2011年自贡蜀光中学自主招生考试题(数学)

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2012自贡市蜀光中学自主招生考试卷数学

2012年自贡市蜀光中学自主招生考试数学试题（试卷满分：150分考试时间：120分钟）注意事项： 1、第Ⅰ卷为客观题（选择题），答案用2B 铅笔涂在机读卡相应位置，答在试卷上无效；2、第Ⅱ卷为主观题，答案应写在答题卷相应．．上，解答应写出文字说明、证明过程或演算步骤，答在试卷上或则答在错误的位置上无效。

3、试结束后，试卷、机读卡、答题卡一并收回。

第Ⅰ卷（选择题共48分）一、选择题（每小题4分，共48分）1、已知a 为实数，则代数式221227a a +-的最小值为…………【】 A. 0 B. 3 C. 33 D. 92、一名考生步行前往考场， 10分钟走了总路程的41，估计步行不能准时到达，于是他改乘出租车赶往考场，他的行程与时间关系如图所示（假定总路程为1），则他到达考场所花的时间比一直步行提前了……………【】A ．26分钟Ｂ．24分钟Ｃ．22分钟 D ．20分钟 3、已知△ABC 中，AB = AC ，∠BAC = 90°，直角 ∠EPF 的顶点P 是BC 中点，两边PE 、PF 分别交AB 、AC 于点E 、F ，给出以下四个结论：① AE = CF ；② EF = AP ； ③△EPF 是等腰直角三角形；④ S 四边形AEPF =12S △ABC ．当 ∠EPF 在△ABC 内绕顶点P 旋转时（点E 不与A 、B 重合），上述结论中始终正确的有……………………………………【】 A ．1 个 B ．2个 C ．3 个 D ．4个4、2012年欧洲杯足球赛小组赛，德国、荷兰、葡萄牙、丹麦所在的B 组被称为“死亡之组”。

每个小组4个队进行单循环比赛，每场比赛胜队得3分，败队得0分，平局时两队各得1分。

小组赛完后，总积分最高的2个队出线进入下轮比赛。

如果总积分相同，还要按净胜球数排序。

德国队要保证出线，这个队至少要积……… 【】 A.8分 B.7分 C.6分 D.5分5、在△ABC 中，a 、b 、c 分别为∠A 、∠B 、∠C 的对边，若∠B ＝60°，则bc ab ac +++的值为…………【】 A. 21B.22 C. 1 D.2CPBEFA6、编号为①、②、③、④、⑤的五条赛艇，其速度依次为每小时1v 、2v 、3v 、4v 、5v 千米，且满足1v ＞2v ＞3v ＞4v ＞5v ＞0，其中，水v 为河流的水流速度（千米/小时），它们在河流中进行追逐赛规则如下：（1）五条艇在同一起跑线上，同时出发，①、②、③、④是逆流而上，⑤号艇顺流而下。

2011年四川省自贡市初中毕业生考试数学试卷和答案-推荐下载

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对全部高中资料试卷电气设备，在安装过程中以及安装结束后进行高中资料试卷调整试验；通电检查所有设备高中资料电试力卷保相护互装作置用调与试相技互术关，系电通，力1根保过据护管生高线产中0不工资仅艺料可高试以中卷解资配决料置吊试技顶卷术层要是配求指置，机不对组规电在范气进高设行中备继资进电料行保试空护卷载高问与中题带资2负料2，荷试而下卷且高总可中体保资配障料置各试时类卷，管调需路控要习试在题验最到；大位对限。设度在备内管进来路行确敷调保设整机过使组程其高1在中正资，常料要工试加况卷强下安看与全22过，22度并22工且22作尽22下可护都能1关可地于以缩管正小路常故高工障中作高资；中料对资试于料卷继试连电卷接保破管护坏口进范处行围理整，高核或中对者资定对料值某试，些卷审异弯核常扁与高度校中固对资定图料盒纸试位，卷置编工.写况保复进护杂行层设自防备动腐与处跨装理接置，地高尤线中其弯资要曲料避半试免径卷错标调误高试高等方中，案资要，料求编试技5写、卷术重电保交要气护底设设装。备备置管4高调、动线中试电作敷资高气，设料中课并技3试资件且、术卷料中拒管试试调绝路包验卷试动敷含方技作设线案术，技槽以来术、及避管系免架统不等启必多动要项方高方案中式；资，对料为整试解套卷决启突高动然中过停语程机文中。电高因气中此课资，件料电中试力管卷高壁电中薄气资、设料接备试口进卷不行保严调护等试装问工置题作调，并试合且技理进术利行，用过要管关求线运电敷行力设高保技中护术资装。料置线试做缆卷到敷技准设术确原指灵则导活：。。在对对分于于线调差盒试动处过保，程护当中装不高置同中高电资中压料资回试料路卷试交技卷叉术调时问试，题技应，术采作是用为指金调发属试电隔人机板员一进，变行需压隔要器开在组处事在理前发；掌生同握内一图部线纸故槽资障内料时，、，强设需电备要回制进路造行须厂外同家部时出电切具源断高高习中中题资资电料料源试试，卷卷线试切缆验除敷报从设告而完与采毕相用，关高要技中进术资行资料检料试查，卷和并主检且要测了保处解护理现装。场置设。备高中资料试卷布置情况与有关高中资料试卷电气系统接线等情况，然后根据规范与规程规定，制定设备调试高中资料试卷方案。

2011年四川省自贡市初中毕业生考试数学试卷和答案

2011年四川省自贡市初中毕业生学业考试数学试卷本试卷分第I卷（选择题）和第Ⅱ卷（非选择题）两部分。

第Ⅰ卷1至2页，第Ⅱ卷3至10页，满分150分，考试时间为120分钟。

考试结束后，将试卷第Ⅰ卷、试卷第Ⅱ卷和答题卡一并交回。

装订时将第Ⅱ卷单独装订。

第Ⅰ卷（选择题共36分）注意事项：（1）答第Ⅰ卷前，考生务必将自己的姓名，准考号、考试科目涂写在答题卡上。

（2）每小题选出答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦擦干净后，再选涂其它答案标号，不能答在试卷中。

一、选择题（共12个小题，每小题3分，共36分）1．-6的倒数是（）A．6 B．-6 C．16D．16-2．函数21--=xxy中，自变量x的取值范围是（）A．x≥1 B．x＞1 C．x≥1且x≠2 D．x>1且x≠23．将不等式组1010xx+≥⎧⎨->⎩的解集在数轴上表示，下列表示中正确的是（）A．B．C．D ．4．己知1x、2x是方程2630x x++=的两个实数根，则2112xxxx+的值等于（）A．-6 B．6 C．10 D．-105．由七个大小相同的正方体组成的几何体如图所示，则它的左视图是（）6．下列调查中，适宜采用全面调查（普查）方式的是（）A．对我市中学生心理健康现状的调查B．调查我市冷饮市场雪糕质量情况C．调查我国网民对日本因地震引发的福岛核事故的看法D．对我国首架大型民用飞机各零部件质量的检查7．已知⊙1O的半径为2cm，⊙2O的半径为3cm，圆心1O、2O的距离为4cm，则两圆的位置关系是（）A．相离B．相交C．内切D．外切8．已知直线l经过点A(1, 0)且与直线y＝x垂直，则直线l的解析式为（）A．y＝-x＋1 B．y＝-x-1 C．y＝x＋1 D．y＝x-19．若圆的一条弦把圆分成度数比为1∶3的两条弧，则优弧所对的圆周角为（）A．45°B．90°C．135°D．270°10．有下列函数：①y＝-3x②y＝x-1 ③y＝-1x(x>o) ④y＝x2＋2x＋1,其中函数值y随自变量x增大而增大的函数有（）A．①②B．②④C．②③D．①④11．某位同学用棱长为1的正方体积木在水平桌面上堆成如图所示的图形，然后把露出的表面都染成红色，则表面被他染成红色的面积为（）A．37 B．33 C．24 D．2112．已知A、B两个口袋中都有6个分别标有数字0、1、2、3、4、5的彩球，所有彩球除标示的数字外没有区别。

2011年四川省自贡市初中毕业生学业考试数学参考答案及评分标准

绝密★启用前 [考试时间：2011年6月12日上午9∶00－11∶00]2011年四川省自贡市初中毕业生学业考试数学参考答案及评分标准第Ⅰ卷(选择题共36分)一、选择题：(每小题3分，共36分)1．D2．C3．A4．C5．D 6．D7．B8．A9．C10．C 11．B 12．A绝密★启用前2011年四川省自贡市初中毕业生学业考试数学参考答案及评分标准第Ⅱ卷(非选择题共114分)说明：一、如果考生的解法与下面提供的参考解法不同，只要正确一律给满分，若某一步出现错误，可参照该题的评分意见进行评分。

二、评阅试卷时，不要因解答中出现错误而中断对该题的评阅，当解答中某一步出现错误，影响了后继部分，但该步以后的解答未改变这一道题的内容和难度，后来发生第二次错误前，出现错误的那一步不给分，后面部分只给应给分数之半；明显笔误，可酌情少扣；如有严重概念性错误，则不给分；在同一解答中，对发生第二次错误起的部分不给分。

三、涉及计算过程，允许合理省略非关键性步骤。

四、在几何题中，考生若使用符号“”进行推理，其每一步应得分数，可参照该题的评分意见进行评分。

二、填空题：(每小题4分，共计24分)13．3.2×10614．9-π15．相切 16．2 17．4 18．πa 121三、解答题：(每小题8分，共计32分) 19．解：原式＝4×22＋1-32- (2＋1) ···························································· (5′) ＝22＋1-32-2-1 ········································································ (7′)＝-22 ······································································································· (8′)20．解：2y 2＋y (y -1)＝(y -1)(3y -1) ·············································································· (2′)2y 2＋y 2-y ＝3y 2-4 y ＋1 ······················································································ (4′)3y ＝1，y ＝31········································································································ (6′) 经检验经y ＝31是原方程的解 ············································································· (7′)∴原方程的解为y ＝31························································································· (8′)21．(1)每个图形2分，共6分(2)有3对全等三角形 ································································································· (2′) 22．(1)56………… (2′) (2)36，36…………(6′) (3)19…………(8′) 四、解答题：(共2个题，每题10分)23．(1)证明 ∵AB ∥CD ，∠CDB ＝∠CAB∴∠CDB ＝∠CAB ＝∠ABD ＝∠DCA ································································· (1′) ∴OA ＝OB ，OC ＝OD ，从而AC ＝BD ······························································· (2′)在ACB 与BDA 中，AB ABCAB DBA AC BD =⎧⎪∠=∠⎨⎪=⎩∴ACB ≌BDA ································································································· (4′)(2)解：过点C 作CG//BD ，交AB 延长线于G ， ······························································ (5′)∵DC //AG ，CG //BD∴四边形DBGC 为平行四边形 ··········································································· (6′) ∵ACB ≌BDA∴AD ＝BC ，即梯形ABCD 为等腰梯形∴AC ＝BD ＝CG ···································································································· (8′) ∵AC ⊥BD 即AC ⊥CG ，又CF ⊥AG ∴CF ＝21AG ，又AG ＝AB ＋BG ＝m ＋n ∴CF ＝21(m ＋n ) ·································································································· (9′) 又四边形DEFC 为矩形，故其周长为2(DC ＋CF )＝2(m ＋2nm +)＝3m ＋n ······························································································································· (10′)24．解：(1)当x ＋2≥0即x ≥-2时， ···················································································· (1′)原方程化为x 2＋2(x ＋2)-4＝0，即x 2＋2x ＝0 ················································· (3′) 解得x 1＝0，x 2＝-2 ···························································································· (4′) ∵x ≥-2，故x 1＝0，x 2＝-2是原方程的解 ···················································· (5′) (2)当x ＋2<0即x <-2时 ····························································································· (6′)原方程化为x 2-2(x ＋2)-4＝0，即x 2－2x －8＝0解得x 1＝4，x 2＝－2 ···························································································· (8′) ∵x <－2，故x 1＝4，x 2＝－2均舍去． ······························································ (9′) 综上所述，原方程的解为x 1＝0，x 2＝-2． ···················································· (10′)五、解答题：(共2个题，每题12分，共24分) 25．解：(1)四边形B C 1DA 是菱形……………………(1′)理由如下： ∵∠ABC ＝120°，AB ＝BC ∴∠A ＝30° ………………………………(2′) 由题意可知∠A 1＝∠A ＝∠ABA 1＝30° ································································· (3′) ∴A 1C 1//AB ，同理AC //BC 1 ∴四边形BC 1D A 是平行四边形． ··········································································· (5′) ∵AB ＝BC 1，∴四边形BC 1DA 是菱形． ································································· (6′) (2)过点E 作EG ⊥AB 于点G ················································································ (7′) ∵∠A ＝∠ABE ＝30°，AB ＝1，∴AG ＝GB ＝21·················································· (9′) ∵cos ∠A ＝AEAG ， AE ＝A AGcos ＝12cos30︒＝33 ················································ (11′)∴DE =A D －AE ＝1-33． ······················································································· (12′) 26．解：(1)由A0) 得，OA ＝3…………………(1′)由AC ＝2 得， OC ＝22AO AC -＝1 ……(2′)∴在Rt AOC 中，sin ∠CAO ＝ACOC＝21……(3′)(2)连接OB ，过D 作DE ⊥x 轴于点E ………(5′)∵OD 切⊙B 于O ，∴OB ⊥OD ……………(6′) ∵在Rt AOC 中，sin ∠CAO ＝21， ∴∠CAO ＝∠BOA ＝30° ····················································································· (7′) ∴∠DBO ＝60°，从而∠ODB ＝30°∴OD ＝OA ＝3 ··································································································· (8′) ∵∠DOE ＝60°，DO ＝3∴OE ＝21OD ＝23，DE ＝OD ·sin 60°＝23∴点D 坐标为(－23，23)················································································· (10′)设反比例函数解析式为y ＝xk，由其图象过点D∴23，k＝··················································································· (11′)∴该反比例函数解析式为y＝4x，即y······································· (12′)六、解答题：(本题满分14分)27．解：(1)取a ＝1，得抛物线y ＝x 2＋2x ＋3，其顶点为 P 1(-1，2) ································· (1′).取a ＝-1，得抛物线y ＝-x 2＋2x ＋3，其顶点为P 2(1，4) ······························ (2′)由题意有P 1、P 2在直线上，设直线的解析式为y ＝kx ＋b ，则⎩⎨⎧=+=+-42b k b k ··········································································································· (3′) 解得13k b =⎧⎨=⎩ ∴直线的解析式为y ＝x ＋3． ········································· (4′) (2)∵抛物线y ＝ax 2＋2x ＋3的顶点P 坐标为(－a 1，3－a1)， ······································ (5′) 显然P (-a 1，3-a1)在直线y ＝x ＋3上， ····························································· (6′) 又1a-能取到除0以外的所有实数 ········································································· (8′) ∴在y ＝x ＋3上仅有一点(0，3)不是该抛物线的顶点． ········································ (9′) (3)猜想：对于抛物线y ＝ax 2＋bx ＋c (a ≠0)，将其顶点的横坐标减少a 1，纵坐标增加a1分别作为点A 的横、纵坐标；将该抛物线顶点的横、纵坐标都增加a1分别作为点B 的横、纵坐标，则A 、B 两点在抛物线y ＝ax 2＋bx ＋c (a ≠0)上． ··········································· (11′)证明如下：∵抛物线y ＝ax 2＋bx ＋c (a ≠0)的顶点坐标为(2b a-，a b ac 442-)∴点A 坐标为(22b a+-，a b ac 4442+-)点B 的坐标为(a b 22+-，a b ac 4442+-) ······································································· (12′)∵22b x a +=-时，y ＝ax 2＋bx ＋c ＝a 222⎪⎭⎫ ⎝⎛+a b ＋b ⎪⎭⎫ ⎝⎛+-a b 22＋c ＝a b ac 4442+- ∴A (－ab 22+，a b ac 4442+-)在抛物线y ＝ax 2＋bx ＋c (a ≠0) ···································· (13′)同理有B (ab 22+-，a b ac 4442+-)也在上述抛物线上，故结论成立． ···················· (14′)。

自贡市蜀光中学2011年高中自主招生考试英语试题

2011年自贡市蜀光中学自主招生考试英语试题注意事项：1、全卷满分150分，考试时间为90分钟。

2、试卷分为两部分，第Ⅰ卷为选择题100分，做在机读卡上；第Ⅱ卷为主观题50分，做在试卷上，考生只交机读卡和第Ⅱ卷。

第Ⅰ卷选择题（共100分）Ⅰ.单项选择题（每题1分，共30分）1. It’s my son’s birthday next week, and I have to do my best for that, ?A. isn’t itB. is itC. haven’t ID. don’t I2. It was twenty years______ they met again.A. whenB. sinceC. untilD. before3. , I only eat food that good.A. To be honest; tasteB. To honest; tastesC. Being honest; tastingD. To be honest; tastes4. –Have Max and Tina sold out all of the English dictionaries?--Yes, completely. ______ is left.A. NoneB. NothingC. No oneD. Neither5. –The experiment has failed.--I suggest you _____ again.A. tryingB. will tryC. would tryD. try6. The heavy snow increased the difficulty they had the mountains.A. to climbB. climbingC.climbed D. climb7. －Did the meeting end late?－No. It was not yet five I got home.A.b eforeB. thatC. untilD. when8. The letter “X” can an unknown number.A. be used to expressB. be used to expressingC. use to get expressD. used for expressing9. I’ll do whatever I can my English .A. improveB. to improveC. have improvedD. to improving10. Nancy’s birthday party is near. What clothes to attend it ?A. you expect I will wearB. you expect will I wearC. do you expect I will wearD. do you expect will I wear11. It was not until dark he foundhe thought was the correct way to solve the problem.A. that, whatB. what; thatC. when;what D. when; that12. The question at the meeting last week is very important.A. discussingB. discussedC. being discussedD. to be discussed13. This is the one of the best films that greatly us.A. is … encouragedB. has … encouragedC. are … encouragedD. have … encouraged14. You should make it a rule to leave your booksyou can find themA. whenB. whereC. thenD. which15. What a table! I’ve never seen such a thing before.It is______ it is long.A. half not as wide asB. widenot as half asC. not half as wide asD. as wideas not half16. Victor apologized for to tell me the change in the plan.A.his being not ableB. him not to be ableC. his not being ableD. him to be not able17. You things about. Look, what a mess in your room.A. always throwB. have always thrownC. are always throwingD. have always been throwing18. ______ on the top of the town , and you can see the whole city.A. StandingB. To standC. StoodD. Stand19．There were plenty of TV sets in the store, so I could hardly know which to buy.A.t o chooseB. choosingC. to be chosenD. to choose from20. The reason why he has been such a success ishe never gives up.A. becauseB. thatC. forD. why21. Just after finishing doing the homework, .A. the doorbell rang loudB. Nancy heard the doorbell ring.C. someone knocked at the doorD. the doorbell was rung22. How the big forest fire has remains to be a mystery.A. broken outB. broken upC. taken placeD. turned up23. nice, the food has a good sale.A. TasteB. TastedC. TastingD. To taste24.－Of the two apples, which one do you prefer?--_______bigger one. It’s______ most delicious one, I think.A. The; aB. The, theC. A, /D. A; the25. It is crucial that I study for it because it30% of the final exam.A. takes upB. is made ofC. is made up ofD. makes up26. The river are covered with trees is very clean.A. which banksB. of which banksC. whose the banksD. the banks of which27. I returned from America last month . I there for two years.A. stayB. stayedC. had stayedD. have stayed28. Only then ______ how much trouble had been caused..A. she realizedB. she had realizedC. had she realizedD. did she realize29. They provide homes many endangered animals and help to educateabout caring for them.A. with; the publicB. to; publicC. for; a publicD. for; the public30. The old buildings at present were built 50 years ago.A. pulled downB. are pulled downC. being pulled downD. to be pulled downⅡ. 完形填空（每题1分，共30分）AHundreds of years ago, news was ca rriedfrom place to place by people on foot or by horse. It 31 days, weeks and sometimes months for people to receive news. Now it is possible to send words and pictures around the world in seconds. Billions of people learn about news stories of their own country 32 the other countries every day, either by watching TV or reading newspapers.Newspapers have been an important part of 33 life since the 18th century. Many countries have hundreds of 34 newspapers. How do newspaper editors 35 which news stories to print? Why do they print some stories and not 36 ? What makes a good newspaper story?Firstly, it is important to report new stories. TV stations can report news much 37 than newspapers. Yet, newspapers give more about the same story. They may also 38 the story in another way, or they may print completely different stories from those on TV.Secondly, a news story has to be interesting and unusual. People don’t want to read stories about everyday life. 39 ,many stories are about some kind of danger and seem to be “bad”news. For example, newspapers 40 print stories about planes landing safely, 41 they print stories about plane accident.Another factor（因素）is also very important in many news stories. Many people are interested in news in 42 countries, but more 43 to read stories about people, places and events in their own country. 44 the stories on the front page inChinese newspapers are usually very 45 the ones in British, French and American newspapers.( )31. A. spent B. took C. cost D. paid( )32. A. or B. and C. as well D. also( )33. A. political B. law C. everyday D. meaningful( )34. A. strange B. different C. fresh D. healthy( )35. A. learn B. guess C. decide D. discuss( )36. A. another B. other C. the other D. others( )37. A. clearer B. better C. faster D. slower( )38. A. look at B. look for C. look into D. look through( )39. A. Or rather B. W hat’s more C. W hat’s worse D. As a result( )40. A. usually B. never C. ever D. sometimes( )41. A. instead B. therefore C. somehow D. anyway( )42. A. big B. small C. foreign D. dangerous( )43. A. prefer B. send C. intend D. turn( )44. A. But B.So C. Yet D. Altogether( )45. A. similar to B. the same as C. differentfrom D. equal toBThe amount of usable water has always been of great interest in the world. 46 springs and streams sometimes means control, particularly in the 47 areas like the desert. The control is possible even without possessions(拥有)of large areas of rich land. In the early days of the American west gun fights were not uncommon for the water resources, and laws had to be 48 to protect the water rights of the 49 and the water resources accordingly(按照情形).As is known to us all, there is not 50 water in all places for everyone to use as much as he likes. Deciding on the 51 of water that will be used in any particular period 52 careful planning, so that people can manage and use water more 53 .Farmers have to change their use of water 54 the water supply forecast.The 55 water supply forecast is based more on the water from the 56 than from the below. Interest is rising in the ways to increase rainfall by man－made methods, and to get water from the winter snow on mountain 57 .With special equipment, some scientists are studying the ways in which the mountain snow can be 58 ,and with the help of a repeater station(增音站),they send the gathered data(数据)to the base station. The operator at the base station can get the data at any time by 59 a button. In the near future, the forecast(预报)and use of water will probably 60 on the advanced knowledge of snow on mountains, not of water underground.( )46. A. Using B. Holding C. Owning D. Finding( )47. A. dry B. distant C. deserted D. wild( )48. A. made B. designed C. signed D. written( )49. A. winners B. settlers C. fighters D. supporters( )50. A. plentiful B. enough C. any D. much( )51. A. type B. quality C. amount D. level( )52. A. requests B. requires C. means D. suggests( )53. A. effectively B. easily C. conveniently D. actively( )54. A. leading to B. owing to C. according to D. sticking to( )55. A. correct B. further C. average D. early( )56. A. clouds B. sky C. air D. above( )57. A. rocks B. tips C. tops D. trees( )58. A. frozen B. used C. wasted D. saved( )59. A. touching B. knocking C. pressing D. turning( )60. A. insist B. lean C. depend D. callⅢ. 阅读理解(每题2.5分，共40分）AYears ago, I lived in a building in a large city. The building next door was only a few feet away from mine. There was a woman who lived there, whom I had never met, yet I could see her seated by her window each afternoon, sewing or reading.After several months had gone by, I began to notice that her window was dirty. Everything was unclear through the dirty window. I would say to myself, “I wonder why that woman doesn’t wash her window. It really looks terrible.”One bright morning I decided to clean my flat, including washing the window on the inside.Late in the afternoon when I finished the cleaning, I sat down by the window with a cup of coffee for a rest. What a surprise! Across the way, the woman sitting by her window was clearly visible. Her window was clean!Then it dawned on me. I had been criticizing her dirty window, but all the time I was watching hers through my own dirty window.That was quite an important lesson for me. How often had I looked at and criticized others through the dirty window of my heart, through my own shortcomings?Since then, whenever I wanted to judge someone, I asked myself first, “Am I looking at him through my own dirty window?”Then I try to clean the window of my own world so that I may see the world about me more clearly.61、The writer couldn’t see everything clearly through the window because .A. the woman’s window was dirtyB. the writer’s window was dirtyC. the woman lived nearbyD. the writer was near－sighted62、“It dawned on me”probably means“”.A. I began to understand itB. it cheered me upC. I knew it grew lightD. it began to get dark63、It’s clear that .A. the writer had never met the woman beforeB. the writer often washed the windowC. they both worked as cleanersD. they lived in a small town64、From the passage, we can learn .A. one shouldn’t criticize others very oftenB. one should often make his windows cleanC. one must judge himself before he judges othersD. one must look at others through his dirty windowsBHow many of us would temp(做临时工)for three years while we waited for the perfect job? Not many of us, perhaps. But Wentworth Miller, the Prison Break star, said he chose to wait even longer time until he found the right job.“Actually I think it might have been three or four years until I was lucky enough to get guest roles on TV shows,” said Miller, 34, who rose to international fame thanks to Prison Break in 2006. That kind of patience and strong will was showed in Prison Break. Miller plays engineering wizard Michael Scofield, who tries everything to break out of a Chicago prison with his brother.Miller said he didn’t seem fated(注定的)for a career in the arts, despite his passion for acting. After graduating from Princeton with an English degree, he moved at his parents’request to Los Angeles to look for a stable life. He started work in a little company that made television movies. This meant simply faxing, walking the boss’dog and going to the store for the boss’ lunch.However, Miller realized he still had questions about his choice. He decided to give up the job. But the boss said he was making a mistake and offered him a well－paid assistant position.“I finally realized that if I did that well－paid job, it would be great if I was successful, but I would always wonder a bout the acting. If I did the acting and was successful I would never wonder about that job,”he explained. He gave up and temped for many people in the entertainment industry. But now, he’s a hot star.65、Miller rose to his fame through .A. A Night in the MuseumB. PrisonBreakC. Crouching Tiger, Hidden DragonD. The Happy Big Feet66、In the little company that made television movies,Miller did the following EXCEPT .A. faxing and filingB.walking the boss’ dogC. going to the store for the boss’lunchD.playing an engineering wizard67、From what Miller said in the last paragraph, wecan see .A. acting is more important than moneyB. Miller was eager to achieve successC. the pay for the job was not high enoughD. Miller made a wrong decision68、The best title for the passage is .A. One has to temp before he gets a role to playB. Where there is will, there is a wayC. “Prison” job is just perfectD. Passion for actingCPaul received an automobile from his brother as a Christmas present. On Christmas Eve when Paul came out of his office, a boy walking around the shiny new car, admiring it. “Is this your car, sir?” he asked.Paul nodded. “My brother gave it to me for Christmas.”The boy was astounded.” You mean your brother gave it to you and it cost you nothing? Boy, Iwish…”He hesitated.Of course Paul knew what he was going to wish for. He was going to wish he had a brother like that.“I wish,”the boy went on,“that I could be a brother like that.”Paul looked at the boy in astonishment and said, “Would you like to take a ride in my automobile?”“Oh yes, I’d love that.”After a short ride, the boy said, “Sir, would you mind driving in front of my house?” Paul smiled. He thought he knew what the boy wanted. He wanted to show his neighbors that he could ride home in a big automobile. But Paul was wrong again. When Paul stopped in front of the boy’s house, the boy rushed out of the car. Then in a little while the boy came back, but he was not coming fast. He was carrying his little crippled(残废的)brother. “There she is , Buddy, just like I told you just now. His brother gave it to him for Christmas and it didn’t cost him a cent. Some day I’m going to give you one just like it and then you can see for yourself all the pretty things in the Christmas windows that I’ve been trying to tell you about.”69. Paul thought the boy wished to .A. get a car from Paul’s brotherB. get a car from the boy’s own brotherC. give a car to PaulD. give a car to the boy’s own brother70. The underlined word “astounded”in the secondparagraph probably means .A. disappointedB. annoyedC. surprisedD. worried71.The boy wanted the new car to be stopped in frontof his house because .A. he wanted to show off(炫耀)to his neighborsB. he wanted his brother to ride in this carC. he wanted Paul to visit his houseD. he wanted his brother to have a look at it72. In the sentence “There she is, Buddy, just like Itold you just now.” “she” refers to .A. Paul’s carB. BuddyC. the boy’ssister D. Paul’s sisterDAmerican Rivers reports that there are more than 250,000 rivers in the United States. Combined, they flow for more than five and one-half million kilometers.The largest and most famous river in the United States is the Mississippi. It starts near the northern border of the United States and flows through the center of the country for more than 3,700 kilometers. About 250 smaller rivers flow into the Mississippi. The mouth of the Mississippi empties into the Gulf of Mexico. At that point, more than sixteen million liters of water flows every second.However, the Missouri River is the longest river in the United States. It flows for about 4,000 kilometers. It begins in the Rocky Mountains of North America. It flows along theborders of seven states before it empties into the Mississippi River near the city of Saint Louis, Missouri.Three rivers that join together in the north central state of Montana form the Missouri River. The water is clear there. But, as it moves east and south. the Missouri River turns brown as it collects huge amounts of dirt from the land. That is why many people call the Missouri River “The Big Muddy”.Some people say the Columbia River in the northwest is the most beautiful river in America. It flows the Canadian province of British Columbia into the United States through the state of Washington. The Columbia River is the largest river that empties into the Pacific Ocean.Another famous river is the Rio Grande. It is the longest river in the state of Texas. It forms the border between Texas and Mexico.Finally, the oldest river in the United States is the New River. It begins in the Appalachian Mountains of North Carolina and flows north through parts of Virginia and West Virginia. The New River also may be the second oldest in the world. It is funny how something so old can be called new. 73．What is the subject discussed in the text?A. American riversB. American water resourcesC. American fresh waterD. American lakes 74．Why is the Missouri river called “The Big muddy”?A. Because it carries sand from the Rocky mountainB. Because t brings a lot of dirt from land into the riverC. Because the color of its water is brownD. Because it flows through the state of Montana75．The mouth of the Missouri river is .A. the Gulf of MexicoB. the AtlanticC. the MississippiD. the pacific76．Which of the following statement is TRUE? .A. The Mississippi is the longest river in the worldB. More than 16m tons of water flows into the Gulf of Mexico every secondC. The Rio Grande separates Texas and FloridaD. The origin of the Columbia River is in Canada四．句型转换 (一空一词，每空1分，共10分) 答案填在答题处。

第十八讲 2011年自主招生数学试卷

第十八讲 2011年自主招生数学试卷1.设*n N ∈，15n ≥. 集合A 、B 都是{}1,2,,I n =⋅⋅⋅的真子集，A B =∅，A B I =.证明：集合A 或B 中，必有两个不同的数，它们的和为完全平方数.2.设()2(0)f x ax bx c a =++>，方程()f x x =的两个根是1x 和2x ，且10x >，211x x a->，又10t x <<.试比较()f t 与1x 的大小.3.求函数(){}2max 1,5f x x x =+-的最小值，并求出相应的x 的值.4.已知()f x 是定义在R 上的不恒为0的函数，且对于任意的,a b R ∈，有()()()f ab af b bf a =+.(1)求()0f ，()1f 的值；(2)判定函数()f x 的奇偶性，并证明你的结论；(3)若()22f =，()2n n f u n -=()*n N ∈，求数列{}n u 的前n 项和n S .F E D CB A 5.已知关于x 的方程()()22211ax a x +=-，1a >. 证明方程的正根比1小，负根比1-大.6.设a ，b 是两个正数，且a b <. 当[],x a b ∈时，246y x x =-+的最小值为a ，最大值为b ，求a ，b 值.7.某生产队想筑一面积为1442m 的长方形围栏，围栏一边靠墙. 现有铁丝网50m ，筑成这样的围栏最少要多少铁丝网？已有的墙最多利用多长？最少利用多长？8.在正方形ABCD 中，过一个顶点D 作对角线CA 的平行线DE ，若CE CA =，且CE 交边DA 于点F . 求证：AE AF =.9.设圆满足：①截y 轴所得弦长为2；②被x 轴分成两段弧，其弧长比为3:1，在满足上述条件的圆中，求圆心到直线:20l x y -=的距离最小的圆的方程.10.设数列{}n a 的前n 项和为n S ，点*(,)()n S n n N n ∈均在函数32y x =-的图像上. (1)求数列{}n a 的通项公式；(2)设13n n n b a a +=⋅，n T 数列{}n b 的前n 项和，求最小正整数m ，使得20n m T <对所有*n N ∈都成立.11.已知函数()24f x x =-+，12()()()n n S f f f n n n=++⋅⋅⋅+， 1,2,n =⋅⋅⋅. 若不等式11n n n n a a S S ++<恒成立，求实数a 的取值范围.。

2012年自贡市蜀光中学自主招生考试

2012年自贡市蜀光中学自主招生考试理综试题（二）、物理选择题（每小题只有1个正确答案，每题3分，共24分） 11、如图，A 、B 两物体叠放在一起，用手托住，让它们靠在粗糙墙边，然后释放，使它们同时由静止开始沿竖直墙面下滑。

已知M A ＞M B ，则物体B （）A 、只受一个力B 、只受两个力C 、只受三个力D 、只受四个力12、一艘轮船正在海面上航行，如果某时刻地球对周围物体的引力减小一半，则船会（）A 、向上浮起一些B 、向下沉一些C 、即不上浮也不下沉D 、无法确定 13、原子弹与核电站的根本区别是（） A 、原子弹利用核裂变，核电站利用核聚变 B 、原子弹利用核聚变，核电站利用核裂变C 、原子弹对聚变的链式反应不加控制，核电站控制聚变的链式反应D 、原子弹对裂变的链式反应不加控制，核电站控制裂变的链式反应 14、一定质量的水体积为a ，全部结成冰后的体积变为b ；一定质量的冰体积为c ，全部化成水后的体积变为d ，则（）A 、b 比a 小101,d 比c 小91 B 、b 比a 大101，d 比c 大101C 、b 比a 大91，d 比c 小101D 、b 比a 小91，d 比c 大9115、如图所示的控制电路，要使3RR AB （3个电阻的阻值都是R ），应选（）A 、S 1、S 2闭合，S 3、S 4断开B 、S 1、S 3闭合，S 2、S 4断开C 、S 1、S 4闭合，S 2、S 3断开D 、S 2、S 3闭合，S 1、S 4断开16、如图，四根完全相同的弹簧，在弹性限度内都受到相同的拉力F 作用，则下列说法正确的是（）A 、b 图弹簧的长度比a 图的弹簧长B 、d 图中弹簧的长度最长C 、c 、d 两图中的弹簧一样长D 、条件不足，无法判断17、五个阻值均为R 的电阻连接成如图的四边形ABCD ， A 、B 、C 、D 中任意两点之间的电阻值不可能是（）A 、RB 、5R C 、2RD 、85R18、如图所示，某种“汤勺”示意图，由一细长柄AB与一半球BC 构成，且AB 与半球相切，切点为B ，已知半球的半径为R ，AB 柄的长度为L ，1:8: R L ,现用一细线系住A 点，并将细线竖直悬挂，如果不计“汤勺”的质量，则“汤勺”内水的最大高度为（）A 、R 31B 、R 43C 、R 21D 、R 32DCBACB (a)（弹簧左端固定在墙上）甲图乙图物理第Ⅱ卷（共76分）二、填空题（每小题4分，共32分）19、如图所示的简单的机械是由固定斜面和滑轮组成，若斜面长L与斜面高h的比值为2，整个机械的效率为90%，则使用该机械将重物沿斜面缓慢拉上的过程中，作用力F与重物重力G的比值为。

自贡市蜀光中学2008年高中自主招生考试数学doc

自贡市蜀光中学2008年高中自主招生考试数学试题注意事项：1、全卷满分为100分，考试时间为90分钟。

2、试卷分为二部分。

第Ⅰ卷为选择题，共20分。

答案用铅笔做在机读卡上；第Ⅱ卷为主观题，做在试卷上。

第Ⅰ卷：选择题（共20分）1、如果函数y=kx+b 的图象不经过第四象限，则函数y=kx 2+bx-1的大致图象是（）2、为给一个正方体的八个顶点染色，要求相邻的两个顶点颜色不能相同，则至少需要（）颜色A 、1种B 、2种C 、3种D 、4种3、已知114a b -=则2227a ab ba b ab---+的值等于（）A 、6B 、-6C 、215 D 、27- 4、如果不等式组x+8＜4x-1的解集是x ＞3，则m 的取值范围是（）x ＞mA 、m ≤3 、m ＜3 C 、m ≥3 D 、m ＞35、若分式212x x m-+ 无论x 取任何实数总有意义，则m 的取值范围（）A 、m ≤1B 、m ＜1C 、m ≥1D 、m ＞1 6、分式226121022x x x x ++++的最小值是（）A 、3B 、4C 、6D 、不存在7、对于实数a 、b 定义两种运算○+和*，使a ○+b=ab ，a*b=ba(a ≠0)则使（a ○+x ）.(a*x) ＜40的正整数x 的个数是（） A 、3 B 、4 C 、5 D 、68、如图，平行四边形ABCD 中，F 是AD 的中点，E 在AB 上，且AE=2BE ，FE 的延长线交CB 的延长线于G ，则S △AOF ：S △COG = A 、2：1 B 、2：5 C 、4：1 D 、4：25第8题图9、如图，抛物线y=-x 2+2(m+1)x+m+3与x 轴交于A 、B 两点且OA ：OB=3：1，则m 的值是（） A 、0 B 、53- C 、0或53- D 、5310、如图，Rt △ABC 中，∠C=90°，D 在BC 上且DB=DA ，∠DAC=60°，则tanB=（）A 、B 、2CD 、二、填空题（20分）1、等腰三角形的一个外角等于100°，则这个等腰三角形的顶角是2、用“·”和“—”按一定规律组成下面的图形，请你用n （n 是正整数）的代数式分别表示第n 图中“·”和“—”的个数，分别是，第1图第2图第3图 3、已知a 、b 、c 是实数，且13ab a b =+，14bc b c =+，15ca c a =+ 则abcab bc ca=++4、已知x 、y 、z 满足x+y=5，z 2=xy+y-9，则x+2y+3z=5、不等式组 9x －a ≥0的整数解恰为1，2，3，那么适合这个不等式组的 8x-b ＜0最大整数a= ，b=三、解答题（共60分） 1、（6分）化简求值。

自贡初三数学试题及答案

自贡初三数学试题及答案一、选择题（每题3分，共30分）1. 下列哪个选项是无理数？A. 1.5B. √2C. 0.3333D. 2.718282. 一个数的平方等于16，这个数是：A. 4B. -4C. 4或-4D. 以上都不对3. 函数y=3x+2的图象不经过哪个象限？A. 第一象限B. 第二象限C. 第三象限D. 第四象限4. 一个三角形的两边长分别为3和4，第三边长可能是：A. 1B. 7C. 1或7D. 以上都不对5. 一个圆的直径是10厘米，那么它的半径是：A. 5厘米B. 10厘米C. 20厘米D. 15厘米6. 一个数的绝对值是5，那么这个数可能是：A. 5B. -5C. 5或-5D. 以上都不对7. 一个数的立方等于-27，这个数是：A. 3B. -3C. 3或-3D. 以上都不对8. 一个数的倒数是1/2，那么这个数是：A. 2B. -2C. 2或-2D. 以上都不对9. 如果一个角是直角的一半，那么这个角是：A. 45°B. 90°C. 180°D. 360°10. 一个等腰三角形的底角是45°，那么顶角是：A. 45°B. 90°C. 135°D. 180°二、填空题（每题4分，共20分）1. 一个数的平方根是2，那么这个数是______。

2. 如果一个数的相反数是-5，那么这个数是______。

3. 一个数的绝对值是8，那么这个数可能是______或______。

4. 一个圆的周长是31.4厘米，那么它的直径是______厘米。

5. 一个等边三角形的每个内角是______度。

三、解答题（每题10分，共50分）1. 解方程：2x + 5 = 15。

2. 已知一个直角三角形的两条直角边长分别为3和4，求斜边长。

3. 一个数乘以它的倒数等于1，求这个数。

4. 一个圆的半径增加2厘米，那么它的面积增加了多少？5. 一个等腰三角形的顶角是100°，求底角的度数。

自贡市蜀光中学2007年高中自主招生考试

自贡市蜀光中学2008年高中保送生考试英语试题注意事项：1、全卷满分100分，考试时间为90分钟。

2、试卷分为两部分，第Ⅰ卷为选择题75分，做在机读卡上；第Ⅱ卷为综合语言知识题25分，做在试卷上，考生只交机读卡和第二卷。

第Ⅰ卷（共75分）一、单项选择题：（共15分；每小题1分，满分15分）从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。

1. old lady with white hair spoke French wellat meeting.A. An; an; theB. The; the; aC. The;不填; anD. The;不填;the2. I prefer at home to outside.A. staying; playingB. to stay; playC. staying; playD. to stay; playing3. She began to something but stopped when she heard theteacher .A. tell; sayingB. speak; talkingC. say; speakingD. talk; telling4. Most of the people to the party were my former schoolmates.A. invitedB. invitingC. were invitedD. have been invited5. Can you make sure the gold ring?A. where Alice had putB. where had Alice putC. where Alice has putD. where has Alice put6. we know, China is a developing country.A. ThatB. WhenC. AsD. Like7. All is needed is time.A. the thingB. thatC. whatD. which8. do you think will teach us maths next term?A. WhomB. WhoC. What d. That9. If you , you would catch the bus.A. hurryB. are hurryC. did hurryD. hurried10. Did you remember the days they spent in Sydney!A. whereB. whenC. thatD. what11. We worked late into the night, for the birthday party.A. prepareB. preparingC. prepared d. were preparing12. E-mail, as well as telephones, an important part in dailycommunication.A. is playingB. have playedC. are playingD. play13. You to the meeting this afternoon if you have somethingimportant to do.A. needn’t to comeB. don’t need comeC. don’t need comingD. needn’t come14. The mountain is that one.A. two times as longer asB. twice the height ofC. three times higher ofD. twice high than15. Miss Zhao often helps us we are in trouble.A. whateverB. howeverC. wheneverD. whoever二、完形填空（共20分,每空1分）One day a police officer managed to get some fresh mushrooms(蘑菇). He was so 16 what he had bought that he offered to 17 the mushrooms with his brother officers. When their breakfast arrived 18 , each officer found some mushrooms on his plate.“Let the dog 19 a piece first,”suggested one careful office who was afraid that the mushroom 20 be poisonous(有毒的).The dog seemed to enjoy his mushroom, and the officers then began to eat their meal, saying that the mushrooms had a very strange 21 quite pleasant taste.An hour 22 , however, they were all shocked 23 the gardener rushed in and said seriously that the dog was dead. At once the officers jumped into their cars and rushed to the nearest hospital. They had a very 24 time 25 the mushrooms that 26 in their stomachs.When they 27 to the police station, they sat down and started to discuss the mushroom poisoning. Each man explained the pains(痛苦) that 28 had felt and they agreed that 29 had grown 30 on the way to the hospital. The gardener was called to tell the way 31 the poor dog had died. “Did it feel pain before death?” asked one of the officers,32 very pleased that he had escaped a 33 death himself. “No,”the gardener looked rather 34 . “It was killed the moment a car 35 it.”16. A. sure of B. careless about C. pleased with D. disappointed17. A. share B. grow C. wash D. cook18. A. tomorrow B. the next day C. the day after D. next day19. A. check B. smell C. try D. examine20. A. must B. should C. might D. may21. A. besides B. but C. and D. or22. A. later B. after C. past D. over23. A. until B. while C. before D. when24. A. hard B. busy C. exciting D. unforgettable25. A. get rid B.getting rid of C.to get rid of D. get rid of26. A. remaining B. left C. remained D. leaving27. A. hurried B. drove C. went D. returned28. A. nobody B. anybody C. somebody D. everybody29. A. this B. these C. it D. they30. A. better B. worse C. well D. good31. A. what B. in that C. which D. in which32. A. to feel B. feeling C. felt D. having felt33. A. strange B. painful C. peaceful D. natural34. A. afraid B. surprising C. happy D. surprised35. A. struck B. knocked C. hit D. beat三、阅读理解：（共40分，每空2分））AMany children use the Internet to get useful knowledge and information, and to relax in their free time. But some of them are not using it in a good way. Here are some rules to make sure you are safe and have fun on the Internet.·Make rules for Internet use with your parents. For example, when you can go online, for how long and what activities you can do online.·Don’t give your password(密码)to anyone else, and never give out the following information: your real name, home address, age, school, phone number or other personal information.·Check with your parents before giving out a credit card number.·Never send a photo of yourself to someone in email unless your parents say it’s OK.·Check with your parents before going into a chat room. Different chat rooms have different rules and attract different kinds of people. You and your parents will want to make sure it’s a right place for you.·Never agree to meet someone you met on the Internet without your parent’s permission. Never meet anyone you met online alone.·Always remember that people online may not be who they say they are. Treat everyone online as if they were strangers.·If something you see or read online makes you uncomfortable, leave the site. Tell a parent or teacher right away.·Treat other people as you’d like to be treated. Never use bad language.·Remember—not everything you read on the Internet is true.36. The writer tells children to .A. send their own photos to himB. make rules for Internet use with parentsC. believe everything they read on the InternetD. give out their personal information37. It is good for children to on the Internet.A. give password to othersB. get useful knowledge and informationC. give out a credit card numberD. go into a chat room as they’d like to38. What shouldn’t be done when you are on line? .A. Using bad languageB. Sending message and emailsC. Leaving the site if you feel uncomfortableD. Treating everyone online as strangers39. If your parents don't agree, never .A. read anything on the InternetB. relax in your free timeC. have a face-to-face meeting with anyone you met onlineD. treat other people as you’d like to be treated40. The best title for this passage is .A. How to use computersB. Surfing on the InternetC. Information on the InternetD. Internet safety rulesA. 564839B. 445987C. 876333D. 22330042. offers help in finding a roommate.A. Banbury HouseB. Three SeasonsC. Sturitin HostelD. First Shop43. If you live in Banbury House, you have to .A. do cooking by yourselfB. do cleaning by yourselfC. travel by trainD. take a school bus44. The articles above are mainly for .A. family accommodationB. student accommodationC. travel accommodationD. cheap accommodation45. The four texts above are most probably .A. lettersB. noticesC. invitationsD. advertisementsCIf you live in the country in northern Europe, you’ll share your garden with all sorts of birds, animals and insects. The swallows(燕子)will travel 8,000 kilometres or more to southern Africa. They’ll come back in the spring.In warm countries, where the winters are not very long or very cold, hibernation(冬眠)is not necessary. And in very cold parts of the world, like the far north of Russia, not many animals hibernate(冬眠); the ground is so hard that they cannot make a deep hole to spend the winter in. But animals in a large part of northern hemisphere(北半球)spend every winter fast asleep.A bear is a half-hibernating animal. A she-bear chooses her wintering place much more carefully because she is likely to have cubs(小熊)in it. It is nearly a cave, and she covers the floor with grass or leaves to be sure of extra warmth. She hides as much food as possible in it. She sleeps until January, when the cubs are born. Even then she doesn’t try to come out of hibernation. The cubs stay with her, drinking her milk and growing bigger and stronger week by week until spring arrives. To keep milk supply going, the she-bear eats the food from her secret stores.46. The swallows travel a very long distance from the north to the south,because .A. they like travellingB. they want to find their food thereC. they want to visit their friends thereD. it is warm in the south47. In northern Europe people who live in the country allkinds of birds, animals and insects.A. hateB. live onC. get on well withD. like eating48. In warm places, animals .A. need hibernatingB. don’t need hibernatingC. never go outD. do much exercise49. According to the passage, a she-bear has her babies in .A. springB. winterC. summerD. autumn50. In the last sentence, “going” means “”.A. movingB. passingC. lastingD. becomingDSomething interesting happened during the last Christmas shopping hour in London A poor man, who, though no fault of his own, found himself locked in a big store late on Christmas Eve. No doubt the store was crowded with people buying presents and the assistants were dead beat and wanted to go home. It seemed that all the necessary checks were made before the store was locked, and the assistants went home to enjoy the three-day holiday.However, the man was still in the store. When he realized that, he decided to make the best use of it. In the store, of course, there was plenty of food, drink and bedding. There must have been radios and television sets, which no one could tell whether the man had ever used. When the store reopened, the man was discovered in bed with a large number of empty bottles beside him. He seemed to have been very happy. Everyone else was enjoying Christmas, so he saw no reason why he should not do the same. Happily enough, he let the police take him away. Perhaps he had a better Christmas than usual. It was reported that the man would have to stay in prison for seven days. It seemed, however, the judge was not going to do anything for the store, as he said that the store had become better known through the story in the newspapers and on television.51. The poor man went into the big store in order to .A. buy some drinks for ChristmasB. go around the store and take a lookC. spend the Christmas EveD. help the assistants sell goods52. According to the context, the underlined part “dead beat” in thepassage means .A. very carelessB. not happyC. too hungryD. very tired53. When the man found he was locked in the store, he .A. became very frightenedB. managed to find the way outC. decided to enjoy his stay in the storeD. started to do something good for the store54. At last people found out .A. the man’s story made the store known to many peopleB. the man had destroyed some of the TV sets and radiosC. it was not necessary to put the man into prisonD. it was not right for the judge not to do anything for the store55. Why did the author write the article? .A. To tell an interesting experience on Christmas EveB. To complain about the problems with ChristmasC. To describe the life of a poor manD. To explain the reason why the store became famous第二卷答题卷(25分) 四、句型转换：（共5分） 1.I didn ’t know where to go the next day. （改为复合句） I didn ’t know I go the next day. 2. His father saw him stand at the door （改为被动语态） He seen stand at the door. 3. He joined the army three years ago.（同义句） is three years he joined the army. 4. I have never seen Alice. He hasn ’t, either. （同义句） I have never seen Alice, he. 5. Unless you work hard, you won ’t succeed.（同义句） hard work, you will not be . 五、根据短文内容及首字母提示完成短文中所缺的单词，使短文意思连贯、通顺。

自贡市2011年初中毕业生升学考试数学题

一、选择题1.A.2.A .3.C4.C5.A6.B二、填空题7.4 8. 158 9.2 10.三、解答题 11.(1)27 (2)81-=x 542=x12. 解：（1）证明：连接FO 并延长交⊙O 于Q ，连接DQ 。

∵FQ 是⊙O 直径，∴∠FDQ＝90°。

∴∠QFD ＋∠Q＝90°。

∵CD⊥AB，∴∠P＋∠C＝90°。

∵∠Q＝∠C，∴∠QFD＝∠P。

∵∠FOE＝∠POF，∴△FOE∽△POF。

∴OE OF OF OP=。

∴OE·OP＝OF 2＝r 2。

（2）当点E 在AB （或BA ）的延长线上时，（1）中的结论成立。

理由如下：依题意画出图形（如图），连接FO 并延长交⊙O 于M ，连接CM 。

∵FM 是⊙O 直径，∴∠FCM＝90°。

∴∠M＋∠CFM＝90°。

∵CD⊥AB，∴∠E＋∠D＝90°。

∵∠M＝∠D，∴∠CFM＝∠E。

∵∠POF＝∠FOE，∴△POF∽△FOE。

∴OE OF OF OP=，∴OE.OP＝OF 2＝r 2。

13. 解：（1）12231111355151331535 (277)a a a a ⨯⨯===⨯⨯'=== （2）∵123111,,133557a a a ===⨯⨯⨯∴1(21)(21)n a n n =-+ ∴2011.......5(2201)(2201)1599a '==⨯-⨯⨯+ （3） 1232011...1111 (13355740214023)111111(1...)23354021402311(1)2402314022240232011............................(8)4023a a a a ++++=++++⨯⨯⨯⨯=-+-++-=-=⨯'= 14. 解：（1）把y ＝4代入y ＝－43x ＋163，得x ＝1。

自贡市蜀光中学自主招生考试卷数学答案

p2012年自贡市蜀光中学自主招生考试数学答案一、选择题：（每小题4分，共48分）1—6 BBCBCA 7—12 BDDBAD 二、填空题：（每小题5分，共30分）13、（2）（4）（5） 14、8 15、213，4- 16、21 17、11 18、161 三、解答题：（每题12分，共72分） 19、（1）解：原方程化为)4)(1(52)3)(2(1)2)(1(1+++=+++++x x x x x x x （2分）411131212111+++=+-+++-+x x x x x x （4分） ∴－.4131+=+x x 解得27-=x . （5分）经检验27-=x 是原方程的根.（6分）（2）解：因324=+-x ax得4－a x ＝3x ＋6，即(3＋a)x ＝－2. ① （1分）当a ＝－3时，方程①无解，∴原方程无解. （3分）当a ≠－3时，.32a x +-=若,232-=+-x即a ＝－2时，原方程无解.（5分）故当a ＝－2或a ＝－3时，原方程无解. （6分）20、解：连结AE ，其与BD 的交点就是所示的点P. （2分）∵点A 、C 关于BD 轴对称，∴PA ＝PC.∴点A 、P 、E 在一条直线上时， PC ＋PE 的值最小.（4分）连结DE.由已知得△ABD 和△BCD 都是靠边三角形. 又E 是BC 的中点，∴∠DEC ＝90°，∠CDE ＝30°，∠ADE ＝90°（8分）在Rt △DCE 中，DE 2＝DC 2－CE 2＝42－22＝12，在Rt △ADE 中，AE 2＝AD 2＋DE 2＝42＋12＝28，∴AE ＝27cm.即PC ＋PE 的最小值为为27cm.（12分）21、解：原式4)()1()1()1(2222-=----++-=a b a b a b ，即2222)(4)1(4])()1[(2a b a b +--=+-，整理得a b 2)1(62=-，即a b =-2)1(3 （4分）由于1=+b a ，∴)1)(1(1)1(32b b b b +-=-=-，整理得0)133)(1(=----b b b ，∴01=-b 或042=-b . （8分）当01=-b ，即1=b 时，0=a ，不合题意。

蜀光中学八年级下数学半期试题

蜀光中学初二下学期半期考试数学试题（时间120分钟，共150分）一、选择题（每小题3分，共36分）请将唯一正确答案的代号填在题后的表格中，填在其他地方不计分。

1、下列计算中，正确的是A. 633a a a =+B. 532)(a a =C. 842a a a =⋅D. a a a =÷342、若分式112--x x 的值为0，则x 的值为A. 1B. -1C. ±1D.23、对于反比例函数xk y 2=(0≠k )，下列说法不正确．．．的是 A. 它的图象分布在第一、三象限 B. 点（k ，k ）在它的图象上 C. 它的图象是中心对称图形 D. y 随x 的增大而增大4、用科学记数法表示-0.0000064记为A.-64×10-7B.-0.64×10-4C.-6.4×10-6D.-640×10-85、在直角坐标中，点A ，点B 的坐标分别为（－4，0），（0，3），则AB 的长为A.2B.2.4C.5D.6 6、已知反比例函数y =xa(a ≠0)的图象，在每一象限内，y 的值随x 值的增大而减少，则一次函数y =-a x +a 的图象不经过．．．Ａ．第一象限Ｂ．第二象限Ｃ．第三象限Ｄ．第四象限7、计算：a a --11)1(的结果为 1.1.1.1.------a D aC a B aA8、若关于x 方程)2(423-+=-x x x a x 有增根，则增根只可能是 A 、0 B 、2 C 、0或2 D 、19、直线l 1：y ＝k 1x ＋b 与直线l 2：y ＝k 2x 在同一平面直角坐标系中的图象如图所示，则关于x 的不等式k 1x ＋b ＞k 2x 的解为A 、x ＞－1B 、x ＜－1C 、x ＜－2D 、无法确定10、某市需要铺设一条长为4000米的管道，为减少施工影响，实际施工时×××。

四川省自贡市市蜀光中学高三数学文模拟试题含解析

四川省自贡市市蜀光中学高三数学文模拟试题含解析一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，只有是一个符合题目要求的1. 在△ABC中，，，，则△ABC的面积为（）A. 1B. 2C.D.参考答案：C【分析】根据余弦定理可以求出,再利用同角的三角函数关系求出，最后用三角形面积公式求出面积. 【详解】由余弦定理可知，因为，所以，因此，故本题选C.【点睛】本题考查了余弦定理、同角三角函数关系、三角形面积公式.重点考查了运算能力.2. 某程序框图如图所示，该程序运行后输出的值是()A. B.C. D.参考答案：A略3. 如图所示，网格纸上小正方形的边长为l，下图画出的是某几何体的三视图，则该几何体的体积为( )A.12B.18C.24D.36参考答案：B4. “勾股圆方图”是我国古代数学家赵爽设计的一幅用来证明勾股定理的图案，如图所示在“勾股圆方图”中，四个相同的直角三角形与中间的小正方形拼成一个大正方形。

若直角三角形中较小的锐角满足，则从图中随机取一点，则此点落在阴影部分的概率是A. B. C. D.参考答案：D5. 若O为△ABC所在平面内一点，且满足，则△ABC的形状为A、正三角形B、直角三角形C、等腰三角形D、以上都不对参考答案：答案：C6. “直线与抛物线相切”是“直线与抛物线只有一个公共点”的（）A．充分非必要条件B．必要非充分条件C．充要条件D．非充分非必要条件参考答案：A【考点】必要条件、充分条件与充要条件的判断．【专题】简易逻辑．【分析】根据充分必要条件的定义，结合直线和抛物线的位置关系进行判断即可．【解答】解：”直线与抛物线相切”能推出“直线与抛物线只有一个公共点”，是充分条件，而“直线与抛物线只有一个公共点”推不出”直线与抛物线相切”，不是必要条件，如图示：，直线和抛物线的对称轴平行时只有1个交点，但不相切，故选：A．【点评】本题考查了充分必要条件，考查直线和抛物线的关系，是一道基础题．7. 将函数的图象上各点的横坐标伸长到原来的2倍，再向左平移个单位，所得图象的一条对称轴的方程是A． B． C. D．参考答案：C，，，.8. 若以F1（﹣3，0），F2（3，0）为焦点的双曲线与直线y=x﹣1有公共点，则该双曲线的离心率的最小值为（）A．B．C．D．参考答案：B【考点】抛物线的简单性质．【专题】计算题；方程思想；综合法；圆锥曲线的定义、性质与方程．【分析】根据e=，可得a越大e越小，而双曲线与直线相切时，a最大，将直线方程与双曲线方程联立，即可求得结论．【解答】解：由题意，c=3，∴e=，∴a越大e越小，而双曲线与直线相切时，a最大设双曲线为=1，把直线y=x﹣1代入，化简整理可得（9﹣2m）x2+2mx﹣10m+m2=0由△=0，解得：m=5，于是a=，e==．故选：B．【点评】本题考查直线与双曲线的位置关系，考查双曲线的几何性质，解题的关键是确定双曲线与直线相切时a最大．9. 已知全集是实数集R，={ },N={1,2,3,4},则（ R M）N等于（）A．{4} B.{3, 4} C.{2, 3, 4} D.{1, 2, 3, 4}参考答案：B10. 曲线在点(1,1)处的切线的倾斜角为（）A. 30°B. 45°C. 60°D. 135°参考答案：D【分析】求出函数的导数，在处的导数就是切线的斜率，然后求出倾斜角即可．【详解】解：可得，，，设切线的倾斜角为，可得故选D．【点睛】本题考查直线的倾斜角，利用导数研究曲线上某点切线方程，考查计算能力，是基础题．二、填空题:本大题共7小题,每小题4分,共28分11. 已知点（x，y）满足约束条件则的最小值是。

四川省自贡市市蜀光中学高一数学理上学期期末试卷含解析

四川省自贡市市蜀光中学高一数学理上学期期末试卷含解析一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，只有是一个符合题目要求的1. 设变量满足约束条件，则的最大值为（）A． 2 B． C．D．4参考答案：B略2. 计算的结果等于（）A．B．C．D．参考答案：A3. 今有一组实验数据如下表所示：则最佳体现这些数据关系的函数模型是（）A． B． C． D．参考答案：C 4. 已知各顶点都在一个球面上的正四棱柱（其底面是正方形，且侧棱垂直于底面）高为，体积为，则这个球的表面积是（）Ａ.Ｂ.Ｃ.Ｄ.参考答案：C略5. 函数的零点个数是（）A. 1B. 2C. 3D. 4参考答案：B【分析】先求函数的定义域，然后解方程f（x）＝0，即可解得函数零点的个数．【详解】要使函数有意义，则x2﹣4≥0，即x2≥4，x≥2或x≤﹣2．由f（x）＝0得x2﹣4＝0或x2﹣1＝0（不成立舍去）．即x＝2或x＝﹣2，∴函数的零点个数为2个．故选：B．【点睛】本题主要考查函数零点的求法和判断，先求函数的定义域是解决本题的关键，属于易错题．6. 下列函数图象中，能用二分法求零点的是（）A．B．C．D．参考答案：C【考点】函数的零点；函数的图象．【专题】函数的性质及应用．【分析】根据函数只有满足在零点两侧的函数值异号时，才可用二分法求函数f（x）的零点，结合所给的图象可得结论．【解答】解：由函数图象可得，A中的函数没有零点，故不能用二分法求零点，故排除A．B 和D中的函数有零点，但函数在零点附近两侧的符号相同，故不能用二分法求零点，故排除．只有C中的函数存在零点且函数在零点附近两侧的符号相反，故能用二分法求函数的零点，故选C．【点评】本题主要考查函数的零点的定义，用二分法求函数的零点的方法，属于基础题．7. 图l是某县参加2011年高考的学生身高条形统计图，从左到右的各条形表示的学生人数依次记为、、…、(如表示身高(单位：)在[150，155)内的学生人数)．图2是统计图l中身高在一定范围内学生人数的一个算法流程图．现要统计身高在160～180(含160，不含180)的学生人数，那么在流程图中的判断框内应填写的条件是（）A．B． C． D．参考答案：B略8. 下列各组函数中是同一函数的是( )A．与y=x B．与y=x C．y=x0与y=1 D．与y=x参考答案：D【考点】判断两个函数是否为同一函数．【专题】函数思想；定义法；函数的性质及应用．【分析】分别判断两个函数的定义域和对应法则是否一致，否则不是同一函数．【解答】解：A.=x，函数的定义域为（﹣∞，0）∪（0，+∞），两个函数的定义域不相同，不是同一函数．B.=|x|，两个函数的对应法则不相同，不是同一函数．C．y=x0=1，函数的定义域为（﹣∞，0）∪（0，+∞），两个函数的定义域不相同，不是同一函数．D.=x，两个函数的定义域和对应法则相同是同一函数，故选：D【点评】本题主要考查判断两个函数是否为同一函数，判断的标准就是判断两个函数的定义域和对应法则是否一致，否则不是同一函数．9. 对于用“斜二侧画法”画平面图形的直观图，下列说法正确的是（）A．等腰三角形的直观图仍是等腰三角形B．梯形的直观图可能不是梯形C．正方形的直观图为平行四边形D．正三角形的直观图一定是等腰三角形参考答案：C【考点】LD：斜二测法画直观图．【分析】根据斜二侧画法画水平放置的平面图形时的画法原则，可得：等腰三角形的直观图不再是等腰三角形，梯形的直观图还是梯形，正方形的直观图是平行四边形，正三角形的直观图是一个钝角三角形，进而得到答案．【解答】解：根据斜二侧画法画水平放置的平面图形时的画法原则，可得：等腰三角形的直观图不再是等腰三角形，梯形的直观图还是梯形，正方形的直观图是平行四边形，正三角形的直观图是一个钝角三角形，故选：C【点评】本题考查的知识点是斜二侧画法，熟练掌握斜二侧画法的作图步骤及实质是解答的关键．10. 设等差数列的前项和为，，则等于A．10 B．12 C．15 D．30参考答案：C二、填空题:本大题共7小题,每小题4分,共28分11. 若，则___________,_____________；参考答案：12. 已知，函数的最小值为__________．参考答案：5【分析】变形后利用基本不等式可得最小值。

四川省自贡市市蜀光中学高三数学文月考试题含解析

四川省自贡市市蜀光中学高三数学文月考试题含解析一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，只有是一个符合题目要求的1. 设函数，若不等式有解，则实数的最小值为( )A. B. C.D.参考答案：D2. 设i为虚数单位，复数等于A. B. C. D.参考答案：A略3. 已知满足,记目标函数的最大值为7，最小值为1，则（）A．2 B．1C．-1 D．-2参考答案：D考点：简单线性规划.【易错点睛】先根据红豆条件画出可行域，再利用几何意义求最值，表示直线在轴上的截距，只需求出可行域在轴上的截距最大最小值时所在的顶点即可.本题主要考查了简单的线性规划，以及利用几何意义求最值的方法，属于基础题.本题的难点在于约束条件中含有参数，如何利用目标函数的最值来确定最值.4. 阅读如图的程序框图，运行相应的程序，输出的结果为（）A．-B．C．3 D．参考答案：C考点：程序框图．专题：图表型；算法和程序框图．分析：根据所给数值执行循环语句，然后判定是否满足判断框中的条件，一旦满足条件就退出循环，输出结果．解答：解：模拟执行程序框图，可得i=0，A=3i=1，A=不满足条件i＞2015，i=2，A=不满足条件i＞2015，i=3，A=3不满足条件i＞2015，i=4，A=…不满足条件i＞2015，i=2015=3×671+2，A=不满足条件i＞2015，i=2016=3×672，A=3满足条件i＞2015，退出循环，输出A的值为3．故选：C．点评：本题主要考查了循环结构，是直到型循环，先执行循环，直到满足条件退出循环，属于基础题5. 已知数列{a n}满足：，则( )A. 16B. 25C. 28D. 33参考答案：C【分析】依次递推求出得解.【详解】n=1时，，n=2时，，n=3时，，n=4时，，n=5时，.故选：C【点睛】本题主要考查递推公式的应用，意在考查学生对这些知识的理解掌握水平.6. 设集合，，则=（）A． B． C．D．参考答案：B略7. “”是“函数在区间上为增函数”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参考答案：A8. 函数的零点所在的大致区间是A. B.C. D.参考答案：B9. 设a大于0，b大于0.A.若2a+2a=2b+3b，则a＞bB.若2a+2a=2b+3b，则a＞bC.若2a-2a=2b-3b，则a＞bD.若2a-2a=a b-3b，则a＜b参考答案：A若，必有．构造函数：，则恒成立，故有函数在x＞0上单调递增，即a＞b成立．其余选项用同样方法排除．故选A10. 复数，其中i为虚数单位，则的虚部为（）A. －1B. 1C. iD.－i参考答案：A【分析】根据复数共轭的概念得到，再由复数的除法运算得到结果即可.【详解】虚部为-1，故选A.【点睛】本题考查了复数的运算法则、复数的共轭复数等，考查了推理能力与计算能力，属于基础题,复数问题高考必考，常见考点有：点坐标和复数的对应关系，点的象限和复数的对应关系，复数的加减乘除运算，复数的模长的计算.二、填空题:本大题共7小题,每小题4分,共28分11. 已知下列命题：1函数的单调增区间是.2要得到函数的图象，需把函数的图象上所有点向左平行移动个单位长度.3已知函数，当时，函数的最小值为．4在[0,1]上至少出现了100次最小值，则.其中正确命题的序号是_参考答案：②③④12. 已知函数，若，则不等式的解集为__________，若存在实数b，使函数有两个零点，则a的取值范围是__________．参考答案：【分析】将a=1代入原函数，可得的解析式，可得不等式的解集；分a的情况进行讨论，可得有两个零点时候，a的取值范围.【详解】解：由题意得：，当a=1时，，可得：（1）当时，，可得；（2）当时，，可得，综合可得的解集为；由，只有一个零点时，，可得，当时，此时，只有一个零点，当时，有两个零点，同理，当时，此时，只有一个零点，当时，有两个零点，故可得的取值范围是【点睛】本题主要考查分段函数与函数的性质，综合性强，注意分类讨论思想的运用.13. 已知，且是第三象限的角，则的值为．参考答案：由题意得，根据三角函数的平方关系，所以，故答案为：14. 已知圆x2＋y2－4x－9＝0与y轴的两个交点A，B都在某双曲线上，且A，B两点恰好将此双曲线的焦距三等分，则此双曲线的标准方程为________．参考答案：＝115. 已知平面向量，的夹角为60°，，，则参考答案：16. 已知奇函数f（x）是定义在R上的连续函数，满足f（2）=，且f（x）在（0，+∞）上的导函数f'（x）＜x2，则不等式f（x）＞的解集为．参考答案：（﹣∞，2）【考点】利用导数研究函数的单调性；导数的运算．【分析】构造函数F （x ）=f（x）﹣x3+1，则F（x）为减函数，且F（0）=0，从而得出f（x）＜x3﹣1即F（x）＜0的解集．【解答】解：设F（x）=f（x）﹣x3+1，∵f'（x）＜x2∴F′（x）=f′（x）﹣x2＜0，∴F（x）在（0，+∞）上递减，又F（2）=f（2）﹣=0，故不等式的解集是：（﹣∞，2），故答案为：（﹣∞，2）．【点评】本题考查了导数与函数单调性的关系，奇函数的性质，属于中档题．17. 若抛物线上一点到其焦点的距离为3，延长交抛物线于，若为坐标原点，则= .参考答案：三、解答题：本大题共5小题，共72分。

四川省自贡市市蜀光中学高三数学理期末试卷含解析

四川省自贡市市蜀光中学高三数学理期末试卷含解析一、选择题：本大题共10小题，每小题5分，共50分。

在每小题给出的四个选项中，只有是一个符合题目要求的1. 下列函数中既是奇函数，又在区间[－1,1]上单调递减的是( )A．f(x)＝sinx B．f(x)＝－|x＋1| C．f(x)＝ (a x＋a－x) D．f(x)＝ln参考答案：【知识点】函数的奇偶性与单调性. B3 B4【答案解析】D 解析：显然选项A，B不正确，而C中函数是偶函数，所以C不正确，所以选D.【思路点拨】根据函数的图像排除A，B选项，根据奇偶性定义排除C,从而选D.2. 已知数列的前n项和为，=n2+n，数列的前n项和=则n=A. 1B. 8C. 9D. 10参考答案：C略3. 已知数列，，，成等差数列,，,,,成等比数列，则的值为或参考答案：A略4. 已知向量，，若m+n与共线，则等于( )(A) (B)(C)(D)参考答案：A5. 已知函数f(x)＝(x2－a)ln x，曲线y＝f(x)上存在两个不同点，使得曲线在这两点处的切线都与y轴垂直，则实数a的取值范围是A.(－，0)B.(－1，0)C.(－，＋∞)D.(－1，＋∞)参考答案：A6. 已知，则“”是“”的（）A．充分必要条件B．充分不必要条件C．必要不充分条件D．既不充分也不必要条件参考答案：A7. 将函数的图象向左平移个单位长度后得到函数的图象如图所示，则函数的解析式是（）A. B.C. D.参考答案：A根据函数g （x ）的图象知， =﹣=，∴T=π，∴ω==2；由五点法画图知，x=时，ωx+φ=2×+φ=，解得φ=；∴g （x ）=sin （2x+）；又f （x ）向左平移个单位后得到函数g （x ）的图象，∴f （x ）=sin[2（x ﹣）+]=sin （2x ﹣）．故选：A ．8. 执行如图所示的程序框图，则输出的i 的值是（）A ．3B ．4C ．5D ．6参考答案：B【考点】程序框图．【分析】由已知中的程序框图可知：该程序的功能是利用循环结构计算并输出变量i 的值，模拟程序的运行过程，分析循环中各变量值的变化情况，可得答案．【解答】解：第一次执行循环体后，S=2，不满足退出循环的条件，i=2；再次执行循环体后，S=6，不满足退出循环的条件，i=3；再次执行循环体后，S=14，不满足退出循环的条件，i=4；再次执行循环体后，S=30，满足退出循环的条件，故输出的i 值为4，故选：B ．9. 根据下列算法语句, 当输入x 为60时,输出y 的值为(A) 25 (B) 30 (C) 31 (D) 61 参考答案：C故选择C10. 已知函数f(x)是定义在R 上的奇函数，当x≥0时，.若,f(x-1)≤f(x),则实数a 的取值范围为A ．[]B ．[]C ．[]D ．[]参考答案：B二、填空题:本大题共7小题,每小题4分,共28分11. 已知，直线，，则直线的概率为．参考答案：由已知，若直线与直线垂直，则，使直线的，故直线的概率12. 已知命题p：?x∈[1，2]，x2﹣a≥0；命题q：?x∈R，x2+2ax+2﹣a=0，若命题“p且q”是真命题，则实数a的取值范围为．参考答案：a≤﹣2或a=1考点：命题的真假判断与应用．专题：计算题．分析：根据命题“p且q”是真命题，得到两个命题都是真命题，当两个命题都是真命题时，第一个命题是一个恒成立问题，分离参数，根据x的范围，做出a的范围，第二个命题是一元二次方程有解问题，利用判别式得到结果．解答：解：∵“p且q”是真命题，∴命题p、q均为真命题，由于?x∈[1，2]，x2﹣a≥0，∴a≤1；又因为?x∈R，x2+2ax+2﹣a=0，∴△=4a2+4a﹣8≥0，即（a﹣1）（a+2）≥0，∴a≤﹣2或a≥1，综上可知，a≤﹣2或a=1．故答案为：a≤﹣2或a=1点评：本题考查命题真假的判断与应用，是一个综合题，这种题目一般是以解答题目出现，是一个不错的题目，但解起来容易出错．13. 在直角梯形中，，点是梯形内或边界上的一个动点，点是边的中点，则的最大值是参考答案：6略14.关于x的不等式的解集为R，则实数a 的取值范围为．参考答案：（﹣1，+∞）【考点】二阶行列式的定义．【专题】计算题；转化思想；定义法；矩阵和变换．【分析】由二阶行列式展开法则得x 2﹣2x﹣a＞0的解集为a，由此能求出实数a的取值范围．【解答】解：∵的解集为R，∴x2﹣2x﹣a＞0的解集为a，∴△=4+4a＜0，解得a＜﹣1，∴实数a的取值范围为（﹣1，+∞）．故答案为：（﹣1，+∞）．【点评】本题考查实数的取值范围的求法，是基础题，解题时要认真审题，注意二阶行列式展开法则的合理运用．15. 已知两个不共线的单位向量，，若，则．参考答案：16. 如图，是圆的直径，是圆的切线，切点为，平行于弦，若，，则 .参考答案：4由于，，而，因此，，，，，，，，故，由于切圆于点，易知，由勾股定理可得，因此.17. 已知焦点在轴上的双曲线的渐近线方程是，则此双曲线的离心率是____________；参考答案：因为焦点在轴上的双曲线的渐近线方程式，所以可设双曲线的方程为，整理得，所以有即所以，所以双曲线的离心率为。