you is to move a single muscle. Now! Ready!"The 20 people sit like stone images while he counts. He is saying ..o.. hundred and eighty.."when, out of the corner of his eye, he sees the snake emerge and make for the bowl of milk. Four orfive screams ring out as he jumps to slam shut the balcony doors.“There is your proof!" the host says.“A man has just shown us real control."“Just a minute," the American says, turning to his hostess,“How did you know that cobrawas in the room?"A faint smile comes across the woman's face as she repli es. “Because it was lying across myfoot.""21.What is the argument between the army officer and the young girl about?A. Whether women are afraid of mice.B. Whether men are calmer than women.C. Whether men are cleverer than women.D. Whether women would make suitable soldiers.22. Why is the servant asked to put out some milk?A. To play a trick.B. To serve the guests.C. To attract the snake .D. To feed the hostess's pet.23. Why does the scientist suggest the guests play a game?A. He doesn't want anyone to panic.B. He intends to test the officer's theory.C. He sees there was a snake in the room.D. He wants to entertain the other guests.24. What does the author imply through the hostess's final statement?A. The army officer's opinion is wrong.B. The hostess understood the American's intention.C. The American was surprised by the snake's presence.D. The hostess has had previous experience dealing with snakes.B25. What caused musicals to move in a new direction during the 1930's?A. The development of new musical instruments.B. The audience s demand for more realistic art forms.C. The rising popularity of other types of entertainment.D. The greater acceptance of black performers by white audiences.26. In which period did musical theatre become more complex and dramatic?A. Pre - 1900.B. 1900- 1929.C.1940- 1949.D.1950- 1959.27. What can be reasonably inferred about the musical West Side Story?A. It told its story in a new way.B. It was based on a true story.C. It was a non-Broadway show.D. It was not very successful at first.CIn 1874 Francis Galton, a British professor, analysed a sample of English scientists and foundthe vast majority to be first-born sons. This led him to theorise that first-born children enjoyed aspecial level of attention from their parents that allowed them to advance intellctually. Half acentury later Alfred Adler, an Austrian psychologist, made a similar argument relating to personality.First-born children, he suggested, were more diligent, while the later-born were more outgoing andemotionally stable. Many subsequent studies have explored these ideas, but their findings have beenvaried - some supporting and some rejecting the original conclusions.The main problem with the previous studies is that they were too small - often limited to afew dozen individuals. This would be true even if the statistical methodsneeded to analyse the datawere simple, but they are not. Distinguishing birth-order effects from those caused by family sizecomplicates matters, meaning still bigger samples must be analysed to obtain meaningful results.To overcome the limitation of these earlier studies, German social scientist Dr. HelmetSchmukle and his colleagues analysed three huge sets of data from America, Britain and Germany.These data sets, though collected for other purposes, included personality and intelligence tests on20, 186 people at different stages of their lives. The American tests were on individuals aged between29 and 35. The British tests were conducted on 50-year-olds. The German tests ran the whole span ofadult life, from 18 to 98.Birth order, they found, had no effect on personality: first-borns were no more, nor less,likely than their younger siblings to be hardworking, outgoing or anxious. But it did affectintelligence. In a family with two children, the first child was more intelligent than the second60% of the time, rather than the 50% that would be expected by chance. On average, thistranslated to a difference of 1.5 IQ points between first and second siblings. That figure agreeswith previous studies, and thus looks confirmed.It is, nevertheless, quite a small difference - and whether it is enough to account for Galton'soriginal observation is unclear. In any event, it is certainly not deterministic. Galton was theyoungest of nine.28. Alfred Adler concluded that first-born children were.A. more stableB. more sociableC. more intelligentD. more hardworking29. What does the underlined“they" in paragraph 2 refer to?A. The data.B. The analyses.C. The previous studies.D. The statistical methods.30. Why was Schmukle's study considered superior to previous research?A. It involved a wider age range.B. It had a much larger sample size.C. It included a larger number of countries.D. It was conducted over a longer period of time.31. Why does the author mention Galton's family background in the last paragraph?A. To confirm Galton's difficult upbringing.B. To suggest Galton's theory may not be correct.C. To compare his experience with Galton's parents.D. To explain why Galton was interested in birth order.DPhotography has opened our eyes to a multitude of beauties, things we literally could nothave seen before the invention of the frozen image. It has greatly expanded our notion of whatis beautiful, what is aesthetically(审美上) pleasing. Items formerly considered trivial, and notworth an artist's paint, have been revealed and honored by the photograph: things as ordinary as afence post, a chair, a vegetable. And as technology has developed, photographers have exploredcompletely new points of view: those of the microscope, the eagle, the cosmos.What is it that delights the human eye and allows us to claim that a photograph is beautiful?Photography depends on the trinity of light, composition, and moment. Light literally makes therecording of an image possible, but in the right hands, light in a photograph can make the image soar. The same is true with composition. What the photographer chooses to keep in or out of theframe is all that we will ever see - but that combination is vital. And the moment that the shutter ispressed, when an instant is frozen in time, provides the whole image with meaning. When thethree - light, composition, and moment - are in balance, there is visual magic.Light, composition, and moment come together in a photograph to bring us the ultimatereality: a view of the world unknown prior to the invention of the camera. Before photography, thebasic artistic rules of painting were rarely broken. Images were made to please, not to capturereality. But as photography evolved, painterly rules were often reacted in the pursuit of fresh vision.Photographers became interested in the real world, good and bad, and it was the accidental detail thatwas celebrated. Photography invited the world to see with new eyes - to see photographically - andall of the arts have drawn new inspiration from this change.With these basic aesthetic tools, photographers have evolved from scientists longing to“fix"an image - any image - to artistic revolutionaries. Photographs have created a new way of seeing,changed our ideas of beauty and, most importantly, made art more democratic. They have given usvisual proof that the world is grander than we imagined, and that there is beauty, often overlooked,in nearly everything.32. Before the invention of photography, which of the following was least likely to appear in anartistic work?A. A great person.B. A lovely insect.C. A grand building.D. A beautiful landscape.33. What is the function of paragraph 2?A. To argue that photographic beauty is subjective.B. To explain the evolution of the concept of beauty.C. To describe the elements that make a successful photo.D. To illustrate different types of photographic techniques.34. How has photography affected other art forms?A. It has reduced their popularity.B. It has forced them to change their rules.C. It has changed their methods of composition.D. It has provided them with new points of view.35. What does the author mean by saying photography has“made art more democratic" ?A. It has expanded the concept of artistic beauty.B. It has challenged the status of traditional art forms.C. It has enabled the development of new artistic tools.D. It has allowed more people to take part in creative activities.第二节(共5小题;每小题2分，满分10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。

2019届广州市普通高中毕业班综合测试（二）数学（文科）2019届广州市普通高中毕业班综合测试（二）数学（文科）参考答案评分说明:1．本解答给出了一种或几种解法供参考，如果考生的解法与本解答不同，可根据试题的主要考查内容比照评分参考制订相应的评分细则．2．对计算题，当考生的解答在某一步出现错误时，如果后继部分的解答未改变该题的内容和难度，可视影响的程度决定后继部分的给分，但不得超过该部分正确解答应得分数的一半；如果后继部分的解答有较严重的错误，就不再给分．3．解答右端所注分数，表示考生正确做到这一步应得的累加分数． 4．只给整数分数．选择题不给中间分．一、选择题二、填空题13 14．53 15．1,8⎡⎫+∞⎪⎢⎣⎭16．2,05⎡⎤-⎢⎥⎣⎦ 三、解答题17．解：（1）因为tan tan 2(tan tan )cos cos A BA B B A+=+， 所以sin sin sin sinB 2cos cos cos cos cos cos A B A A B A B A B⎛⎫+=+⎪⎝⎭．…………………………………1分 化简得()2sin cos cos sin sin sin A B A B A B +=+．……………………………………2分 即()2sin sin sin A B A B +=+．……………………………………………………………3分 因在ABC ∆中，A B C ++=π，则()()sin sin sin A B C C π+=-=．………………4分 从而sin sin 2sin A B C +=．…………………………………………………………………5分 由正弦定理，得2a b c +=．所以=2a bc+．…………………………………………………………………………………6分 （2）由（1）知2a bc +=，且2c =，所以4a b +=．…………………………………………7分因为=3C π，所以()222222cos 22a b ab ca b c C ab ab+--+-==．…………………………9分 即122cos32ab abπ-=． 所以4ab =．…………………………………………………………………………………10分所以11sin 4sin 223ABC S ab C ∆π==⨯⨯= 所以△ABC．…………………………………………………………………12分18．（1）证明：取AD 的中点O ，连结OP ，OB ，BD ，因为底面ABCD 为菱形，60BAD ∠=，所以AD AB BD ==．…………………………………1分因为O 为AD 的中点，所以BO AD ⊥． ……………2分 在△PAD 中，PA PD =，O 为AD 的中点，所以PO AD ⊥． ………………………………………3分 因为BO PO O =，所以AD ⊥平面POB ．………4分 因为PB ⊂平面POB ，所以AD PB ⊥．……………5分 （2）解法1：在Rt △ PAD 中，2AD =，所以1PO =．因为底面ABCD 是边长为2的菱形，60BAD ∠=，所以BO =分在△PBO 中，1PO =，BO =2PB BC ==，因为222PO BO PB +=，所以PO BO ⊥．……………………………………………………7分【6-7分段另证：在△APD 中，90APD ∠=，O 为AD 的中点，所以12PO AD AO ==． 在△ BOP 和△ BOA 中，因为PO AO =，PB AD AB ==，BO BO =，所以△ BOP ≅△ BOA ．所以90BOP BOA ∠=∠=．所以OP OB ⊥．】 由（1）有PO AD ⊥，且ADBO O =，AD ⊂平面ABCD ，BO ⊂平面ABCD ，D CBAPO所以PO ⊥平面ABCD ．……………………………………………………………………8分 在△PBC 中，由（1）证得AD PB ⊥，且//BC AD ，所以BC PB ⊥．因为2PB BC ==，所以2PBC S ∆=．……………………………………………………9分 在△ABC 中，2AB BC ==，120ABC ∠=，所以1sin 2ABC S AB BC ABC =⨯⨯⨯∠=．……………………………………………10分 设点A 到平面PBC 的距离为h ，因为A PBC P ABC V V --=，即1133PBC ABC S h S PO ∆=．…………………………………………11分所以ABC PBC S PO h S ∆===．所以点A 到平面PBC分 解法2：因为//AD BC ，BC ⊂平面PBC ，AD ⊄平面PBC ， 所以//AD 平面PBC ．所以点A 到平面PBC 的距离等于点O 到平面PBC 的距离．………………………………6分 过点O 作OH PB ⊥于点H ．…………………………7分由（1）证得AD ⊥平面POB ，且//AD BC ，所以BC ⊥平面POB ．因为OH ⊂平面POB ，所以BC ⊥OH ．因为PB BC B =，PB ⊂平面PBC ，BC ⊂平面PBC ，所以OH ⊥平面PBC ．…………………………………8分 在Rt △ PAD 中，2AD =，所以1PO =． 因为底面ABCD 是边长为2的菱形，60BAD ∠=，所以BO =分在△PBO 中，1PO =，BO =2PB BC ==，H O P A BCD因为222PO BO PB +=，所以PO BO ⊥．………………………………………………10分【9-10分段另证：在△APD 中，90APD ∠=，O 为AD 的中点，所以12PO AD AO ==．在△ BOP 和△ BOA 中，因为PO AO =，PB AD AB ==，BO BO =，所以△ BOP ≅△ BOA ．所以90BOP BOA ∠=∠=．所以OP OB ⊥．】在△PBO 中，根据等面积关系得PB OH PO OB ⨯=⨯．………………………………11分所以PO OB OH PB ⨯===． 所以点A 到平面PBC的距离为2．……………………………………………………12分19．解：（1）根据上表中的样本数据及其散点图：（ⅰ）262739414953565860614710x +++++++++==．……………………2分（ⅱ）rni ix y nx y-=∑=…………3分==…………………………………4分=分6.56≈54.18≈，所以0.98r ≈．……………………………………………………………………………………6分 由样本相关系数0.98r ≈，可以推断人体脂肪含量和年龄的相关程度很强．………………7分（2）因为回归方程为ˆˆ 1.56ybx =+，即ˆ 1.56a =． 所以ˆ27 1.56ˆ0.5447y a bx --==≈．【或利用()()()121ˆn iii ni i x x y y bx x==--=-∑∑()1221ni ii ni i x y nx yx n x==-=-∑∑837.80.541548=≈】………………10分 所以y 关于x 的线性回归方程为ˆ0.54 1.56yx =+． 将50x =代入线性回归方程得ˆ0.5450 1.5628.56y=⨯+=．……………………………11分 所以根据回归方程估计年龄为50岁时人体的脂肪含量为28.56%．………………………12分【结论没写28.56%扣1分】20．解：（1）设(),M x y ，()00,P x y ，则点Q 的坐标为()0,0x ．因为2PM MQ =，所以()()000,2,x x y y x x y --=--，…………………………………………………………1分即00,3.x x y y =⎧⎨=⎩ …………………………………………………………………………………2分因为点P 在抛物线236y x =上，所以20036y x =，即()2336y x =．…………………………………………………………3分所以点M 的轨迹C 的方程为24y x =．……………………………………………4分（2）解法1：设直线1x my =+与曲线C 的交点坐标为A 211,4y y ⎛⎫ ⎪⎝⎭，222,4y B y ⎛⎫⎪⎝⎭，由21,4,x my y x =+⎧⎨=⎩得2440y my --=． 由韦达定理得+1y 2y =4m ，1y 2y =4-．………………………………………………5分设点200,4y T y ⎛⎫ ⎪⎝⎭，则10220101444AT y y k y y y y -==+-．…………………………………………6分 所以直线AT 的方程为2000144y y y x y y ⎛⎫-=- ⎪+⎝⎭．令1x =-，得点D 的坐标为010141,y y y y ⎛⎫-- ⎪+⎝⎭．………………………………………………7分同理可得点E 的坐标为020241,y y y y ⎛⎫-- ⎪+⎝⎭．……………………………………………………8分如果以DE 为直径的圆过x 轴某一定点(),0N n ，则满足0ND NE •=．……………9分 因为010********,1,y y y y ND NE n n y y y y ⎛⎫⎛⎫--•=--•-- ⎪ ⎪++⎝⎭⎝⎭()()()2212001220012124161++y y y y y y n y y y y y y -++=+++．所以()2200200416161++044y my n y my --+=+-．…………………………………………………10分 即()2140n +-=，解得1n =或3n =-．………………………………………………11分 故以DE 为直径的圆过x 轴上的定点()1,0和()3,0-．…………………………………12分 解法2：直线1x =与曲线C 的交点坐标为()1,2A '，()1,2B '-，若取()0,0T '，则A T ''，B T ''与直线1x =-的交点坐标为()1,2D '--，()1,2E '-， 所以以D E ''为直径的圆的方程为()2214x y ++=．该圆与x 轴的交点坐标为()1,0和()3,0-．所以符合题意的定点只能是()11,0N 或()23,0N -．………………………………………6分设直线1x my =+与曲线C 的交点坐标为A 211,4y y ⎛⎫ ⎪⎝⎭，222,4y B y ⎛⎫⎪⎝⎭，由21,4,x my y x =+⎧⎨=⎩得2440y my --=．由韦达定理得+1y 2y =4m ，1y 2y =4-．………………………………………………7分设点200,4y T y ⎛⎫ ⎪⎝⎭，则1022101444AT y y k y y y y -==+-．…………………………………………8分 所以直线AT 的方程为2000144y y y x y y ⎛⎫-=- ⎪+⎝⎭．令1x =-，得点D 的坐标为010141,y y y y ⎛⎫-- ⎪+⎝⎭．…………………………………………………9分同理可得点E 的坐标为020241,y y y y ⎛⎫-- ⎪+⎝⎭．……………………………………………………10分若点()11,0N 满足要求，则满足110N D N E •=． 因为0102110102442,2,y y y y N D N E y y y y ⎛⎫⎛⎫--•=-•- ⎪ ⎪++⎝⎭⎝⎭()()212001220012124164+y y y y y y y y y y y y -++=+++20020041616=4+044y my y my --+=+-．……11分所以点()11,0N 满足题意． 同理可证点()23,0N -也满足题意．故以DE 为直径的圆过x 轴上的定点()1,0和()3,0-．……………………………………12分21．（1）解：当21=a 时，217()(2)ln 422f x x x x x =++-+， 函数)(x f 的定义域为),0(+∞，………………………………………………………………1分 且()2ln 3f x x x x'=++-．…………………………………………………………………2分 设()2ln 3g x x x x=++-， 则()()222221122()1x x x x g x x x x x +-+-'=-+==()0x >． 当01x <<时，()0g x '<；当1x >时，()0g x '>，即函数()g x 在()0,1上单调递减，在()1,+∞上单调递增，………………………………3分 所以当0x >时，()()10g x g ≥=（当且仅当1=x 时取等号）．…………………………4分 即当0x >时，()0f x '≥（当且仅当1=x 时取等号）．所以函数()f x 在),0(+∞单调递增，至多有一个零点. ………………………………………5分 因为(1)0f =，1=x 是函数)(x f 唯一的零点.所以若21=a ，则函数()f x 的所有零点只有1=x ．………………………………………6分 （2）证法1：因为2()(2)ln 47f x x x ax x a =++-+，函数)(x f 的定义域为),0(+∞，且2()ln 24x f x x ax x+'=++-．…………………………7分 当12a ≥时，()2ln 3f x x x x'≥++-，………………………………………………………9分 由（1）知032ln ≥-++x xx ．……………………………………………………………10分 即当0x >时()0f x '≥，所以()f x 在()0,+∞上单调递增．…………………………………………………………11分 所以)(x f 不存在极值．……………………………………………………………………12分证法2：因为2()(2)ln 47f x x x ax x a =++-+， 函数)(x f 的定义域为),0(+∞，且2()ln 24x f x x ax x+'=++-．……………………7分设2()ln 24x m x x ax x+=++-， 则2221222()2ax x m x a x x x +-'=-+=()0x >．设)0( 22)(2>-+=x x ax x h ，则()m x '与)(x h 同号． 当21≥a 时，由2()220h x ax x =+-=，解得1104x a --=<，2104x a-+=>．…………………………………8分可知当20x x <<时，()0h x <，即()0m x '<，当2 x x >时，()0h x >，即()0m x '>， 所以()f x '在()20,x 上单调递减，在()2,x +∞上单调递增．………………………………9分 由（1）知032ln ≥-++x xx ．………………………………………………………………10分 则2222222()ln 3(21)(21)0f x x x a x a x x '=++-+-≥-≥． 所以2()()0f x f x ''≥≥，即()f x 在定义域上单调递增．………………………………11分 所以)(x f 不存在极值．……………………………………………………………………12分22．（1）解法1：因为直线l 的参数方程为⎩⎨⎧+=+=ααsin 3,cos 2t y t x （t 为参数），当=2απ时，直线l 的直角坐标方程为2x =．……………………………………………1分 当2απ≠时，直线l的直角坐标方程为()tan 2y x α=-．…………………………3分因为222,cos x y x ρρθ=+=，……………………………………………………………4分因为8cos 22+=θρρ，所以2228x y x +=+．所以C 的直角坐标方程为08222=--+x y x ．………………………………………5分解法2：因为直线l 的参数方程为⎩⎨⎧+=+=ααsin 3,cos 2t y t x （t 为参数），则有sin2sin sin cos,cos sin cos,x ty tαααααααα=+⎧⎪⎨=+⎪⎩………………………………………………2分所以直线l 的直角坐标方程为()sin cos 2sin 0x y αααα---= ．…………3分 因为222,cos x y x ρρθ=+=，……………………………………………………………4分因为8cos 22+=θρρ，所以2228x y x +=+．所以C 的直角坐标方程为08222=--+x y x ．……………………………………………5分 （2）解法1：曲线C 的直角坐标方程为08222=--+x y x ，将直线l 的参数方程代入曲线C 的方程整理，得05)cos 2sin 32(2=-++t t αα．……6分 因为020)cos 2sin 32(2>++=∆αα，可设该方程的两个根为1t ，2t ，则()122cos t t αα+=-+ ，125t t =-．…………………………………………7分所以12AB t t =-===分整理得)2cos 3αα+=，故2sin 6απ⎛⎫+= ⎪⎝⎭分 因为0α≤<π，所以63αππ+=或263αππ+=， 解得6απ=或2απ= 综上所述，直线l 的倾斜角为6π或2π．………………………………………………10分解法2：直线l 与圆C 交于A ，B 两点，且AB =，故圆心)0,1(C 到直线l 的距离1)22(92=-=d ．………………………………6分 ①当2απ=时，直线l 的直角坐标方程为2=x ，符合题意．………………………7分 ②当0,,22αππ⎡⎫⎛⎫∈π⎪ ⎪⎢⎣⎭⎝⎭时，直线l 的方程为0tan 23tan =-+-ααy x ．所以1tan 1|tan 230tan |2=+-+-=αααd ，………………………………………………8分tan α=解得6απ=．………………………………………………………………………………9分 综上所述，直线l 的倾斜角为6π或2π．…………………………………………………10分23．（1）解：当1a =时，由()f x x >，得2111x x -->+．……………………………1分当12x ≥时，2111x x -->+， 解得3x >． 当12x <时，1211x x -->+，解得13x <-．…………………………………………4分综上可知，不等式()1f x x >+的解集为 133x x x ⎧⎫><-⎨⎬⎩⎭或．………………………5分（2）解法1：由1()(1)2f x f x <+，得1212122a x a x --<+-． 则22121a x x >--+．……………………………………………………………………6分 令()22121g x x x =--+， 则问题等价于min (())a g x >因为123,,211()61,,22123,,2x x g x x x x x ⎧-+<-⎪⎪⎪=-+-≤≤⎨⎪⎪->⎪⎩…………………………………………………………9分min 1()22g x g ⎛⎫==- ⎪⎝⎭．所以实数a 的取值范围为(2,)-+∞．…………………………………………………………10分 解法2：因为2121(21)(21)x x x x --+≤--+，………………………………………6分 即221212x x -≤--+≤，则21212x x --+≥-．……………………………………7分所以()2121212212g x x x x x =--++-≥-+-≥-，…………………………………8分 当且仅当12x =时等号成立．……………………………………………………………………9分 所以min ()2g x =-．所以实数a 的取值范围为(2,)-+∞．………………………………………………………………10分（注：文档可能无法思考全面，请浏览后下载，供参考。

2019年广州市普通高中毕业班综合测试（二）文科数学本试卷共6页，23小题，满分150分。

考试用时120分钟。

注意事项：1．答卷前，考生务必将自己的姓名和考生号、试室号、座位号填写在答题卡上，用2B 铅笔在答题卡的相应位置填涂考生号，并将试卷类型(B)填涂在答题卡相应位置上。

2．作答选择题时，选出每小题答案后，用2B 铅笔在答题卡上对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其他答案。

答案不能答在试卷上。

3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液。

不按以上要求作答无效。

4．考生必须保证答题卡的整洁。

考试结束后，将试卷和答题卡一并交回。

一、选择题：本题共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,则= A. {0,1,3,5} B. {0,2,4,6}C. {1,3,5}D. {2,4}2.已知复数在复平面内对应的点在第三象限，则实数的取值范围是（ ）A.B.C.D.3.某公司生产，，三种不同型号的轿车，产量之比依次为，为检验该公司的产品质量，用分层抽样的方法抽取一个容量为的样本，若样本中种型号的轿车比种型号的轿车少8辆，则（ ）A. 96B. 72C. 48D. 364.执行如图所示程序框图，则输出的值是（ ）A. 21B. 22C. 23D. 245.从某班5名学生（其中男生3人，女生2人）中任选3人参加学校组织社会实践活动，则所选3人中至少有1名女生的概率为（ ）A. B. C. D.6.函数的部分图像如图所示，则函数的解析式为（）A. B.C. D.7.设等比数列的前n项和为，则下列等式中一定成立的是A. B.C. D.8.已知双曲线的渐近线方程为，则此双曲线的离心率为（）A. B. C. D.9.一个圆锥的体积为，当这个圆锥的侧面积最小时，其母线与底面所成角的正切值为（）A. B. C. D.10.设，且1是一元二次方程的一个实根，则的取值范围为A. B. C. D.11.在三棱锥中..，，则该三棱锥的外接球的表面积为（）A. B. C. D.12.已知函数与的图像上存在关于轴对称的点，则实数的取值范围为（）A. B. C. D.二、填空题：本题共4小题，每小题5分，共20分．13.已知向量，向量，则=__________14.《莱茵德纸草书》是世界上最古老的数学著作之一.书中有一道这样的题目：把100个面包分给5个人，使每人所得份量成等差数列，且较大的三份之和的是较小的两份之和，则最小一份的量为___. 15.若函数在上单调递增，则实数的取值范围是_____.16.己知点P 在直线上，点Q 在直线，的中点为，且，则的取值范围是____．三、解答题：共70分，解答应写出文字说明、证明过程和演算步骤，第17～21题为必考题，每个试题考生都必须做答．第22、23题为选考题，考生根据要求做答． （一）必考题：共60分．17.中角，，的对边分别为，，，己如.（1）求的值： （2）若，，求的面积. 18.如图，在四棱锥中，底面是边长为2的菱形，，，且，.（1）求证：： （2）求点到平面的距离.19.科研人员在对人体脂肪含量和年龄之间关系的研究中，获得了一些年龄和脂肪含量的简单随机样本数据，如下表：根据上表的数据得到如下的散点图．(1)根据上表中的样本数据及其散点图： (i)求;(ii)计算样本相关系数（精确到0.01），并刻画它们的相关程度． (2)若y 关于x 的线性回归方程为，求的值（精确到0.01），并根据回归方程估计年龄为50岁时人体的脂肪含量。