2021年武汉外国语学校高中招生资格综合能力测试题(附答案)
武汉外校初升高资格生考试有答案
2015武汉外国语学校初升高资格考试III 英语（总分60分）第一部分第一部分 单项选择（共15小题，每小题1分，满分15分）分）1. ---_________! The door of the classroom has been left open all night.---Oh, I'm not the one to blame. A. Thank goodness B. Come on C. All right D. My goodness 2. ---Can you show me ________way to the Jordan's ?---Sorry, I'm afraid I can't because there isn't______ Jordan in the community. A. the; the B. the; a C. a; the D. the; / 3. ---Ten dollars a pair? I think it's a bit expensive.---If you take five pairs, the price for each will ____ to five dollars. A. take down B. put down C. break down D. come down 4. ---It is many years _____ they ____married.---As I know, they just celebrated their 30th wedding anniversary last month. A. before; had got B. when; got C. since; gotD. that; had got 5. ---The advertisement says this big store provides all kinds of refrigerators.---I think it wants to tell us we_____ go to any other store. A. needn't B. can't C. mustn'tD. may not 6. _________all of them have done a good job, only one can be chosen for the position. A. If B. As C. WhileD. Since 7. Attention please ! All passengers must have the luggage _____two hours before your planes take off. A. to check B. checked C. checkD. checking 8. We have ___the TV sets and marked on each box "Look out", "Easily broken stuff". A. packed B. taken C. carriedD. delivered 9. Teenagers who don't take exercise or ______diet is high in fat will be likely to gain weight. A. that B. which C. whatD. whose 10. After thinking it over, he finally agreed with my suggestion that we _____ the date. A. changed B. had changed C change D. would change 11. ---Do you know that she failed Physics in the final-term exam?---Yes, but I have no idea _____ she did it. She is always good at it. A. how B. why C. thatD. what 12. Lucy, _____for years to be a reporter, finally took a position at Wuhan Evening Daily. A. having struggled B. to struggle C. strugglingD. struggled 13. It is known to all that it is Jim who broke the chair. Don't talk to me as if I ___it.A. have doneB. didC. had doneD. would do 14. Only after they had negotiated for several months _____an agreement. A. they reached B. did they reach C. they reachD. do they reach 15. ---I tried my best but I still couldn't work out the meaning of the poem.---____________. Read more. A. I'm afraid not B. It's up to you C. I'm sorry D. You are not alone第二部分第二部分 完形填空（共15小题，每小题1分，满分15分）分）I lived with my father on a small farm in Virginia. Farm days were happy but there were sometimes some things you didn’t expect. One day, I was sent by my father to buy some tools for our farm. As a 17-year-old boy, I liked 16 better than driving our truck, 17 this time I couldn’t cheer up. My father had told me I’d have to ask for credit(赊账) at the store.Seventeen is a/an 18 age, when a young man wants respect more than anything else. It was 1976, and the ugly 19 of racial discrimination(歧视) was still a fact of life. I had seen my friends ask for credit and then stand, head down, while the store owner 20 whether they were good for it. I knew black youths just like me who were 21 like thieves by the store clerk each time they went into a store.My family was honest. We paid our debts. But before harvest, cash was short. Would the store owner 22 us?Wall James, the store owner, stood behind the cash desk, talking to a farmer. I nodded as I passed him on my way to the shelves. When I brought my 23 to the cash desk, I said 24 , “I need to put this on credit.”The farmer gave me a 25 The farmer gave me a 25 look. But Wall’s face didn’t change. “Sure,” he said quickly. “Your dad is look. But Wall’s face didn’t change. “Sure,” he said quickly. “Your dad is 26 26 good for it.” He good for it.” He good for it.” He 27 27 27 to the other man. “This boy is one of John Tuck’s sons.”to the other man. “This boy is one of John Tuck’s sons.”The farmer nodded in a neighborly way. I was filled with pride. “John Tuck’s son.” Those there words had opened a door to an adult’s respect and trust.That day I discovered that the good name my parents had 28 brought our whole family the respect of our neighbors. Everyone knew what to 29 from a Tuck: a decent person who kept his word and respected himself 30 much to do wrong.16. A. everything B. anything C. nothing D. something 17. A. so B. yet C. and D. though 18. A. pridefulB. excitingC. respectfulD. excellent 19. A. object B. habit C. intention D. shadow 20. A. suspected B. questioned C. found D. figured 21. A. caught B. accused C. watched D. separated 22. A. trust B. blame C. charge D. believe 23. A. bargains B. orders C. sales D. purchases 24. A. excitedly B. friendly C. carefully D. casually 25. A. trustful B. distrustful C. proud D. confident 26. A. always B. sometimes C. never D. frequently 27. A. replied B. turned C. pointed D. introduced 28. A. givenB. deservedC. earnedD. wasted29. A. give B. receive C. demand D. expect 30. A. so B. enough C. too D. very三.阅读理解（共10小题，每小题2分，满分20分） 第一节，（共5小题，每小题2分，满分10分）Humor can make the conversation more interesting. If you intend using humor in your talk to make people smile, you must know how to identify shared experiences and problems. Your humor must be relevant to the audience and should help to show them that you are one of them or that you understand their situation and are in sympathy with their point of view. Depending on whom you are addressing, the problems will be different. If you are talking to a group of managers, you may refer to the disorganized methods of their secretaries; if you are addressing secretaries, you may want to comment on their disorganized bosses.Here is an example, which I heard at a nurses' gathering, of a story which works well because the audience all shared the same view of doctors. A man arrives in heaven and is being shown around by an Angel. He sees wonderful accommodations, beautiful gardens, sunny weather and so on. Everyone is very peaceful, polite and friendly until, waiting in a line for lunch, the new arrival is suddenly pushed aside by a man in a white coat, who rushes to the head of the line, grabs his food and stomps over to a table by himself. "Who is that?" the new arrival asked the Angel. "Oh, that's God." came the reply, "but sometimes he thinks he's a doctor."If you feel awkward being humorous, you must practice so that it becomes more natural. Include a few casual and apparently off-the-cuff remarks which you can deliver in a relaxed and unforced manner. Often it's the delivery which causes the audience to smile, so speak slowly and remember that a raised eyebrow or an unbelieving look may help to show that you are making a light-hearted remark.Look for the humor. It often comes from the unexpected. A twist on a familiar quote "If at first you don't succeed, give up" or a play on words or on a situation. Look at your talk and pick out a few words or sentences which you can turn about and inject with humor. 31:To make your humor work, you are supposed to ________.A. make fun of the disorganized people.B. address different problems to different people.C. show sympathy for your listeners.D. take advantage of different kinds of audience32: The joke about the doctors implies that, in the eyes of nurses, they are ________. A. very clear about their godlike roleB. very busy even during lunch hours.C. impolite to new arrivalsD. not fond of having lunch with the nurses33:What ’s the possible meaning of the underlined word in paragraph3? ________.A. intentionalB. urgentC. unpreparedD. excellent 34:To achieve the desired result, humorous stories should be delivered ________.A. as casually as possibleB. as awkwardly as possibleC. in well-worded languageD. as quickly as possible35: The best title for the text may be ________.A. Different Humor methodsB. Various kinds of humorC. Add humor to speechD. Use humor effectively第二节第二节 （共5小题，每小题2分，满分10分）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，选项中有两处为多余选项。
2021年武汉外校初中招生综合测试之数学部分及其参考答案
2021年武汉外校初中招生综合测试之数学部分及其参考答案2021年武汉外校初中招生综合测试之数学部分及其参考答案（B卷） 2021年武汉外校初中招生综合测试（B卷）第一部分基础知识检测第1题8分，第2题至第8题2分，满分22分 1、计算：（每小题2分，共8分）（1）（78.6－0.786×25＋75%×21.4）÷15×2001 解答：原式=（0.786×100－0.786×25＋0.75×21.4）÷15×2001 =[0.786×(100－25)＋75×0.214] ÷15×2001 =[0.786×75＋75×0.214] ÷15×2001 =(0.786＋0.214)×75÷15×2001 =1×75÷15×2001=5×2001 =10005 （2）1.65÷（1/4＋0.8）－（0.5＋1/3）×(24/35) 解答：原式=1.65÷(21/20) －(5/6) ×(24/35) =11/7－4/7 =1 （3）【2（5/14）×（2/3）－62.5%】÷【（13/12＋6.375）÷11（14/15）】解答：原式=（11/7－5/8）÷【（179/24）÷（179/15）】=（53/56）÷（5/8） =53/35（4）2－[（7/16）×2(2/3)＋1/7）×1(10/11)]÷[12(1/3)－3.75÷(5/14）)解答：原式=2－（7/6＋1/7）×(21/11)÷（37/3－21/2） =2－(55/42)×(21/11)÷(11/6) =2－(5/2)÷(11/6) =2－15/11 =7/112、小明和小红用火柴棒搭正方形，下图是小明搭出的正方形：（图）已知小红有91根火柴棒，如果也按照这种方式搭正方形，可搭出_________个正方形。
武汉外校初升高资格生考试有答案
2015武汉外国语学校初升高资格考试III 英语（总分60分）第一部分单项选择（共15小题，每小题1分，满分15分）1. ---_________! The door of the classroom has been left open all night.---Oh, I'm not the one to blame.A. Thank goodnessB. Come onC. All rightD. My goodness2. ---Can you show me ________way to the Jordan's ?---Sorry, I'm afraid I can't because there isn't______ Jordan in the community.A. the; theB. the; aC. a; theD. the; /3. ---Ten dollars a pair? I think it's a bit expensive.---If you take five pairs, the price for each will ____ to five dollars.A. take downB. put downC. break downD. come down4. ---It is many years _____ they ____married.---As I know, they just celebrated their 30th wedding anniversary last month.A. before; had gotB. when; gotC. since; gotD. that; had got5. ---The advertisement says this big store provides all kinds of refrigerators.---I think it wants to tell us we_____ go to any other store.A. needn'tB. can'tC. mustn'tD. may not6. _________all of them have done a good job, only one can be chosen for the position.A. IfB. AsC. WhileD. Since7. Attention please ! All passengers must have the luggage _____two hours before your planes take off.A. to checkB. checkedC. checkD. checking8. We have ___the TV sets and marked on each box "Look out", "Easily broken stuff".A. packedB. takenC. carriedD. delivered9. Teenagers who don't take exercise or ______diet is high in fat will be likely to gain weight.A. thatB. whichC. whatD. whose10. After thinking it over, he finally agreed with my suggestion that we _____ the date.A. changedB. had changed C change D. would change11. ---Do you know that she failed Physics in the final-term exam?---Yes, but I have no idea _____ she did it. She is always good at it.A. howB. whyC. thatD. what12. Lucy, _____for years to be a reporter, finally took a position at Wuhan Evening Daily.A. having struggledB. to struggleC. strugglingD. struggled13. It is known to all that it is Jim who broke the chair. Don't talk to me as if I ___it.A. have doneB. didC. had doneD. would do14. Only after they had negotiated for several months _____an agreement.A. they reachedB. did they reachC. they reachD. do they reach15. ---I tried my best but I still couldn't work out the meaning of the poem.---____________. Read more.A. I'm afraid notB. It's up to youC. I'm sorryD. You are not alone第二部分完形填空（共15小题，每小题1分，满分15分）I lived with my father on a small farm in Virginia. Farm days were happy but there were sometimes some things you didn’t expect. One day, I was sent by my father to buy some tools for our farm. As a 17-year-old boy, I liked 16 better than driving our truck, 17 this time I couldn’t cheer up. My father had told me I’d have to ask for credit(赊账) at the store.Seventeen is a/an 18 age, when a young man wants respect more than anything else. It was 1976, and the ugly 19 of racial discrimination(歧视) was still a fact of life. I had seen my friends ask for credit and then stand, head down, while the store owner 20 whether they were good for it. I knew black youths just like me who were 21 like thieves by the store clerk each time they went into a store.My family was honest. We paid our debts. But before harvest, cash was short. Would the store owner 22 us?Wall James, the store owner, stood behind the cash desk, talking to a farmer. I nodded as I passed him on my way to the shelves. When I brought my 23 to the cash desk, I said 24 , “I need to put this on credit.”The farmer gave me a 25 look. But Wall’s face didn’t change. “Sure,” he said quickly. “Your dad is 26 good for it.” He 27 to the other man. “This boy is one of John Tuck’s sons.”The farmer nodded in a neighborly way. I was filled with pride. “John Tuck’s son.” Those there words had opened a door to an adult’s respect and trust.That day I discovered that the good name my parents had 28 brought our whole family the respect of our neighbors. Everyone knew what to 29 from a Tuck: a decent person who kept his word and respected himself 30 much to do wrong.16. A. everything B. anything C. nothing D. something17. A. so B. yet C. and D. though18. A. prideful B. exciting C. respectful D. excellent19. A. object B. habit C. intention D. shadow20. A. suspected B. questioned C. found D. figured21. A. caught B. accused C. watched D. separated22. A. trust B. blame C. charge D. believe23. A. bargains B. orders C. sales D. purchases24. A. excitedly B. friendly C. carefully D. casually25. A. trustful B. distrustful C. proud D. confident26. A. always B. sometimes C. never D. frequently27. A. replied B. turned C. pointed D. introduced28. A. given B. deserved C. earned D. wasted29. A. give B. receive C. demand D. expect30. A. so B. enough C. too D. very三.阅读理解（共10小题，每小题2分，满分20分）第一节，（共5小题，每小题2分，满分10分）Humor can make the conversation more interesting. If you intend using humor in your talk to make people smile, you must know how to identify shared experiences and problems. Your humor must be relevant to the audience and should help to show them that you are one of them or that you understand their situation and are in sympathy with their point of view. Depending on whom you are addressing, the problems will be different. If you are talking to a group of managers, you may refer to the disorganized methods of their secretaries; if you are addressing secretaries, you may want to comment on their disorganized bosses.Here is an example, which I heard at a nurses' gathering, of a story which works well because the audience all shared the same view of doctors. A man arrives in heaven and is being shown around by an Angel. He sees wonderful accommodations, beautiful gardens, sunny weather and so on. Everyone is very peaceful, polite and friendly until, waiting in a line for lunch, the new arrival is suddenly pushed aside by a man in a white coat, who rushes to the head of the line, grabs his food and stomps over to a table by himself. "Who is that?" the new arrival asked the Angel. "Oh, that's God." came the reply, "but sometimes he thinks he's a doctor."If you feel awkward being humorous, you must practice so that it becomes more natural. Include a few casual and apparently off-the-cuff remarks which you can deliver in a relaxed and unforced manner. Often it's the delivery which causes the audience to smile, so speak slowly and remember that a raised eyebrow or an unbelieving look may help to show that you are making a light-hearted remark.Look for the humor. It often comes from the unexpected. A twist on a familiar quote "If at first you don't succeed, give up" or a play on words or on a situation. Look at your talk and pick out a few wordsor sentences which you can turn about and inject with humor.31:To make your humor work, you are supposed to ________.A. make fun of the disorganized people.B. address different problems to different people.C. show sympathy for your listeners.D. take advantage of different kinds of audience32: The joke about the doctors implies that, in the eyes of nurses, they are ________.A. very clear about their godlike roleB. very busy even during lunch hours.C. impolite to new arrivalsD. not fond of having lunch with the nurses33:What’s the possible meaning of the underlined word in paragraph3? ________.A. intentionalB. urgentC. unpreparedD. excellent34:To achieve the desired result, humorous stories should be delivered ________.B. as awkwardly as possibleA. as casually as possibleC. in well-worded languageD. as quickly as possible35: The best title for the text may be ________.A. Different Humor methodsB. Various kinds of humorC. Add humor to speechD. Use humor effectively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，选项中有两处为多余选项。
武汉外国语学校2011年高中招生资格考试综合能力测试题(word版附答案)
武汉外国语学校2011年高中招生资格考试综合能力测试题第六部分：填空题（本大题共5小题，每小题6分，共30分） 1．如果一个数能表示成2222x xy y ++（x ，y 是整数），我们称这个数为“好数”． 则在1，2，3，…，19中全部的“好数”为_________．2．已知2290129(21)x a a x a x a x +=+++⋅⋅⋅，则213579()a a a a a ++++202468()a a a a a -++++的值为________． 3．下图是用12个全等的等腰梯形镶嵌成的图形，则这个图形中等腰梯形的上底长与下底长的比是________．4．已知正五边形广场ABCDE 的周长为2000米．甲，乙两人分别从A ，C 两点同时出发，沿A B C D E A →→→→→→⋅⋅⋅方向绕广场行走，甲的速度为50米/分，乙的速度为46米/分．那么出发后经过______分钟，甲、乙两人第一次行走在同一条边上．5．如图，根据指令，机器人在平面上能完成下列动作：先从原点O 沿正东偏北α（090α︒≤≤︒）方向行走一段时间后，再向正北方向行走一段时间，但何时改变方向不定．假定机器人行走速度为10米/分钟，则机器人行走2分钟可能落点区域的面积是________平方米．第七部分：解答题（本大题共3小题，每小题10分，共30分）6．如图，矩形ABCD 的长AD 为a ，宽AB 为b ，E 、F 分别是BC 、AD 上的点，且AE 、CF 是相距为h 的平行线，求AF 的长．（用a 、b 、h 表示）FEDCBA7．如图，已知点P 是抛物线21416y x =+上的任意一点，记点P 到x 轴距离为1d ， 点P 与点(0,8)F 的距离为2d ． （1）证明：12d d =；（2）若直线PF 交此抛物线于另一点Q （异于P 点），试判断以PQ 为直径的圆与x 轴的位置关系，并说明理由．8．如下左图，阴影部分是陆地，折线ABCDE 是河岸，今要将河岸拉直，需在线段DE 上找一点M ，将河岸ABCDM 变成线段AM ，并且河面面积保持不变． 请你在图中画出线段AM （保留作图痕迹），并说明理由．参考答案1．【解析】222222()x xy y x y y ++=++，特征：“好数”就是两个整数的平方和．好数有1、2、4、5、8、9 、10、13、16 、17、182．【解析】令1x =-，024*******()()1a a a a a a a a a a ++++-++++=；令1x =，024*******()()9a a a a a a a a a a +++++++++=； ∴024685a a a a a ++++=，135794a a a a a ++++=．∴22221357902468()()549a a a a a a a a a a ++++-++++=-=3．【解析】由图中横边可以看出：横边可以看成是3个等腰梯形的下底组成；假如把上面三个小梯形的上底平移到最下面的三个小梯形的上底处，可以发现横边 也可以看成是6个等腰梯形的上底组成． ∴等腰梯形的上底长与下底长的比是1：24．【解析】由正五边形广场ABCDE 的周长为2000米，可得其边长为400米；甲、乙两人分别从A ，C 两点同时出发时距离是800米，若甲、乙两人第一次行走在同一条边上时，极有可能此时距离为一条边长400米， 此时时间为400(5046)100÷-=分．而就在此时，甲、乙分别在CD 、ED 中点处，不再同一条边上，需继续前行， 则甲至少还需走200米，即4分，此时甲在点D ，乙在边DE 上， 也就是说出发后经过104分钟，甲乙两人第一次行走在同一条边上．5．【解析】设改变方向的点为M ，过M 作x 轴的垂线，垂足为N ，根据速度和时间求出OM PM +的长，在OPM ∆中然后根据三角形的两边之和大于第三边列出一个不等式，然后在OMN ∆中，根据两边之和大于第三边列出另外一个不等式，然后 再根据x 大于等于0，y 大于等于0，在平面直角坐标系中画出相应的平面区域为 一个弓形，如图所示，利用四分之一圆的面积减去等腰直角三角形的面积即可求出 弓形的面积．2020Oy x依题意10220OM PM +=⨯=米， 在OPM ∆中，OM PM OP +≥（当O 、M 、P 共线时等号成立） ∴20OP ≤，即22400x y +≤，在OMN ∆中，OM ON MN ≤+（当O 、M 、N 共线时等号成立） ∴OM MP ON MN MP x y +≤++=+，∴20x y +≥．∴区域2240020:00x y x y S x y ⎧+≤⎪+≥⎪⎨≥⎪⎪≥⎩为弓形则面积为2211202010020042ππ⨯-⨯=-（平方米）6．【解析】过F 向AE 作垂线，垂足为M ，易证Rt DFC Rt MAF ∆∆∽，所以，有AF MFCF CD=设AF x =，有22()x h ba xb =-+ 化简得：2222222()2()0h b x ah x a b h --++=①若h b =，则222a b AF a+=；②若b h a <≤，则222222ah bh a b h AF h b -+-=-③若0h b <<，则222222ah bh a b h AF h b -+-=-7．【解析】（1）设P 为抛物线上一点，故P 的坐标为21(,4)16t t +； 则P 到x 轴距离211416d t =+． P 到点(0,8)F 的距离2222211(48)41616d t t t =++-=+；化简可得12d d =． （2）相切；设Q 到x 轴的距离为m ，到F 的距离为n ， 根据（1）的结论，有m n =，过PQ 的中点作x 的垂线，设其长度为h ，易得11()2h m d =+，同时有21()()2PQ n d m d h =+=+=， 故以PQ 为直径的圆与x 轴相切．8．【解析】连接BD ，过C 作CF ∥BD 交DE 于F ，则BDC BDF S S ∆∆=．连接AF ，过B 作BM ∥AF 交DE 于M ，则ABM FBM S S ∆∆=，连接AM 即为所求．。
武汉外国语学校2012年高中招生资格考试综合能力测试题(word版附答案)
武汉外国语学校2012年高中招生资格考试综合能力测试题第六部分 选择题（本大题共5小题，每小题4分，共20分）66．某女士从一个商场买了三条围巾，每条a 元，又从另一个商场买了两条围巾，每条b 元，后来她又以每条2a b+元的价格把围巾全部卖给了别人，结果发现亏本了，原因是（ ）A ．a b >B ．a b <C ．a b =D ．与a 和b 的大小无关67．若关于x 的方程61(1)(1)1tx x x -=+--有增根，则它的增根是（ ）A ．0B ．1C ．1-D ．1和1-68．用线段将左图中的点连接起来，每个点至少连接一次，不可能构成选项中的哪个 图形（ ）A． B．C． D．69．如图1，把一个边长为1的正方形纸片经过三次对折后沿中位线（虚线）剪下一部分得到图2，则图2展开得到的纸片的面积为（ ）图1上折右折右下方折沿虚线剪开图2A ．34 B ．12 C ．38D ．31670．有8名羽毛球运动员进行选拔赛．若已知：①水平高的总是能战胜水平低的；②没有任何两名选手水平一样．若要选出水平最高的两名选手，若要选出水平最高的两名选手，至少需要比赛（ ）场．A ．7B ．9C ．11D ．13第七部分 填空题（本大题共5小题，第6-7小题每题5分，第8-10小题每题6分，共28分） 71．如果关于x 的不等式30x m -≤的正整数解是1，2，3，那么m 的取值范围是___________．72．如图，在平面直角坐标系中，OCB ∆的外接圆与y轴交于A ，60OCB ∠=︒，45COB ∠=︒，则OC =___________．CB AOyx73．将红、白、黄三种小球，装入红、白、黄三个盒子中，每个盒子中装有相同颜色的小球．已知：①黄盒中的小球比黄球多；②红盒中的小球与白球不一样多；③白球比白盒中的球少．则红、白、黄三个盒子中装有小球的颜色依次是___________．74．如图，在ABC ∆中，90ACB ∠=︒，6BC =，8AC =，PQ ∥AB ，点P 在AC 上（与点A 、C 不重合），点Q 在BC 上．若在AB 上存在点M ，使PQM ∆为等腰直角三角形，则PQ =___________．QPCBA75．请根据下列图形的规律在横线上填写适当的图形第八部分 解答题（本大题共3小题，共32分） 76．（本题满分10分）某工厂为保护环境，决定购买6台机器用于污水处理．现有A 型、B 型两种机器供 选择，其中每种机器的价格和每台机器的年污水处理量如下表所示．经过预算， 本次购买机器所需的资金不能超过34万元． （1）按该工厂的要求，可以有几种购买方案？A 型B 型 价格（万元/台） 7 5 每台年处理量（吨） 100 60（2）若该工厂购进的6台机器的年污水处理能力不能低于380吨，为了节约资金， 应选择哪种购买方案？77．（本题满分10分）已知实数p ，q ，r ，满足p q r ≤≤，且0pq qr rp ++=，1pqr =． 求最大的实数m ，使不等式p q m r +≥恒成立，并说明理由． 78．（本题满分12分）如图，在平面直角坐标系中，A 、B 两点的坐标分别为(0,2)-，(0,8)，以AB 为一边作正方形ABCD ，再设以CD 为直径的半圆为P ，x 轴交半圆P 于点E ，交边CD 于点F ．（1）求线段EF 的长；（2）连接BE ，试判断直线BE 与P 的位置关系，并说明你的理由；（3）直线BE 上是否存在点Q ，使得以Q 为圆心、r 为半径的圆，既与y 轴相切 又与P 外切？若存在，试求r 的值；若不存在，请说明理由．参考答案66．【解析】此题考察了不等式的应用，是七年级的内容．根据题意列出不等式：3252a ba b ++>⨯，解出a b >67．【解析】此题考察了分式方程的解法以及增根的概念，是八年级的内容．首先将分式方程化为整式方程：26(1)1t x x -+=-，化简得270x tx t ++-=……①根据题意，若有增根，只能是1和1-，将1代入①式得到3t =，所以1是增根； 将1-代入①式得到60-=，不成立，所以1-不是增根． 即它的增根是1．68．【解析】此题考察了学生的观察能力，通过观察四个选项和题目所给的图形可以发现，D 选项的图形在右上部分多出了一个点，这是不可能形成的． 即此题选D69．【解析】此题考察了四边形以及三角形的基础知识．根据题目的条件，对折三次后，纸片的厚度为原来的八倍，所以减去的纸片面积为小三角形面积的八倍．减去的小三角形的面积为111124432⨯⨯=，所以减去的纸片的面积为118324⨯=，所以剩下的纸片的面积为34．70．【解析】此题考察了逻辑思维能力．根据题意，采取淘汰制的赛法，任意分为4组，选出4名胜利者，然后4名胜利者 任意分为2组，选出2名胜利者，再打1场，选出水平最高者，这样总共有7场． 注意，在第二场比赛选出的2名选手中，除了第一名，另外一个不一定是第二名， 因为有可能在第一场比赛的时候，第二名就被第一名打败了，所以，在三场比赛中， 被第一名打败的3位选手再选出水品最高的，需要2场比赛，这样就选出了水品 第二高的选手．所以总共需要9场比赛．71．【解析】此题考察了一元一次不等式的知识，是七年级的内容．根据题意，得到3mx ≤，又因为正整数解是1，2，3，那么可以得到m 的取值范围是：912m ≤<72．【解析】此题考察了直角坐标系与圆结合的计算问题，属于九年级的内容．根据题意，可知AB 是直径，连接AB ，由60OCB ∠=︒，得到60OAB ∠=︒，因为OA =，所以AB =连接AC ，因为45COB ∠=︒，得到ABC ∆是等腰直角三角形，所以2CB CA ==．在AOC ∆中，作AD CO ⊥，所以得到CD =，1OD =，所以1OC =+73．【解析】此题考察了推理判断的能力．根据题意，假设红、白、黄三个盒子中所装的小球分别是A 、B 、C ，则由②知， A 不是白球，由③知，B 也不是白球，所以C 是白球．由③知，B 比白球多，由①知， 白球比黄球多，所以B 是红球，那么A 是黄球．所以答案是：红、白、黄三个盒子中所装小球的颜色分别是黄、红、白74．【解析】此题考察了等腰三角形的知识，是八年级的内容．此题有两种情况：（1）当PQ 为直角边时，可以作图如下：MQPC BA此时PQ QM =．根据题意可知，::::3:4:5CQ PC PQ MB MQ BQ ==，假设3CQ a =，则5PQ a =，即5MQ a =，所以254BQ a =，所以3764BC a ==，所以2437a =，所以120537PQ a ==；（2）当PQ 为斜边时，可以作图如下：ED M PQABC此时PM MQ =，作PD AB ⊥、QE AB ⊥．假设3BE b =，那么4QE EM DM PD b ====，163AD b =， 所以49103AB b ==，所以3049b =，所以240849PQ b ==， 综上，此题的答案是12037或2404975．【解析】此题考察的是轴对称的知识，是八年级的内容．观察图形发现，每一幅图都是由数字1，2，3，4，5和7通过轴对称得到的，所以横线上应该填写的是76．【解析】此题考察了不等式的应用，是七年级的内容．需要根据题目的意思列出不等式，再根据实际情况，确定出有几种方案，然后算出 每种方案的费用，得出最优方案．（1）设购买A 型机器x 台，则购买B 型机器6x -台，根据题意，有： 75(6)34x x +-≤，解得2x ≤．因为x 是非负整数，所以x 的取值可以是0，1，2． 所以有3种方案：一、购买2台A 型机器，4台B 型机器； 二、购买1台A 型机器，5台B 型机器； 三、购买0台A 型机器，6台B 型机器．（2）方案一的污水处理能力是2100460440⨯+⨯=吨； 方案二的污水处理能力是1100560400⨯+⨯=吨； 方案三的污水处理能力是010*******⨯+⨯=吨；根据题意，只有方案一和方案二的污水处理能力大于380吨． 方案一购买机器所需的资金是：274534⨯+⨯=万元； 方案二购买机器所需的资金是：175532⨯+⨯=万元；所以，选择方案二既满足污水处理能力的要求，所用的资金也最少．77．【解析】此题考察了不等式的性质以及基本不等式的相关内容，是高一的内容，属于超纲范围．此题首先需要根据题意确定出三个参数的正负，然后根据题目所给的关系式， 把m 分离出来，再根据“小于恒成立即小于最小值”，利用基本不等式求出 分离m 之后那部分的最小值即可．因为p q r ≤≤，且1pqr =，所以得到0r >．因为p q r ≤≤，且0pq qr rp ++=，所以得到0p <． 又因为1pqr =，所以得到0q <．则p q m r +≥变形为：()p q p q m rr+-+≤=． 由01pq qr rp pqr ++=⎧⎨=⎩得1110p q r ++=．变形得到111p q r +=-．所以()11()()2p q q p p q r p q p q-+=++=++．又因为224q p p q ++≥=（当且仅当p q =时等号成立） 所以()4p q r-+≥． 要使式子恒成立，即4m ≤．所以满足条件的最大实数m 的值是4．78．【解析】此题考察了圆的几何性质以及全等和相似三角形等内容，并且与直角坐标系相结合，是一道综合性的大题，属于九年级的内容．此题第一问比较简单，利用勾股定理进行计算即可；第二问是要证明切线，用最常 见的连接半径证明垂直就行；第三问比较难，通过图形可以知道这个圆是存在的， 然后构造直角三角形，利用勾股定理算出半径即可． （1）由题意得，10CD =，连接EP ，则5EP =． 因为2FD =，所以3PF =．在Rt PEF ∆中，由勾股定理得4EF = （2）由（1）得6OE =， 因为8OB =，所以10BE =．连接BP ，则BPC BPE ∆∆≌，所以BE PE ⊥． 即BE 与圆P 相切．（3）连接PQ ，∵Q 与P 外切，∴5PQ r =+． 过Q 作QM y ⊥轴于M ，交CD 于N ．∵Q 与y 轴相切，∴QM r =，∴10QN MN QM r =-=-．∵MQ ∥OE BMQ BOE ⇒∆∆∽BM MQ BO OE ⇒=8463r rBM ⨯⇒==．∴453rNP NF PF =-=-．在Rt QNP ∆中，222QN NP PQ +=2224(10)(5)(5)3rr r ⇒-+-=+．2163909000r r ⇒-+=，解得：r。
2013年武汉外校高中资格生考试 答案
武汉外国语学校2013年高中招生资格考试综合能力测试题答案21-25 BDCCB26-30 CBDDD31-35 CBBCA36-40 CDBCB41-45 DAADA46-50 what minds before best neither51-55 man′s might luck waiting offered56-60 well-mannered saying thanks stars more 61-65 hand is However tips because66-70 BDCCB71、4组分析：可将原方程视为关于x的二次方程，将其变形为x2+yx+（2y2-29）=0由于该方程有整数根，根据判别式△≥0，且是完全平方数由△=y2-4（2y2-29）=-7y2+116≥0解得y2≤116/7≈16.57y2 0 1 4 9 16△116 109 88 53 4显然只有y2=16时，△=4是完全平方数，符合要求当y=4时，原方程为x2+4x+3=0，此时x1=-1，x2=-3当y=-4时，原方程为x2-4x+3=0，此时x3=1，x4=3所以，原方程的整数解为x1=-1 x2=-3 x3=1 x4=3y1=4 y2=4 y3=-4 y4=-472、5.573、英、法74 分析：因为AC=15 ，CD=12，所以AD=9，同理，BD=16，所以AB=25，所以三角形ABC 是直角三角形。
因为CE 是ACB 的平分线，所以角ACE 是45度， 接下去求得DE 的长度，再用余弦定理，可求得CE 的长度。
75、-30，-276、解析：（1）设购进甲种服装x 件，则乙种服装是（200-x ）件，根据两种服装共用去32400元，即可列出方程，从而求解；（2）设购进甲种服装y 件，则乙种服装是（200-y ）件，根据总利润（利润=售价-进价）不少于26700元，且不超过26800元，即可得到一个关于y 的不等式组，解不等式组即可求得y 的范围，再根据y 是正整数整数即可求解；（3）首先求出总利润W 的表达式，然后针对a 的不同取值范围进行讨论，分别确定其进货方案． 解 答 解：（1）设购进甲种服装x 件，则乙种服装是（200-x ）件，根据题意得：180x+150（200-x ）=32400，解得：x=80，200-x=200-80=120（件），则购进甲、乙两种服装80件、120件；（2）设购进甲种服装y 件，则乙种服装是（200-y ）件，根据题意得：≥≤（320-180）y+（280-150）（200-y ）26700（320-180）y+（280-150）（200-y ）26800， 解得：70≤y ≤80，又∵y 是正整数，∴共有11种方案；（3）设总利润为W 元，W=（140-a ）y+130（200-y ）即W=（10-a ）y+26000．①当0＜a ＜10时，10-a ＞0，W 随y 增大而增大，∴当y=80时，W 有最大值，即此时购进甲种服装80件，乙种服装120件；②当a=10时，（2）中所有方案获利相同，所以按哪种方案进货都可以；③当10＜a ＜20时，10-a ＜0，W 随y 增大而减小．当y=70时，W 有最大值，即此时购进甲种服装70件，乙种服装130件．77、附图分析，可点击放大78、分析：（1）若a=1，0x =-2，0y =6， ∵ ∴∵点A （1，A y ）,B(0, B y ),C(-1, C y )在抛物线y=2x +4x+10上， ∴A y =15， 211()()()a b c ax bx c c a b c ++-++--+=10，C y =7 ∴A B C y y y -=15107-=5 （2）由0﹤2a ﹤b ，得0x = -2b a ﹤-1 由题意，如图过点A 作AA 1⊥x 轴于点A 1，则AA 1=A y , OA 1=1 连接BC ，过点C 作C D ⊥y 轴于点D ， 则BD=B y -C y ， CD=1过点A 作AF//BC ，交抛物线于点E （x 1，E y ）,交X 轴于点F （2x ，0）则∠FAA 1=∠CBD ∴Rt △AFA 1∽Rt △BCD. ∴1AA BD = 1FA CD , 即A B Cy y y -=211x -=1-2x 过点E 作EG ⊥AA 1于点G ，易得△AEG ∽△BCD ∴AG BD =EG CD , 即A E B Cy y y y --=1-1x ∵点A （1，A y ）,B(0, B y ),C(-1, C y ), E （x 1，E y ）在抛物线y=a 2x +bx+c 上，∴A y =a+b+c, B y =c , C y =a-b+c , E y =a 21x +b 1x +c∴211()()()a b c ax bx c c a b c ++-++--+=1-1x 解得1x = -2（1x =1舍去）。
武汉外国语学校高中部强基班招生考试题
武汉外国语学校高中部强基班招生考试题一、选择题1、As preparations were not completed in time,the conference had to be till the next Tuesday.A.put awayB.CancelC.put asideD.postponed2、with the size of the whole earth,the highest mountain does not seem high at all.A.When comparedpareC.While comparingparing3、It's only a short way to the station,so we might as wA.GoodB.nowC.QuickD.well4、Liquids are like solids they have a definite volume.A.in thatB.for thatC.with thatD.at that5、Since she can speak Japanese fluently,she has an advantage other job applicants.A.ToB.inC.OverD.against6、Yesterday's English examination looked simple,but it turned out to be easy.A.nothing butB.everything butC.something butD.anything but二、完型填空A boy and a girl catch a bird and（）it in a birdcage(鸟笼).They like it（）and（）it every day.A cat sees the bird and wants（）her supper.（）the bird is in the cage.She can't catch it.So she is very（）.One day，she opens the door of the cage（）wants to catch it.But the bird fillies away.The cat（），and she has（）.Thetwo children（）and see the bird isn't in.They are very angry and put the cat into the cage.1、A.take B.put C.carry D.bring2、A.well B.very C.much D.very much3、A.see B.look C.have a look D.have a look at4、A.have it for B.has is for C.to have it for D.to has it so5、A.But B.And C.So D.Then6、A.angry B.happy C.glad D.tired7、A.but B.and C.so D.or8、A.can to fly B.can fly C.can't to fly D.can't fly9、A.no ways B.some ways C.any way D.not way10、e back to home e back home e to homeD.back home三、阅读理解All of us communicate with one another l as well as with words.Most of the time we're not aware that we're doing it.We gesture with eyebrows or hands,meet someone else eyes and look away,or change positions in a chair.These actions we assume are occasional.However in recent years res hers have discovered that there is a system to them almost as consistent and understandable as language.One important kind of body language is eyebehavior.Americans are careful about how and when they meet one another eyes.In our normal conversation,each eye contact lasts only about a second before one or both of us look away.When two Americans look searchingly into each other's eyes,they become more intimate.There fore,we carefully avoid this,except in suit situations.Researchers who are engaged in the study of communication through body movement are not prepared to spell out a precise vocabulary of gestures.When an rubs his nose,it may mean he is disagreeing with someone or refusing something.But there are other possibleinterpretations,too.Another example:when a student in conversation with a pro fess or holds the older man's eyes a little longer than usual it can be a sign of respect,it can be a challenge to the professor's authority,or it can be something else entirely.The researchers look for patterns in the situation,not for a separate meaningful gesture.Communication between human beings would be just dull if it were all done with words.1、How can people communicate with each other besides language?By gesture2、Like language,gesture is_a consistent and understandable system3、According to the second paragraph,an American will feel uncomfortable if ks into his eyes for too long4、If a student holds his pro eyes a little longer in a conversation,what can it mean?Respect or a challenge or something else It can be a sign of respect,it can be a challenge to the professor's authority,or it can be something else entirely5、What is the main idea of the passage?Body language is as important as words Communication between human beings would be just dull if it were all done with words and we can communication with other actions 答案：一、D、A、D、A、C、A二、1-5 BDDCA 6-10 ABDAB三、1、By gesture/body language/no.2、a consistent and understandable system3、looks into his eyes for too long4、Respect or a challenge or something else.5、Body language is as important as words.。
2015年武汉外国语学校高中招生资格综合能力测试题（附答案）
2015年武汉外国语学校⾼中招⽣资格综合能⼒测试题（附答案）武汉市外国语学校2015年⾼中招⽣资格考试数学试题⼀、填空题（共13题，每⼩题5分，满分65分）1．化简：)12)(12(2)12)(12(2)12)(12(2)12)(12(2)12)(12(2655544433322211++++++++++++++＝____2．对于任意的有理数a ，⽅程2x 2－(a ＋1)x －(3a 2－4a ＋b )＝0的根总是有理数，则b 的值为____3．如图，矩形ABCD 中，AB ＝6，BC ＝4，在AB 、BC 、CD 和DA 上分别取点E 、F 、G 、H ，使得AE ＝AH ＝CF ＝CG ，则四边形EFGH ⾯积的最⼤值为_______4．⼝袋A 中装有标号分别为1到10的10个红球，⼝袋B 中装有标号分别为1到8的8个⿊球．现在从两个⼝袋中随机各取出⼀个球，则红球标号⽐⿊球标号⼤的概率为__________5．如图，直线三⾓形ABC 中，∠C ＝90°，BC ∶AC ＝4∶3，圆O 是三⾓形ABC 的内切圆，点D是斜边AB 的中点，则sin ∠ODA ＝__________6．已知a ＋b ＝2，4)1()1(22-=-+-ab b a ，则ab ＝__________7．已知实数x 、y 满⾜：x 4＋x 2＝3，32424=+y y ，则444yx +＝_______8．如图，在等边三⾓形内，三个半径相等的圆两两外切，并且每个圆都和等边三⾓形的两条边相切．若三⾓形的边长为4，则图中夹在三个圆之间的阴影部分的⾯积为__________（⽤含π的代数式表⽰）9．已知A 、B 、C 、D 、E 是反⽐例函数xy 16=（x ＞0）图象上的五个整点（即横纵坐标都是整数的点），分别以这些点向横轴或纵轴作垂线段，由垂线段所在的正⽅形边长为半径作四分之⼀圆周的两条弧，组成如图所⽰的五个橄榄形（阴影部分）．若取圆周率π为3.14，则这五个橄榄形的⾯积总和是__________10．下列四张图中，只有⼀张图的曲线满⾜拿住曲线的两端拉直后不会打结，请将该图对应的序号填在横线上__________11．如图，在三⾓形ABC 中，AB ＝AC ，∠ABD ＝∠CBE ，BE ＝DE ．若BC ＝1，则点C 到BD 所在直线的距离为__________12．对于正整数n ，记n !＝1×2×3×……×(n －1)×n ，例如：4!＝24，5!＝120，则2015!的尾部（从个位往前计数）连续的0的个数是__________13．1789年的发过巴黎，⼀位对后世有深重影响的伟⼤数学家在这⾥诞⽣，他的名字叫柯西，柯西的⼀⽣对数学领域有着很⾼的建树和造诣，很多数学定理和公式都⽤他的名字来命名，如著名的柯西不等式：(ac ＋bd )2≤(a 2＋b 2)(c 2＋d 2)，在该式中a 、b 、c 、d 可以是任意实数，当且仅当ad ＝bc 时等号成⽴，根据该式，对于有意义的实数x ，则x x 221-++的最⼤值为__________三、解答题（共2题，第14题10分，第15题15分，满分25分）14．已知函数1312+-=x y ，当a ≤x ≤b 时，y 的最⼩值为2a ，最⼤值为2b ，求a 、b 的值15．平⾯直⾓坐标系中，点F 坐标为(0，1)，点A 是抛物线241x y =上异于原点O 的任意⼀点(1)过A 作直线l ：y ＝－1的垂线，垂⾜为M ，求证：AF ＝AM (2)设直线AF 与抛物线的另⼀交点为B ，判断以AB 为直径的圆与直线l ：y ＝－1的位置关系并证明(3)过B 作直线l ：y ＝－1的垂线，垂⾜为N ，求证：A 、O 、N 三点共线(4)若AF ＝3BF ，求△AOB 的⾯积求x x 221-++的最⼤值。
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武汉外国语学校 2021 年高中招生资格考试数学试题
一、填空题（每题7 分，共10 题共70 分）
1.设的整数部分为x，小数部分为y，则x2
＋
1
xy＋y2的值为
2
2.若关于x、y 的方程组
⎧a1x +b1 y =c1
的解为
⎧x = 5
，则方程组
⎧5a1x + 3b1y= 4c1的解为
⎨
a x +
b y =c
⎨
y =6
⎨
+ 3b y = 4c
⎩ 2 2 2 ⎩ ⎩5a2 x 2 2
3.学生玩游戏，他们按以下规则轮流在黑板上写数．规则：①每人每次各选一个从1 到10 中的数字轮流写在黑板上；②不能写已写在黑板上的数的约数；如：黑板上写着“9”的话，以后不能写1、3、9．③不能弃权不写．最后，没数可写的人失败．在这个游戏中，如果巧妙地选数的话，那么先写的人必胜．则1 到10 的数中最先可以写的数字是
4.某城堡的城墙围成如下图PQRS 的形状，其中PQ＝40 m，QR＝45 m，RS＝20 m，SP＝20 m，且∠PSR＝90°，有一名卫兵在城墙外，按顺时针方向沿着与城墙最近的距离保持2 m 的路径巡逻，绕一圈回到出发点，则他总共走了米
5.数x、y、z 满足方程+
| x +y -z |
= 4 ，则的末位数字为
4
6.模型赛车手遥控一辆赛车，先前进1m，然后，原地逆时针方向旋转角a（0°＜α＜180°）．被称为一次操作．若五次操作后，发现赛车回到出发点，则角α为
7.在直角坐标系中，正方形A1B1C1O1、A2B2C2C1、…、A n B n C n C n－1 按如图所示的方式放置，其中点A1、A2、A3、…、A n 均在一次函数y＝kx＋b 的图象上，点C1、C2、C3、…、C n 均在x 轴上．若点B1 的坐标为(1，1)，点B2 的坐标为(3，2)，则点B n 的坐标为
8.如图，锐角三角形ABC 内接于半径为R 的⊙O，H 是三角形ABC 的垂心，AO 的延长线与BC 交于点M，若OH⊥AO，BC＝10，OA＝6，则OM 的长
9.满足不等式n200＜5300的最大正数n 等于
10.某条件下的汽车测试中，驾驶员在一次加满油后的连续行驶过程中从汽车仪表盘得到如下信息：
时间油耗（升/100 公里）可继续行驶距离（公里）
10:00 9.5 300
11:00 9.6 220
注：油耗=
加满油后已用油量
加满油后已行驶距离
，可继续行驶距离=
汽车剩余油量
，
当前油耗
平均油耗=
指定时间内的用油量
指定时间内的行驶距离
从上述信息可以推断在10：00~11：00 这1 小时内（填上所有正确判断的序号）
① 向前行驶的里程为80 公里；② 向前行驶的里程不足80 公里；
x + 9 +x - 7
③ 平均油耗超过9.6 升/100 公里；④ 平均油耗恰为9.6 升/100 公里；
⑤ 平均车速超过80 公里/小时
二、解答题（每题10 分，共三题共30 分）
11.数x、y、z、t 满足不等式(x＋y＋z＋t)2≥4(x2＋y2＋z2＋t2)．问是否存在实数a 使得(x－a)(y －a)＋(z－a)(t－a)＝0？若存在，请证明：若不存在请说明理由
12.梯形ABCD 中，∠ADC＝Rt∠，BC＝CD＝12．∠ABE＝45°；点E 在DC 上．AE、BC 的延长线相交于点F，若AE＝10，S＝S
＋S△C EF，试求S 的值
△ADE
13. 考试中有333 名同学答对1000 道试题，至多答对3 题者为不及格，至少答对6 题者为优秀，已知不是所有同学答对题的个数的奇偶性都相同，成绩不及格者和成绩优秀者人数哪个多？
武汉外国语学校2014 年高中招生资格考试数学答案。