【正文】 即 52OM PQ ? ，當且僅當 25OM P Q??時等號成立 . 因此 OM PQ 的最大值為 52 . （ 3）橢圓 C 上不存在三點 ,D E G ，使得 62O D E O D G O E GS S S? ? ?? ? ? 證明：假設(shè)存在 1 1 2 2( , ) , ( , ) , ( , )D u v E x y G x y滿足 62O D E O D G O E GS S S? ? ?? ? ? 由（ 1）得 2 2 2 2 2 21 2 1 22 2 2 2 2 21 2 1 23 , 3 , 3 。2 , 2 , 2 .u x u x x xv y v y y y? ? ? ? ? ?? ? ? ? ? ? 解得 2 2 2 2 2 21 2 1 23 。 1 .2u x x v y y? ? ? ? ? ? 因此 12,ux x 只能從 62? 中選取， 12,v y y 只能從 1? 中選取 . 因此 ,D E G 只能在 6( , 1)2??這四點中選取三個不同點 而這三點的兩兩連線中必有一條過原點 與 62O D E O D G O E GS S S? ? ?? ? ?矛盾 所以橢圓 C 上不存在滿足條件的三點 ,D E G . 2022年普通高等學校招生全國統(tǒng)一考試 (山東卷 ) 英語 本試卷分第 Ⅰ 卷和第 Ⅱ 卷兩部分，共 12 頁。滿分 150 分?？荚囉脮r 120 分鐘。考試結(jié)束后，將本試卷和答題卡一并交回。 注意事項： 1. 答題前，考生務(wù)必用 毫米黑色簽字筆將自己 的姓名、座號、準考證號、縣區(qū)和科類填寫在答題卡和試卷規(guī)定的位置上。 2. 第 Ⅰ 卷每小題選出答案后，用 2B 鉛筆把答題卡上對應(yīng)題目的答案標號涂黑；如需改動，用橡皮擦干凈后，再選涂其他答案標號。 3. 第 Ⅱ 卷必須用 毫米黑色簽字筆作答，答案必須寫在答題卡各題目指定區(qū)域內(nèi)相應(yīng)的位置，不能寫在試卷上；如需改動，先劃掉原來的答案，然后再寫上新的答案；不能使用涂改液、膠帶紙、修正帶。不按以上要求作答的答案無效。 第 Ⅰ 卷（共 105 分） 第二部分 英語知識運用（共兩節(jié)，滿分 35 分） ( 第一節(jié) 語法和詞匯知識（共 15 小題；每小題 1 分，滿分 15 分） 從 A、 B、 C、 D 四個選項中，選出可以填入空白處的最佳選項，并在答題卡上將該項涂黑。 your timeit?s just______ short distance from here to ______ restaurant. 。the B. the 。 a C. a 。 the 。a ?m sorry ,I broke the vase. Oh,__________ It wasn?t very expensive . A. that?s all right B. you?d better not C. I?m afraid not D. as you wish ways to praise your children often, ___ you?ll find they will open their hearts to you . A. or B. still C. but D. and two girls are so alike that strangers find ___________difficult to tell one from the other. A. it B. them C. her D. that are broadening the bridge to ___________ the flow of traffic. A. put off B. turn on C. speed up D. work out ?m afraid he?s more of a talker than a doer, which is _____he never finishes anything. A. that B. when C. why D. where over there there?s a very long, winding path _________up to the house. A. to lead B. leads C. led D. leading had his camera ready _______ he saw something that would make a good picture. A. even if B. in case C. if only D. so that 29.——Are you going to Tom?s birthday party? —— might have to work. A. Don?t mention it B. Thank you C. Sounds great D. It depends ?m sorry I don?t phone you, but I?ve been very busy _________ the past couple of weeks A. beyond B. with C. over D. among I got on the bus ,I_________I had left my wallet at home. A. was realizing B. have realized C. realized D. would realize town has narrow streets and small houses _______ are built close to each other. A. that B. where C. what D. they ?ve offered her the job, but I didn?t know_____________ she?ll accept it A. where B. what C. which D. whether ?s a in our office that when it?s somebody?s birthday, they bring in a cake for us all to share. A. balance B .tradition C. concern D. relationship was surprised to find the fridge empty。 the children _______ everything! A. had been eating B. have eaten C. had eaten D. have been eating 第二 節(jié) 完形填空（共 20 小題；每小題 1 分，滿分 20 分） I first went to hear a live rock concert when I was eight years old. My brother and his friends were all 36 of a heavy metal group called Black Wednesday. When they 37 that Black Wednesday were going to perform at our local theatre. They all bought 38 for the performance. However, at the last minute, one of the friends couldn?t go, so my brother 39 me the ticket. I was really 40 ! I remember the buzz（嘈雜聲） of excitement inside the theatre as we all found our 41 .After a few minutes， the lights went down and everybody became 42 .I could barely make out the stage in the 43 .We waited. Then there was a roar from the crowd, like an explosion, as the first members of the band 44 the stage. My brother leaned over and shouted something in my ear, but I couldn?t 45 what he was saying. The first song was already starting and the music was as 46 as a jet engine. I could 47 the drum beats and the bass notes in my stomach. I can?t recall any of the songs that the band played. I just 48 that I really enjoyed the show and didn?t want it to 49 .But in the end, after three encores（加演） , the show finished. We left the 50 and walked unsteadily out onto the pavement. I felt a little dizzy, as if I had just 51 from a long sleep. My ears were still 52 with the beat of the last song. After the 53 , I became a Black Wednesday fan too for a few years before getting into other kinds of music. Once in a while, 54 , I listen to one of their songs and 55 I?m back at that first show. B. fans C. friends D. volunteers 37 A. discovered B. thought C. predicted B. drinks C. tickets D. clothes . offered B. returned C. found B. excited C. embarrassed D. encouraged 41. A. space B. entrance C. spots 42. A. quiet C. serious D. nervous 43. A. silence B. darkness C. noise D. smoke upon B. got through C. stepped onto D. broke into . hear C. repeat D. bear 46 .A. hard C. sweet D. fast 47. A. touch C. enjoy D. digest 48. A. remember B. understand C. believe