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珠海市2012~2013学年第一学期普通高中学生学业质量监测高三理科数学试题参考答案及评分标准

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiat ed le arni ng education gui de party members in a ccorda nce with their own situati on, target the problems to, base d on the w ork d one. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educat ional efforts to realiz e the party's ide ologi cal a nd politica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nches s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout substance, S ham mules. To im plement t he educati on management system for b asic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unqualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax party continued reorga nization as a n importa nt task, finis h perfect org anization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work ini tiative s
珠海市 2012~2013 学年第一学期普通高中学生学业质量监测
高三理科数学试题参考答案及评分标准

一、选择题:CABD AADB

二、填空题:

9.函数 y ? sin x 的导函数 y? ?



x

10.在递增等比数列{an}中, a2 ? 2, a4 ? a3 ? 4 ,则公比 q =



11.某学校三个社团的人员分布如下表(每名同学只参加一个社团):

合唱社

粤曲社

武术社

高一

45

30

a

高二

15

10

20

学校要对这三个社团的活动效果进行抽样调查,按分层抽样的方法从社团成员中抽取 30 人,结果合

唱社被抽出12 人,则这三个社团人数共有_______________.

12.在△ABC 中,内角 A,B,C 的对边分别为 a,b,c,已知 C= ? ,

y

3

b ? 3 ,若△ABC 的面积为 3 3 ,则 c =



2

13.如图,F1,F2 是双曲线

C:

x2 a2

? y2 b2

? 1(a>0,b>0)

的左、右焦

点,过 F1 的直线 l 与 C 的左、右两支分别交于 A,B 两点.若 | AB | : | BF2

| : | AF2 |=3 : 4 : 5,则双 曲线的离心率为

.

B A

F1

O

F2 x

(二)选做题(14-15 题,考生只能从中选做一题)
14.(坐标系与参数方程选做题)在直角坐标系 xOy 中, 已知曲线 C1 :

(第 13 题图)

?x ? t ? 2

? ?

y

?

1?

2t

, ( t 为参数)与曲线 C2



?x

? ?

y

? 3cos? ? 3sin?

,(?

为参数)相交于两个点

A

、B

,则线段

AB

的长



.

D

15.(几何证明选讲选做题)如图,PAB、PCD 为⊙O 的两条割

若 PA=5,AB=7,CD=11,AC=2,则 BD 等于

.

P

C
O
A B
(第15题图)

线,

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so t hat the majority of party members and fully qualified, compre he nsive skill s of grass -root s party organi zations, grass -roots party level upgrade . Comrades, do a "two" learni ng educati on is of great significa nce, re spons ibilitie s, carry sig nifica nt implicati ons .

City levels party and ge neral members cadres, t o dee p aware ness "two le arn a do" learni ng education of importanc e and nee d, to height of political consci ously and full of political e nthusiasm, put "two lear n a do" lear ning e ducation carr ied out good, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Fiv e" good start, and spee d up constr uction more high e col ogical vitality ha ppi nes s of City provi des str ong powerful g uarantee. Tw o, starting from the revere d Constit ution re spe cted the party Constit ution was XI Jinpi ng, Ge neral Se cretary to the part y's request, 18 six pl enary se ssi on of the Central Commissi on for di sci pline ins pe ction re port "five experie nce" first.

Full strictly administeri ng the part y, first of all, to exalt the party Constitution, a nd pi pe the whole part y, the ruling party of the party Constit ution. Revered

Constitution reflected i n awe. Party a party of ide als and beliefs purpose, s ummed up the party's fine traditi on a nd style ; a cle ar party members a nd w hat ca n be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constituti on to a we and wary eye e nha nci ng the s acred se nse of res ponsi bility and missi on.

Hearts filled with party Constitution, hold t he party li ne, BA obligati ons unconditi onally carry out party members , accordi ng to the Constituti on of directi on tow ards sta ndar ds efforts. Res pect reflecte d in t he study the party Constituti on mea ns. S ome party members joi ned the party Constit ution on the s helf, not to le arn, s ome long-term party accordi ng to the Constituti on of the party's organization, the party is not required t o pay members hip due s, loose conce pt, party orga nizations of the party orga nization, and tur ned a blind eye on the task s ass igned by t he Orga nization, were forgotte n, forgotten vow s performa nce t he party Constitution.

row, ever -spirali ng increase i n the lear ning proce ss. Res pect party lines refle cted in practi ce. Two t o learn a basic Constituti on Party rules, ser ies of s peeches , the key to be qualifie d party members . To be qualified party members, sta ndards are not high, but if he doe s take a ruler of the party Consti tution to "card", truly it is not easy. Carry out study and e ducation, every party must contr ol the party's eight obligations, ask , look for gaps, identify problems, clear dire ction, work t o solve spe cific pr oblems . Actively practici ng in the production life of the eight obligations, to play a vanguar d and exemplary role, truly a party ba nner. " Two" fight to highlig ht grass-r oots party organizati ons

Constitution is the fundame ntal standard of our Communists are slim, t he party Constitution to re peatedly lear n, pra ctice , thinki ng, lear ning a nd t hinki ng, thi nking a nd row,

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a cc orda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd p olitica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nche s s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout substance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unq ualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax party continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s

9、

x cosx ? sin x x2

10、2

11、150 12、 7

13、 13 14、 4 15、 6
三、解答题:12+12+14+14+14+14=80 16.(本小题满分 12 分)
设向量 a= (2,sin? ) ,b= (1, cos? ) ,θ 为锐角.
(1)若 a·b=163,求 sinθ+cosθ 的值; (2)若 a∥b,求 sin(2θ+π3)的值.

17.(本小题满分 12 分) 某中学校本课程共开设了 A,B,C,D 共 4 门选修课,每个学生必须且只能选修 1 门选修课,现有该
校的甲、乙、丙 3 名学生: (1)求这 3 名学生选修课所有选法的总数; (2)求恰有 2 门选修课没有被这 3 名学生选择的概率; (3)求 A 选修课被这 3 名学生选择的人数的数学期望.

18.(本小题满分 14 分) 已知某几何体的直观图和三视图如下图所示,其正视图为矩形,侧视图为等腰直角三角形,俯视图为
直角梯形

(1)求证: BC // 平面C1B1N ; (2)求证: BN ? 平面C1B1N ;

(3)设 M



AB

中点,在 BC

边上找一点 P

,使 MP

//

平面 CNB1 ,并求

BP PC

的值.

4
8 主视8图
4
4 俯 8 视图

侧视图

19.(本题满分 14 分)

已知椭圆 C : x2 a2

?

y2 b2

? 1(a ? b ? 0) ,左、右两个焦点分别为 F1 、F2 ,上顶点 A(0, b) ,?AF1F2 为

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importance and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the Central Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nhancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, an d turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

row, ever -spirali ng increase i n the lear ning proce ss. Res pect party lines refle cted in practi ce. Two t o learn a basic Constituti on Part y rules, ser ies of s peeches , the key to be qualifie d party members . To be qualified party members, sta ndards are not high, but if he doe s take a ruler of the party Consti tution to "card", truly it is not easy. Carry out study and e ducation, every party must control the party's eight obligations, ask , look for gaps, id entify problems, clear dire ction, work t o solve spe cific pr oblems .

2
Actively practici ng in the production life of the eight obligations, to play a vanguar d and exemplary role, truly a party ba nner. "Two" fight to highlig ht grass-r oots party organizati ons

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a ccorda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd politica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nches s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout subst ance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unqualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax part y continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s
正三角形且周长为 6.
(1)求椭圆 C 的标准方程及离心率;
(2)O 为坐标原点, P 是直线 F1 A 上的一个动点,求| PF2 | ? | PO | 的最小值,并求出此时点 P 的坐
标.

20.(本小题满分 14 分)

已知函数 f (x) ? 1 ax2 ? 2x , g(x) ? lnx . 2
(1)如果函数 y ? f (x) 在[1, ??) 上是单调减函数,求 a 的取值范围;

(2)是否存在实数 a ? 0 ,使得方程 g(x) ? f ?(x) ? (2a ?1) 在区间 (1 , e) 内有且只有两个不相等的实

x

e

数根?若存在,请求出 a 的取值范围;若不存在,请说明理由.

21.(本题满分 14 分)

已知正项数列?an? 的前 n

项和为 Sn

,且

Sn

?

an (an ? 4

2)

(n ? N*) .

(1)求 a1 的值及数列?an? 的通项公式;

(2)求证:

1 a13

?

1 a23

?

1 a33

?

?

1 an3

?

5 32

(n?N*) ;

(3)是否存在非零整数 ? ,使不等式 ?(1? 1 )(1? 1 ) ? ? (1? 1 ) cos ? an?1 ?

a1

a2

an

2

1 an ?1

对一切 n ? N* 都成立?若存在,求出 ? 的值;若不存在,说明理由.

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importan ce and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the C entral Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nh ancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, and turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

珠海市 2012~2013 学年第一学期普通高中学生学业质量监测高三理科数3 学试题参考答案及评分标准第 row, ever-spiraling increase in the learning process. Respect party lines reflected in practice. Two to learn a basic Constitution Party rules, series of speeches, the key to be qualified party members. To be qualified party members, standards are not high, but if he doe s take a ruler of the party Constitution to "card", truly it is not easy. Carry out study and education, every party must control the party's eight obligations, ask, look for gaps, identify problems, clear direction, work to solve specific problems. Actively practicing in the production life of the eight obligations, to play a vanguard and exemplary role, truly a party banner. "Two" fight to highlight grass-roots party organizations

3

页(共

8

页)

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a cc orda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd p olitica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nche s s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout substance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unq ualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax party continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s
高三理科数学参考答案和评分标准

三、解答题: 16.(本小题满分 12 分)
解:(1) 因为 a·b=2+sinθcosθ=163,所以 sinθcosθ=16.

……………… 3 分

所以 (sinθ+cosθ)2=1+2 sinθcosθ=43.

又因为 θ 为锐角,所以 sinθ+cosθ=2 3 3.

……………… 6 分

(2) 解法一 因为 a∥b,所以 tanθ=2.

……………… 8 分

所以 sin2θ=2 sinθcosθ= s2ins2iθn+θccoossθ2θ= t2ant2aθn+θ 1=45,

cos2θ=cos2θ-sin2θ= csoins22θθ-+scions22θθ= 1t-an2taθn+2θ1=-35.……………… 10 分

所以 sin(2θ+π3 )=12sin2θ+ 23cos2θ =12×45+ 23×(-35 )=4-130 3 .
解法二 因为 a∥b,所以 tanθ=2. 所以 sinθ=2 5 5,cosθ= 55.

……………… 12 分 ……………… 8 分

因 此 sin2θ

=2 sinθcosθ=45, cos2θ=cos2θ-sin2θ-



-?

0

1

2

3

35. ……………… 10 分

所以 sin(2θ+π3 )=12sin2θ+ 23cos2θ =12×45+ 23×(-35 )=4-130 3 .

……………… 12 分

17、(本小题满分 12 分)
解析:(Ⅰ)每个学生有四个不同选择,根据乘法法则,选法总数 N= 4? 4? 4 ? 64 …… 3 分
(Ⅱ) 恰有 2 门选修课这 3 名学生都没选择的概率为

P2

?

C42C32 A22 43

?

2? 3? 3? 2 4?4?4

?9 16

……………… 7 分

(Ⅲ) 设 A 选修课被这 3 名学生选择的人数为? ,则? =0,1,2,3

P( ?

=0)=

33 43

?

27 64

P(?

=1)=

C31 ? 32 43

?

27 64

P( ?

=2)=

3? C31 43

?

9 64

P(? =3)=

C 33 43

?

1 64

……………… 9 分

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importance and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the Central Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nhancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, an d turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

row, ever -spirali ng increase i n the lear ning proce ss. Res pect party lines refle cted in practi ce. Two t o learn a basic Constituti on Part y rules, ser ies of s peeches , the key to be qualifie d party members . To be qualified party members, sta ndards are not high, but if he doe s take a ruler of the party Consti tution to "card", truly it is not easy. Carry out study and e ducation, every party must control the party's eight obligations, ask , look for gaps, id entify problems, clear dire ction, work t o solve spe cific pr oblems .

4
Actively practici ng in the production life of the eight obligations, to play a vanguar d and exemplary role, truly a party ba nner. "Two" fight to highlig ht grass-r oots party organizati ons

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a ccorda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd politica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nches s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout subst ance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unqualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax part y continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s

? 的分布列是

P

27 27

9

1

64

64

64

64

………… 10 分

E? ? 0 ? 27 ? 1? 27 ? 2 ? 9 ? 3 ? 1 ? 3 64 64 64 64 4

………… 12 分

18. 解 :( 1 ) 证 明 : ? 该 几 何 体 的 正 视 图 为 矩 形 , 侧 视 图 为 等 腰 直 角 三 角 形 , 俯 视 图 为 直 角 梯 形 , ? BA, BC, BB1 两 两 互 相 垂 直 。 以 BA, BC, BB1 分 别 为 x, y, z 轴 建 立 空 间 直 角 坐 标 系 , 则 N (4,4,0), B1 (0,8,0) , C1(0,8,4), C(0,0,4) , B(0,0,0) ……………… 2 分

∵ BC ? (0,0,4) , B1C1 ? (0,0,4) , BC ? B1C1 ,∴ BC // B1C1 ∵ B1C1 ? 平面C1B1N , BC ? 平面C1B1N , ∴ BC // 平面C1B1N …… 4 分

(2)? BN ? B1N ? (4,4,0) ? (4,?4,0) ? 16 ?16 ? 0, BN ? B1C1 ? (4,4,0) ? (0,0,4) ? 0

? BN ? B1N, BN ? B1C1 ,又 B1N ? B1C1 ? B1

? BN ? 平面C1B1N

……………… 8 分

C

C1

(3)设 P(0,0, a) 为 BC 上一点,? M 为 AB 的中

P

B

? M (2,0,0) , MP ? (?2,0, a) , NC ? (?4,?4,4)

设平面的一个法向量为 n ? (1, x, y) ,则有

AM N





B1

n ? NC, n ? NB1 ,则有 n? NC ? 0, n? NB1 ? 0, ∴ (1, x, y) ?(?4,?4,4) ? 0,(1, x, y) ?(?4,4,0) ? 0 ,得 x ? 1, y ? 2 , ∴ n ? (1,1,2) ,…10 分

? MP //平面 CNB1 ,? n ? MP ,于是 MP? n ? (?2,0, a) ? (1,1,2) ? ?2 ? 2a ? 0

解得: a ? 1

……………………… 12 分

? MP ? 平面 CNB1 ,? MP //平面 CNB1 ,此时 PB ? a ? 1 ,

? BP ? 1 PC 3
(注:此题用几何法参照酌情给分)

………………………………… 14 分

19、(本题满分 14 分)

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importan ce and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the C entral Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nh ancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, and turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

珠海市 2012~2013 学年第一学期普通高中学生学业质量监测高三理科数5 学试题参考答案及评分标准第 row, ever-spiraling increase in the learning process. Respect party lines reflected in practice. Two to learn a basic Constitution Party rules, series of speeches, the key to be qualified party members. To be qualified party members, standards are not high, but if he doe s take a ruler of the party Constitution to "card", truly it is not easy. Carry out study and education, every party must control the party's eight obligations, ask, look for gaps, identify problems, clear direction, work to solve specific problems. Actively practicing in the production life of the eight obligations, to play a vanguard and exemplary role, truly a party banner. "Two" fight to highlight grass-roots party organizations

5

页(共

8

页)

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a cc orda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd p olitica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nche s s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout substance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unq ualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax party continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s

? a ? 2c 解:(Ⅰ)解:由题设得 ??a ? a ? 2c ? 6
?? a 2 ? b2 ? c2

……………… 2 分

解得: a ? 2,b ? 3 , c ? 1…… 3 分

故 C 的方程为 x 2 ? y 2 ? 1 . …… 5 分 离心率 e ? 1

43

2

(2)直线 F1 A 的方程为 y ? 3(x ?1) ,…… 7 分

………………… 6 分

设点 O 关于直线 F1 A 对称的点为 M (x0 , y0 ) ,则

? y0

?? ?

x0

?

3 ? ?1

?

???x0 ?

?

?

3 2

(联立方程正确,可得分至

8

分)

? y0 ?? 2

?

3( x0 ? 1) 2

? ??

y

0

?

3 2

所以点 M 的坐标为 (? 3 , 3 ) 22

……………………………… 9 分

∵ PO ? PM , PF2 ? PO ? PF2 ? PM ? MF2 ,…… 10 分

| PF2 | ? | PO | 的最小值为| MF2 |?

(? 3 ?1)2 ? ( 3 ? 0)2 ?

2

2

7

…………… 11 分

3 ?0

直线 MF2 的方程为

y

?

2 ?3

(x ?1) ?1

即y ??

3 (x ?1) 5

2

…………… 12 分

?



?y ?

?

?

3 5

(x

? 1)

?

???x ?

?

?

2 3

,所以此时点

P

的坐标为

? ?

y

?

3(x ? 1)

? ??

y

?

3 3

(? 2 , 3 ) …………… 14 分 33

20.解:(1)当 a ? 0 时, f (x) ? 2x 在[1, ??) 上是单调增函数,不符合题意.…1 分

当 a ? 0 时,y ? f (x) 的对称轴方程为 x ? ? 2 ,由于 y ? f (x) 在[1, ??) 上是单调增函数,不符合题意. a

当 a ? 0 时,函数 y ? f (x) 在[1, ??) 上是单调减函数, 则 ? 2 ? 1 ,解得 a ? ?2, a

综上, a 的取值范围是 a ? ?2.

…………………………………4 分

(2)把方程 g(x) ? f ?(x) ? (2a ?1) 整理为 lnx ? ax ? 2 ? (2a ?1) ,

x

x

即为方程 ax2 ? (1? 2a)x ? lnx ? 0 .

……………………5 分

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importance and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the Central Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nhancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, an d turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

row, ever -spirali ng increase i n the lear ning proce ss. Res pect party lines refle cted in practi ce. Two t o learn a basic Constituti on Part y rules, ser ies of s peeches , the key to be qualifie d party members . To be qualified party members, sta ndards are not high, but if he doe s take a ruler of the party Consti tution to "card", truly it is not easy. Carry out study and e ducation, every party must control the party's eight obligations, ask , look for gaps, id entify problems, clear dire ction, work t o solve spe cific pr oblems .

6
Actively practici ng in the production life of the eight obligations, to play a vanguar d and exemplary role, truly a party ba nner. "Two" fight to highlig ht grass-r oots party organizati ons

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a ccorda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd politica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nches s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout subst ance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unqualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax part y continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s

设 H (x) ? ax2 ? (1? 2a)x ? lnx (x ? 0) ,原方程在区间( 1 , e )内有且只有两个不相等的实数根, 即为函 e

数 H (x) 在区间( 1 , e )内有且只有两个零点. ……6 分 e

H ?(x) ? 2ax ? (1? 2a) ? 1 ? 2ax2 ? (1? 2a)x ?1 ? (2ax ?1)(x ?1) …………7 分

x

x

x

令 H ?(x) ? 0,因为 a ? 0 ,解得 x ? 1或 x ? ? 1 (舍) 2a
当 x ? (0,1) 时, H ?(x) ? 0 , H (x) 是减函数;

…………………8 分

当 x ? (1, ??) 时, H ?(x) ? 0, H (x) 是增函数.……10 分

H (x) 在( 1 , e )内有且只有两个不相等的零点, e

??H ?

(1) e

?

0,

只需 ?H (x)min ? 0, …………13 分

??H (e) ? 0,

?



? ? ?? ?

a e2 H

? (1)

1? 2a e
?a?

? (1

1 ?

? (1 2a)

? ?

2a)e ? e2
1?a ?

a? 0,

e2

? 0,

??ae2 ? (1 ? 2a)e ?1 ? (e2 ? 2e)a ? (e ?1) ? 0,

??

? e2 ? e



?a ???a

? ?

2e 1,

?

1

,

? ?a ?

1? e

,

?? e2 ? 2e

解得1 ? a ? e2 ? e , 所以 a 的取值范围是(1, e2 ? e ) . …………………14 分

2e ?1

2e ?1

21.(1)由

Sn

?

an (an ? 4

2)

.

当 n ? 1 时, a1

?

S1

?

a1

(a1 ? 4

2)

,解得

a1

? 2 或 a1

? 0 (舍去).

……2 分

当 n ? 2 时,

由 an

?

Sn

? Sn?1

?

an (an ? 2) 4

?

an ?1 (an ?1 4

? 2)

?

an 2

?

a2 n?1

?

2(an

? an?1)



∵ an ? 0 ,∴ an ? an?1 ? 0 ,则 an ? an?1 ? 2 ,

∴?an? 是首项为 2,公差为 2 的等差数列,故 an ? 2n . ………………4 分

另法:易得 a1 ? 2, a2 ? 4, a3 ? 6 ,猜想 an ? 2n ,再用数学归纳法证明(略).

(2)证法一:∵

1 an3

?

1 (2n)3

?

1 8n ? n2

?

1 8n(n2

?1)

?

1 8(n ?1)n(n ?1)

? 1 [ 1 ? 1 ](n ? 2) ,……4 分 16 (n ?1)n n(n ?1)

∴当 n

?

2

时,

1 a13

?

1 a23

?

1 a33

?

? 1 ?1?1?1? an3 23 43 63

?1 (2n)3

? 1 ? 1 [( 1 ? 1 ) ? ( 1 ? 1 ) ? ? 1 ? 1 ]

23 16 1? 2 2? 3 2? 3 3? 4

(n ?1)n n(n ?1)

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importan ce and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the C entral Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nh ancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, and turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

珠海市 2012~2013 学年第一学期普通高中学生学业质量监测高三理科数7 学试题参考答案及评分标准第 row, ever-spiraling increase in the learning process. Respect party lines reflected in practice. Two to learn a basic Constitution Party rules, series of speeches, the key to be qualified party members. To be qualified party members, standards are not high, but if he doe s take a ruler of the party Constitution to "card", truly it is not easy. Carry out study and education, every party must control the party's eight obligations, ask, look for gaps, identify problems, clear direction, work to solve specific problems. Actively practicing in the production life of the eight obligations, to play a vanguard and exemplary role, truly a party banner. "Two" fight to highlight grass-roots party organizations

7

页(共

8

页)

carried out "practi ce li ne pi one er standard, a nd post spurs" "members concentrated s ervice m onths", activities, e ducation gui de members always everyw here bearing i n mind i dentit y, ba sed j ob post, active play r ole. To develop differentiated le arni ng education gui de party members in a cc orda nce with their own situati on, target the problems to, base d on the w ork done. Pay attention to the r oom a nd room for grass-r oots party organi zations, grass -roots party organizati ons have more a utonomy in educati on, maki ng educati on more gr ound, full of vitality, good effect. Fi nall y, hig hlight t he normal long -term. To hig hlight the characteristi cs of recurrent e ducation, with l ong flowing, continuous line of pers everance the persevera nce to promote educational efforts to realiz e the party's ide ologi cal a nd p olitica l construction of routine i nstituti onali zation. With the party bra nch as the base unit. Play the rol e of party bra nche s s hould be, is t he key to e ducati ona l succe ss. Ea ch branch must take stri ct educati on a nd manag ement res ponsi bility of party member s, educati on based on l earni ng to make specific arra ngements, f ully mobilize the enthusia sm of party members involve d in t he e ducati on, ens ure the Organi zation in place , measure s in place , put in pl ace . To t he party organizati on a s the basi c form. In t he standardi zed development of learning , make learni ng more effective efforts, a nd wi ll adhere to t he good party group, orga nized party, party members and the General Assem bly, tell a good party le cture s, ca n drive a g ood topic a bout, preve nt showy wit hout substance, S ham mules. To im plement t he educati on management system for basic support. Democratic mut ual eval uation on party members i n accor dance wit h the reg ulations, t he real performance criteria a nd order esta blis hed, sound carefully dis pose of unq ualified party members, t o further im prove the dredge ex port team, pure s elf clea ning me cha nism. Party lea ding cadre s shoul d a dhere t o and impleme nt the central group lear ning system, to w hich branch of learni ng excha nges, participati on i n a dual organizati on wit h comrades. F ocus on recurrent e ducation, you also nee d to conti nue t o strengt hen t he buil ding of gras s-roots party organizati ons. Now, the city also has 88 village party organi zations are weak and lax, first Secretary of the village, but conv ersion requires a pr oce ss. Rece ntly, t he city's party organizati on focus ed investigati on, che ck out a total of "lost" members 4,50 7, "Pocket" members 1037, find there are 640 "lost" party members ar e not conta cted 1 48 "Pocket" party members and implementati on of orga nizationa l relations hips. Educational manag ement of party members i nto the Organizati on, t here is a l ot of work to do. Weak a nd lax party continued reorga nization as a n importa nt task, finis h perfect organization, wit h a good team, Good system. S peci al highlights of grass -roots party orga nizations, to be dealt with first in pla ce, further education, reorga nization, transformation and educati onal i nteraction. In short, thr ough soli d and effective work initiative s

? 1 ? 1 [1 ? 1 ] ? 1 ? 1 ? 1 ? 5 .… 7 分 8 16 2 n(n ?1) 8 16 2 32

当n

? 1时,不等式左边 ?

1 a13

?

1 8

?

5 32

显然成立.

……………… 8 分

证法二:∵ n3 ? 4n(n ?1) ? n(n2 ? 4n ? 4) ? n(n ? 2)2 ? 0 ,∴ n3 ? 4n(n ?1) .



1 an3

?

1 (2n)3

?

1 8n3

?

1 32n(n

?1)

?

1 32

(1 ? n ?1

1) n

(n

?

2)

.……4



∴当 n

?

2 时,

1 a13

?

1 a23

?

1 a33

?

?

1 an3

?

1 23

?

1 43

?

1 63

?

?

1 (2n)3

?

1 23

?

1 [(1? 32

1) 2

?

(1 2

?

1) 3

?

? ( 1 ? 1)] ? 1 ? 1 (1? 1) ? 1 ? 1 ? 5 .……7 分 n ?1 n 8 32 n 8 32 32

当n

? 1时,不等式左边 ?

1 a13

?

1 8

?

5 32

显然成立.

……8 分

(3)由 an

? 2n ,得 cos ? an?1 2

?

cos(n ?1)?

?

(?1)n?1 ,

设 bn ? (1? 1 )(1? 1 ) ? 1 ? (1? 1 )

a1

a2

an

,则不等式等价于 (?1)n?1? ? bn . an ?1

bn?1 ?

an ?1

?

2n ?1

?

bn

? ?1 ?

?

1 an?1

? ? ?

an?1 ?1

???1 ?

1 2n ?

2

? ??

2n ? 3

2n ? 2

?

(2n ?1)(2n ? 3)

4n2 ? 8n ? 4 ? 1,……9 分 4n2 ? 8n ? 3

∵ bn ? 0 ,∴ bn?1 ? bn ,数列?bn? 单调递增.

…………………… 10 分

假设存在这样的实数 ? ,使得不等式 (?1)n?1? ? bn 对一切 n ? N* 都成立,则



当 n 为奇数时,得 ?

? (bn )min

? b1

?

23 3



……11 分



当 n 为偶数时,得 ??

? (bn )min

? b2

?

85 15

,即 ?

??8 5 15

. ……12 分

综上, ? ?(? 8 5 , 2 3 ) ,由 ? 是非零整数,知存在 ? ? ?1 满足条件.…… 14 分 15 3

涉及重大决策事项、要人任免目安排和额度资金使用等,具有行政执法许可部门管理审批自由裁量务定权的领导岗位。broken probl em, fill the s hort Board, so that t he majority of party member s and fully qualified, compre hensive skill s of grass-r oots party organizati ons, grass -root s party level upgrade. Comrade s, do a "two" learning e ducation is of great signifi cance, res ponsi bilities, carry signifi cant impli cations.

City levels party and general member s cadre s, to deep awar enes s "two learn a do" lear ning educati on of importance and ne ed, to height of politica l cons ciously and full of political e nthusiasm, put "two lear n a do" learning e ducation carrie d out g ood, for coordi nation advance "four a full" strategy layout, and a chieve d "Thirtee n-Five" good start, a nd spee d up construction more hig h ecologi cal vitality ha ppi ness of City provi des strong powerful guarantee. Two, starting from the revered Constituti on res pe cted the party Constituti on wa s XI Jinping , General Secretary to the party's request, 1 8 six ple nary ses sion of the Central Commission for dis cipline i nspecti on report "five experience" first.

Full strictly administering the party, first of all, to exalt the party Constituti on, a nd pipe t he whole party, the r uling party of the party Constitution. Revered

Constitution reflected i n awe. Party a party of ideal s and beliefs purpose , summed up the party's fine traditi on a nd style ; a clear party members and w hat can be done a nd w hat must be done, w hat ca nnot be done. Each Communist Party Constitution to awe a nd wary eye e nhancing the sacre d sense of respons ibility a nd mis sion.

Hearts filled with party Constitution, hold t he party line, BA obligations unconditionally carry out party members, accor ding to t he Constit ution of directi on tow ards sta ndar ds efforts. Respect reflecte d in the study t he party Constit ution means . Some party members joi ned the party Constit ution on t he shelf, not to lear n, some l ong -term party accordi ng to the Constituti on of the party's orga nization, the party is not require d to pay member shi p dues, loose conce pt, party orga nizations of the party organi zation, an d turne d a bli nd eye on the tasks as si gned by the Organi zation, were forgotten, forgotte n vows performance the party Constituti on.

Constitution is the fundamental standard of our Communi sts are slim, the party Constit ution t o repeate dly learn, practi ce, thi nking, l earni ng and t hinki ng, thi nking a nd row,

row, ever -spirali ng increase i n the lear ning proce ss. Res pect party lines refle cted in practi ce. Two t o learn a basic Constituti on Part y rules, ser ies of s peeches , the key to be qualifie d party members . To be qualified party members, sta ndards are not high, but if he doe s take a ruler of the party Consti tution to "card", truly it is not easy. Carry out study and e ducation, every party must control the party's eight obligations, ask , look for gaps, id entify problems, clear dire ction, work t o solve spe cific pr oblems .

8
Actively practici ng in the production life of the eight obligations, to play a vanguar d and exemplary role, truly a party ba nner. "Two" fight to highlig ht grass-r oots party organizati ons



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