江苏省洪泽中学06届高三全真模拟试卷

2006年高考模拟试卷 数 学 试 题（理科）考生须知:1. 本卷满分150分, 考试时间120分钟.2. 答题前, 在答题卷密封区内填写学校、班级和姓名.3. 所有答案必须写在答题卷上, 写在试题卷上无效.4. 考试结束, 只需上交答题卷. 参考公式：如果事件A 、B 互斥，那么P （A+B ）=P （A ）+P （B ） 如果事件A 、B 相互独立，那么P （A ·B ）=P （A ）·P （B ）如果事件A 在一次试验中发生的概率是P ，那么n 次独立重复试验中恰好发生k 次的概率P n（k ）=k n kkn P PC --)1(球的体积公式：334R Vπ=（其中R 表示球的半径） 球的表面积公式S=4πR 2（其中R 表示球的半径）第I 卷（选择题，共50分）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，只有一项是符合题目要求的,请将答案填写在答卷纸上)1. 已知=>==>==B A x y y B x x y y A x 则},1,)21(|{},1,log |{2 ( ）A ．),21(+∞B ．（2,21）C ．)21,0( D ．（0，2）2.命题甲：α是第二象限角；命题乙：sin tan 0αα<，则命题甲是命题乙成立的 ( )A. 必要不充分条件B.充分不必要条件C. 充要条件D. 既不充分也不必要条件3．已知直线:4350,()l x y AB m λλ++==为非零实数，如果直线l 与直线AB 平行，则可推算出：与m 共线的一个单位向量是（ ）A ．34(,)55B ．34(,)55-C ．43(,)55D ．43(,)55- 4．定义运算a c ad bc b d =-，复数z 满足11z ii i=+，则复数z 的模为（ ）A ．1+B C ．1- D5．把正方形ABCD 沿对角线AC 折起，当A 、B C 、D 四点为顶点的三棱锥体积最大时，直线BD 与平面ABC 所成的角的大小为（ ）0.30.1A ．90°B ．60°C ．45°D ．30°6．为了解某校高三学生的视力情况，随 机地抽查了该校100名高三学生的视力情况，得到频率分布直方图（如右图）. 由于不慎将部分数据丢失，但知道前4组 的频数成等比数列，后6组的频数成等差数列，设最大频率为a ，视力在4.6到5.0 之间的学生数为b ，则a , b 的值分别为 A. 0.27,78 B. 0.27,83 C. 2.7,78D. 2.7,837. 以椭圆221169144x y +=的右焦点为圆心，且与双曲线221916x y -=的渐近线相切的圆的方程为 ( )A. 221090x y x +-+=B. 221090x y x +--=C.221090x y x ++-=D.221090x y x +++=8．从黄瓜、白菜、油菜、扁豆4种蔬菜品种中选出3种，分别种在不同土质的三块土地上， 其中黄瓜必须种植，不同的种植方法共有（ ）A ．24种B ．18种C ．12种D ．6种9．△ABC 中，a 、b 、c 分别为∠A 、∠B 、∠C 的对边.如果a 、b 、c 成等差数列，∠B=30°，△ABC 的面积为23，那么b =（ ） A ．231+ B ．31+C ．232+ D ．32+10．经济学中的“蛛网理论”（如图），假定某种商品的“需求—价格”函数的图象为直线l 1,“供给—价格”函数的图象为直线l 2，它们的斜率分别为k 1、k 2，l 1与l 2的交点P 为“供给—需求”均衡点，在供求两种力量的相互作用下，该商品的价格和产销量，沿平行于坐标轴的“蛛网”路径，箭头所指方向发展变化，最终能否达于均衡点P ，与直线l 1、 l 2的斜率满足的条件有关，从下列三个图中可知最终能达于均衡点P 的条件为 ( )1k 0二、填空题：（本大题共4小题，每小题4分，共16分．把答案填在答题卷上） 11．已知函数)24(log )(3+=xx f ，则方程4)(1=-x f 的解=x __________。

2006高考模拟试题（一）2006.10 说明：本套试卷分第Ⅰ卷和第Ⅱ卷两部分，满分150分。

考试时间：120分钟。

第Ⅰ卷（三部分，共115分）第一部分：听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A，B，C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1．What’s the most probabl e relationship between the two speakers?A. They are host and guest.B. They are waiter and customer.C. They are husband and wife.2．Where did this conversation take place?A. At the hospital.B. At the airport.C. At the post office.3．Why will the woman go to London?A. To have a look at London.B. To go with her friend.C. To spend the weekend.4．What’s the woman’s job?A. She is a saleswoman.B. She is a waitress.C. She is a hotel clerk.5．How is the weather now?A. It’s snowing.B. It’s raining.C. It’s clear.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A，B，C三个选项中选出最佳选项，并标在试卷的相应位置。

2005-2006学年度第一学期高三年级统一调研模拟英语试卷第一部分：听力（共两节，满分30分）第一节（共5小题，每小题1.5分）请听下面5段对话，选出最佳选项。

每段对话仅读一遍。

1.Where is Tom going to finish his homework?A. At homeB. In the classroomC. In the library2.How does the man prefer to go to work?A. By trainB. By carC. By bus3.What’s the girl’s advice?A. The boy should work harder.B. The boy shouldn’t work too hard.C. The boy should make good use of the time.4.What is the man used to?A. Wearing no hat in cold weather.B. Going out without a hat in cold weather.C. Covering his head on a cold winter day.5.When doesn’t the woman like to go to the zoo?A. On FridaysB. On SundaysC. On Saturdays第二节（共15小题；每小题1.5分）请听下面5段对话或或独白，选出最佳答案。

每段对话或读白读两遍。

请听第6段材料，回答第6至8题。

6．Who sent a new camera to the man?A. His motherB. His uncleC. His sister7.What did the man’s sister give him as a birthday present?A. A blue tieB. A wonderful pictureC. A new suit8.Where does Uncle Robert live?A. In the man’s homeB. In New YorkC. In the countryside请听第7段材料，回答第9至11题9.How much did the woman’s package post cost?A.$10.80B.$5.90C.$5.94 10.Which way did the woman choose to mail her package?A. First classB.A cheaper wayC. An expensive way11.Where does the woman mail her package to?A. New YorkB. ParisC. Her hometown请听第8段材料，回答第12至14题。

2006年高考模拟试题理科综合能力测试本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，第Ⅰ卷1至5页，第Ⅱ卷6至14页。

考试结束，将试题卷和答题卡一并交回。

第Ⅰ卷（选择题共21题每题6分共126分）注意事项：1．答第Ⅰ卷前，考生务必将自己的姓名、准考证号、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，用橡皮擦干净后，再选涂其他答案标号，不能答在试题卷上。

以下数据可供解题时参考： 相对原子质量（原子量）：H 1 O 16 Ne 20 Na 23 S 32 Fe 56 Cu 64Ⅰ卷一、选择题（本题包括13小题。

每小题只有一个选项符合题意）1．下列关于体温调节的叙述中，正确的是 （ ） A ．下丘脑是感觉体温变化的主要中枢，是形成冷觉和热觉的部位 B ．冷觉感受器分布在皮肤，温觉感受器分布在内脏器官C ．寒冷环境中出现“寒战（或战栗）”是立毛肌收缩的结果D ．在炎热环境中大量排汗并未带走热量，只有汗液蒸发才使热量散失2.下列关于光合作用强度的叙述，正确的是 （ ） A ．在一枚叶片从幼到老的生长发育过程中，其光合作用强度是不会改变的B ．在植物群落的垂直方向上，占据不同空间的植物叶片的光合作用强度有差异C ．植物的光合作用强度只受到环境因素的影响，与基因型无关D ．若光照强度相同，则阳生植物的光合作用强度高于阴生植物 3.图1示一人工种子。

下列与人工种子的培育生产过程有关的叙述中不正确．．．的是 （ ）B.胚状体是由愈伤组织分化而成，离体细胞只有形成愈伤组织才能表现出全能性D.胚状体是由未分化的、具有分裂能力的细胞构成 4.下列诸项陈述正确的是 （ ）A.从国外引进的一种豆科植物在某地栽培不结根瘤，是因为该地土壤无根瘤菌B.提高农田的光照强度，增大田间的昼夜温差均是提高作物产量的重要措施C.2,4-D 的生产和使用，有效地解决了某些温室作物果实的发育、成熟问题D.利用鱼垂体的提取物可促使雌鱼排卵，因为垂体含有促性腺激素 5．图2表示发生在某动物精巢内形成精子的过程中，一个细胞内（不考虑细胞质）DNA 分子数量的变化。

2006年高考模拟测试数学1 第Ⅰ卷（选择题 共60分）一、选择题：本大题共12小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知集合}121|{},72|{-<<+=≤≤-=m x m x B x x A 且≠B φ，若A B A =⋃则（ ）A ．43≤≤-mB ．43<<-mC ．42<<mD ．42≤<m 2．函数)2(542≤+-=x x x y 的反函数的图象是（ ）3．若R b a ∈,，则31a 31b >成立的一个充分不必要的条件是 （ ）A.0>abB.a b >C.0<<b aD.0)(<-b a ab4．实数x 满足θsin 1log 3+=x ,则|9||1|-+-x x 的值为（ ）A ．8B ．－8C ．8或－8D ．与θ有关5．如图，正三棱锥A —BCD 中，点E 在棱AB 上，点F 在棱CD 上，并使λ==FDCFEB AE ，其中+∞<<λ0，设α为异面直线EF 与AC 所成的角，β为异面直线EF 与BD 所成的角，则α+β的值为（ ）A ．6π B ．4πC ．2πD ．与λ有关的变量6．已知点F 1，F 2分别双曲线12222=-by a x 的左，右焦点，过F 1且垂直于x 轴的直线与双曲交于A ，B 两点，若△ABF 2是锐角三角形，则该双曲线的离心率e 的范围是（ ）A ．（1，+≦）B ．（1，1+2）C ．（1，3）D ．（1－21,2+）7．函数)(x f y =与)(x g y =有相同的定义域，且对定义域中任何x ，有1)()(,0)()(=-=+-x g x g x f x f ，若g (x )=1的解集是{x|x =0}，则函数F （x ）=)(1)()(2x f x g x f +-是（ ）A ．奇函数B ．偶函数C ．既是奇函数又是偶函数D ．非奇非偶函数8．在轴截面是直角三角形的圆锥内，有一个体积最大的内接圆柱，则内接圆柱的体积与圆锥的体积的比值是 （ ）A ．83B ．94 C ．73 D ．21 9．当n ∈N 且n ≥2时，1+2+22+…+24n -1=5p+q ，其中p,q 为非负整数，且0≤q ＜5，则q 的值为（ ） A.0 B.2 C.2 D.与n 有关10．过曲线C ：x 2+ay 2=a 外一点M 作直线l 1交曲线C 于不同两点P 1，P 2，线段P 1P 2的中点为P ，直线l 2过P 点和坐标原点O ，若l 1⊥l 2，则a 的值为 （ ） A ．1 B ．2 C ．－1 D ．无法确定 11．在△ABC 中，如果4sinA+2cosB=1,2sinB+4cosA=33,则∠C 的大小是 （ ）A ．30°B ．150°C ．30°或150°D ．60°或120°12．若函数ax xy +=2的图象如图，则a 的取值范围是 （A ．（－≦,－1）B ．（－1，0）C ．（0，1）D ．（1，+≦）第Ⅱ卷 (非选择题)二、填空题：本大题共4小题，每小题4分，共16分，把答案填在题中横线上。

洪泽县中学2006届高三周练数学试卷一. 选择题:(题共12小题, 每小题5分，共60分) 1. 已知集合}3x 3|N x {A ≤≤-∈=,则必有 ( )A. A 1∈-B. A 0∈C. A 3∈D. A 2∈2. 不等式0x 32x ≥--的解集是 ( ) A. )3,2( B. )3,2[ C. ]2,( -∞ D. ),3(∞+3. 函数x cos x2sin )x (f =的最小正周期是 ( )A. 2πB. πC. 2πD. 4π4. 若)3,2( a =, )x ,4( b =, 且 a ∥b , 则x 的值为 ( )A. 38- B . 38C. －6D. 65. 下列函数中, 在区间)1,0( 上为减函数的是 ( )A. )x 1(log y 31-= B. 2x x 22y -= C. x 1)31(y -= D. )x 1(31y 2-=6. 如果,2y lg x lg =+则y 1x 1+的最小值是 ( )A. 2B. 21C. 51D. 2017. 若一等数列的前7项的和为48, 前14项的和为72, 则它的前21项的和为 ( )A. 96B. 72C. 60D. 488. 两位同学一起去一家单位应聘, 面试前单位负责人对他们说:“我们要从面试的人中招聘3人,你们俩同时被招聘进来的概率是701”.根据这位负责人的话可以推断出参加面试的人数为 ( )A. 21B. 35C. 42D. 709. 设l 1、 l 2为直线, α为平面.下面四个命题中, 正确的是 ( )C. l 1、l 2与所成的角相等⇒ l 1∥l 210. 离心率为黄金比215-的椭圆称为“优美椭圆”. 设1by a x 2222=+)0b a (>>是优美椭圆, F 、A 分别是它的左焦点和右顶点, B 是它的短轴的一个端点, 则AB F ∠等于( )A. 60°B. 75°C. 90°D. 120° 11. 设函数x cos b x sin a )x (f ⋅-⋅=图象的一条对称轴方程为4x π=, 则直线0c by ax =+-的倾斜角为 ( )A. 4πB. 43πC. 3πD. 32π12. 设函数1x 3x 2)x (f -+=. 若函数)x (g y =的图象与)1x (f y 1+=-的图象关于直线x y =对称,则)3(g 的值为 ( )A. 27B. 29C. 3D. 5二. 填空题：(本大题共4小题；每小题4分，共16分)13. 在n5)x1x (-的展开式中, 第4项是常数项, 则n ＝ . 14. 过点)2,1(P 且在坐标轴上截距相等的直线方程为 .15. 若曲线x x )x (f 4-=在点P 处的切线平行于直线0y x 3=-, 则点P 的坐标为 .16．圆x 2＋y 2＝2上到直线x －y －4＝0距离最近的点的坐标是_________． 17. 将容量为100的样本数据按从小到大的顺序分成8个组，如下表：则第六组的频率为 .18. 半球内有一内接正方体, 正方体的一个面在半球的底面圆内. 若正方体的棱长为6, 则半球的体积为 . 三. 解答题：(本大题6小题，共74分)19. (本题12分) 已知向量)1,x (sina =, )21,x (cos -= b . (1) 当b a ⊥时, 求||b a +的值; (2) 求函数)()x (f b a a -⋅=的值域.解: ,1x sin ||22+=a ,41x cos ||22+=b 21x cos x sin -⋅=⋅b a …… (3分)(1),b a ⊥ ∴.0=⋅b a ……(4分) 又2222|||2|)(||b |b a |a b a b a +⋅+=+=+,4941x cos 1x sin 22=+++=∴.23||=+b a ……(7分)(2)21x 2sin 211x sin )()x (f 222+-+=⋅-=⋅-=-⋅=b a a b a a b a a ……(8分)).4x 2sin(22221x 2sin 2112x 2cos 1π+-=+-+-=……(10分)∴]222,222[)x (f +-∈ .……(12分) 20.（本题12分）已知: 如图, 长方体AC 1中, 棱AB ＝BC ＝3, 棱BB 1＝4, 连结B 1C, 过点B 作B 1C 的垂线交CC 1于点E, 交B 1C 于点F. (1) 求证: A 1C ⊥平面EBD;(2) 求点A 到平面A 1B 1C 的距离;(3) 求ED 与平面A 1B 1C 所成角的大小. 解: (1)连结AC.在长方体AC 1中, A 1C 在底面ABCD 上的射影为AC, AC ⊥BD,∴AC 1⊥BD. ……(2分)在长方体AC 1中, A 1C 在平面BB 1C 1C 上的射影为B 1C,B 1C ⊥BE, ∴A 1C ⊥BE. ……(3分)又BD BE ＝B, ∴A 1C ⊥平面EBD. ……(4分) (2) ∵BF ⊥B 1C, BF ⊥AB 1, B 1C A 1B 1＝B 1, ∴BF ⊥平面A 1B 1C 1, ……(5分)又∵A 1B 1∥AB, A 1B 1⊂平面A 1B 1C,AB ⊄平面A 1B 1C, ∴AB ∥平面A 1B 1C, 点A 到平面A 1B 1C 的距离即为点 B 到平面A 1B 1C 距离, 也就是BF. ……(7分) 在△B 1BC 中, 易知224343BF +⨯=512=, 点A 到平面A 1B 1C 的距离为512.……(8分)(3)连结A 1D 、FD. 由(2)知BE ⊥平面A 1B 1C, 即BE ⊥平面A 1B 1CD,∴∠EDF 为ED 与平面A 1B 1C 所成的角. ……(9分)矩形B 1BCC 1中, 易求得B 1F ＝516, CF ＝59, EF ＝,2027F B CF BF 1=⋅ EC ＝.49F B BB FC 11=⋅ 又在Rt △CDE 中, 415CD EC ED 22=+=,……(11分),259BD EF EDF sin ==∠即ED 与平面A 1B 1C 所成角为259arcsin .……(12分)21.(本题满分12分)已知正方形ABCD 的外接圆方程为 x2+y2－24x+a=0 (a<144)，正方形一边CD 所在直线的方向向量为(3,1)，（1）求正方形对角线AC 与BD 所在直线的方程；（2）若顶点在原点焦点在x 轴的抛物线E 经过正方形在x 轴上方的两个顶点A 、B ，求抛物线E 的方程。

06届高三数学第一轮模拟试卷一（立几、解几、概率等）命题人：江阴市成化高级中学 张龙伍一、选择题：本大题共10小题，每小题5分，共50分。

1、编号为1、2、3、4、5的五个人分别去坐编号为1、2、3、4、5的五个座位，其中有且只有两个人的编号与座位号一致的坐法有( ) A ．10种 B ．20种 C ．30种 D ．60种2、正三棱锥的侧面都是直角三角形，侧棱与底面所成的角为α，则α等于( )A ．36arcsinB ．33arccosC ．22arctanD ．6π 3、设有如下三个命题：甲：相交直线l 、m 都在平面α内，并且都不在平面β内；乙：直线l 、m 中至少有一条与平面β相交；丙：平面α与平面β相交．当甲成立时，( ) A ．乙是丙的充分而不必要条件 B ．乙是丙的必要而不充分条件C ．乙是丙的充分且必要条件D ．乙既不是丙的充分条件又不是丙的必要条件 4、将一个各个面上均涂有颜色的正方体，锯成64个同样大小的小正方体，从这些小正方体中任取一个，其中恰好有2面涂有颜色的概率是 （ ）A 、916 B 、2764 C 、38 D 、11325、等体积的球和正方体，它们的表面积的大小关系是（ ）A ．正方体球S S >B ．正方体球S S <C ．正方体球S S =D ．正方体球S S 2=6、地球半径为R ，则南纬60°纬线圈的长为 （ ）A ．R 3πB ．R 2πC ．R πD ．R7则样本在(10 , 50)上的频率为 ( ) (A)20. (B)4. (C)2. (D)107.8、若函数f (x )=32ax bx cx d +++的图象如图所示，则一定有（ ）A a <0 b >0 c >0 d <0B a <0 b <0 c >0 d <0C a <0 b >0 c <0 d <0D a <0 b <0 c <0 d <09、有80个数，其中一半是奇数，一半是偶数，从中任取两数，则所取的两数和为偶数的概率为 ( ) (A)7939. (B)801. (C) 21. (D)8141.10、设{a n }是等差数列，从{a 1，a 2，a 3，··· ，a 20}中任取3个不同的数，使这三个数仍成等差数列，则这样不同的等差数列最多有（ ）(A)90个 . (B)120个. (C)180个. (D)200个. 二、填空题：本大题共4小题，每小题4分，共16分。

2006年江苏省某校高中入学综合调研数学试卷一、填空题（共48分）1. 计算：√2√5−2√6−√6=________．2. 设x为正整数，且满足{|x−2|<3x2−2x−3≥0，则x＝________．3. 在△ABC中，P是线段AB上的点、Q是线段AC延长线上的点，且AP:PB＝2:1，AQ:QC ＝4:1，PQ和BC交于M，则BM:MC＝________．4. 已知abc≠0，k=a+b−cc =a−b+cb=b+c−aa，一次函数y＝kx+k2−2k+2图象上两点为P1(x1, y1)，P2 (x2, y2)且|x1−x2|＝2，则|P1P2|＝________√2或2√5．三、标题5. 如图：圆O内挖去一个平行四边形ABCD，现将图形用一直线切开，使其面积被平分．（将作图痕迹保留，用字母表示该直线为PQ）四、标题6. 设a、b满足a2+b2−2a＝0，则2a−b的最大值为________+√5．7. 在△ABC中，AC＝CD且∠CAB−∠B＝30∘，则∠BAD＝________．8. 已知：0<a<1，−1<b<0，则a，ab，a−b，a+b这四个数中最大的数为________．9. 某商店有A种练习本出售，如买一本为0.30元，买一打（12本）为3.00元，买10打以上每打为2.70元，某年级有227人，每人需要一本，则最少需付________元．10. 设sinα、cosα是方程x2−√mx+12=0的两根，△ABC的三边分别为sinαcosα12m，则△ABC的形状是________三角形．11. 如图：直角梯形ABCD中，AD // CB，∠DCB＝90∘，AD<CB，E为CD上一点，∠ABE ＝45∘，AE＝10，BC＝CD＝12，则CE＝________．12. 设x、y满足10x2−16xy+8y2+6x−4y+1＝0，则x−y＝________．二、解答题（共52分）13. 解方程组：{4x2(x+y)2+4x(1−y)x+y+2=0x−xy x+y −xx+y+12=0．14. 在某一次自行车1000米场地追逐赛中（一圈为1000米），甲运动员的战术为：第一分钟的速度为1000米/分，以后每分钟递增200米，到第5分钟时由于体力下降，则以每分钟递减200米，直至最低速度为600米/分，乙运动员的战术为1200米/分匀速前进．比赛规则规定：两人同时、同地、同向出发，追上一圈者获胜．问：（1）甲运动员在最高时速时，能否追上乙．（2）比赛结束时，比赛进行了多长时间．15. 方程x3+(1−3a)x2+2a2x−2ax+x+a2−a＝0有且只有一个根．求a的取值范围．16. 在△ABC中，H为垂心，M为BC上的中点，AD为BC上的高，且AD＝BC(AC> AB)．求证：HD+HM＝MC．17. 已知一次函数y＝kx+m，二次函数y＝2ax2+2bx+c和y＝ax2+bx+c−1的图象分别为l、E1、E2，l交E1于B、C两点，且满足下列条件：I)b为整数．II)B(2−2√2, 3−2√2)，C(2+2√2, 3+2√2)．Ⅲ）两个二次函数的最小值差为1．（1）如l与E2交于A、D两点，求|AD|值．（2）问是否存在一点P，从P出发作一射线分别交E1、E2于P1，P2，使得PP1:PP2为常数，并简述你的理由．2006年江苏省某校高中入学综合调研数学试卷答案1. 22. 3或43. 2:14. 25. 连接平行四边形的顶点，得出平行四边形的对角线交点，再连接圆心，即可平分图形面积．6. 27. 15∘8. a−b9. 51.310. 直角11. 4或612. −0.2513. 令xx+y =a，原方程组可化为：{4a2+4a(1−y)+2=0a(1−y)−a+12=0①-②×4可得：4a2+4a＝0，解得：a＝0或−1，当a＝0时不符合题意，（舍去），当a＝−1时，可得x＝−x−y，代入原方程可得：{x=14y=−12．14. 根据题意可知，第4分钟时到达最高时速，甲行驶的路程为：1000+1200+1400+ 1600＝5200米．乙行驶的路程为：1200×4＝4800米．5200−4800＝400<1000．甲在最高时速时没有追上乙．第5分钟时，甲的时速为1400米/分，甲领先乙5200−4800+200＝600米．第6分钟不变，第7分钟甲领先乙400米，第8分钟甲领先乙0米，此时甲的速度也成为600米/分．(1200−600)(x−8)＝1000，x=293．比赛结束时，比赛进行了293分钟．15. ∵ x3+(1−3a)x2+2ax−2ax+x+a2−a＝0，∴ x3−3ax2+2a2x+x2−(2a−1)x+a2−a＝0，∴ x(x−a)(x−2a)+(x−a)[x−(a−1)]＝0，∴ (x−a)[x2−(2a−1)x−(a−1)]＝0，∵ 方程x3+(1−3a)x2+2a2x−2ax+x+a2−a＝0有且只有一个根，∴ x2−(2a−1)x−(a−1)＝0无解，∴ △＝(2a−1)2+4(a−1)<0，∴ 4a2−3<0，∴ −√32<a <√32． 16. 连CH ，∵ H 为垂心，∴ CH ⊥AB又∵ AD ⊥BC ，∴ △ABD ∽△CHD ，设AD ＝BC ＝1，BD ＝x ，则CD ＝1−x ，DM =12−x ， ∵ AD BD =CD DH ，AD x =BC−x DH ，∴ DH ＝(1−x)x ，HM 2＝DH 2+DM 2＝[(1−x)x]2+(12−x)2 =[x(1−x)−12]2 ∵ AC >AB ，BD ＝x <12 ∴ x(1−x)＝x −x 2=−(x −12)2+14<14，∴ HM ＝−x(1−x)+12HD +HM ＝(1−x)x −x(1−x)+12=12=BC 2=CM ， ∴ HD +HM ＝CM ．17. 把B 、C 点的坐标代入一次函数y ＝kx +m ，解得：k ＝1，m ＝1∵ B 、C 在E 1上，将B 、C 坐标代入其二次函数，∴ 3−2√2=2a(2−2√2)2+2b(2−2√2)+c3+2√2=2a(2+2√2)2+2b(2+2√2)+c经化简得：8a +2b ＝1①将E 1，E 2的函数是化简y 1=2a(x +b 2a )2+c −b 22a所以y 1最小值=c−b 22ay 2=a(x +b 2a )2+c −1−b 24a所以y 2最小值：c −1−b 24a根据两个二次函数的最小差值为1|c −b 22a −(c −1−b 24a )|＝1化简得到|1−2b 21−2b |＝1再化简绝对值得到b ＝0（其中能够得出b 2+2b −1＝0，但是，要求b 为整数，所以，此式舍去）再根据上面我写的①式，得到a =18根据B 、C 坐标可知x b 和x c 之间的距离为4√2应有 |x b −x c |＝4根号2即(x b −x c )2＝32②因为y ＝x +m （之前得出了k ＝1），y ＝2ax 2+2bx +c 的交点位B 、C有x +m ＝2ax 2+2bx +c 整理得2ax 2+(2b −1)x +c −m ＝0 则x b +x c ＝4 ③x b ×x c ＝4(c −m)④②③④整理化简得到m −c ＝1⑤A ，D 是E 2与l 的交点，所以，x +m ＝ax 2+bx +c −1 再根据④式，化简整理得到ax 2+(b −1)x −2＝0所以，x a +x d ＝(1−b)/a ，x a ×x d =−2a 所以，(x a −x d )2=(1−b a )2−4(−2a ) 所以，得到|x a −x d |＝8√2，即|AD|＝8√2；存在，当m ＝k >0时，14x 2−34mx +k =x +m ，得x 1＝0，x 2＝3m +4>0．∴ 点A(0, m)．显然，经过点A 且平行于x 轴的直线与抛物线的另一交点即为点P 1(3m, m)． 又∵ 由题意，点P 2只能有一解，再结合抛物线的对称性，可知点P 2只能重合于点D ． 设DE 与AP 1交于点G ，由DG ＝AG ，即m −(k −916m 2)=32m ，得m =83．∴ 点P 1(8, 83)、点P 2(4, −43)．故存在点P．。

2006年普通高等学校招生全国统一考试英语试卷 (江苏卷) [ 2007-1-27 ]第二部分：英语知识运用（共两节, 满分45分）第一节：单项填空（共15小题，每小题1分，满分15分）21. --- I think I’ll give Bob a ring.--- You _______. You haven’t been in touch with him for ages.A. willB. mayC. have toD. should22. My most famous relative of all, _______ who really left his mark on America, was Rob Sussel, my great-grandfather..A. oneB. the oneC. heD. someone23. --- I don’t suppose the police know who did it.--- Well, surprisingly they do. A man has been arrested and ________ now.A. has been questionedB. is being questionedC. is questioningD. has questioned24. This new model of car is so expensive that it is _______ the reach of those with average income.A. overB. withinC. beyondD. below25. --- Are you going to have a holiday this year?--- I’d love to. I can’t wait to leave this place _______.A. offB. outC. behindD. over26. The committee is discussing the problem right now. it will _______ have been solved by the end of next week.A. eagerlyB. hopefullyC. immediatelyD. gradually27. Although medical science __ control over several dangerous diseases, what worries us is that some of them are returning.A. achievedB. has achievedC. will achieveD. had achieved28. --- It took me ten years to build up my business, and it almost killed me.--- Well, you know what they say. _________.A. There is no smoke without fireB. Practice makes perfectC. All roads lead to RomeD. No pains, no gains29. The owner of the cinema needed to make a lot of improvements and employ more people to keep it running, ___ meantspending tens of thousands of pounds.A. whoB. thatC. asD. which30. Whenever he was asked why he was late for class, he would answer carelessly, always ______ the same thing.A. sayingB. saidC. to sayD. having said31. _______ environmental damage is done, it takes many years for the ecosystem (生态系统) to recover.A. Even ifB. If onlyC. WhileD. Once32. --- There is a story here in the paper about a 110-year-old man.--- My goodness! I can’t imagine _________ that old.A. to beB. to have beenC. beingD. having been33. I wish you’d do ________ talking and some more work. Thus things will become better.A. a bit lessB. any lessC. much moreD. a little more34. A poet and artist ________ coming to speak to us about Chinese literature and painting tomorrow afternoon.A. isB. areC. wasD. were35. We haven’t settled the question of ______ it is necessary for him to study abroad.A. ifB. whereC. whetherD. that第二节完型填空（共20小题；每小题1.5分，满分30分）I know I should have told the headmaster at the time. That was my real 36 .He had gone out of the study for some 37 , leaving me alone. In his absence I looked to see 38 was on his desk. In the 39 was a small piece of paper on which were written the 40 “English Writing Prize 1949. History Is a Serious of Biographies (人物传记)”.A(n) 41 boy would have avoided looking at the title as soon as he saw the 42 . I did not. The subject of the English Writin g Prize was kept a 43 until the start of the exam so I could not 44 reading it.When the headmaster 45 , I was looking out of the window.I should have told him what had 46 then. It would have been so 47 to say: “I’m sorry, but I 48 the title for the English Wr iting Prize on your desk. You’ll have to 49 it.”The chance passed and I did not 50 it. I sat the exam the next day and I won. I didn’t 51 to cheat, but it was still cheatinganyhow.That was thirty-eight years 52 when I was fifteen. I have never told anyone about it before, 53 have I tried to explain tomyself why not.The obvious explanation is that I could not admit I had seen the title 54 admitting that I had been looking at the things on hi s desk. 55 there must have been more behind it. Whatever it was, it has become a good example of how a little mistake can trap (使陷入) you in a more serious moral corner (道德困境).36. A. plan B. fault C. grade D. luck 37. A. reason B. course C. example D. vacation38. A. this B. which C. that D. what 39. A. drawer B. corner C. middle D. box40. A. names B. words C. ideas D. messages 41. A. honest B. handsome C. friendly D. active42. A. desk B. paper C. book D. drawer 43. A. question B. key C. note D. secret44. A. help B. consider C. practise D. forget 45. A. disappeared B. stayed C. returned D. went46. A. existed B. remained C. happened D. continued 47. A. tiring B. easy C. important D. difficult48. A. saw B. gave C. set D. made 49. A. repeat B. defend C. correct D. change50. A. take B. have C. lose D. find 51. A. remember B. learn C. mean D. pretend52. A. past B. ago C. then D. before 53. A. either B. never C. nor D. so54. A. by B. besides C. through D. without 55. A. But B. Though C. Otherwise D. Therefore第三部分：阅读理解（共20小题，每题2分，满分40分）AThe Marches were a happy family. Poverty, hard work, and even the fact that Father March was away with the Union armie s could not down the spirits of Meg, Jo, Amy, and Marmee, as the March girls called their mother.The March sisters tried to be good but had their share of faults. Pretty Meg was often displeased with the schoolchildren she t aught; boyish Jo was easy to become angry; golden-haired schoolgirl Amy liked to show up; but Beth, who kept the house, was lo ving and gentle always.The happy days passed and darkness came when a telegram arrived for Mrs. March. “Your husband is very ill,” it said, “co me at once.” The girl tried to be brave when their mother left for the front. They waited and prayed. Little Beth got scarletfever (猩红热) when she was taking care of the sick neighbor. She became very ill but began to recover by the time Marmeewas back. When Father came home from the front and at that joyful Christmas dinner they were once more all together.Three years later the March girls had grown into young womanhood. Meg became Mrs. Brooke, and after a few family trou bles got used to her new state happily. Jo had found pleasure in her literary efforts. Amy had grown into a young lady with a talen t for design and an even greater one for society. But Beth had never fully regained her health, and her family watched her with lov e and anxiety.Amy was asked to go and stay in Europe with a relative of the Marches. Jo went to New York and became successful in he r writing and had the satisfaction of seeing her work published there. But at home the bitterest blow was yet to fall. Beth had know n for some time that she couldn’t live much longer to be with the family and in the spring time she died.News came from Europe that Amy and Laurie, the grandson of a wealthy neighbor, had planned to be married soon. Now J o became ever more successful in her writing and got married to Professor Bhaer and soon afterwards founded a school for boy s.And so the little women had grown up and lived happily with their children, enjoying the harvest of love and goodness tha t they had devoted all their lives to.56. The members of the March family were Father March, Mrs. March and their _______.A. four daughtersB. five daughtersC. son and four daughtersD. son and five daughters57. Who was the most successful in career (事业) among the March girls?A. JoB. BethC. AmyD. Meg58. Which of the following would be the best title for the passage?A. The march FamilyB. The March ParentsC. The March GirlsD. The March Relatives59. It can be inferred from the passage that the March family had ______.A. both happiness and sadnessB. wealthy neighborsC. more girls than boysD. a lot of rich relativesBThe first reality TV show in the world was called Expedition Robinson and it was shown in Sweden in 1997. Half the popul ation of the country watched the final event and a new kind of TV program was born. Two years later in Holland , the first series of Big Brother was filmed. Again, it was a great success and the final program was watched by 15 million people. Now more than 20 countries around the world have Big Brother or Expedition Robinson on their TV screens. The ordinary people who take part i n the programs are known by millions of people in their own countries and reality TV has become big, big business.For the TV producers, reality TV is a dream come true because many of the programs cost nothing to make. At some poin t, the television viewers are asked to telephone the program to vote or to apply to take part in the show. It is the cost of these telep hone calls that pays for the shows. One of the most popular shows is Pop Idol. In the show a group of attractive young people are made into pop stars. TV viewers vote for their favorite person on the show. The winner makes a record and millions of copies of the record are sold. His or her pictures are published on the covers of magazines or on the front pages of newspapers, and then, they are quickly forgotten.But not everyone is happy about reality TV. In Portugal, two TV channels got into trouble because they showed too much o f the personal lives of the people in the shows. In France, reality TV is called “rubbish TV” and the TV studios of Big Brother wer e attacked three times in one week. In Greece, Big Brother was described as “ against human rights and civilization”.61. Those who take part in the reality TV shows are usually _____.A. common peopleB. pop TV starsC. attractive peopleD. famous film stars62. Who would pay for the cost of the reality TV shows according to the passage?A. TV producers who make reality TV showsB. TV actors who take part in reality TV shows.C. TV viewers who telephone reality TV showsD. TV companies which broadcast reality TV shows63. It can be concluded from the passage that ______.A. everyone is happy about reality TV.B. reality TV will do well in many countries.C. all the people in Europe are in favor of reality TVD. reality TV will not be broadcast in any countries.CI II64. According to Advertisement 1, the famous yearly competition is ______.A. a music competitionB. an eating competitionC. a cooking competitionD. a pleasure-taking competition65. People who come to watch the competition earliest may _______.A. get the best watching positionB. get the best food.C. watch whatever they want toD. take good pictures66. The best title for Advertisement 2 would be _______.A. The VikingsB. Reliving of the VikingsC Frojel D. A Viking Reliving Society67. From the advertisement we know that Frojel used to be ______.A. a Viking club.B. a family-based societyC. a European islandD. a trading centerDIn a recently published book, I came across some exercises with interesting names such as fishbone diagrams, lotus flowers a nd clustering. As I used these exercises in my classes, I noticed that students were interested. They said more and wrote more. The y enjoyed expressing their ideas and sharing them in groups. They were no longer passively waiting for the bell , but actively taki ng part in the lesson. I find that creativity can act as a way to increase participation and improve fluency.Creativity has become a popular word in recent years. Scholars in arts, psychology, business, education and science are all w orking to get a deeper understanding of it. Robert J. Stemberg is a creativity specialist and Yale professor of psychology. He defin es creativity as “the ability to produce work that is both new (original) and appropriate(applicable to the situation ) ”. this definitio n is useful, as we want our students to use language in a new way and to use it correctly and properly. Mot scholars say there are t wo types of creativity: big “C” creativity and small “c” creativity. Big “C” creativity refers to genius level thinking that results i n artistic masterpieces and scientific breakthroughs. Small “c” creativity refers to everyday level thinking that can be used in any s ituation our emphasis is on the latter. While it goes without saying that any of our students could go on to be the next Picasso or E dison, our aim is to help students produce more ideas and use language in a new way.68. The underlined words “waiting for the bell ” in the first paragraph probably means______.A. longing for a phone callB. hoping to have a bellC. expecting the end of the classD. waiting to speak in the class69. It can be inferred from the passage that the author thinks the exercises in the book were _____.A. popularB. usefulC. scientificD. creative70. When you use a familiar word in a new way, you are ________.A creative in the sense of big “C” creativity.B. creative in the sense of small “c” creativity..C. not creative in the sense of big “C” creativity..D. not creative in the sense of small “c” creativity.71. The main purpose of the passage is to _________.A. show how useful the book is.B, explain what creativityC. discuss how one can be creativeD. tell what reaching aims atEA new eight-kilometer road is under construction that links the port area with motorway system. It is expected to carry 20,000 trucks and cars a day, which greatly reduces the overcrowded traffic in the center of the city. As part of the project, two four-kil ometer road tunnels are being built below the central area of the city, one for traffic to the north and the other for the traffic to th e south. The two tunnels are about 20 meters below the surface and are 12 meters wide, providing for two lanes of traffic in each d irection.In the upper part of the tunnel two air-conditioning pipes remove the waste gas of trucks and cars and keep the quality of ai r inside the tunnel. The lighting is at the top of the tunnel, practically at its highest point. There will also be electric signs at freque nt intervals. They show traffic conditions ahead and can be seen clearly by drivers. The wall is made up of four main elements, wh ich include a waterproofing covering and, on the inside of the tunnel, a concrete lining.Each tunnel is roughly round and the lower part of the tunnel is somewhat flat. The surface of the road lies on the base, whi ch is made of concrete and steel. The drainage system, just below the road surface on one side, removes any extra liquid, particula rly water. In the event of fire, the fire main, which is made of steel, pipes water to many fire hydrant stations at regular intervals al ong the length of the tunnel. The fire main is at the side of the tunnel and at the level of the road surface. Other systems in the tunn el will include emergency phones.72. Each of the tunnels under construction is _____.A. eight kilometers long and twenty meters wideB. eight kilometers long and six meters wideC. four kilometers long and twenty meters wideD. four kilometers long and six meters wide73. Which part of the tunnel in the diagram is used to pipe out extra water?A. 1B. 3C. 5 D 674. Driving in the tunnel, one can know the traffic conditions ahead through______.A. the lightsB. the electric signsC. the trucks and the carsD. the emergency phones75. The passage is mainly about _____.A. the construction of a roadB. the design of a roadC. the construction of two tunnelsD.the design of two tunnels第四部分：写作（共两节，满分35分）第一节：对话填空请认真阅读下列对话，并根据各题所给的首字母的提示，在答题卡右栏中标有题目的横线上，写出一个英语单词的完整、正确的形式，使对话通顺。

2006年普通高等学校招生全国统一考试模拟试卷数学（文
史类）
佚名
【期刊名称】《高校招生：高考升学版》
【年(卷),期】2006()5
【总页数】4页(PI0001-I0004)
【正文语种】中文
【中图分类】G
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