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1、四川省成都七中2012届高三年级二诊模拟考试理科数学及答案成都七中高2012级高三二诊模拟考试 数学试题(理科) 一(选择题(每小题5分，共60分，在每小题给出的四个选项中，只有一项是符合要求() 2i1Z,、复数的虚部是 ( ) 1，iA.iB.,iC.1D.,12yx-ax+2,log，a2、若函数在区间上为减函数，则的取值范围是( ) a(,1A.(0,1)B.2,，,)C.2,3)D.(1,3)1310,ABCtanC,tanA,cosB,3、在中，则 ( ) 210A.,1B.1C.3D.,2O,ABC、已知4三点在球心为，半径为的球面上，且三棱锥为正四面体，那么A,BA,B,CO3
2、两点间的球面距离为 ( ) ,2A.B.C.,D., 323,ABC5、已知点是边长为的等边的中心，则 ( ) O(OA，OB),(OA，OC),11111A.B.,C.D., 9966,6、以,(x)表示标准正态总体在区间(,x)内取值的概率，若随机变量服从正态分布2，则概率P(|,|,), ( ) N(,),1,A.,(,，),(,)B.,(1),(,1)C.,()D.2,(,，,),nn,1aSana,2a，a,2，27、已知数列满足且，为数列的前项和，则nnn1nn,1(S，2)2012log, ( ) 2A.2013B.2012C.2011D.2010 minor injury ra
3、te is less than 0.8%. 15.2.3 construction safety management system in order to achieve security objectives and develop safety management system: (1) construction contract responsibility system for production safety and security before the approach to establish effective safety production responsibil
4、ity system, enabling all staff to clarify their security responsibilities, project manager and construction team, subcontractors enter into a construction contract, specification for safe behaviour. (2) safety instruction and safety training before the approach of safety education for all employees,
5、 comes into play in the construction and regular lectures on security, security awareness and staff training in special positions. (3) safety information regularly check the implementation of the safety and security reports submitted in a timely manner, appropriate security measures, develop safety
6、plans, active contact with Labor departments to ensure information transfer, the transfer, collection, management. (4) security system according to the standard case, the whole construction process of security checks to eliminate hidden dangers, and by checking and reward and punishment system to en
7、hance the safety awareness of staff, ensuring smooth safety guidelines and regulations, ensure the security goals of the. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, reinforced wood-mode processing plants, construction of living 22xy28、若抛物线与
8、双曲线有相同的焦点下，点是两曲线,1(a,0,b,0)y,2px(p,0)A22abAF,x的一个交点，且轴，若为双曲线的一条渐近线，则的倾斜角所在的区间可能是 ll( ) , A.(0,)B.(,)C.(,)D.(,)4644332112，b9、为正实数，且，,1，则的最大值为 ( ) a,bab2ab1953A.B.C.D. 216164x,R10、已知定义在上的函数满足下列三个条件，,对任意的都有;y,f(x)f(x，4),f(x)R?对任意的，都有;?的图像关于轴对称。则0,x,x,2f(x),f(x)y,f(x，2)y1212的大小关系为 ( ) f(4.5),f(6.5),f(7)
9、A.f(4.5),f(7),f(6.5)B.f(4.5),f(6.5),f(7) C.f(7),f(4.5),f(6.5)D.f(6.5),f(7),f(4.5)22xy2,1(a,0,b,0)11、双曲线的渐近线与抛物线相切，则该双曲线的离心率为 y,x，122ab( ) A.3B.2C.5D.612、用红、黄、蓝三种颜色去涂图中标号为的个小正方形，使得任意相邻(有公共边)1,2？99的小正方形所涂颜色都不相同，且标号为“3,5,7”的小正方形涂相同的颜色，则符合条件的所有涂法共有( )种 1 2 3 A.18B.36C.72D.1084 5 6 二、填空题(共4小题，每小题4分，共16分)
10、 7 8 9 x,0,y,xkz,x，3y13、已知满足条件为常数，若得最大值为x,y,2x，y，k,0,8，则 。 k,314、直径为的球的内接正四面体的体积= 。 mode processing plants, construction of living-inforced woodurity goals of the. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, rehe secd and punishment system t
11、o enhance the safety awareness of staff, ensuring smooth safety guidelines and regulations, ensure to the standard case, the whole construction process of security checks to eliminate hidden dangers, and by checking and rewarding tontact with Labor departments to ensure information transfer, the tra
12、nsfer, collection, management. (4) security system accorf the safety and security reports submitted in a timely manner, appropriate security measures, develop safety plans, active ction on security, security awareness and staff training in special positions. (3) safety information regularly check th
13、e implementaraining before the approach of safety education for all employees, comes into play in the construction and regular lectures ofety ttion team, subcontractors enter into a construction contract, specification for safe behaviour. (2) safety instruction and saproduction responsibility system
14、, enabling all staff to clarify their security responsibilities, project manager and construcafety ) construction contract responsibility system for production safety and security before the approach to establish effective s15.2.3 construction safety management system in order to achieve security ob
15、jectives and develop safety management system: (1minor injury rate is less than 0.8%. 2 22xy15、若点和点分别为椭圆的中心和左焦点，点为椭圆上任意一点，则，,1OP,FPOFP43的最大值为 。 A,R16、设集合，集合中的任意元素满足运算“”，且运算“”具有 ,Aa,b,Aa,a,0如下性质，对任意的，(1);(2); a,b,c,A(3);给出下列命题: (a,b),c,a,c，b,c，c0,Aa,Aa,0a,0,a,;?若则;?若且则 (1,1),1,01,A其中正确命题的序号是 (写出所有正确命
16、题的序号) 三、解答题(共6题，17题21题每题12分，22题14分，共74分) 222,ABC17、a,c,ac,bc在中，分别是角的对边，已知且 a,b,cA,B,Cb,ac,(1)求的大小; ，AA,f(x),cos(,x,)，sin(,x)(,0)(2,)设且的最小正周期为，求在的最f(x)f(x)0,22大值。 18、甲、乙两名运动员一次试跳2米成功的概率分别为0.7,0.6且每次试跳成功与否相互之间没有影响。 求:(1)甲试跳3次，第3次才成功的概率; (2)甲、乙两人在第一次试跳中至少有一个成功的概率; (3)甲、乙两人各试跳两次，甲比乙的成功次数恰好多一次的概率。 19、在直三
17、棱柱中，AA,AB,BC,3,AC,2,D是中点. AC1BC/平面ABD(1)求证:; 11BABD(2)求点到平面的距离; 11第3页，共13 页 (3)求二面角的余弦值。 A,DB,B111220、已知函数， f(x),alnx，x,(1，a)x(x,0)2(1)求的单调区间; f(x)(2)若在内恒成立，求实数的取值范围; af(x),0(0,，,)111n*(3)求证:。 ，？，,n,N,ln2ln3ln(n，1)n，1x21、已知椭圆的对称中心为原点，焦点在轴上，左，右焦点分别为F和F，且，|FF|,2CO12123点在该椭圆上。 (1,)2(1)求椭圆的方程; C122FF(2)
18、过的直线与椭圆相交于A,B两点，若,AFB的面积为，求以为圆心且与直lC1227线相切的圆的方程。 l111aab？,bab,1,b,2b，1,1,(，)22、数列满足，若数列满足 1nnnn1n，1nbbb12n,1* (n,2,n,N)bb,b,b(1)求及; n234urity goals of the. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, rehe secd and punishment system to enhan
19、ce the safety awareness of staff, ensuring smooth safety guidelines and regulations, ensure to the standard case, the whole construction process of security checks to eliminate hidden dangers, and by checking and rewarding tontact with Labor departments to ensure information transfer, the transfer,
20、collection, management. (4) security system accorf the safety and security reports submitted in a timely manner, appropriate security measures, develop safety plans, active ction on security, security awareness and staff training in special positions. (3) safety information regularly check the imple
21、mentaraining before the approach of safety education for all employees, comes into play in the construction and regular lectures ofety ttion team, subcontractors enter into a construction contract, specification for safe behaviour. (2) safety instruction and saproduction responsibility system, enabl
22、ing all staff to clarify their security responsibilities, project manager and construcafety ) construction contract responsibility system for production safety and security before the approach to establish effective s15.2.3 construction safety management system in order to achieve security objective
23、s and develop safety management system: (1minor injury rate is less than 0.8%. mode processing plants, construction of living-inforced wood4 a，1b*nn(2)证明; ,(n,2,n,N)abn，n，1111110*(3)求证:。 (1，)(1，)？(1，),(n,N)aaa3n12成都七中高2012级二诊模拟试题参考答案 一、选择题 2i(1,i)1Z,i，1？、理 C 虚部为1; (1，i)(1,i)B,x|1,x,4？A:B,x|2,x,4 文 C
24、 。 第5页，共13 页 2x,2x，2a,22、 C 当时，在上为减函数，排除; (,1y,logA22x,4x，22a,4 当时，在上为减函数，但不恒大于0， x,4x，2(,1y,log4排除B; 323x,x，22 当时，在上不为减函数。 a,y,log(,13221013、 A 。 sinB,tanB,？tanC,tan(A，B),1103,O,ABC？，AOB,？,3,4、 D 为正四面体，所求距离为。 332335、 D |OA|,|OB|,|OC|,？OA，OB，OC,0323312,()()()()()cos120 ？OA，OB,OA，OC,OC,OB,366、理 B ,，,
25、P,(|,|,),P,(，,),P,(,),(),(),(1),(,1) ,2, 文 A 切线方程为 y|,(3x,2)|,1？y,x,1x,1x,1nn,1nn,17、理 A 由得，而 a,2a，a,2，2a,2,(a,2)1nn,1nn,1n201220111 ，即 a,2？a,2,(a,2),？,(a,2),0n20122011120122(1,2)(S，2)2201220132012？S,2，2，？2,2,2？log,2013 201221,222q4a,4a，a 文 C 设公比为，由题设， ？4aq,4a，aq？q,4q，4,02131114a(1,q)1 ？q,2？S,1541,q
26、2p22PPPPp222224F(,0),C,A(,P),a，bc,a，b8、理D 由及，又 ,1222224ab2222222ba，b4(a，b)abt,0 即，令，则 ,1？(),4,4,02222aabba-inforced woodurity goals of the. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, rehe secd and punishment system to enhance the safety awa
27、reness of staff, ensuring smooth safety guidelines and regulations, ensure to the standard case, the whole construction process of security checks to eliminate hidden dangers, and by checking and rewarding tontact with Labor departments to ensure information transfer, the transfer, collection, manag
28、ement. (4) security system accorf the safety and security reports submitted in a timely manner, appropriate security measures, develop safety plans, active ction on security, security awareness and staff training in special positions. (3) safety information regularly check the implementaraining befo
29、re the approach of safety education for all employees, comes into play in the construction and regular lectures ofety ttion team, subcontractors enter into a construction contract, specification for safe behaviour. (2) safety instruction and saproduction responsibility system, enabling all staff to
30、clarify their security responsibilities, project manager and construcafety ) construction contract responsibility system for production safety and security before the approach to establish effective s15.2.3 construction safety management system in order to achieve security objectives and develop saf
31、ety management system: (1minor injury rate is less than 0.8%. mode processing plants, construction of living6 42, ，设倾斜角为，则 t,4t,4,0？t,2，22b, 。 tan,2，22,3？,(,),a3242()4yy2A3A 文A ，设，则 (2,),(,)AyGF(1,0),B(2,0)，(),1,？y,1AA3323？A(2,1)？|AF|,221111113139，b22(1)()()9、 B ,，,，,，,， 2222416ababaaaaaaa13119, 当时，
32、取最大值。 16a4b410、 A 对?对任意的，都有说明在 ,0,20,x,x,2f(x),f(x)f(x)1212x,2 单增，对,由周期为，对?对称轴方程为 f(,x，2),f(x，2)？4？f(7),f(3),f(1)f(6.5),f(2.5),f(1.5)f(4.5),f(0.5)y2011、C 设切点，则切线的斜率为2x，由题意 P(x,y),2x,y,2x00000x0bb2222？y,x，1？x，1,2x？x,1？,2,e,1，(),5 又 00000aa112、D 解:标号为“3,5,7”三条相同颜色有种涂法，当“3,5,7”涂 C31 好后，“2,4,1”有两类涂法，一类“
33、2,4”同色有种。此时“1” C2111 有种，共有=4种涂法; CCC2222 另一类“2,4”不同色有种，此时“1”只有1种，共2种涂法， A2“2,4,1”共有6种涂法，同理“6,8,9”也有6种涂法， ？3，6，6,108 总共有种涂法。 ？13、填空题 y,x(3)理 -6 由可行域知，目标函数的最大值在与2x，y，k,0的交点处 Z第7页，共13 页 kkk4 取得，联立方程可得交点为 (,)？Z,k,k,8？k,63333文 -9 画出满足不等式组的可行域可知 Z,3,2，6,9min114、 将该正四面体放置于一个棱长为的正方体中，则它们有相同的外接球 ， a3111？3a,3
34、,a,1？V,1，1，1,(，1，1，1)，4, 323222xyy200015、6 ，设，则 P(x,y)13(1)F(,1,0)，,？y,0004342 ？FP,(x，1,y),OP,(x,y)？OP,FP,x(x，1)，y00000002x11220 = x(x，1)，3(1,),x，x，3,(x，2)，200000444时，有最大值6 OP,FP？,2,x,2？x,20016、? ,正确 ？0,a,b,c？?？a,b,c,a,c，b,c，c？(1,1),1,1,1，1,1，1,0，0，1,1？错 b,c,a 在中先取得 (a,b),c,a,c，b,c，c(a,a),1,a,a，a,a，
35、a？0,a,a 又取得， b,0,c,a(a,0),a,a,a，0,a，a？a,a,0故 ?正确 a,0,a？0,a,aa,a？a,0二、解答题 22222222217、(1) ？b,ac,a,c,ac,bc？a,c,b,bc？b，c,a,bc2221b，c,abc,cos0？A,又？,x,？A, ,2223bcbche secd and punishment system to enhance the safety awareness of staff, ensuring smooth safety guidelines and regulations, ensure to the stan
36、dard case, the whole construction process of security checks to eliminate hidden dangers, and by checking and rewarding tontact with Labor departments to ensure information transfer, the transfer, collection, management. (4) security system accorf the safety and security reports submitted in a timel
37、y manner, appropriate security measures, develop safety plans, active ction on security, security awareness and staff training in special positions. (3) safety information regularly check the implementaraining before the approach of safety education for all employees, comes into play in the construc
38、tion and regular lectures ofety ttion team, subcontractors enter into a construction contract, specification for safe behaviour. (2) safety instruction and saproduction responsibility system, enabling all staff to clarify their security responsibilities, project manager and construcafety ) construct
39、ion contract responsibility system for production safety and security before the approach to establish effective s15.2.3 construction safety management system in order to achieve security objectives and develop safety management system: (1minor injury rate is less than 0.8%. mode processing plants,
40、construction of living-inforced woodurity goals of the. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, re8 ,3133,(2)f(x),cos(x,)，sinx,cosx，sinx，sinx,cosx，sinx62222,2, ？,3sin(x，),？,2？f(x),3sin(2x，)x,0,662,72x，,？x,时,f(x),3max666618、解:设“甲第次试跳才成功”为
41、事件“乙第次试跳成功”为事件， ABiiii由题意得且相互独立() A,BP(A),0.7,P(B),0.6,i,1,2,3iiii(1)“甲第3次试跳才成功”为事件， AAA？P(AAA),0.3,0.3,0.7,0.063123123即第3次才成功的概率为0.063 C (2)“甲、乙两人在第一次试跳中至少有一人成功”为事件， P(C),1,P(A)P(B),1,0.3，0.4,0.8811(3)设“甲在两次试跳中成功次”为事件 M(i,0,1,2)ii“乙在两次试跳中成功j次”为事件N(j,0,1,2) j甲比乙成功的次数恰好多一次为事件 DP(D),P(MN，MN),P(MN)，P(M
42、N),P(M)P(N)，P(M)P(N)102110211021 则 1221,C,0.7，0.3，0.4，0.7，C，0.6，0.4,0.302422所求概率为0.3024 AC19、解:取中点，为中点， ACFD11DF,平面ABCAB,BC则，又 ？BD,AC？DF,DC,DB两两垂直关系如图 则 C(1,0,0)B(0,22,0)A(,1,0,3)1A(,1,0,0)D(0,0,0)B(0,22,3)1 ABD设平面的一个法向量为 m,(x,y,z)1111第9页，共13 页 AB,(1,22,3)AD,(1,0,3)11,，22,3,0xyz,0mAB,1111 又令 ？,x,3z,
43、0m,AD,011,1,x,3,则z,1,y,0？m,(3,0,1)又BC,(1,22,3)11平面 ？BC/ABD？BC,m,3，1，0，(,22)，1，(,3),0？BC,m1111d(2) 设到平面的距离为，则 BABDBB,(0,0,3)1113310BB,m3101d, 到平面的距离为 BABD？111010|m10设平面的一个法向量为， DBBn,(x,y,z)1222DB,(0,22,0)DB,(0,22,3)1,22y,0,0nDB,2 则取，则 ,x,1,y,z,0n,(1,0,0),222,22y，3z,0n,DB,022, 设二面角为 A,DB,B11m,n310310c
44、os,？ 则所求二面角的余弦值为。 1010|m|n|2x(1a)xa(x1)(xa),，,f(x)19、理解:, xxa,0 (1)当时，在递减，在递增; f(x)(0,1)(1,，,)0,a,1 当时，f(x)在(a,1)递减，在递增; (0,a),(1,，,)a,1 当时，f(x)在(0,，,)递增; a,1f(x)(1,a)递减，在(0,1),(a,，,)递增 当时，在。 1a,0？f(1),af(1),0(2) 当时，此时f(x),0不成立。 21a,0f(1),a,0f(x) 当时，由(1)在(0,+)上的最小值为 ,2inforced woodurity goals of the
45、. 15.2.4, safety and facilities management (1) configuration of safety equipment: material, repair shop, rehe secd and punishment system to enhance the safety awareness of staff, ensuring smooth safety guidelines and regulations, ensure to the standard case, the whole construction process of securit
46、y checks to eliminate hidden dangers, and by checking and rewarding tontact with Labor departments to ensure information transfer, the transfer, collection, management. (4) security system accorf the safety and security reports submitted in a timely manner, appropriate security measures, develop saf
47、ety plans, active ction on security, security awareness and staff training in special positions. (3) safety information regularly check the implementaraining before the approach of safety education for all employees, comes into play in the construction and regular lectures ofety ttion team, subcontr
48、actors enter into a construction contract, specification for safe behaviour. (2) safety instruction and saproduction responsibility system, enabling all staff to clarify their security responsibilities, project manager and construcafety ) construction contract responsibility system for production safety and security before the approach to establish effective s